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Title: A New Century of Inventions

Author: James White

Release date: June 15, 2013 [eBook #42951]

Language: English

Credits: Produced by Chris Curnow, Harry Lamé and the Online
        Distributed Proofreading Team at http://www.pgdp.net (This
        file was produced from images generously made available
        by The Internet Archive)


*** START OF THE PROJECT GUTENBERG EBOOK A NEW CENTURY OF INVENTIONS ***




Produced by Chris Curnow, Harry Lamé and the Online
Distributed Proofreading Team at http://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)







  Transcriber's Notes:

  Italics have been transcribed as _italics_, small capitals as ALL
  CAPITALS, superscripts as ^{text}. [sqrt] represents square root, [lb]
  represents the pound-symbol, [***] an asterism, and [oe] the oe-
  ligature.

  More Transcriber's Notes may be found at the end of this text.




  A NEW
  CENTURY OF INVENTIONS,
  BEING
  Designs & Descriptions
  OF
  ONE HUNDRED MACHINES,
  RELATING TO
  _ARTS, MANUFACTURES, & DOMESTIC LIFE_.


  By JAMES WHITE, CIVIL ENGINEER.


  Connoissons le principe--
  Nourrissons nous des Elemens.

  Girard Syn. fr.


  Manchester:

  PRINTED FOR THE AUTHOR, BY LEECH AND CHEETHAM, WRIGHT'S-COURT,
  MARKET-STREET.

  AND SOLD BY

  W. AND W. CLARKE, MARKET-PLACE; E. THOMSON, MARKET-STREET;
  T. SOWLER, ST. ANN'S-SQUARE, MANCHESTER.

  G. WILSON, 49, ESSEX-STREET, STRAND; LONGMAN, HURST, REES, ORME,
  AND BROWN, PATERNOSTER-ROW, LONDON.

  AND BY THE PRINCIPAL BOOKSELLERS IN THE UNITED KINGDOM.

  1822.


Entered at Stationers' Hall.




PREFACE.


It has been my lot, during a long and eventful passage through life, to
have my attention forcibly drawn to a multitude of Mechanical Subjects;
the present review of which permits me to hope, that in making them
publicly known, I should render an important service to the Arts and to
Society. But the manner of doing this has been so long a question with
me, that I have sometimes feared my ability would be extinct before I
could do it at all. The reasons, however, that urge me to make the
attempt acquire strength with the lapse of time: and whenever my
declining health bespeaks the approach of that "night in which no man
can work," I feel deep regret, that this tribute should not have been
thrown into the treasury of human knowledge while yet, by the favour of
a good Providence, the means of doing it were more fully at my disposal.

I have determined therefore to publish these Inventions. Not because
they have been matured into a regular System of Mechanical truth; but
because they consist of _many_ distinct objects of immediate
application:--coupled with _some_ ideas of a more comprehensive nature,
that may probably extend the usefulness of this admirable study, in the
hands of Artists yet unborn.

The form, or rather the title of this work, has but one example, that of
the illustrious Marquis of Worcester; whose name may, perhaps, prolong
the remembrance of mine: an event the rightful anticipation of which, I
confess, would give me pleasure. Not that I either covet or regard what
is commonly called popular applause: but the approbation of the wise and
good I do regard, and aspire to obtain; since that alone seems to fulfil
the adage--"Vox populi vox dei."

On the subject of our respective Inventions, my views are somewhat
different from those of the Noble Marquis; whose description of his
labours, as the custom then was, seems chiefly calculated to excite the
desire of knowing them better: whereas my wish is to infuse, at once,
the knowledge of my subjects into every head capable of receiving it.

This Work then, treats less of Theory than Practice. What are called
Principles in Mechanics, are, and must be, founded on numerous
suppositions; to present which to "the mind's eye" requires often a
_forest_ of signs, which some readers _will_ not, and others _can_ not
penetrate; so that, for many, Theory might as well not exist. This evil
is increased when, as it sometimes happens, these suppositions are laid
so far from reality, as to leave the result, though correctly deduced,
further from the truth than the point to which a sound understanding
unassisted by science, would have carried it. To this extreme
discrepance of views between theoretical and practical men, may be
ascribed their well-known antipathy to each other--in indulging which,
they are alike to blame! since no theory inconsistent with fact can be
complete; nor any fact be adduced, that a perfect theory will not
account for and confirm.

Happily these discussions do not affect my present purpose. For although
I shall offer nothing contrary to sound theory, I do not consider that
as my subject; but make it my business to present rational methods of
producing useful effects.--In other words to describe these Inventions
as connected with immediate Practice. And if, hereafter, it should
become desirable to resume the discussion of any _principle_ relating to
these subjects, I shall cheerfully enter upon it; but hasten, mean
while, to do what seems more important--to place the subjects themselves
beyond the danger of being wholly lost, whatever may befall me in the
course of those events which are still among the secrets of Heaven.

In the pursuit of knowledge, in general, it is often desirable to trace
it from its _upper_ source; and to know all the circumstances that have
attended its progress, down to the very moment when it falls under our
observation. Nor is it a matter of indifference to examine the minutest
form which talent assumed, in the young mind whose subsequent efforts
have engaged our attention, or gratified us with more varied and solid
productions. In this view I have presumed to think myself justified in
commencing this Work, by a succinct reference to those feeble efforts
which marked my first steps in this career. Young I then was, and my
musings puerile indeed! But they were original: they were the links of a
chain which time has not yet snapt asunder--and of which my honoured
Father saw the connection with my subsequent labours, long before I
thought, myself, of any thing but working for the purposes of amusement;
or, in the childish phraseology, of "playing at work."

[Illustration]

Should any reader then enquire what were my first avocations? the answer
would be, I was (in imagination) a Millwright, whose Water-wheels were
composed of Matches. Or a Woodman, converting my chairs into _Faggots_,
and presenting them exultingly to my Parents: (who doubtless caressed
the workman more cordially than they approved the work.) Or I was a
Stone-digger, presuming to direct my friend the Quarry-man, _where_ to
bore his Rocks for blasting. Or a Coach-maker, building Phætons with
_vaneer_ stripped from the furniture, and hanging them on springs of
Whalebone, borrowed from the hoops of my Grandmother. At another time, I
was a Ship Builder, constructing Boats, the sails of which were set to
a side-wind by the vane at the mast head; so as to impel the vessel in a
given direction, _across a given Puddle_, without a steersman. (See
Plate 2. Fig. 3.) In fine, I was a Joiner, making, with one tool, a
plane of most diminutive size, the [relative] perfection of which
obtained me from my Father's Carpenter a profusion of tools, and dubbed
me an artist, wherever his influence extended. By means like these I
became a tolerable workman in all the mechanical branches, long before
the age at which boys are apprenticed to any: not knowing till
afterwards, that my good and provident Parent had engaged all his
tradesmen to let me work at their respective trades, whenever the more
regular engagements of school permitted.

Before I open the list of my intended descriptions, I would crave
permission to exhibit _two_ more of the productions of my earliest
thought--namely, an Instrument for taking Rats, and a Mouse Trap:
subjects with which, fifty years ago, I was vastly taken; but for the
appearance of which, here, I would apologize in form, did I not hope the
considerations above adduced would justify this short digression. If
more apology were needful.... Emerson himself describes a Rat-trap: and
moreover, defies criticism, in a strain I should be _sorry_ to imitate!
my chief desire being to instruct at all events, and to please if I can:
without, however, daring to attempt the elegant PROBLEM, stated and
resolved in the same words--"Omne tulit punctum, qui miscuit utile
dulci."

[Illustration]

The town of Cirencester (my native place) is intersected by several
branches of the river Churn, whose waters are pure and transparent, and
whose banks, formerly, were much perforated by the industry of the Rats
that had made them their residence. These holes had generally two
openings; one at or near the surface of the ground, and the other near
the bottom of the river: so that the rats could range the fields from
the former, and dive into the water from the latter--where they were
often seen gliding along the bottom, either up or down the stream. The
Instrument for taking them in these circumstances, was no other than my
Father's Walking-stick, (represented at A. Fig. 1. Plate 2.) connected
with the curve B by the joint C; the curve having a string fastened to
it, which, passing through the body of the stick, rose to the hand at D,
for the purpose of closing the fork at the proper moment. The Machine,
thus constructed, was put over the rat's back while in the act of
diving; and by pulling the string C D, he was sufficiently pinched to be
drawn out of the water, where a Dog stood ready to dispatch him.

On the Mouse-trap (Fig. 2. and 4.) more thought was bestowed. It
appeared adviseable (I remember) to lay the deceptive plan rather deep:
and to lull the little animal into a false security till the snare had
taken full effect; and even then to hide from her some of its horrors
till she was far enough from this vestibule of misery, _not_ to deposit
there any of those tokens of distress that might deter other mice from
following her example. The trap then, consisted of a _long_ passage,
formed spirally round the surface of a Cone, like the figures we have of
the Tower of Babel. This passage is uncovered in Fig. 4 to shew the
entrance E, and the subsequent gates F G H, &c. which like the valves of
a pump, gave easy entrance to the victim, but forbade her return. At the
length of a mouse from the outer gate E, was placed the first bait N,
say a small rind of cheese, well toasted to allure, but nailed down to
prevent its removal. Its position was further indicated by a train of
meal reaching from it to the outer gate E; which latter was nicely hung
on pivots inclined a little to the perpendicular, so as to open with
ease but never fail to close itself again. It had besides an horizontal
plate O, fixed to its bottom on the inside, so that if the mouse
attempted to open it that way, she trode on this plate and destroyed the
result of her own efforts.

When, therefore, the little wretch had passed this barrier, she was in
reality taken: but unconscious yet of danger, she nibbled the first bait
with pleasure, and then skipped forward in search of more substantial
food: but to obtain this she must pass more of these faithless gates, F
G H, &c. which with progressive effort she opened, and at length found
the inner compartments replete with good things, on which she fed to
satiety, and then only began to think of her situation. Nor yet, with
_much_ alarm: for at the end of this labyrinth, so easy of access, she
hoped to find an easy exit. But alas, these hopes were illusive.
Instead of light, she found the _dark_ gallery O; the least evil of
which was to be too narrow for two mice abreast, since it overhung a
tremendous cavern, Q, that entirely occupied the Cone below, and was
filled with water deep enough to drown her, were she to fall, or be
jostled into it. And one of these disasters she could hardly escape! for
other mice would not fail to be beguiled into this cruel Bastille; to
reach the same spot; and finally, to plunge her into this watery grave.

Having endeavoured to recollect the substance of these youthful attempts
to unite cause and effect, or to fulfil a given purpose by preconcerted
means, I now turn to things of greater importance, and more worthy to be
the theme of my readers' attention. The subjects to be presented will
observe a miscellaneous order; since they have not only originated at
different periods, but offer likewise different degrees of interest--to
_equalize_ which throughout the Work, appears a desirable attempt. As to
the _manner_ of treating each subject, it will be, generally, to
describe the Machines by a reference to the Figures; and then to add
some remarks on their date, construction, properties, and uses.




  PART FIRST.
  A NEW CENTURY OF
  Inventions.


  A
  DYNAMOMETER;
  OR,
  _Machine for measuring Power and resistance while in Motion_.

Dynamics being a science that relates to bodies in motion--comprehending
not their weight only, or their velocities only, but the product of the
one by the other; so the Dynamometer is a mean of measuring both these
circumstances together, and thus of making known the _momentum_ of a
power or resistance in motion. As this Machine has a connection more or
less intimate with almost every other, it seems entitled to the first
place in this collection. Its description follows:

In Plate 3, Fig. 1 and 3, M M, represent two cheeks, standing parallel
to each other, and forming a cage or frame by means of the cross bars E
and the nuts F G. A P, Fig. 2, is the principal axis of the Dynamometer,
fixed to the wheel R N of which it is the centre of motion. It has a
square end A, formed to receive the wheels and other supplemental parts,
to be mentioned below. After the square A, comes a bearing E, to fit the
steps in the frame; and beyond the wheel R N is a cylindrical part O,
fitted to the hollow axis T of the wheel or frame I K, (Fig. 4); and in
fine the form P of this shaft fits and turns in the _cannon_ of the
axis B H, of the wheel C D; so as, when put together and connected with
the frame I K, to assume the form C R F G of the third figure. L P, Fig.
3 and 4, are two intermediate wheels (thus placed to balance each other
on the common centre T) whose axes turn on proper steps in the frame I
K; and which by their teeth connect the motion of this frame with that
of _both_ the wheels R N, and C D.

Such are the parts of the Dynamometer properly so called; and they are
shewn as in their places in Plate 1, where the parts above described, as
far as visible, are marked with the same letters. Moreover, this figure
shews a scale-bason P, to receive the weights used to measure equable
powers, as will be seen hereafter.

Plate 4 contains some of the auxiliary parts of this Machine. But before
we proceed to describe them, it may be proper to observe that the
_measuring power_, by the action of which at K, (Plate 1) the energy of
the _force_ is transmitted to the _resistance_, must, to meet every
case, be susceptible of change, according as the resistance or force to
be measured is uniform or convulsive. For example, in a mill grinding
corn, driven by a fall of water, the whole process is sensibly uniform,
and a weight at P is the proper measurer. But if it were desired to
measure the effect of a pump driven by water, or of a tilt hammer worked
by a Steam Engine, then the measuring power at P must be a spring: for
in these cases the _vis inertiæ_ of a weight would add to its force of
gravity when suddenly raised, or detract from it when the resistance
should suddenly give way. Whenever therefore, the force and resistance
are both _equable_, a weight will best measure them; and when _either_
is convulsive, a spring: but a spring so equalized as to offer the same
resistance at every degree of tension it may have to sustain.

In the 6th. and 7th. Figures, (Plate 4) these demands are fulfilled. The
first represents a barrel-spring, similar to that of a watch, but
_surrounded_ by a fusee, the increasing radii of which compensate for
the increased tension of the spring in the barrel G; so that the action
of the system on the chain is always the same.

The 7th. Figure exhibits a spring adapted to heavier purposes. It is a
cylinder nicely bored and hermetically closed at bottom; in which works
a Piston P plunged in oil, which when forcibly drawn up forms a vacuum
in the cylinder, into which the atmosphere endeavouring to enter, acts
like a spring on the Piston; and preserves the same stress whatever be
the height of this Piston in the cylinder.

This then, is also an _equalized Spring_, such as these experiments
require; but it is _not_ my invention. I first saw a vacuum used, as a
spring, by my noble Patron, the late Earl Stanhope: to whose mechanical
attainments, I owe this tribute of applause on the present occasion.

In the three Figures of this Plate, 8, 9, 10, are shewn two of the means
I use for creating those factitious resistances that are sometimes
wanted in the process of measuring power. In Fig. 8, E H F, is a gripe
or brake, such as millers use to stop their wind-mills with; fixed under
L, it surrounds the wheel E H, and is then fastened to the end F of the
lever K L. The brake is thus pressed with greater or less force against
the wheel, as the weight I is placed more or less distant from the
fulcrum L of the lever. By these means a resistance of the equable kind
is produced, capable of being adapted to _any_ power it may be wished to
measure; which makes this Dynamometer a real _tribometer_ or measurer of
friction.

The second kind of resistance brought forward in this Plate, is a
Pendulum P (Fig. 9 and 10,) set a vibrating by a pallet-wheel A B,
connected with the axis of resistance; and working in the pallets N. It
appears besides, in the Figure, that the times of vibration can be
changed by the mechanism T N R, which raises or lowers the ball P. This
then, is another resistance, such as we sometimes want: but it is also a
mean of finding the quantity of resistance that a vibrating body opposes
to motion, when oscillating in times _not_ those due to its length as a
pendulum. In other words it is a mean of measuring _vis inertiæ_
itself--which an _astounding_ modern writer declares does not exist!

I hasten to give a description of certain other parts relating to the
measuring system: and some methods of connecting with the Dynamometer
the several kinds of forces it may be desirable to examine.

In Plate 5, Fig. 12, A X represents a Crank or Handle with a variable
radius, the intent of which is to adapt a man's strength to the velocity
and intensity of any resistance he may have to overcome. The manner is
this: B is a Screw pressing on the quadrant, and fixing the arm C X to
any required angle with the part A C: thus determining the virtual
radius of the handle.

Fig. 14, shews a method of applying to the Machine the force of a man
pumping: for the catch N permits the handle O to rise alone, but carries
round the wheel R, at every downward stroke, while the fixed catch C
secures all the forward motion thus given. The same Figure shews, at B,
the force of a man in the act of _rowing_: for the catch M permits the
lever V M to recede when the man _fetches_ his stroke, and carries the
wheel round when he _takes_ it. An operation, by the bye, which I think
the best mode of employing human strength, if every possible advantage
is taken of the method.

The 13th. Figure shews the last method I shall now offer of adapting
power to the Dynamometer. T S represents the Piston of a Steam Engine,
the rod of which is formed of _two_ bars, including between them the
chains F G and F D, the first of which is single, merely to carry back
the acting wheel; and the last double, to draw round the ratchet wheel
E, by the catch O, at every stroke of the Piston.

I must obviate here an objection that may strike some readers. This
Piston T S, acts only one way, like that of an atmospheric engine, a
thing now quite out of date! I answer that this figure is chiefly
intended to give the _idea_; and shew a rotatory Steam Engine that
_might_ act without a fly. I will add, that it is my intention some day
to bring forward a method of using these suspended actions, better than
by a mere ratchet wheel: and especially without incurring danger from
the length of the ratchet teeth, or the blow they suffer at the
beginning of the strokes. But of this more hereafter.

A short description will suffice for the mechanism of the 18th. figure
(Plate 6), which is intended to convert the alternate pressure of a
man's feet into rotatory motion, and then to measure his _power_. To do
this two catches A B, take into the teeth of the same wheel M, and each
catch carries an arm, P, embracing somewhat stiffly the boss of the
wheel. The treadles have a common centre at E, and are fastened to the
same rope going over a pulley, F, so as for the depression of the one to
raise the other. Again, the pulling bars C D, are connected with the
treadles, and from the form of the catches, it is evident (since the
levers move with some stiffness), that the first effect of an ascending
motion will be to draw the rising catch out of the teeth, and keep it
out until arrived at its greatest height; when the very beginning of
its descending motion will bring the catch into the teeth again, and
thus carry round the wheel at every downward movement of the treadle;--a
method this of making a ratchet work without rattling upon the wheel.

The mechanism shewn in figure 19, is intended to produce another of our
factitious resistances; and it serves likewise to make experiments on
the resistance of the air. It is a fly, meeting with an _equable_
resistance as does the fly in the striking train of a clock. The wheel
W, is put on the axis of resistance of the Dynamometer; and its teeth
geer in those of the vertical shaft L H. This latter is perforated from
above, and has an open mortice all along its body, which a small bar
penetrates, meeting at bottom the ring H, to which it is fastened by a
pin going through the mortice. Again, this ring H, is moved, downward,
by the rollers of the sliding bracket P, which has its motion from the
wheel and rack G: and finally, the leaves I K slide in the horizontal
frame; and when the machine turns _would_ obey the centrifugal force and
fly outward; but are withheld by the cords N O, which passing over the
pulleys N O, and under those L M, are then fixed to the frame above L.
When, now, this Machine is used, and the fly made to revolve swiftly,
the leaves I K, oppose a certain resistance to the rotatory motion; and
if _this_ be too feeble, the key G must be turned backward, which will
permit the ring H to rise, and the wings I K to recede from the centre.
But if this resistance is already too strong, the key G must be turned
forward, and the wings brought nearer: between which extremes, a point
will easily be found where the resistance of the air will _expend_ just
power enough to balance that brought into the Dynamometer through the
_power-axis_; and thus to keep the measuring weight in the position
required for any given experiment.

There remains only one part to be described as belonging to this
Machine. It is represented in Plate 5, fig. 15, and is a graduated bar,
made to fit in the holes K, of the measuring cylinder I K Plate 1: and
to carry one of the arcs A A, which thus serves to extend, virtually,
the radius of that cylinder to any required dimension.

It is now time to shew something of the manner of using this Dynamometer
in the measurement of forces. Let the object then be to measure the
power expended by a Horse in drawing a Carriage.

To do this, we fix a Drum (see fig. 16,) of equal radius with the
measuring cylinder, on the power axis A; and a similar Drum to the
resisting axis H. After firmly fixing the Machine, we place the Carriage
at a distance behind it in the plane of the Drum H; and carry a rope
from that Drum to the Carriage: on the other hand, we fill the first
Drum A, with a coil of rope, to which the Horse is harnessed; and while
he travels in the plane of the Drum A, the scale P (Plate 1,) is loaded
with weights, until the Carriage follows the horse's motion without any
(or with little) agitation to the scale P: at which moment the _power_
employed _is equal to one half the weight at P, multiplied by the space
gone through both by the Horse and the Carriage_.

If it were now desired to find the power of a man turning a crank or
handle, we should take that given in the figure 12, and fix it to the
power-axis A. We should also take the fly-system shewn in fig. 19, and
place it on the axis-of-resistance H. Then causing the man to turn the
Machine, we should put _twice_ as much weight into the scale P, as his
strength was thought able to bear. Then if he thought the work too
heavy, we should draw inward the leaves of the fly, and take away part
of the weight P, until the man were satisfied he could work with
convenience: and when, as before, the weight P should overcome the
resistance of the fly I K, without either rising or falling, (sensibly)
then the _power_ expended would be _one half of the weight P, multiplied
by the space described by the man's hand in the act of turning the
handle_.

It may occur to some of my readers that in these experiments the whole
effect is not actually _measured_: since the space described by the
horse or the man's hand, must be determined after the experiment. I
answer that these quantities, necessarily _variable_, must bear an
inverse proportion to the weight P: and in all cases, this weight
multiplied by that space, must give the _power_ or momentum required.
Besides, it is most easy to add a piece of mechanism that shall count
the number of turns, and express them _in space_, by the inspection of a
graduated scale. Nor need we stop here. The duration, in time, of any
experiment, may also be recorded by the Machine itself. These are things
so naturally connected with the subject, that I cannot feel it
necessary, with so much before me, to attempt exhausting them. But
_this_ I engage to do: if any serious difficulty should actually stop
any reader in this career of investigation, I will obviate such
difficulty at some convenient future period. And mean while those
persons who have aptitude for such subjects, will find in this Machine,
ample scope for extending their enquiries; and comparing many mechanical
realities with the deductions of Theory, thus amending and conciliating
the conclusions both of Theory and Practice.

I have said above, that the weight or spring acting on the measuring
cylinder at K, _must_ be equalized: but in reference to _some_
applications of this Machine to real use, I would modify that precept a
little. I should, indeed, always like the principal action to be of a
constant nature: with a supplementary part of less intensity, prepared
to add something to the former; and this, for the purpose of meeting
spontaneously the case of any unexpected addition of the moving power.
Thus in Plate 1, if P be a weight _nearly_ adapted to a given
resistance, I would (to prevent accident, from its being overraised by
any sudden jerk of the power,) hang one or more heavy chains under the
scale, which drawn from the ground to a certain length, would add a
known quantity to the measuring power; and transmit with a certain
softness to the work, the unequal action of the _mover_.

One word on the _friction_ of this Machine. All friction must of course
be avoided as much as possible; but as it will be nearly the same in
every class of experiments, it is not of great importance. The same may
be said of the _vis inertiæ_ of the parts, _in convulsive motions_. The
parts would, of course, be made as light as a proper strength would
permit. My mechanical readers will easily supply these small items of
foresight; to anticipate the whole of which would make this Work
interminable.


  OF A NEW KIND OF
  BARREL SPRING,
  _To lengthen the going of Clocks, Jacks, &c._

Although this invention does not properly constitute a _new Spring_, yet
it produces effects both new and important. It protracts almost
indefinitely the action of a barrel Spring, and thus reduces
considerably the number of wheels in a clock or other spring-driven
machine. This effect is produced by _setting the two ends of the spring
at variance_; or making them _act one against another_: for as these
opposite tendencies can be made nearly equal, one end of the spring will
be wound up _almost_ as much as the other end runs down: thus prolonging
the effect in any desired proportion. It will be making known the
principle, to describe the _first motion_ of a clock founded upon it.

In Plate 7, fig. 1, A is the spring barrel, to which is fixed a _wheel_,
B, of 96 teeth, working in C, a pinion of 17. E is another _wheel_ of 92
teeth, working in F, a pinion of 22: both pinions being _fixed_ on the
same arbor, I G. The smaller wheel E, turns on a round part of the axis
H D; and is connected with its motion in the backward direction only, by
a ratchet wheel R, fixed on a square part of the same arbor. _As usual_,
this latter has a cylindrical boss within the barrel A, to which the
_inner_ end of the spring is hooked; as its outer end is, to the rim of
the barrel; and thus does the wheel B (when the clock is wound up) tend
to turn _forward_ as shewn by the arrow B; while the wheel E, tends to
turn _backward_ in the direction of E, the second arrow. But these
opposite tendencies are _not_ equal; because the wheel B is larger, and
acts _disadvantageously_ on C, the smallest pinion; while the wheel E is
smaller, and acts to _advantage_ on the larger pinion F: so that there
is a decided tendency in the whole to turn _backward_. Now, to find
precisely what is the effect of that tendency, we observe that when the
barrel and the larger wheel B, have made _one_ revolution round the
common axis H D, the pinions C and F will both have made 96/17 of a
revolution (being the quotient of the division of the wheel B by the
pinion C:) and since the larger pinion of 22 teeth, works in the smaller
wheel of 92 teeth; this latter wheel in the same time will have made
96/17 of 22/92 of a revolution, or 1,350 of a turn very nearly. The
difference then between this quantity and unity, namely the decimal
0,350, is what the spring has really _gone down_ during one turn of the
barrel. And as the whole number of coils in the spring are 10, the
number of turns of the barrel to uncoil it entirely, will be 10/0,350 or
10000/350 equal to 28,57 nearly: instead of _ten revolutions_ which it
would have been on the common principle.

It is almost superfluous to add that this prolongation of the time might
have been greater, had I not been confined to the above numbers, for
want of others _more nearly alike_, and having a common difference, on
my engine.

An important remark here presents itself, viz. that the best properties
of this invention are unattainable by the use of the common
_geering_--the friction of whose teeth would have absorbed the small
rotatory tendency thus retained; and in which system, also the working
diameters of the wheels could not have been defined with sufficient
exactitude. This then, is one of the cases in which (as I have observed
in a former work) my late Patent System of Geering has "given rise to
machines that could not have existed without it,"--which it does by
possessing exclusively the property of realizing (sensibly) the whole
calculated effect; and working without commotion or assignable friction.
It may please some of my readers to be informed that this System, and
the means of executing it in every dimension, will hold a prominent
place in some future page of this essay.

Referring again to the figure 1, the teeth X X, Y Y, are there placed to
give a first idea of this principle: and they are unaccompanied by
others, to avoid the confusion of lines that would have arisen from
attempting to shew all the teeth, in their due position, on so small a
scale. These things will claim all our attention when the System itself
comes under examination.

The above representation of this Machine may leave a technical
difficulty on the minds of clock makers relative to the _winding up_ of
this spring; which, in the present state of things, will suspend, for
the time, it's action on the pendulum: for in order to effect it, (in a
reasonable number of turns) the introduction of the key _must_, by a
proper check-piece, be made to stop the wheel B, and leave it again at
liberty when the key is taken out: in which case ten turns of the key
will effect the winding, although the Machine should be calculated to
_give out_ forty turns in the uncoiling of the spring. But if the wheels
B and E had changed places; that is, if E had been fixed to the barrel
A, and B been connected with the ratchet wheel R, then the act of
winding up would have taken place in the opposite direction; or in that
which tends to _keep up_ the motion of the pendulum, in which case,
however, the machinery of the clock must have borne the _whole_ stress
of the spring during the act of winding, instead of the small portion it
sustains when the two ends counteract each other.

But I anticipate another objection to this method of employing a barrel
spring: which is the inequality of stress, when the spring is much or
little wound. The answer is, that many clocks and watches are made to go
well without fusees; either by modifying the thickness of the springs,
or employing only a few of the middle coils. My Invention may, perhaps,
help to nurse this System to perfection: if not, its influence will be
the more confined, but in no wise destroyed.


  OF
  A PARALLEL MOTION,
  _Being a combination of the Crank with the Epicycloid_.

A B, Plate 7, fig. 2 and 3, is a ring or wheel fixed to the frame C D;
and having all round it's inside, teeth directed to the centre. F is a
wheel of half the diameter, and exactly half the number of teeth of the
wheel A B. It turns on a Crank-arm, E F, whose radius is equal to one
quarter of the diameter of the fixed wheel A B--in the centre of which
the axis of this Crank finds it's due position. The latter, therefore,
so conveys the wheel F round the inside of the fixed wheel A B, that the
teeth of both are constantly _geering_ to a proper depth: and a stud
being fixed on the face of the wheel F, opposite the middle of any
tooth, a, directly over the centre of the Crank E, this stud describes
the perpendicular diameter of the large wheel: and will either receive
motion from the rod R of a Steam Engine Piston, so as to give the fly I
K, a rotatory motion; or communicate to a Pump-piston a reciprocating
motion, drawn from the rotatory one of the fly, when _that_ is the
effect desired to be produced.

This Invention will be remembered, as having procured me a remunerating
Medal from the late Napoleon Bonaparte, then first Consul of the French
Republic. That period, however, (1801) was not the real date of this
production, although then first made _public_. I have proof, on the
contrary, of its existence with me several years before; and it is
generally ascribed to me by the publicists. I might quote in particular
Doctor Gregory: who likewise mentions its having been executed by
Messrs. Murray and Wood, of Leeds, subsequently to it's exhibition at
Paris. The Doctor commits, however, a small error in calling me an
Anglo-American; but this is accounted for by my then living in a country
where to be an Englishman was itself a crime! and where some kind
friends, wishing to hide me from the relentless decrees of the day, felt
justified in using this sort of pious fraud in my favour: a resource
from which, though I did _not_ authorize it, I reaped no small
advantage; and still think of with gratitude, though not with unmixed
approbation.

I think it a duty more imperious than agreeable, to expostulate a little
with Messrs. Lanz & Betancourt, on their apparent partiality in giving
an account of this Machine. In their work on the construction of
machines, art. 97, page 37, they make M. de la Hire the inventor of it,
by the terms in which they introduce his treatise on Epicycloids: and
they leave me the thread-bare merit of having "_presented a model_ of
this movement at the last exposition but one," &c. Now, although I do
not attach great importance to this kind of misrepresentation, I cannot
but observe, that neither my Machine or their description of it can be
called a Theorem! nor especially a theorem relating solely to the
Epicycloid, as M. de la Hire's was. These Gentlemen knew that he
insisted principally on the application of this curve to the teeth of
wheels, _with which my Invention has nothing to do_. On the contrary, my
Machine is a combination of two curves at least, on which de la Hire
says absolutely _nothing_. Is this then inadvertency? or is it uncandid
nationality? I hope, the former.

A further remark on the utility of this System as a first motion, may be
of use in this place. It respects the _geering_ of the fixed and
moveable wheels A B, and F, on the _perfection_ of which depends the
truth of the statement, that the stud, a, describes a diameter of the
large wheel. Now, perfection is too much to be expected from common
teeth when of the necessary strength; so that my Patent Geering is an
indispensable complement to this Invention: as by its use, the principle
is made practically true; this line becoming really straight, and this
motion, under proper circumstances, being unattended with noise or
commotion. In a word, I cannot move a step in this mechanical field,
without meeting with instances where the new System shews its
superiority to the old: whence it becomes a duty for me to commence the
consideration of this subject in the very next _part_ of this
publication.


  OF
  A SYSTEM OF CONCENTRIC PULLEYS,
  _Already known as White's Patent Pulleys_.

These Pulleys have been frequently described since I first entered my
_specification at the Patent Office_. The Authors of the Encyclopedia
Britannica; the Rev. Mr. Joyce, in his juvenile philosophy; and Dr.
Gregory in his mechanics, have all adverted to them. In the latter work,
I find the following quotation from my own description, thus introduced:

A very considerable improvement in the construction of pulleys has been
made by Mr. James White, who obtained a Patent for his Invention, of
which _he_ gives the following description: "Fig. 4, Plate 7, _of this
work_, shews the Machine, consisting of two pullies, Q and R; the former
fixed, the other moveable. Each of these has six concentric grooves,
capable of having a line put round them, and thus of acting like as many
different pulleys having diameters equal to those of the grooves.
Supposing then, each groove to be a distinct pulley, and that all these
diameters were equal, it is evident, that if the weight 144 were to be
raised by pulling at S, till the pulleys touched each other, the first
pulley must receive the length of line as many times as there are parts
of the line hanging between it and the lower pulley. In the present
case there are 12 lines, b, d, f, &c. hanging between the two pulleys,
formed by its revolution about the six upper and six lower grooves.
Hence as much line must pass over the uppermost pulley as is equal to 12
times the distance of the two. But, from an inspection of the figure, it
is plain that the second pulley R S, cannot receive the full quantity of
line by as much as is equal to the distance betwixt it and the first. In
like manner, the third pulley receives less than the first, by as much
as is equal to the distance between the first and the third; and so on
to the last which receives only 1/12 of the whole: for this receives
it's share of line n, from a _fixed_ point in the upper frame which
gives it nothing: while all the others in the same frame receive the
line partly by moving to meet it, and partly by the line coming to meet
them."

"Supposing now these pulleys to be equal in size, and to move freely as
the line determines them, it appears from the nature of the system, that
the number of their revolutions, and consequently their velocities, must
be in proportion to the number of suspending parts, that are between the
fixed point above-mentioned, (n) and each pulley respectively. Thus the
outermost pulley would go twelve times round in the time that the pulley
under which the part n of the line passes, (if equal to it) would
revolve only once; and the intermediate times and velocities would be a
series of arithmetical proportionals of which, if the first term were
l, the last would always be equal to the whole number of terms. Since
then, the revolutions of equal and distinct pulleys are measured by
their velocities, and that it is possible to find _any_ proportion of
velocity on a single body running on a centre, viz. by finding
proportional distances from that centre; it follows, that if the
diameters of certain grooves in the same body be exactly adapted to the
above series, (the line itself being supposed inelastic and of no
magnitude) the necessity of using several pulleys in each frame will be
obviated, and with that some of the inconveniences to which the use of
the common pulley is liable."

"In the figure referred to the coils of rope, by which the weight is
supported, are represented by the lines a, b, c, &c. a is the line of
traction commonly called the fall, which passes over and under the
proper grooves, until it is fastened to the upper frame just above n. In
practice, however, the grooves are not arithmetical proportionals; nor
can they be so, for the diameter of the rope employed must be deducted
from each term, without which, the small grooves to which the said
diameter bears a greater proportion than to the larger ones, will tend
to rise and fall faster than the latter, and thus introduce worse
defects than those which they were intended to obviate."

"The principal advantage of this kind of pulley is, that it destroys
lateral friction, and that kind of shaking motion which are so
inconvenient in the common pulley; and lest, says Mr. White, (I quote
Dr. Gregory) this circumstance (of a long pin) should give the idea of
weakness, I would observe, that to have pins for pulleys to run upon, is
not the only, nor perhaps the best method: but that I sometimes use
centres fixed in the pulleys, and revolving on a short bearing in the
side of the frame, by which strength is increased, and friction much
diminished: for to the last moment of duration, the motion of the pulley
is circular, and this very circumstance is the cause of it's not wearing
out in the centre as soon as it would, assisted by the ever increasing
irregularities of a gullied bearing.--These pullies when well executed,
apply to Jacks and other Machines of that nature with great advantage:
both as to the time of their going and their own durability: and it is
possible to produce a System of pulleys of this kind, composed of six or
eight parts only, and adapted to the pocket, which by means of a skain
of sewing silk, would raise more than a hundred weight."

There are several real and solid advantages attending the use of this
pulley; some of which are only hinted at in this description. I have
thought, therefore, it might be useful to introduce here an account of
some trials which the System underwent a few years ago at
Portsmouth,--at the request of an Officer of the Navy, who had
_re-invented_ it with some ingenious additions to my ideas. Not being at
present in correspondence with that Gentleman, I hardly think myself at
liberty to mention his name; but fully so to give an extract from the
report which followed these experiments--in which the superiority of
the System _in respect of power_, is made evident, although some less
favourable circumstances prevented its adoption on that occasion.

"With a view to comparison, it was settled with Lieutenant S. that his
blocks should be made to correspond with the treble and double 16 inch
blocks of a 24 gun ship, which carry a 4-1/2 inch rope. The sheeves in
the new blocks are fixed upon the pin, revolving therewith, and are of
different diameters proportioned to the velocity of the parts of the
rope that pass over them; they are also reeved with a double rope so
that there are two grooves of each size, the diameter of the smallest
groove in this tackle being 2-8/12, and of the largest 15 inches. The
diameter of the sheeves of the common blocks would have been (as usually
made) 9-1/8 to the bottom of the grooves, but were reduced at the
request of Lieutenant S. in the treble block to 8-1/8, and in the double
block to 8-7/8, in order that the sum of the diameters of the sheeves in
each tackle should be the same. The Lieutenant intending in the first
instance, to have used a roller under the pin, for the purpose of
diminishing friction, but afterwards laying aside this idea on account
of it's complication, was the reason that he had not made his sheeves in
the same proportion with the common blocks: the weight and length of the
respective blocks are as follows:

                                   Weight.      Length.

  Lieutenant S.'s treble blocks    131lbs.     24 Inches.
  Common             ditto         78  "       16   "
  Lieutenant S.'s double block     73  "       21   "
  Common             ditto         60  "       16   "
  Lieutenant S.'s single block     22  "       17   "
  Common             ditto         34  "       16   "

"Lieutenant S.'s blocks were reeved with a 2-1/2 inch double rope, and
the common block with a 4-1/2 inch single rope, and both tackles
suspended from a beam, and their respective falls let over the single
blocks, so as to keep the weight applied as a power, just clear of the
weight to be lifted, thus forming a power of six to one; the following
experiments were made:

   Weight very          Power required              Power required
  slowly lifted.  with Lieutenant S.'s blocks.  with the common blocks.
     [lb]s.                 [lb]s.                       [lb]s.
      336                     88                          124
      672                    169                          252
     1344                    312                          448
     2688                    588                          808
     5376                   1101                         1344.

"After reeving the common blocks with a 3-1/2 inch rope in lieu of a
4-1/2 inch rope, it was as follows: 5376 1101 1232.

"It must be observed, that the double 2-1/2 inch rope in Lieutenant
S.'s blocks, is not of equal strength with the single 4-1/2 inch rope
first used in the common blocks; and that his blocks had an undue
advantage in the first experiment over the common blocks, in respect to
the pliability of the rope. The rope should therefore, be taken larger
in the one or smaller in the other case, on this account: The common
blocks were reeved in the last experiment, with a 3-1/2 inch rope, which
is as near as may be of the same strength as the double 2-1/2 inch rope.

"In these experiments it was observable, that the tar was much more
squeezed out of the parts of the rope that passed over the smallest
sheeves in Lieutenant S.'s blocks, than out of those passing over the
larger sheeves, or out of those passing over the sheeves of the common
blocks; by which, as well as by the nature of the thing, we judge that
with blocks requiring such small sheeves, the ropes would be more
crippled and broken than by the common blocks, especially if any
constant strain or weight in motion, as on ship board, should be held by
them. In regard to our opinion of the merits of the blocks proposed by
Lieutenant S. compared with common blocks, we beg leave to submit, that
the mechanical principle of them is very inviting, and it is not to be
wondered that an ingenious person should pursue the idea; yet _allowing
there would be a saving of power_, which is attained in so great a
degree with the common blocks, but considering the greater complication,
weight, and expence of these blocks, and their greater disposition to
cripple the ropes, we do not perceive any application of them on ship
board, for which we could recommend them in preference to common blocks;
neither do we perceive any purposes on shore, for the services of the
dock yards in which to recommend their application in preference to the
other powers in use."

To this account of the result of these experiments, I beg leave to add
what seems to be a great improvement of this System: namely, a method by
which the diameters of the larger pulleys are considerably lessened; and
thus the principal, if not the only objection, obviated. It has been
before observed, that the larger pulleys, as Q R, are the ultimate terms
of an arithmetical progression, beginning at unity; and that
consequently they cannot be very small, even though the first terms
should be so. If a first pulley were only one inch in diameter, the
_twelfth_ pulley would be twelve inches,--where we see a large and
inconvenient difference. But this evil I now obviate, by placing at the
beginning of the series, one or more _loose pulleys_, over which to
_reeve_ the cord, before the concentric or fixed grooves begin; thus
lowering the _ratio_ of the progression, and keeping the larger pulleys
within bounds. For example, the smallest fixed pulley (supposed as
before, to be one inch in diameter) I now make the _second_ of the
series instead of the first: and therefore, the second _fixed pulley_ is
to the first as 3 to 2, instead of being as 2 to 1; for the same reason,
the third fixed pulley is to the second as 4 to 3; and in a system of
12 pulleys, (with one loose one) the respective terms will be as
follows:

  Terms  1----2----3----4----5----6----7----8----9---10---11---12
       loose;2/2; 3/2; 4/2; 5/2; 6/2; 7/2; 8/2; 9/2;10/2;11/2;12/2

or 6 inches for the largest pulley, instead of 12 inches given by the
last progression.

So likewise, if we take _two_ loose pulleys, (which will not add much to
the complication of the Machine) and make the third term 1 inch, the
fourth will become 4/3, shewing the _ratio_ of the progression to be
1/3, so that the series of 12 terms will stand thus:

  Terms,  1-----2----3---4----5----6----7----8----9---10---11---12
        loose;loose; 1; 4/3; 5/3; 6/3; 7/3; 8/3; 9/3;10/3;11/3;12/3; or,

four inches for the largest groove in the concentric part of the System.

Now we saw before, that the first and last pulley were in diameter to
each other, as 1 to 12; whereas, here, with only two loose pulleys,
these extremes are but as 1 to 4: dimensions much more convenient and
manageable. The 5th. figure of the Plate 7, is intended to shew
graphically, the effect of this modification of the principle. In that
figure, if the line a, be the diameter of the _first_ pulley, that of
the sixth pulley will be shewn by the line b c; but if the same line a
be made the _second_ pulley, the diameter of the sixth will be shewn by
the line e d; only 2/3 of the former. And in fine, if the same a, be the
third pulley, the sixth will have it's diameter reduced to the line f
g, only one half of what it was in the first case. In a word, the more
loose pulleys are put before the fixed ones begin, the nearer to
cylindrical will the general form become; and the more conveniently may
pulleys be used for general purposes. I might even assert, that if
_one_, or at most two loose pulleys had been used in the above-mentioned
experiments, the result would have been as favourable to the System,
with respect to the _weight of the tackle and stress on the ropes_, as
it was in respect of _power_; where it's advantages were important and
undeniable.


  OF
  A POWER-WHEEL,
  _Turned by heated Air, Gas, &c._

This Wheel (see Plate 8, fig. 1,) is technically called a Bucket-wheel.
It is plunged almost entirely in water, oil, mercury (or other heavy
fluid) contained in the vessel A B. It's axis carries a _waved_ wheel a
b, on which rolls a friction-pulley p, running on a pin in the mortice
of the bar c d. This bar works the pump f; which by the descent of it's
_loaded_ Piston, drives _cold_ air (or gas) into the tube g,
communicating with _several_ collateral ones placed _across_ the vessel,
so as to convey the air to h, below and beyond the centre of the wheel.
A fire being made at F under this vessel, the water (or other fluid) is
brought to a proper heat; and if then the pump f, be made to give a
stroke or two, air will be forced from the tubes at h, which having been
heated in the passage, will bubble up into the buckets h, i, k, &c. and
turn the wheel so as to perpetuate it's own supplies from the Pump, and
furnish a surplus of _power_ for other purposes. This results from the
fact, that air (for example) in rising to the temperature of boiling
water, expands, under the pressure of the atmosphere, to about three
times the volume it occupied at the mean temperature: so that it resists
the entrance into the vessel as _unity_, and acts (when heated) as 3:
leaving a power of _two_, in the form of a rotatory motion.

It will occur to many readers, that azotic gas or nitrogen, might be
used with advantage to turn this wheel: only adding to the Machine a
_long_ returning tube, leading from the top of the vessel, through air
or water, to the _suction valve_ of the pump f; and _that_ in order to
bring down the temperature of the gas from the heat it had acquired in
the vessel, to the mean temperature; at which this gas is said to occupy
only 1/7 of the space it fills when at the heat of boiling water.

I have now to observe that this invention was _executed_ in 1794, of
which abundant proof remains. Since then, it has been proposed by other
persons, and is I think, patentized either in France or England: but a
different method is employed of introducing the cold _air_, namely an
inverted screw of Archimedes, whose manner of working I do not entirely
recollect. What I here wish to observe is, that this concurrence of idea
between others and myself, gives me no pain; since it would be more
strange if it did not happen, while so many active minds are ransacking
nature for the very purpose of unveiling her secrets. Only I think it
incumbent upon me to use every method, consistent with truth and honour,
to avoid being thought unjust enough to purloin other people's ideas,
and call them my own.


  OF
  AN EQUABLE PUMP,
  _Or Machine for raising Water without interruption or concussion_.

This Machine is represented in Plate 8, fig. 2 and 3. It is composed of
two barrels A B, both of them forming part of the column of water to be
raised; connected together by a crooked tube C, of equal diameter, out
of which the lower Piston-rod passes through a stuffing box into the
air: as does the upper Piston-rod at D, where the column leaves the Pump
to pass upward. The two Pistons fixed to the rods E and F, are of the
bucket kind; made as thin and light as possible; their valves opening
upwards and their motions being such, generally, that when one of them
is drawn up, the water rises through the other, _then descending_: But
here lies both the novelty and utility of this Machine; these upward and
downward motions are _not_ reciprocal: Both Pistons fall faster than
they rise, and thus leave an interval of time _when they both rise
together_; during which their valves, respectively, close by their own
weight _before_ the column of water falls upon them. In such manner,
indeed, that the column never _falls_ at all. By this important
arrangement, the work is constantly going on, and _no commotion_ occurs
to absorb _Power_ uselessly, or to destroy, prematurely, the Machine;
circumstances which _constantly_ attend every Pump Machine acting by
merely reciprocal motion.

This non-reciprocity then, I produce by several methods; one of which
(perhaps the most easily understood) is that shewn in fig. 2: There, A B
are two friction-rollers, made as large as possible, rolling on the
curves C X, the ascending and descending parts of which are essentially
_unequal_. For example, the rising part of the curve occupies 2/3 of the
whole circumference; and the falling part 1/3 only; so that both curves
recede from the centre at the same time, during 1/6 of a revolution, at
the two opposite positions, A C and X Y. Applying then, these curves and
levers to the Pump-barrels represented in fig. 3, we obtain that
_continuity of uniform motion_, which is necessary to doing the greatest
quantity of work with the least power; and to securing the greatest
durability of the Machine. Having hinted at a _minimum_ of power, I must
add here that this Machine appears to promise that result, much more
credibly than any reciprocating pump whatever; especially if to this
continuity of motion we add a certain _largeness_ of dimension that
shall produce the required quantity of water, with the slowest possible
motion of each particle; and even here this _continuative_ principle
helps us much; since pistons and valves of the largest dimensions may be
used without introducing any convulsive, or (what is synonymous) any
destructive effects.

One particular remains to be noticed in fig. 2. It relates to the means
by which the _perpendicularity_ of the motion in the Piston-rods is
secured. The arcs M are portions of cylinders having the bolts Z, for
their centres, and which, _rolling_ up and down against the
perpendicular plane O N, secure a similar motion to the bolts. The
_tenons_ P, are cycloidal, on their upper and lower surfaces; and work
in square or oblong holes in the plane N O, being kept _in_ their holes
by the action of the two springs on a pin let through these tenons: and
thus is the motion of the point Z of the levers M B, a perpendicular
one; and that of the friction rollers A B, very nearly so.

My object in this work, is to make known the principles, and _some_ of
the forms of these Inventions, but my limits will not permit their being
dilated on; else I could give several more useful forms of this Machine:
but, to make room for other subjects, I must hasten forward--reserving
to some future period, many hints respecting the adaptation of those
ideas to particular cases. Those of my readers who love to speculate on
the doctrine of _permutations_, will anticipate how much may be done by
the _combination of a hundred Machines_ with each other: and they will
give me credit for detached items of knowledge--useful in themselves,
though too minute to be severally brought forward. Should, however, the
degree of patronage I have already experienced, be proportionably
extended as the work advances, _I can and will_ follow it up with many
useful hints, tending to shew the extent of some of my present subjects,
and the amplitude of the sphere in which they roll.

It should be observed, in concluding this article, that the present
Machine was executed in France, in 1793, and also proposed to the
Government, as a substitute for the celebrated Machine of Marly. In the
report then published, it was preferred to the whole multitude of former
projects; but left _in equilibrio_ with _one_ modern Machine,--a
competition which prevented it's adoption for the moment--and indeed
till I was _glad to escape the notice_, instead of courting the favour
of the then rapidly succeeding governments.


  OF
  A SIMPLE MACHINE,
  _For Protracting the Motions of Weight-Machinery_.

Let A, Fig. 4 Plate 8, be the barrel-wheel of a Clock, or other Machine,
already in use, and driven by a weight; and let the _similar_ barrel B
be added to the former; the motion of both being connected by the
_unequal_ wheels C D. The rope or chain E F, is then led from the barrel
A under the pulley P to the barrel B: By which arrangement, when the
weight has occasioned _one_ revolution of the barrel and wheel A C,
_those_ B D, will have made a lesser portion of a revolution in the
ratio of the wheel C and D; (namely as 22 to 24,) and that motion will
have _taken up_ 11/12 of the line which the barrel A has _given off_. By
these means, the motion of the whole may be prolonged almost
indefinitely. This System may appear to some persons open to the
objection that the friction of the wheels C D, will absorb so much of
the power, as to leave the rotatory tendency too feeble for it's
intended purpose. But I again take refuge in the well proved property of
my patent geering,--of not impeding (sensibly) the motion of any Machine
in which it is used.

Should it further be suggested, that this is only an awkward parody on
the _differential wheel and axle_, ascribed by Dr. Gregory (in the
introduction to his work, page 4,) to the celebrated George Eckhardt: I
would answer, that I made _that invention also_; though doubtless
_after_ Mr. Eckhardt; and especially after the date of the figure given
by the Doctor, as coming from China, "among some drawings of nearly a
century old;" Of course then, I do not pretend to priority of invention:
but _truth herself_ authorises me to say, that I did invent this Machine
also, _in the night between the 17th. and 18th. of January, 1788, and
drew it in bed by moonlight, that it might not escape me!_ It was the
result of a previous _fit_ of close thinking: and of the conclusion I
_then_ drew, that in whatever way, _slowness_ of motion is obtained by
the connection of two movements, _power_ is invariably gained for the
same reason, and in the same proportion. The fact is, that all my ideas
respecting differential motions, have flowed from this source; as will
be evident to the attentive reader of these pages.


  OF
  AN INSTRUMENT
  _For drawing Portions of Circles, and finding their Centres by
  inspection_.

It is a known property of _an angle_ such as g d f (plate 9 fig. 1) when
touching two fixed points g f, and gliding from one of these points to
the other, to describe a portion of a circle g d f. My object in this
instrument is to determine, by inspection, the radius of such circle in
all cases.

To do this, I connect with the jointed rule m d n, another rule like
itself but shorter g e f, so as that the figure g d e f shall be a
perfect parallelogram: and I then say that knowing the distance of the
points d and e, (the distance d f being given) I know the radius of the
circle of which g d f is a portion. To prove this, a little calculation
is necessary: In the circles A B and a b (fig. 6) draw the lines E D; _f
d_, _d g_, _g f_, _g e_, and _g D_; and bearing in mind the known
equation of the circle, let _d n_ = _x_, _g n_ = _y_; and g D = a, the
absciss, ordinate, and radius respectively. The equation is 2ax - x² =
y²: from which we get _a_ = (y² + x²)/(2x) the denominator of this
fraction being the line _d e_. But further its numerator (_y_² + _x_²)
is equal to the square of the chord g d of the angle E D g, which chord
I call _c_. This gives _a_ = _c_²/(line _d e_); from which equation we
derive this proportion _a_ : _c_ :: _c_ : line _d e_; Putting then the
chord _c_ = 1 (one foot for instance) this proportion becomes _a_ : 1 ::
1 : 1/_a_; whence we draw this useful conclusion, that, whatever portion
of a foot is contained in the line _d e_, (expressed by a fraction
having _unity_ for its numerator) the radius of the circle will be
expressed _in feet_ by the denominator of that fraction. Thus if the
line _d e_, be 1 inch or 1/12 of a foot (and the line _g d_ or _d f_ be
1 foot) the radius of the circle will be 12 feet; and so for every other
fraction. Now in the instrument itself the two points _d_ and _e_, _are
connected by a micrometer-screw_ (not here drawn) of the kind described
in a subsequent article, and by which an inch is divided in 40,000
parts, each of which therefore is the 1/3333.33, &c. part of a foot: so
that if the distance _d e_, were only _one_ of these parts, we should
produce a portion g d f of a circle of 3333.33, &c. feet radius--being
more than half a mile.

I had omitted to observe, that the _points_ or studs, against which the
rulers m n slide, to trace the curve (_by a style in the joint d_,) that
these studs I say are fixed to a detached ruler o p, laid _under_ the
parallelogram on the paper, and having two _stump points_ to hold it
steady: _one_ of the studs being moveable in a slide, in order that it
may adapt the distance f g, to _any_ required distance of the points _d
e_: We note also that the dotted curve g d f is _not_ the very circle
drawn, but one parallel to it and distant one half the width of the
rulers. In fact the mortices of these rulers are properly the acting
lines, and _not their edges_. I expect, for several reasons, to resume
the subject of this instrument before the work closes.


  OF
  AN INCLINED HORSE WHEEL,
  _Intended to save room and gain speed_.

My principal inducements for giving this Wheel the form represented, by
a section, in fig. 3, (see Plate 9) were to save _horizontal room_; and
to gain speed by _a Wheel_ smaller than a common horse-walk,--and _yet_
requiring less obliquity of effort on the part of the horse. With this
intention, the horse is placed _in a conical_ Wheel A B, more or less
inclined, and not much higher than himself: where, nevertheless, his
head is _seen_ to be at perfect liberty out of the cone as at C. The
horse then walks _in_ the cone, and is harnessed to a fixed bar
introduced from the open side where, by a proper adjustment of the
traces, he is made to act partly by his weight, so as to exert his
strength in a favourable manner. This Machine applies with advantage
where a horse's power is wanted, _in a boat or other confined place_:
and it is evident, by the relative diameters of the wheel and pinion A B
and D, (as well as by the small diameter of the wheel) that a
considerable velocity will be obtained at the source of power,--whence,
of course, the subsequent _geering_ to obtain the swifter motions, will
be proportionately diminished.


  OF
  A DIFFERENTIAL COMBINATION OF WHEELS,
  _To count very high numbers, or gain immense power_.

In fig. 2, of Plate 9, (which offers an horizontal section of the
Machine), A B is an axis, to the cylindrical part of which the wheels C
D are fitted, so as to turn with ease in either direction. Each of these
wheels, C and D, has two rims of teeth, _a b_, and _c d_; and between
those _b d_ are placed an intermediate pinion W, connected by it's
centre with the arm _x_, which forms a part of the axis A B. There is
likewise a fourth wheel or pinion Z, working in the outer rims _a c_ of
the wheels C and D. It appears from the figure itself, that the action
of this Machine depends on the greater or lesser _difference_ between
the motion _forward_ of the wheel C, and the motion _backward_ of the
wheel D; for if these opposite motions were exactly alike, the wheels
would indeed all turn, but produce no effect on the arm _x_, or the axis
A B: whereas _this_ motion is the very thing required. Since then the
motion of the bar _x_, and finger _g_ depends on the difference of
action of the wheels C and D on the intermediate pinion W, we now
observe, that in the present state of things, the rims _a_, _b_, _c_,
_d_, have respectively 99, 100, 100, and 101 teeth: and that when _one
revolution_ has been given to the wheel C, the rim _b_ of this wheel
has acted, by 100 of its teeth, on those of the intermediate pinion W;
insomuch that if the opposite wheel D had been immoveable, the arm _x_
would have been carried round the common centre a portion equal to 50
teeth, or one half of it's circumference (which effect takes place
because the pinion W _rolls_ against the wheels C and D, it's centre
progressing only half as fast as it's circumference.) But instead of the
wheel D standing still, it has moved in a direction opposite to the
former, a space equal to 99/100 of a revolution, and brought into the
teeth of the pinion W, 99/100 of 101 teeth; that is, 99 teeth, and 99
hundredths of one tooth: so that the _account_ between the two motions
stands thus:

        The forward motion by the wheel C, is equal to 100,00 teeth.
             And the backward motion by the wheel D, is 99,99   "
                                                       ------
  And the difference in favour of the forward motion is 00,01 of 1
  tooth.

Or, dividing the whole circumference into 101 parts (each one equal to a
tooth of the rim _d_,) this difference becomes 1/100 part of 1/101 =
1/10100 of a revolution of the axis A B, for each revolution of the
wheel C. But we have observed, that the arm _x_ progresses only _half_
as much, on account of the _rolling_ motion: whence it appears that the
wheel C, must make 20200 turns to produce _one_ turn of this axis A B.
And if, with 20 teeth in the pinion Z, we suppose the movement to be
given by the handle _y_, this handle must make _more_ than 20200
revolutions, in the proportion of 99 (the teeth in the wheel) to 20, the
teeth in the pinion Z. Thus the said 20200 turns must be multiplied by
the fraction 99/20 which gives 99990 turns of the handle, for one of the
axis A B. And finally, if instead of turning this Machine by the handle
and pinion _y_ Z, we turned it by an endless screw, taking into the rim
_c_, of 100 teeth; the handle of such screw must revolve 2020000 times
to produce one single revolution of the axis A B; or to carry the finger
_g_, once round the common centre.

The above calculations are founded on the very numbers of a Machine of
this kind I made in Paris: and of which I handed a model to a public man
nearly thirty years ago. I need not add that this kind of movement
admits of an almost endless variety: since it depends both on the
numbers of the wheels and their differences; nay, on the differences of
their differences. I might have gone to some length in these
calculations had I not conceived it more important to bring other
objects into view, than to touch at present the extensive discussions
_this subject_ invites and will doubtless suggest to many. Suffice it
now to say, that here is a simple Machine which gains power (or
occasions slowness), in the ratio of two millions and twenty thousand to
one; giving, (if executed in proper dimensions) to a man of ordinary
strength, the power _of raising, singly, from three to four hundred
millions of pounds_. It may be useful to observe that using this Machine
for an opposite purpose, that of _gaining speed_, _extreme rapidity_ may
be caused by a power acting very slowly on the axis A B; only in that
case, the _difference_ must be enlarged, and the diameters and numbers
of the wheels be calculated _on the principles of perfect
geering_--which is as easy in this Machine as in any other.


  OF
  A CRANE,
  _Which combines_ VARIABLE POWERS _with speed and safety_.

Doctor Gregory (in his Mechanics 2d. volume page 157,) thus introduces
the description of this Crane, and the observations with which he tags
that description.

"The several Cranes described in this article, as preferable to the
common walking Crane, while they are free from the dangers attending
that Machine, lose at the same time one of it's advantages, that is,
they do not avail themselves of that addition to the moving power which
the weight of the men employed may furnish: yet this advantage has been
long since insured by the mechanists on the continent: who cause the
labourers to walk upon an inclined plane, turning upon an axis, after
the manner shewn in the figure referred to under the article
_foot-mill_,--where we have described a contrivance of that kind, well
known in Germany nearly 150 years ago. The same principle has been
lately brought into notice (probably without knowing it had been adopted
before) by Mr. Whyte, (White) of Chevening in Kent: His Crane is
exhibited,--fig. 2 and 4, Plate 10, _as it was described in the
Transactions of the Society for the Encouragement of Arts_."

"A, Plate 9, fig. 4, (of this Work) is a circular inclined plane, moving
on a pivot under it, and carrying round with it the axis E. A person
walking on this plane at A, and pressing against a lever, throws off a
gripe or brake, and thus permits the plane to move freely, and raise the
weight G by the coiling of the rope F, round the axis E. To shew more
clearly the construction and action of the lever and gripe, _a plan_ of
the plane connected with them, is added in fig. 5, where B represents
the lever, and D the gripe: where it is seen that when the lever B is in
the situation in which it now appears, the brake or gripe D, _presses
against the periphery of the plane_; but when the lever B is driven out
to the dotted line H, the gripe D is detached, and the whole Machine
left at liberty to move: a rope or cord of a proper length, being
fastened to B, and to one of the uprights in the frame, to prevent this
lever from being pushed too far towards H, by the man working at the
Crane."

"The _supposed properties_ of this Crane, (says Dr. Gregory) for which
the premium of forty guineas was adjudged by the society to the
Inventor, are as follows:"

"'1. It is simple, consisting merely of a wheel and axle:

"'2. It has comparatively little friction, as is obvious from the bare
inspection of the figure:

"'3. It is durable from the two properties above mentioned:

"'4. It is safe: for it cannot move but during the pleasure of the man,
and while he is actually pressing on the gripe lever:

"'5. This Crane admits of an almost infinite variety of different
powers; and this variation is obtained without the least alteration of
any part of the Machine. If in unloading a vessel, there should be found
goods of every weight, from a few hundreds to a ton and upwards, the
workman will be able so to adapt his strength to each, as to raise it in
a space of time, (inversely) proportionate to it's weight, he walking
always with the same velocity as nature and his greatest ease may teach
him.'"

"'It is a great disadvantage in some Cranes, that they take as long a
time to raise the smallest weight as the largest; unless the man who
works them turn or walk with such velocity as must soon tire him. In
other Cranes, perhaps, two or three powers may be procured; to obtain
which, some pinion must be shifted, or fresh handle applied or resorted
to. In this Crane on the contrary, if the labourer find his load so
heavy as to permit him to ascend the wheel without turning it, let him
only move a step or two towards the circumference, and he will be fully
equal to the task. Again, if the load be so light as scarcely to resist
the action of his feet, and thus to oblige him to _run_ through so much
space as to tire him beyond necessity, let him move laterally towards
the centre, and he will soon feel the place where his strength will
suffer the least fatigue by raising the load in question. One man's
weight applied to the extremity of the wheel would raise upwards of a
ton: and it need not be added that a single sheaved block (at the jib)
would double that power. Suffice it to say that the size of the machine
may be varied in any required degree, and that this wheel will give as
great advantage at any point of its plane as a common walking wheel of
equal diameter; as the inclination can be varied at pleasure, as far as
expediency may require. It may be well to observe that what in this
figure is the frame and seems to form a part of the Crane, must be
considered as part of the house in which it is placed; since it would be
mostly unnecessary should such cranes be erected in houses already
built: and with respect to the horizontal part, by walking on which, the
man who attends the jib, occasionally assists in raising the load, it is
not an essential part of this invention, when the crane and jib are not
contiguous: although, when they are, it would certainly be convenient
and economical.'"

The Doctor continues: "Notwithstanding, however, the advantages which
have been enumerated, Mr. Whyte's (White's) Crane is subject to the
theoretical objection, that it derives less use than might be wished
from the weight of the man or men: for a great part of that weight
(_half_ of it if the inclination be 30 degrees,) lies directly upon the
plane, and has no tendency to produce motion. Besides, when this Crane
is of small dimensions, the effective power of the men is very unequal;
and the barrel too small for winding a thick rope: when large, the
weight of the materials, added to that of the men, put it out of shape
and give it the appearance of an unwieldy moving floor."

The Doctor continues: "We know one large Crane of this construction,
which has an upright post near the rim on each side, to support it, and
keep it in shape; and as much as possible to prevent friction, each post
had a vertical wheel at it's top." (N. B. _I_ never saw, or heard,
before, of this monster.)--"We were informed this Crane was seldom used;
and that it was soon put out of order. Nor, moreover, is it every
situation that will allow the Crane-rope to form a right angle with the
barrel on which it winds; and when this angle is oblique, the friction
must be much increased. The friction arising from the wheels at the top
of the vertical _crutches_ might indeed be _got shut off_, by making the
inclined wheel very strong; but this would add _greatly_ to the friction
of the lower gudgeon of the oblique shaft, and _considerably_ increase
the expence of the Machine."

"There remains then (says Dr. Gregory) another stage of improvement with
regard to the construction of Cranes, in which the weight of the
labourers shall operate without diminution, at the end of an horizontal
lever; and in which the impulsive force thus arising, may be
occasionally augmented by the action of the hands, either in pulling or
lifting"--and then follows the conclusion. "This step in the progress
has been lately effected by Mr. David Hardie, of the East India
Company's Bengal warehouse!"

I cannot follow the author (whoever he be) of the glowing picture next
given of Mr. Hardie's Invention, (to which the obloquy thrown on my poor
abortion is clearly _the foil_) as my readers must already be anxious to
"get shut" of such unmitigated Bathos, bestowed on so trivial a theme.
With respect to my Crane, I shall only say that it fulfilled the
conditions required by the Society, _and obtained the Premium_: and if
on the one hand, the language in which, thirty years ago, I described
it, exhibits the impetuosity of youth, untempered with the moderation of
age, I will say on the other, that if impartial criticism, mechanical
acumen, or comprehensive _science_ are essential components of a
mechanical work _of high pretensions_,--these qualities were seldom more
wantonly abandoned or abused, than in the paragraphs above quoted:
except, perhaps, in the attack of the same work, on the labours and
character of the justly celebrated Watt, whose merits had this author
known how to appreciate, he _could not_ thus have attempted to lessen in
the public esteem.

But to return, this _Diatribe_ begins by comparing my Crane to a foot
mill: and kindly supposes I did not know that its principle existed in
Germany 150 years ago. But the fact is, my object was nothing like that
of the author of the mill in question: the very figure of which, proves
that _he_ had no view to the variation of power by change of place on
the wheel: whereas _that_ is the principal use I make of this "unwieldy
moving floor," as the Doctor _heavily_ terms it. Again, this author
asserts that by making men walk on an _inclined_ plane, I derive less
use than might be wished from their weight; and yet! a page before he
told us that "the mechanists on the Continent had long since insured the
advantage of availing themselves of that addition to the moving power
which the weight of the men may furnish;" so that poor _I_ have the
merit of imitating them without knowing it, and yet of _not_ drawing the
same advantages as they from the self same principle!

But again, "a great part of the weight of the man (_half_ of it, if the
inclination be 30 degrees) lies directly on the plane, and has no
tendency to produce motion," which _one sided truism_ is placed there to
give relief to the portentous _dictum_, which follows:--that "there
remains then another stage of improvement with regard to the
construction of Cranes, in which the weight of the labourers shall
operate without diminution at the end of an horizontal lever: and that
stage has been effected by Mr. D. H. of the East India Company's Bengal
warehouse."

But is this conclusion definitive? are there no countervailing evils?
Will Dr. Gregory presume to say there is no _disadvantage_ attending
this advantage? Did the Doctor ever ascend an upright ladder? and did he
_prefer_ that, to going up an easy flight of stairs? was he ever in the
geometrical stairs of St. Paul's? or in any large _winding_ stair-case?
and if so did he prefer ascending close to the nucleus? or did he
quickly seek a point where the step was _wider than high?_ most
certainly the latter; and why then did he not perceive that if the
weight of my man is diminished one half on the plane, for the very same
reason, a given _elevation_ of his feet (on which his _fatigue_ depends)
will cause a circular motion twice as extensive; yet this is quite as
clear as the Doctor's _ex-parte_ proposition.

But I must wade on a little further, trusting that my readers will exert
a little more patience to follow me: for this same dictum of the
Doctor's accuses indirectly, the Society of Arts of being a set of
blockheads, for remunerating an Invention with only _supposed_
properties. I really wish these self-constituted judges of other
people's labours would utter their oracles with more regard to truth and
propriety! and above all, not mix up their passions (which alas! are not
always purified by science) with their judgement on the merits of other
men's inventions. Had the author of this article been wise enough to
proceed thus, he would not have _supposed_ me capable of offering
_suppositions_ for realities; nor the Society of Arts of rewarding as
genuine, _suppositious_ merit; and still less would he have emblazoned
the very properties he calls _supposed_, with _reality_ written in
glaring characters on every one of them! These properties are in fact
only the transcript of what the society required of the candidates: and
I therefore said my Crane is simple: Can this author say it is not? I
said it has little friction? will he say it has _much?_ I said it is
durable: Is it now possible to contradict this? I said it is safe: and
will Dr. G. say it is not, when it is moveable, _only during the wish of
the workman_: since _whatever_ suspends this wish, (whether accident or
design) the Crane becomes of itself _immoveable_. In fine, I observed,
that this Crane admits of an indefinite number of _powers_, without any
modification of it's parts; and can any one say these are _supposed_
properties? If the Doctor or his coadjutors persist in saying so, I must
_suppose_ them actuated by improper motives; for truth will never bear
them out in these allegations. I take leave to add, that but for the
interests of truth, these strictures had never appeared. Even
self-defence would not have provoked one line of them: But I felt it
incumbent on me to deter, if possible, inadvertency as well as
malevolence, from infesting with the thorns of misrepresentation, the
paths which genius explores, in search of useful knowledge.


  OF
  A DIRECT AND DIFFERENTIAL PRESS,
  _With two Powers: of which_ ONE _immense_.

The effects intended to be obtained from this Press, are to introduce
two distinct powers; the one to raise and lower the pressing cap with
convenient speed; the other to _press_ with _very_ great force. In Plate
10, A B is a frame, the under part of which contains the goods to be
pressed. The toothed wheel C D turns the screw S, and that E F turns the
nut G H, _both the same way_. The long pinions I K, turn both these
wheels C D, and E F; and occasionally one only, as will be seen
presently. L M are two bevil wheels on the axes of the long pinions I K;
and N O, are two similar ones, on the power shaft P Q. This latter shaft
runs in two boxes R T, the _stems_ of which fit and turn in the gudgeons
of the long pinions, or rather suffer these to revolve round _them_:
being pinned on through a circular groove which connects them in the
perpendicular direction only. Finally, the rope and pulleys _indicated_
at X Y Z, serve to raise both shaft and pinions; thus disengaging the
latter from the wheel E F, when the nut G H, is _not_ to be turned. We
may remark, that the parts M T O are _doubled_ in this machinery, at L R
N; merely to take away the side tendency from the screw S: as otherwise
_one half_ of this mechanism would produce the very same effect, and
leave the Machine the more simple. Supposing now, this Press charged
with goods in it's present position,

  The wheel C D, having 69   teeth; } with proportionate
      that  E F,   "    70     "    } diameters.
  The pinions I & K, each 10   "
  The wheels L N & M O equal;

The thread of the screw S, 1 inch; and in fine, the crank V Q, having a
radius of 18 inches.

In this state of things, the motion of the pressing cap W, is to the
motion of the handle V, as 1 to 52164; and, the power gained bears the
same proportion to the strength exerted: for when the handle has made
one revolution, the wheel C D has made 10/69 of a revolution, and the
screw _would have_ gone down 10/69 of a thread, or 10/69 of an inch: but
in the same time the wheel E F has turned the _nut_ 10/70 of a
revolution _in the same direction_; so that the latter has only gone
down 10/69 less 10/70 of an inch; that is, (reducing to a common
denominator) 700/4830 - 690/4830 = 10/4830 = 1/483 of an inch: Now to do
this, the handle Q V has described a circle of three feet in diameter,
or in round numbers 9 feet, or 108 inches; and to complete a descent of
the screw of one thread, (or one inch) the handle must move through a
space 483 times as great; that is, a space of 108 inches multiplied by
483 = 52164 inches: whence we see that the power gained is, as 52164 to
1: and reckoning a man's strength at 150lbs. (exclusive of friction)
that strength exhibits a pressure of _five millions two hundred and
sixteen thousand four hundred pounds_; or upwards of _two thousand three
hundred tons_: a result not unworthy to be mentioned with those of the
hydraulic press; to which it might be still further assimilated by other
proportions in the screw and nut wheels C D, E F. Adverting now, to the
second property of this Machine: namely the simple power intended to act
when the press is to be laden or discharged, the handle V should first
be turned _backward_, until the cap W has slackened upon the goods; and
the long pinions I K be raised by the mechanism X Y Z, which pinions,
then geering only in the wheel C D, will raise the cap 1 inch for every
turn of that wheel; or for every 69/10 turns of the handle V, say in
round numbers for every seven turns: here then is a power of 756 to 1;
very different from the former; yet produced by only a few inches motion
of the long pinions I K.

We remark further, that the figure shews at G H _two_ of a system of
friction rollers, destined to lessen the resistance which the
turning-nut would otherwise oppose to the motion of the Machine. As to
the friction between the screw itself and the nut--see a future article,
in this _part_, tending to lessen or take away the friction of screws in
general.


  OF
  A PERISTALTIC MACHINE,
  _For raising much Water to small heights_.

Physicians will soonest understand the nature of this Machine, from the
name I have given it. It is perhaps the most simple of Water-Machines;
and certainly not the least efficient where it applies. It's name is
taken from the similarity of its action to the creeping of a worm, and
to some of the functions of animal life. Yet it might be explained to
the most unlettered housewife, when in the act of converting certain
long vessels into _chitterlings_; or making room for the materials of a
sausage or black pudding. To be serious: this Machine, in it's simplest
form, (see Plate 11) consists of a flexible tube C D, fig. 2, nailed to
the ground, and connected with a short tube of metal containing two
valves, A B, itself affixed to a box D, filled with water, or into which
water flows. This water runs through the valve A, and distends the tube
C D, on which rolls the body F, similar in form to a land roller. The
Machine acts in the following manner: When the roller is drawn to the
end D of the tube, the water fills the latter through the valve A; and
on the roller's return, this water is forced into the rising tube
through the valve B.

The above is the simplest form of this mechanical trifle: But it has the
disadvantage of an inconstant vibratory motion, not only of the water
but the roller: which latter being heavy, would absorb considerable
power. To remedy this evil, I have given the principle a rotatory form
in fig. 1; where A B C is a spiral tube, duly fastened to the bottom of
a shallow tub D E. At B is seen a conical roller, having the middle of
the bottom of the tub for its summit and centre of gyration. The tube A
B C, occupies rather more than one circumference; so that the cone
presses during a small part of it's revolution on both spires at once:
by which means the Machine _would act_ without even one valve; though it
is better to place one, _under_ the opening A. Now, observe the
operation: as the cone rolls over the tube and round the common centre,
in the direction of the arrow R the water enters behind it, through the
opening A, (for the tub is plunged a few inches into the water) and is
forced by it's pressure into the ascending tube, which is a continuation
of that, A B C. It would be superfluous to add, that these tubes are
shewn in the figures _as cut open_, and presenting their inside to view;
which representation is adopted in order to shew more completely the
valves A and B of the 2d. figure.

An objection may occur to some, at sight of this Machine: namely, that
the roller or cone B, would soon destroy the flexible tubes, by pressing
too hard on their _puckered texture_. But to obviate this difficulty I
have added, in fig. 3, a form of the tube (supposed of leather) which
insures a proper _position_ of the leather under these rollers;
accompanied by ledges A B, on which their surplus weight would bear, so
as to annul every excess of pressure on the tube.

In many of the subjects I shall have to lay before my readers, the
_forms_ are so numerous as to leave some difficulty in judging where the
actual descriptions ought to end. This article itself, small as it is,
offers an example of this: for I could draw several corollaries from the
foregoing, that would offer new degrees of interest: but I am withheld
by the apprehended want of room in the plates. I must at least defer my
first intention, of _multiplying_ examples and shewing the influence of
FORM on mechanical results in general. It will, however, always be open
to me, to resume this subject when the principal object has been
achieved--that of making known the principles of these inventions, with
their most useful forms and properties. I observe, however, what has
just occurred to me, that this Machine would be somewhat more _durable_,
if the water-tube was pressed _between two rollers_, instead of being
contracted from one side, by the action of a single one.


  OF
  A DRAYMAN'S CANTER,
  _Or inclined Plane with increased Power_.

This Machine presents a simple method of increasing the power of the
inclined plane, as used by carters or draymen for loading their carts;
and called by them (in some counties) CANTERS. It admits of a gentle
declivity in those planes: and thus considerably increases their power.
The means consist in the transfer of the declivity from one end of the
Machine to the other. Thus (plate 11, fig. 4) when the cask is rolled up
from A to B, it is _wedged_ in that position by the wedge F; when _so
much_ of its weight is supported by the feet C, (for all the feet are in
pairs) that the end D of the Canter can be raised _with ease_ to E, so
as to _re_-form the plane, in the direction of C E; at which time the
feet D G drop into an upright position, and secure this new state of the
plane. The cask is now rolled back from B to E, where it is found twice
as _high_ as it was at B; and this man[oe]uvre may be repeated several
times according to the number of feet provided, and their length
respectively. The _power_ of an inclined plane, is as its length to its
height: and that power is doubled when the force is applied at the
circumference of a cask or other rolling body. So that, here, the power
being as 16 to 1, if a man can exert an energy of 200_lb._ the cask may
weigh 3200_lb._ and still be raised with ease on this _Canter_, which
therefore is three times as powerful as though the weight was raised
directly from A to F in the usual method.

Should it be suggested, or thought, that this Machine applies only to
_rolling_ bodies, I would just say that it might apply, cæteris paribus,
as well to bodies sliding up the plane; or (using a small truck on the
Machine) it might serve in a cotton warehouse, for piling the bags, &c.
This System is doubtless susceptible of _discussion_, and may require to
be modified for different purposes: but it is by no means devoid of
practical capabilities.


  OF
  A PERPETUAL WEDGE MACHINE,
  _Being a simple Method of gaining Power._

In Plate 12, fig. 5, let A B represent a wheel and axle, of which the
wheel A is divided into 100 teeth; (more or less) and let C represent a
second wheel with one tooth (or several) less than those of the first
wheel A. These two wheels are concentric, for the axis of the wheel A,
turns in the hollow centre of the wheel C; which latter wheel is fixed
to the frame of the Machine, not here represented. D is a pinion that
circulates round the wheel A and C in and along with the frame E as
impelled by the hand acting on the handle F. Thus the circulating pinion
is constantly occupied by means of its wedge formed teeth (of which one
is shewn at D), in bringing the unequal teeth _a b_ of the wheels A and
C _abreast of each other_: whence arises a _slow_ revolution of the
wheel A, and of the axis B round the common centre. For if the number of
the teeth on these wheels (A and C) differ only by unity or _one_, then
must the handle D revolve one turn about that common centre to occasion
1/100 part of a revolution of the wheel A, and of course 100 turns to
move the axis B once round that centre. And if further the wheel A be
three times the diameter of the axis B, the power gained _there_ would
be as 300 to 1, that is a power of 1_lb._ at a distance from the
centre, _only_ equal to the radius of the wheel A, would countervail a
weight of 300_lb._ suspended on the axis B: and supposing a man's
strength to be 100_lb._ he would raise (exclusive of friction)
30000_lb._ by this simple machine.

To shew more fully the essential properties of this Machine, I have
represented only three teeth in all: one _b_ in the fixed wheel C; one a
little smaller _a_, in the wheel A, (since this wheel has _more_ teeth
than the former) and one D in the circulating pinion, whose form and
manner of acting justifies in my apprehension, the name I have given to
the Machine--a perpetual wedge Machine. I shall only add that there
would equally be motion if the teeth of the wheel A instead of being
more numerous than those of the wheel C were less numerous: but the
manner of action would be different and I think less perfect.

This Machine is among the first inventions I carried into real practice
on coming to manhood. It must be about 40 years ago, and was first
constructed as a Crane at the request of the late Doctor Bliss, of
Paddington. It _may_ offer some difficulty as a _Power_ Engine from the
small diameters and the friction thence resulting: but for any Machine
where great _slowness_ is desirable, whether to express slow motion, or
to count high numbers, &c., it still appears to me a very good Machine.


  OF
  A DROPPING-WEIGHT-MOVER;
  _Or Machine for lengthening the Time of going of a Clock, Jack, or
  other Weight-Machine_.

Suppose A B (plate 12, fig. 4) to be the first wheel of a Clock or other
Machine required to _go_ a long time without winding up. This wheel
works into the two pinions _c d_, both of which are connected by
ratchets with the axis E F of the wheel G H, _in one direction only_;
insomuch that whether the wheel A B turn forward or backward, the wheel
G H will always turn the same way. This process is well known in the
mechanical world; and I have merely adapted it to my present invention.
F and G are two tubes, or square vessels, of equal size, containing a
number of balls--the tubes so balanced against each other, that _one_ of
them is always heaviest by the weight of _half a ball_. Suppose for
example that the tube F contains six balls and the tube G five; and that
the tube G is so much heavier than F as only to be outweighed by half a
ball: _That_ half will then be the moving power; and the vessel F will
turn the wheel A B backward, raising the tube G at the same time. But
arriving at the bottom the mechanism m will let go the lowest ball in F,
and then the tube G which is at the top will preponderate and turn the
clock till it also gets to the bottom; when a similar mechanism at _n_,
will disengage one ball from it, by which subtraction the tube F will
resume the ascendency and perpetuate the motion. Thus may the _going_ of
any clock, jack, &c. be protracted to a period almost indefinite. Nor
need it, strictly speaking, be wound up at all. It is only taking care
to drop at proper intervals, an _equal number_ of balls into each tube,
and this reciprocation of movement will become perpetual. The figure of
this little Machine is unfortunately small: and the scapement is but
imperfectly shewn; It has however, only _one_ property that it is
essential to notice; which is that the detent _o_, shall suffer the
cross _m_ to turn only one quarter round at each discharge: and _this_
is insured by the spiral ledge of the four ratchet teeth _m_, which by a
pin fixed to the side of the detent, draw the latter down into the
succeeding tooth as soon as the tube F begins to rise, so that there is
only one ball discharged at each descent of that tube.


  OF
  A MACHINE,
  _To promote Evaporation, with or without Heat_.

The vessel containing the liquid to be evaporated, (see Plate 12, fig.
6,) is long and shallow, and the liquid rises nearly to it's brim. In
this vessel is placed a _long_ hollow drum A B, covered with open
wire-work, or any kind of cloth of a very loose texture. This drum turns
slowly, on the hollow centre C, to which is fitted a stuffing box and
tube, connecting the drum A B, with the pump P; the latter worked by any
convenient power. The pump then, drives air, either hot or cold into the
drum, and thence through the interstices of it's texture; where it comes
in contact with the liquid at _an indefinite number of points_, breaks
the films formed by the liquid, and, saturated thereby, passes into the
open air; thus occasioning a rapid evaporation, which might be increased
either by heating the liquid or the injected air, or both, _ad libitum_.
The whole idea consists in the multitude of points of contact between
the liquid and the drying medium.


  OF
  A CUTTING OR GRATING MACHINE,
  _For Green Roots, Tobacco, &c._

This Machine is composed of a perpendicular axis A B, fig. 7, driven
with considerable velocity by any proper _geering_. C D is a vessel
formed something like a shoe with the toe cut off: its entrance D is
concentric with the shaft A B, and a weight _m_, fastened to it's side,
_equilibrizes_ the weight of the eccentric part C. Around this vessel,
and concentrically with it, is placed a cylindrical _rasp_ or _grater_ E
F, consisting, here, of a number of _blades_ so grooved on one surface
as that by grinding them obliquely on the edge, each one shall form a
line of sharp teeth, which, combined with those of the other blades,
constitute a rasp similar to that used for powdering dye-woods; with
this difference however, that these blades have interstices between
them, through which the pulp escapes outwards, and thus the rasp is kept
clean at all times. When this Machine is used the roots are merely
thrown into the vessel D as into the hopper of a mill, and they are
pressed against the rasp _by their own centrifugal force_; which is made
as strong or weak as desired, by the greater or less velocity of the
Machine.

This Machine owes its origin to the decree of the French Emperor, for
encouraging the making of sugar from beet-root. With the other
mechanicians of Paris I was called upon, by a house engaged in that
trade, to try my hand upon it; and this Machine was the result. It acts
fast and well; and from being less liable to clog, than most of the
others, is I believe superior; though _this_ was never proved by any
comparative experiment. If it were desired to _cut_ any substance with
this machine, the blades would be sharp knives, instead of being
toothed; and they would be placed obliquely to the circumference: but
the process of _grating_ is that for which it was exclusively designed.


  OF
  A SCREW,
  _With greatly diminished Friction_.

My readers will perceive, that I have altered the title given in the
prospectus to this Invention. It has been done in deference to the
opinions of some persons in high reputation in the mechanical world, who
hold that there can be no motion whatever without _friction_. For my own
part I am no believer in several sorts of friction: and must therefore,
require a new definition of friction, before I can flow with the stream.
As the question, however, is not yet before my readers, I shall wave the
discussion at present, and describe this invention, as introducing the
_rolling motion_ into the threads of a screw; thus taking away the
GREATEST PART of the friction on every supposition.

In Plate 12, fig. 8, A is the screw, and B C the nut, bored large enough
to receive the screw, bodily, _without any penetration of their
threads_. Nevertheless, these threads are made to occupy the same
length, in both screw and nut, as though they did enter each other: so
that the two parts running parallel to each other, leave a _square
interstice_ _b_, all along both nut and screw: into which balls of
brass, or _soft_ iron are introduced, which at once restore the
screw-property without it's friction: a friction so considerable in the
common screw, that it always surpasses the effective power, since it
remains closed, (in a vice for example) while holding any object
squeezed with all the force a man can apply. I have mentioned the use of
soft balls: it is in order that they may _all_ act together, and work
themselves to a common bearing. It will appear by fig. 9, that the
_acting_ balls might, or perhaps ought to be, separated from each other
by a set of smaller ones; since in this case, the surface of the
touching balls move the same way, avoiding all friction between _them_;
and leaving the friction only between those surfaces that are exempt
from heavy pressure. These circumstances will be understood by
consulting the direction of the arrows in fig. 9; and I have added two
other sketches, to shew the principle in it's application to _square
threaded screws_, as at fig. 10; or to oblong threaded screws, whose
threads penetrate each other, in fig. 12. I have further, in fig. 8,
sketched one of the methods I propose for supporting the weight of the
descending balls, and returning them again into the nut. Considering the
balls as a _fluid_, I have provided a rising column of them, which the
working of the screw downward will fill: and the weight of the balls
themselves will return them into the nut, when the screw is drawn
upward.


  OF
  A SIMPLE AND POWERFUL
  MICROMETER.

This interesting Machine, see Plate 12, fig. 11, consists of a screw
divided into three parts, _a_, _b_, _c_; the first, _a_, is a mere
cylinder to _centre_ the screw at that end: _c_ is a screw of (suppose)
20 threads to the inch; and _b_ another screw of 21 to the inch. D E
represents the frame of the Machine, the part E being the _fixed_ nut of
the screw C, while the piece _f g_, forms the _moveable nut_ of the
screw C, carrying a finger _g_, along the graduated bar, E _g_ D. If
now, the screw be turned once round by the button H, it will have moved
_to the left_ 1/20 of an inch; while the nut and it's finger _g_ will
have progressed on it's screw 1/21 of an inch _to the right_: and the
difference 1/20 - 1/21 = 1/420 of an inch is what the nut _f_ has really
moved to the left, along the bar E g D. If therefore, the rim of the
button be divided into 100 parts, _one_ of these will represent 1/42000
part of an inch by this Micrometer: and I need not add, that this minute
portion may be rendered still more minute at pleasure. The means of
doing this are evident: It is only making the screws _b_ and _c_ _nearer
alike_ in fineness, or number of threads per inch; as 29 and 30, 30 and
31, &c.

I hope it will be understood, that I do not give any of these Machines
as the only examples I could furnish of the application of the
principles on which they are founded. This very Machine is not a
Micrometer _only_; it might be (if made in proper forms and dimensions)
a vice, a press, or other _power Machine_. It has been already hinted,
that change of form must remain to be considered hereafter.

I have chosen to bring forward this Machine at an early stage of the
work, because it has, inadvertently perhaps, been ascribed to another
person. I refer to an article in the celebrated _programme_ of M.
Hachette, of Paris; with which is combined an essay on the composition
of Machines, by Messrs. Lanz and Betancourt. In the article D 3, at page
10 of that work, are the following words:

"M. de Prony a trouvé une maniere de transformer le mouvement
circulaire, en un autre rectiligne dont la vitesse soit aussi petite que
l'on voudra;" and further on--"l'idée en est extremement simple,
heureuse; elle est d'ailleurs susceptible de plusieurs applications
utiles aux arts." And in page 11, are these words--"C'est ainsi que M.
de Prony est parvenu à une solution aussi simple qu'ingenieuse du
probleme qu'il s'etoit proposé."

For the sake of my English readers, I subjoin a translation of these
passages: "Mr. de Prony has found (or invented) a manner of
transforming a circular movement into a rectilinear one, of which the
velocity shall be as small as may be desired;" and further on "This idea
is extremely simple and happy: and is besides, susceptible of several
useful applications to the arts." And in page 11, are these words--"Thus
has Mr. de Prony given a solution as simple as it is ingenious, of the
problem which he had proposed to himself."

The above account appears in 1808, and M. de Prony does not prevent or
disavow it. Perhaps he had forgotten the circumstance: and perhaps he
did not know of this publication: but I solemnly declare that I shewed
HIM this Micrometer, executed, _fourteen years before!_ that is, while
he and M. Molard were making their report on the Machines proposed for
the Water-works at Marly. I certainly wish to accuse no body in this
affair: but if I did not state the fact as it is, I should, myself, be
stigmatized as a _plagiary!_ I am _forced_, therefore, to take my stand
on the adage--"Fiat justitia ruat c[oe]lum."

In closing the first Part of this Work, I cannot but express my
gratitude for the unexpected _degree_ of support, with which my numerous
Subscribers have honoured me. I presume to offer these pages as a _fair_
Specimen of what they may expect in the four succeeding Parts,--namely,
as it regards the execution: for the _materials_ of what remains,
include objects of greater importance than those preceding. If I have
been fortunate enough to raise any favourable expectations in the minds
of my present readers, I hope they will express those feelings; and thus
induce others to join in bringing to a useful close, a work which is at
least _intended_ to produce unmixed public utility. From criticism, I
expect candour: and should my intentions, though pure, be
misrepresented--should envious tongues or pens assail my labours, or
asperse my character, I will defend both, _after_ I can use my Book as
my shield--that is, after I have fulfilled my Engagements with my
Subscribers: of whom (in expectation of meeting them again _within_
three months) I now respectfully take leave.

  J. W.

  _No. 5, Bedford-street,_

  _Chorlton Row._




  SYNOPSIS,
  (IN ALPHABETICAL ORDER)
  OF THE
  _CENTURY OF INVENTIONS_
  COMPOSING THIS WORK.


_Note. The objects with Numbers after them are those contained in the
present_ PART: _and the Numbers shew the Pages where they stand._


  A

    1 Adding Machine; or Machine to cast up correctly large columns of
      figures.
    2 Air Pump; essay towards completing the vacuum.

  B

    3 Barrel Spring, to lengthen the going of Clocks and other spring-
      driven Machines. 26
    4 Boats (serpentine) for lessening the expence of traction.
    5 Bobbin or Lace (Machine for making) and for covering Whips, &c.
      with great rapidity.
    6 Bowking Machine for Calico Printers.
    7 Bucket Wheels (a combination of) to raise water.

  C

    8 Canals (open) as Hydraulic Machines of great force.
    9 Canter, or inclined Plane for Draymen. 72
   10 Chain to act _equably_ on my wheels.
   11 Chocolate Mill (rotatory.)
   12 Cocks (_equilibrium_) to avoid leakage.
   13 Colour Mill for Calico Printers.
   14 Compasses (bisecting.)
   15 Cotton (Machine for batting.)
   16 Crane, combining _variable powers_ with speed and safety.
      (rewarded by the Society of Arts.) 57
   17 Crank (epicycloidal) or parallel motion. Rewarded by BONAPARTE. 30

  D

   18 Dash Wheel for Calico Printers, acting with greater rapidity than
      usual.
   19 Differential Wheels for gaining immense power. 54
   20 Doffing Machine, of great force for taking Cylinders from their
      Mandrills.
   21 Draw-bench for my twisted pinions.
   22 Dynamometer, for measuring powers and resistances in motion. 15
   23 Dynamometer, second kind.

  E

   24 Engine for cutting my _Patent Wheels_ in small and middling
      dimensions.
   25 Engine for cutting my large bevil Wheels and wooden Models, either
      on my System, or the usual one.
      N. B. These objects will occupy considerable space in the work.
   26 Engraving Machine for Calico Printers, being an important
      application of my Cog or toothed Wheels.
   27 Engraving Machine for large patterns.
   28 Essay to _derive_ power from expanding Solids.
   29 Evaporation (Machine to promote.) 78
   30 _Eyes_ (Machine for making rapidly.)

  F

   31 Fire escape (on a retarding principle.)
   32 ---- (by breaking the fall.)
   33 Fires (Portable Engine to extinguish.)
   34 Fires (Watch Engine always ready for.)
   35 Flax (Machine for breaking) with rapidity.
   36 Forging Bar iron and steel (Machine for.)
   37 Friction (to prevent.)
   38 Friction (to prevent) Thoughts on.

  G

   39 Geering and ungeering (Machine for).
   40   Do.       Do.       for swift motions.
   41 Grating or cutting green Roots, Tobacco, &c. (Machine for.) 79

  H

   42 Helico-Centrifugal Machine, for raising water in large quantities.
   43 Horse Wheel for saving room and gaining speed. 53
   44 Horse Wheel (reciprocating) for Mangles, &c.
   45 Horse Wheel, with means for turning the Horse when he acts in two
      directions.
   46 Horizontal Pump of large produce, driven by wind.
   47 Hot Air as _power_, while heating liquids, rooms, &c.

  L

   48 Lamp for the Table; suspending the oil by it's weight.
   49 Lithographic, or Copper-plate Press, with several curious and
      useful properties.

  M

   50 Machine for clearing turbid liquors.
   51 Machine for driving Boats on Canals, under Tunnels, &c. without
      disturbing the Water.
   52 Machine to assist in taking Medicine, Pills, &c. (Humani nihil
      alienum.)
   53 Mangle (perpetual or rotatory).
   54 Marine-Level (two essays on a.)
   55 Micrometer for measuring very minute spaces. 83
   56 Mirrors to collect Solar Heat, (method of forming.)
   57 Mover, by dropping weights. 76

  N

   58 Nails (Machine for moulding.)
   59 Nails (Machine for forging.)

  P

   60 Pencyclograph, or Instrument for describing portions of Circles,
      and finding their centres by inspection. 51
   61 Peristaltic Machine, for raising _much_ water, to small heights.
      69
   62 Persian Wheel modified, for raising water.
   63 Pitch-fork, for musicians, with variable tones.
   64 Power-wheel by heated Air. 43
   65 Press, direct and differential. 66
   66 Press (eccentric Bar.)
   67 Printing Machine (two coloured.)
   68 Protracting Motion (Machine for.) 49
   69 Pullies (my Patent much improved.) 33
   70 Pump (my equable.) 45
   71 Pump, triple, in one column.
   72 Pump (portable) worked by pedals.
   73 Punch Machine for Engravers.
   74 Punch Machine on another principle.
   75 Do. rotatory, for my Engraving Machine.

  R

   76 Reciprocating Motion, (long) for Mangles, &c.
   77 Reflector parabolico conical, or plano parabolical for light
      houses, &c.
   78 Regulator: (not centrifugal) for Wind or Water Mills, Steam
      Engines, &c.
   79 Retrographic Machine (Machine for Writing backwards) for
      Engravers.
   80 Rotato-gyratory Churn.

  S

   81 Screw, with greatly diminished friction. 81
   82 Screws, (Machine for forging) &c.
   83 Spinning Machines, (my Patent), Eagles, &c.
   84 Spinning Machinery: another system, adapted chiefly to wool.
   85 Spring, to keep a door strongly closed, yet open easily.
   86 Steel Yard, differential: for weighing _vast_ weights with short
      levers.
   87 Syphon, (mechanical) to expel part of the water at the highest
      point.

  T

   88 Tallow (Machine for cutting and trying.)
   89 Tea-table (commodious help for the.)

  V

   90 Ventilator, rotatory, yet by pressure.
   91 Vessel (expanding) for Pumps, Steam Engines, &c.

  W

   92 Washing Apparatus: for Hospitals, &c. _confining the offensive
      matter until cleansed away_: thus promoting salubrity.
   93 Water-wheel, (horizontal) probably the best of the impulsive kind.
   94 The same, for high falls.
   95 Water-wheel, (inclined) employing the weight of the fluid.
   96 Water, (Machine for raising large quantities.)
   97 Weaving by Power: manner of driving the Shuttle, (executed A. D.
      1780.)
   98 Wedge Machine (perpetual.)
   99 WHEELS (my System of cog or toothed.)
  100 Windmill of great power.


ERRATA.

  Page 16, line 17, for fig. read plate.
    "  22,   "   4, for posistion, read position.
    "  22,   "   7, for 17, read 15.
    "  22,   "   9, for fig. read plate.
    "  22,   "  23, for fig. read plate.
    "  24,   "  16, for clylinder at P, read cylinder at K.
    "  24,   "  22, for fig. read plate.
    "  26,   "  16, for E, read C.
    "  28,   "   5, for diamenter, read diameters.
    "  35,   "  10, for inconvencies, read inconveniences.
    "  36,   "   8, for of pulley, read of the pulley.
    "  40,   "  25, for as, read of.
    "  41,   "   4, for loose 1; read loose --
    "  41,   "   5, for pulleys, read pulley.
    "  43,   "  18, for furnish surplus, read furnish a surplus.
    "  43,   "  22, for occpied, read occupied.
    "  46,   "  17, for power, read motion.
    "  49,   "  22, for diffential, read differential.
    "  55,   "  21, }
    "  55,   "  24, } for 20,200, read 20200.
    "  55,   "  26, }
    "  55,   "  28, for 99,990, read ,99990.
    "  58,   "  23, for figures, read figure.
    "  62,   "   2, end the quotation marks at "lifting."
    "  62,   "   8, for gasping, read anxious.
    "  63,   "   7, for wishd, read wished.
    "  64,   "   2, for ladders, read ladder.
    "  66,   "  11, for occasionaly, read occasionally.
    "  67,   "   7, for G N, read L N.
    "  68,   "   2, for _two hundred_, read _three hundred_.
    "  75,   "   4, for 300[lb]s. read 100[lb]s.
    "  82,   "  16, for fig. 9, read fig. 10.
    "  83,   "  11, for an of inch, read of an inch.




  PART SECOND.
  A NEW CENTURY OF
  Inventions.


INTRODUCTION.

In the progress of a work like the present, no competent reason could
have been assigned for omitting to bring forward _my System of Toothed
Wheels_, the Patent for which has lately expired:--a System which a few
years ago, excited in this town, so much interest, aroused so much
animosity, and was treated with so much illiberality:--But which, also,
was fostered with so much public spirit, tried with so much candour, and
adopted with so much confidence. It was I say, incumbent on me to bring
the merits of this System into public view, had it only been to justify
myself for proposing, and my friends for adopting it. But stronger
reasons point now to the same measure. From the intimate connection the
System holds with the subjects of this essay, it _must_ be often
adverted to; and I have been already obliged to speak of it in terms
which can hardly have been understood by those readers who had not
previously considered the general Subject. I should therefore be still
in danger of filling these Pages with unintelligible assertions, did I
not begin by marking out the foundations on which my statements are
built; or by explaining to a certain degree, the _Principles_ of the new
System. Without then abandoning the tacit engagement I have taken with
my unlearned readers--not to entangle them in too much theory, I think
it indispensable to quote the Memoir I read before the Literary and
Philosophical Society of Manchester, in December, 1815; which small
work will form the basis of the _practical_ remarks I shall have to make
on the subject, as _this_ work proceeds. The Memoir is thus introduced
in the transactions of that learned body:


MEMOIR

ON A NEW SYSTEM OF

COG OR TOOTHED WHEELS,

_By Mr. James White, Engineer._[1]

COMMUNICATED BY T. JARROLD, M. D.

(_Read December 29th, 1815._)

[1] N. B. A Patent was taken out for the Invention some years ago.

"The subject of this paper, though merely of a mechanical nature, cannot
fail to interest the Philosophical Society of a town like Manchester, so
eminently distinguished for the practice of mechanical science; unless
as I fear may be the case, my want of sufficient theoretic knowledge or
of perspicuity in the explication, should render my communication not
completely intelligible. To be convinced of the importance of the
subject, we need only reflect on the vast number of toothed wheels that
are daily revolving in this active and populous district, and on the
share which they take in the quantity and value of its productions; and
it is obvious that any invention tending to divest these instruments of
their imperfections, whether it be by lessening their expence,
prolonging their duration, or diminishing their friction, must have a
beneficial influence on the general prosperity. Now I apprehend that all
these ends will be obtained in a greater or less degree, by having
wheels formed upon the new system.

I shall not content myself by proving the above theoretically, but shall
present the society with wheels, the nature of which is to turn each
other in _perfect silence_, while the friction and wear of their teeth,
if any exist, are so small as to elude computation, and which
communicate the greatest known velocity without shaking, and by a steady
and uniform pressure.

Before I proceed to the particular description of my own wheels, I shall
point out one striking defect of the system now in use, without
reverting to the period when mechanical tools and operations were
greatly inferior to those of modern times. Practical mechanics of late,
especially in Britain, have accidentally hit upon better forms and
proportions for wheels than were formerly used; whilst the theoretic
mechanic, from the time of De la Hire, (about a century ago) has
uniformly taught that the true form of the teeth of wheels depends upon
the curve called an epicycloid, and that of teeth destined to work in a
straight rack depends upon the simple cycloid. The cycloid is a curve
which may be formed by the trace of a nail in the circumference of a
cart wheel, during the period of one revolution of the wheel, or from
the nail's leaving the ground to its return; and the epicycloid is a
curve that may be formed by the trace of a nail, in the circumference of
a wheel, which wheel rolls (without sliding) along the circumference of
another wheel.

Let _A B_ (Plate 13, fig. 1.) be part of the circumference of a wheel _A
B F_ to which it is designed to adapt teeth, so formed as to produce
equable motion in the wheel _C_, when that of the wheel _A B F_ is also
equable. Also, let the teeth so formed, act upon the indefinitely small
pins _r_, _i_, _t_, let into the plane of the wheel _C_, near its
circumference. To give the teeth of the wheel _A B F_ a proper form,
(according to the present prevailing system) a style or pencil may be
fixed in the circumference of a circle _D_ equal to the wheel _C_, and a
paper may be placed behind both circles, on which by the rolling of the
circle _D_ on _A B_, will be traced the epicycloid _d_, _e_, _f_, _g_,
_s_, _h_, of which the circle _A B F_ is called the base, and _D_ the
generating circle. Thus then the wheel to which the teeth are to belong
is the base of the curve, and the wheel to be acted upon is the
generating circle; but it must be understood that those wheels are not
estimated in this description at their extreme diameters, but at a
distance from their circumferences sufficient to admit of the necessary
penetration of the teeth; or, as M. Camus terms it, where the
_primitive circles_ of the wheels touch each other, which is in what is
called in this country the _pitch line_.

Now it has been long demonstrated by mathematicians, that teeth
constructed as above would impart equable motion to wheels, supposing
the pins, _r_, _i_, _t_, &c. indefinitely small. This point therefore
need not be farther insisted upon.

So far the theoretic view is clear; but when we come to practice, the
pins _r_, _i_, _t_, previously conceived to be indefinitely small, must
have _strength_, and consequently a considerable _diameter_, as
represented at 1, 2; hence we must take away from the area of the curve
a breadth as at _v_ and _n_ = to the semidiameter of the pins, and then
equable motion will continue to be produced as before. But it is known
to mathematicians that the curve so modified will no longer be strictly
an epicycloid; and it was on this account that I was careful above, to
say that the teeth of wheels producing equable motion, _depended_ upon
that curve; for if the curve of the teeth be a true epicycloid in the
case of thick pins, the motion of the wheels will not be equable.

I purposely omit other interesting circumstances in the application of
this beautiful curve to rotatory motion; a curve by which I acknowledge
that equable motions can be produced, when the teeth of the ordinary
geering are made in this manner. But here is the misfortune:--besides
the difficulty of executing teeth in the true theoretical form, (which
indeed is seldom attempted), _this form cannot continue to exist_; and
hence it is that the best, the most silent geering becomes at last
imperfect, noisy and destructive of the machinery, and especially
injurious to its more delicate operations.

The cause of this progressive deterioration may be thus explained:
Referring again to fig. 1, we there see the base of the curve _A B_
divided into the equal parts _a b_, _b c_, and _c d_; and observing the
passage of the generating circle _D_, from the origin of the curve at
_d_, to the first division _c_ on the base, we shall find no more than
the small portion _d e_, of the curve developed, whereas a second equal
step of the generating circle _c b_, will extend the curve forward from
_e_ to _f_, a greater distance than the former; while a third equal step
_a b_, will extend the curve from _f_ to _g_, a distance greater than
the last; and the successive increments of the curve will be still
greater, as it approaches its summit; yet all these parts correspond to
equal advances of the wheel, namely, to the equal parts _a b_, _b c_ and
_c d_ of the base, and to equal ones of rotation of the generating
circle. Surely then the parts _s g_, _g f_, of the epicycloidal tooth
will be _worn out_ sooner than those _f e_, _e d_, which are rubbed with
so much less velocity than the other, even though the _pressure_ were
the same. But the pressure is not the same. For, the line _a g_ is the
direction in which the pressure of the curve acts at the point _g_, and
the line _p q_, is the length of the lever-arm on which that pressure
acts, to turn the generating circle on its axis (now supposed to be
fixt;) but, as the turning force or rotatory effort of the wheels, is by
hypothesis uniform, the pressure at _g_ must be inversely as _p q_; that
is, inversely as the cosine of half the angle of rotation of the
generating circle; hence it would be infinite at _s_, the summit of the
curve, when this circle has made a semi-revolution.

Thus it appears that independently of the effects of percussion, the
_end_ of an epicycloidal tooth must _wear out_ sooner than any part
nearer its base, (and if so, much more it may be supposed of a tooth of
another form;) and that when its form is thus changed, the advantage it
gave must cease, since nothing in the working of the wheel can
afterwards restore the form, or remedy the growing evil.

Having now shewn one great defect in the common system of wheels, I
shall proceed to develope the principles of the new system, which may be
understood through the medium of the three following propositions.

1. The action of a wheel of the new kind on another with which it works
or _geers_ is the same at every moment of its revolution, so that the
least possible motion of the circumference of one, generates an exactly
equal and similar motion in that of the other.

2. There are but two points, one in each wheel, that necessarily touch
each other at the same time, and their contact will always take place
indefinitely near the plane that passes through the two axes of the
wheels, if the diameters of the latter, at the useful or pressing points
are in the exact ratio of their number of teeth respectively; in which
case there will be no sensible friction between the points in contact.

3. In consequence of the properties above-mentioned, the epicycloidal or
any other form of the teeth, is no longer indispensable; but many
different forms may be used, without disturbing the principle of equable
motion.

With regard to the demonstration of the first proposition, I must
premise an observation of M. Camus on this subject, in his Mechanics,
3d. part, page 306, viz. "if all wheels could have teeth infinitely
fine, their _geering_, which might then be considered as a simple
contact, would have the property required, [that of acting uniformly]
since we have seen that a wheel and a pinion have the same _tangential_
force, when the motion of one is communicated to the other, by an
infinitely small penetration of the particles of their respective
circumferences."

Now suppose that on the cylindrical surface of a spur-wheel _B c_, (fig.
3) we cut oblique or rather _screw-formed teeth_, of which two are
shewn at _a c_, _b d_, so inclined to the plane of the wheel, as that
the end _c_ of the tooth _a c_ may not pass the plane of the axes _A B
c_, until the end _b_ of the other tooth _b d_ has arrived at it, this
wheel will virtually be divided into an infinite number of teeth, or at
least into a number greater than that of the particles of matter,
contained in a circular line of the wheel's circumference. For suppose
the surface of a similar, but longer cylinder, stripped from it and
stretched on the plane _A B C E_ (fig. 4) where the former oblique line
will become the hypothenuse _B C_, of the right angled triangle _C A B_,
and will represent _all_ the teeth of the given wheel, according to the
sketch _E G_ at the bottom of the diagram. Here the lines _A B_ and _C
E_, are equal to the circumference of the base of the cylinder, and _A
C_ and _B E_ to its length; and if between _A_ and _B_, there exist a
number, _m_, of particles of matter, and between _A_ and _C_ a number,
_n_, the whole surfaced _A B C E_ will contain _m n_ particles, or the
product of _m_ and _n_; and the line _B C_, will contain a number =
[sqrt](_m_² + _n_²), from a well known theorem; whence it appears that
the line _B C_ is necessarily longer than _A B_, and hence contains more
particles of matter.[2]

[2] It need hardly be observed, that whatever is true of the whole
triangle C A B, (fig. 4) is true of every similar part of it, be it ever
so small: and in fact, when the hypothenuse B C, is folded again round
the cylinder, from which we have supposed it stripped, the acting part
will be very small indeed; but it will still act in the way here
described, and give tendencies to the wheel it acts on, and to its axis,
precisely proportionate to the quantities here mentioned.

It is besides evident, that the difference between the lines _B C_ and
_A B_, depends on the angle _A C B_; in the choice of which, there is a
considerable latitude. For general use however, I have chosen an angle
of obliquity of 15°, which I shall now assume as the basis of the
following calculations. The tangent of 15°, per tables, is in round
numbers 268 to radius 1000; and the object now is to find the number of
particles in the oblique line _B C_, when the line _A B_, contains any
other number, _t_.

By geometry, _B C(x)_ = [sqrt](_r_² + _t_²) = [sqrt](1000² + 268²) =
1035 nearly; and this last number is to 268, as the number of particles
in the oblique line _B C_ is to the number contained in the
circumference _A B_, of the base of the cylinder. Hence it appears, that
a wheel cut into teeth of this form, contains (virtually) about four
times as many teeth, as a wheel of the same diameter, but indefinitely
thin, would contain. And the disproportion might be increased, by
adopting a smaller angle.

Thus I apprehend it is proved, that the action of a wheel of this kind,
on another with which it geers, is perfectly uniform in respect of
swiftness; and hence the proof that it is likewise so, as to the force
communicated.

Before I proceed to the second proposition, I ought perhaps to
anticipate some objections that have been made to this system of
geering, and which may have already occurred to some gentlemen present.
For example, it has been supposed that the _friction_ of these teeth,
is augmented by their inclination to the plane of the wheel; but I dare
presume to have already proved, that it is this very obliquity, joined
to the total absence of motion in direction of the axes, that _destroys_
the friction, instead of _creating_ it. I acknowledge however, that the
_pressure_ on the points of contact, is greater than it would be on
teeth, parallel to the axes of the wheels, and I farther concede that
this pressure tends to displace the wheels in the direction of the axes,
(unless this tendency is destroyed by a tooth, with two opposite
inclinations.) But supposing this counteraction neglected, let us
ascertain the importance of these objections. First, with regard to the
increase of pressure on the point _D_ of the line _B C_, (representing
the oblique tooth in question,) relative to that which would be on the
line _B E_, (which represents a tooth of common geering:) let _A D_ be
drawn perpendicular to _B C_. If the point _D_ can slide freely on the
line _B C_, (and this is the most favourable supposition for the
objection,) its pressure will be exerted perpendicularly to this line;
and if the point _A_, moves from _A_ to _B_, the point _D_, leaving at
the same moment the point _A_, and moving in direction _A D_, will only
arrive at _D_ in the same time, its motion having been slower than that
of _A_, in the proportion of _A B_ to _A D_; whence by the principle of
virtual velocities, its pressure on _B C_ is to that on _A C_, as the
said lines _A B_ to _D A_.

To convert these pressures into numbers, according to the above data; we
have _A C_ = 1000, _A B_ = 268, _B C_ = 1035; then from the similar
triangles _B A C_, _B D A_, it will be _B C_ : _A C_ :: _A B_ : _A D_ =
268000/1035 = 259 nearly. Therefore the pressure on _B C_, is to that on
_A C_, as 268 to 259, or as 1035 : 1000.

To find what part of the force tends to drive the point _B_, in the
direction _B E_, (for this is what impels the wheels, in the direction
of their axes,) we may consider the triangle _B A C_ as an inclined
plane, of which _B C_ is the length, and _A B_ the height; and the total
pressure on _C B_, which may be represented by _C B_, (1035) may be
resolved into two others, namely, _A B_ and _A C_, which will represent
the pressures on those lines respectively, (268 and 1000.) Hence the
pressure on _B C_, is augmented only in the ratio of 1035 to 1000, or
about 1/29 part by the obliquity; and the tendency of the wheels to move
in the direction of their axes, (when this angle is used,) is the
268/1000 of the original stress, that is, rather more than one quarter.
But since the longitudinal motion of an axis can be prevented by a point
almost invisible applied to its centre, it follows that the effect of
this tendency can be annulled, without any sensible loss of the active
power. It may be added, that in vertical axes, those circumstances lose
all their importance, since whatever force tends to _depress_ the one
and increase its friction, tends equally to _elevate_ the other, and
relieve its step of its load; a case that would be made eminently
useful, by throwing a larger portion of pressure on the _slow-moving_
axes, and taking it off from the more rapid ones.

We now proceed to the second proposition. The truth of the assertions,
contained in this proposition, must, I should suppose, be evident, from
the consideration of two circles touching each other, and at the point
of contact, coinciding with their common tangent at that point. Let _A_
and _B_ be two circles, tangent to each other, (fig. 3) in _e_. _A C_ is
the line joining the centres, and _D F_ the common tangent of the
circles at _e_; which is at right angles with _A C_; and so are the
circumferences of the two circles at the point _e_. For the circles and
tangent coincide for the moment. Hence then I conclude, 1st that a
motion (evanescently small) of the point common to the three lines, can
take place without quitting the tangent _D F_: and 2d. that if there is
an infinite number of teeth in these circles, those which are found in
the line of the centres, will _geer_ together in preference to those
which are out of it, since the latter have the common tangent, and an
interval of space between them.

The truth of this proposition (or an indefinite approximation to truth,)
may be deduced from the supposition that the two circles do _actually_
penetrate each other. To this end let _A B_ _a b_, in fig. 5, be two
equal circles, placed parallel to each other in two contiguous planes,
so as for one to hide the other, in the indefinitely small curvilinear
space _d f e g_. I say that if the arc _d g_ is indefinitely small, the
rotation of the two circles will occasion no more friction between the
touching surfaces, _g e f_ and _f d g_, than there would be between the
two circles placed in the same plane, and touching at the point n the
same common tangent.

For draw the lines _D E_, _f d_, _d g_, _g f_, _g e_ and _g D_; and
adverting to the known equation of the circle, let _d n_ = _x_, _g n_ =
_y_ and _D g_ = _a_, the absciss, ordinate and radius of the circle; we
have 2 _a x_ - _x_² = _y_². From this equation we obtain _a_ = (_y_² +
_x_²)/2_x_, the denominator of this fraction (2_x_) being the width, _d
e_, of the touching surfaces _f d g_, and _f e g_ of the two circles.
But the numerator (_y_² + _x_²) is equal to the square of the chord _g
d_ of the angle _E D g_, which chord I shall call _z_; then we have _a_
= _x_²/2_x_ from which equation we derive this proportion, _a_ : _z_ ::
_z_ : 2_x_ = _z_²/_a_. But in very small angles, the sines are taken for
the arcs without sensible error; and with greater reason may the chords;
if then we suppose the arc _d g_, or the chord _z_, indefinitely small,
we shall find the line _d e_ = 2_x_ = _z_²/_a_, indefinitely smaller;
that is, of an order of infinitessimals one degree lower; for it is well
known that the square of evanescent quantities are indefinitely smaller
than the quantities themselves. And to apply this, if the chord _z_
represent the circular distance of two particles of matter found in the
screw-formed tooth _a c_, of the wheel _B c_, fig. 3, (referred to the
circle _a b_, fig. 5), that distance _z_ will be a mean proportional
between the radius _D g_ of such wheel, and the double versed sine of
this inconceivably small angle.[3]

[3] I ought perhaps to have introduced this reasoning on the 5th. figure
by observing, that every projection of every part of a screw, on a plane
at right angles with the axis of such screw, is a circle; and that
therefore the chord _z_, or the line _g d_, is the true projection of a
proportionate part of any line, _B C_, fig. 4, when wrapped round a
cylinder of equal diameter with the circle _a b_, fig. 5.

I am aware that some mathematicians maintain, that the smallest portion
of a curve cannot strictly coincide with a right line; a doctrine which
I am not going to impugn. But however this may be, it appears certain
that there is no such mathematical curve exhibited in the material
world; but only polygons of a greater or less number of sides, according
to the density of the various substances, that fall under our
observation. I shall therefore proceed to apply the foregoing theory,
not indeed to the ultimate particles of matter, (because I do not know
their dimensions,) but to those real particles which have been actually
measured. Thus, experimental philosophy shews, that a cube of gold of
1/2 inch side, may be drawn upon silver to a length of 1442623 feet, and
afterwards flattened to a breadth of 1/100 of an inch, the two sides of
which form a breadth of 1/50 of an inch: so that if we divide the above
length by 25, we shall have the length of a similar ribbon of metal of
1/2 an inch in breadth, namely, 57704 feet; which cut into lengths of
1/2 an inch, (or multiplied by 24, the half inches in a foot) give
1384896 such squares, which must constitute the number of laminæ of a
half inch cube of gold, or 2769792 for an inch thickness. Let us suppose
then a wheel of gold, of two feet in diameter, the friction of whose
teeth it is proposed to determine. We must first seek what number of
particles are contained in that part of the tooth or teeth, that are
found in one inch of the wheel's circumference; this we have just seen
to be 2769792 thicknesses of the leaves, or diameters of the particles,
such as we are now contemplating.

We shall now have this proportion, (see fig. 4) 268 (_A B_) : 1035 (_B
C_) :: 2769792 (no. of particles in one inch of circumference of base) :
_x_ = 10696771 particles in that part of the line _B C_, which
corresponds with _that_ inch of the circumference. Thus each of the
latter particles measured in the direction _A B_, is equal to the
fraction 1/10696771ths of an inch. And if that fraction be taken for the
arc _g d_, (fig. 5) then to find the length of the line _d e_, (on which
the friction of _this_ and all other geering depends) we must use this
analogy; 12 inch (rad. of wheel) : 1/10696771 of an inch (chord _g d_) ::
1/10696771 of an inch (_g d_) : _d e_, the line required =
1/1273050917917292 of an inch. This result is still beyond the truth, as
we do not know how much smaller the ultimate molecules of gold are.

To advert now to some of the practical effects of this system, I would
beg leave to present a _form_ of the teeth, the sole working of which
would be a sufficient demonstration of the truth of the foregoing
theory. _A_, _B_, (fig. 6) are two wheels of which the primitive circles
or pitch-lines touch each other at _o_. As all the homologous points of
any screw-formed tooth, are at the same distance from the centres of
their wheels, I am at liberty to give the teeth a rhomboidal form, _o t
i_; and if the angle _o_ exists all round both wheels, (of which I have
attempted graphically to give an idea at _D G_,) in this case, those
particles only which exist in the plane of the tangents _f h_, &c. and
infinitely near that plane passing at right angles to it through the
centres _A_ and _B_, will touch each other; and there, as we have
already proved, no sensible motion of the kind producing friction,
exists between the points in actual contact. I might add, as the figure
evidently indicates, that if any such motion did exist, the angles _o_
would quit each other, and the figure of such teeth become absurd in
practice; but on the other hand, if such teeth can exist and work
usefully (which I assert they can, nay that all teeth have in this
system a tendency to assume that form at the working points;) this
circumstance is of itself a practical evidence of the truth of the
foregoing theory, and of what I have said concerning it.

It must have been perceived that I have in some degree anticipated the
demonstration of my third proposition, namely, that the epicycloidal or
any other given form of the teeth, is not essential to this geering. It
appears that teeth formed as epicycloids, will become more convex by
working; since the base of the curve is the only point where they suffer
no diminution by friction; whilst those of every other form, that
likewise penetrate beyond the primitive circles of the wheels, will also
assume a figure of the same nature, by the rounding off of their points,
and the hollowing of the corresponding parts of the teeth they impel;
and that operation will continue till an angle similar to that at _o_,
but generally more obtuse, prevails around both wheels; when all
sensible change of figure or loss of matter will cease, as the wheels
now before you will evince.

On the right of the drawing, (fig. 6) the teeth of the wheel _B_ are
angular, (suppose square) and those of the wheel _C_ rounded off by any
curve _s_, _within_ an epicycloid. All that is necessary to remark in
this case is, that the teeth of the wheel _B_ must not extend _beyond_
its primitive circle, whilst the round parts of those of the wheel _C_,
do more or less extend beyond its primitive circle; whence it becomes
evident, that the contact of such teeth, (if infinite in number) can
_only_ take place in the plane of the common tangent at right angles to
_A B_; also that if these teeth are sufficiently hard to withstand
ordinary pressure, without indentation in these circumstances, there is
no perceptible reason for a sensible change of form; since this contact
only takes place where the two motions are alike, both in swiftness and
direction. A fact I am going to mention may outweigh this reasoning in
the minds of some, but cannot invalidate it. I caused two of these
wheels made of brass, to be turned with rapidity under a considerable
resistance for several weeks together, keeping them always anointed with
_oil_ and _emery_, one of the most destructive mixtures known for
rubbing metals; but after this severe trial, the teeth of the wheels,
_at their primitive circles_ were found as entire as before the
experiment. And why? Certainly for no other reason than that they worked
without sensible friction.

Hitherto nothing has been said of wheels in the conical form, usually
denominated _mitre and bevel geer_. But my models will prove, that they
are both comprehended in the system. The only condition of this unity of
principle is, that the axes of two wheels, instead of being _parallel_
to each other, be always found in _the same plane_. With this condition,
every property above-mentioned, extends to this class of wheels, which
my methods of executing also include, as indeed they do every possible
case of geering.

Being afraid of trespassing on the time of the society, I have
suppressed a part of this paper, perhaps already too long; but I hope I
may be indulged with a few remarks on the application of those wheels to
practical purposes. And first, as to what I have myself seen; these
wheels have been used in several important machines to which they have
given much swiftness, softness or precision of motion as the case
required. They have done more; they have given birth to machines of no
small importance, that could not have existed without them. In rapid
motions they do all that band or cord can perform, with the addition of
mathematical exactness, and an important saving of power. In spinning
factories these properties must be peculiarly interesting; and in
calico-printing, where the various delicate operations require great
precision of motion. In clock-making also, this property is of great
importance in regulating the action of the weight, and thus giving full
scope to the equalizing principle whatever it be. I may add, it almost
annuls the cause of anomaly in these machines, since a given clock will
go with less than 1/4 of the weight usually employed to move it. Another
useful application may be mentioned; in flatting mills, where one roller
is driven by a pinion from the other, there is a constant combat between
the effort of the plate to pass equally through the rollers, and the
action of the common geering, which is more or less convulsive. Whence
the plate is _puckered_, and the resistance much increased, both which
circumstances these wheels completely obviate; and many similar cases
might be adduced.

I shall only add, that my ambition will be highly gratified if, through
the approbation of this learned society, I may hope to contribute to the
improvement and perfection of the manufactures of this county; and if
the invention be found of general utility to my much loved country."

Subsequently to the reading of the above paper, I had occasion to
execute many wheels on this principle; and their appearance, and use,
excited on the one hand much interest, and on the other much opposition.
I had even to complain of real injury in that contest: against which I
defended myself with a warmth that I thought _proportionate_ to the
attack.--But all this was local and temporary: and writing now for a
more enlarged sphere, and perhaps for a more extended period, I feel
inclined to lay aside every consideration, but those immediately
connected with the influence of this work on the public prosperity. I
shall therefore avoid all reference to the names either of my friends
or my opponents. My friends will live in a grateful heart, as long as
memory itself shall last; my enemies, if I have any, will be
forgiven--or, at worst, forgotten; and my System is henceforward left to
wind its way into public notice and usefulness, by its own intrinsic
merits.

       *       *       *       *       *

CERTAIN OBSERVATIONS which I was induced to make on occasion of a
re-print of the above Memoir, may assist in introducing what remains to
be said on the subject. They commence thus:

The foregoing little work, which first brought this subject into public
notice in this town, was not the only method employed to develope its
principles, and urge its adoption. A second paper was read, at the next
meeting of the society, and some time after, a third, at the Exchange
Dining Room; on both which occasions new modes of reasoning were
pursued, and new kinds of proof adduced. On the first, a model was
exhibited of two screw-formed teeth (connected with proper centres)
exactly like those represented in fig. 6; by the action of which on each
other, it became manifest that teeth of this angular shape _do_ work
together without inconvenience, and therefore, that all sensible
friction is, in this case, done away.

On the latter occasion (the lecture at the Exchange) two other methods
were brought forward, to corroborate the principles before stated: (see
Plate 14, fig. 1.) The first was a kind of transparency, in which _a
line of light_ represented the place of contact of two wheels working
together; by the partial and _variable_ obscuration of which, the
successive action of every portion of the teeth was clearly shewn. The
second method consisted of two pair of wheels, _made from loaf sugar_,
the teeth of which were cut one pair in the usual form, and the other on
the new principle. Here, the difference in the effects of the two
methods was so great, that the common teeth were almost immediately worn
or broken down, by the very same kind of impulse that the new wheels
sustained without injury: and with a loss of matter almost
imperceptible, since many thousand revolutions of the wheels took place
without detaching so many _grains_ of sugar!

These _Observations_ include likewise the following remarks:

In adverting to a few of the difficulties we have encountered, it will
appear curious that one of them should spring from a most useful
property of the system: but the paradox is thus explained. As there is
no method more effectual for giving the teeth _a perfect form_, than
working the wheels together, (covering them with an abrasive substance)
we have most frequently chosen to depend on that important property; and
have therefore set the wheels at work as they came from the foundry,
instead of chipping the teeth, as is usual when common wheels are
expected to act well in the first instance. But our wheels being then
full of asperities, their action would be of course imperfect and noisy,
till time had smoothed and equalized the touching surfaces: a state of
things that might well stagger the opinion of a candid observer
unacquainted with the system. Happily however we can now appeal to the
fact of many wheels having _become silent_, that were once referred to
with triumph, as proofs of a radical defect in the principle. It may not
be improper to add here, that if highly finished wheels were
_particularly desired_, we would engage to cut them in metal on this
principle, with all the perfection of surface given to common wheels by
the first masters.

In the use of bevel wheels of this description (with singly inclined
teeth) there is doubtless a tendency to approach toward or recede from
each other; the extent of which (for cylindrical wheels) has been
already determined. This tendency goes, so far, to give a _bend_ to the
shaft; and, if this be _very weak_, to create a degree of friction on
the teeth as the wheels revolve. It is therefore desirable that the
shafts should be rather too strong than too weak; since the principle
can only exist entire, when the wheels in working, are kept in the same
planes which they occupy when at rest. This is too evident to be further
insisted on.

But a greater, or at least a more frequent cause of friction in the
wheels is the motion, endwise, of the shafts, arising from a want of
solidity in the bearers, and especially of connection between them; for
whenever these _are strongly connected_, and the shafts well fitted to
their steps, all circular commotion is ipso facto destroyed; while the
longitudinal tendency produced by the teeth on the shafts _is certainly
an advantage_: because it prevents the shaking that often arises from
their vibration, endwise, when lying on unsteady bearers, or on bearers
between which they have too much liberty.

A few words will make known the process of reasoning by which I arrived
at the idea that forms the basis of this invention. I had been
conferring with a well-known mechanical character, (to whom the art is
greatly indebted)--and hearing his observations on the advantage derived
from having two equal cog wheels connected together, with the teeth of
the one placed opposite the _spaces_ of the other; so as to reduce the
_pitch_ one half, and the friction still more; (since the latter follows
the ratio of the double _versed sines_ of the half-angles between the
teeth respectively:)--and no sooner had I left that gentleman, than my
imagination thus whispered--"What that gentleman says is both true and
important." "But if _two_ wheels thus placed, produce so good an effect,
_three_ wheels (_dividing the original pitch into three_), would produce
a better: and _four_, a better still: And _five_ a better than _that_.
And for the same reason, an indefinite number of such wheels would be
indefinitely better! We must then cut off the corners of all those
teeth, and we shall have one screw-formed line, that will represent an
indefinite number of teeth, and approach indefinitely near to _absolute
perfection!_" Thus did this Invention originate: and it soon appeared to
me, to be the nearest approach of material exactitude to mathematical
precision, that is to be found in the whole circle of practical
mechanics. For not only is the _relative motion_ of the touching points
of two wheels (that is their _friction_), less than the distance between
two of the nearest particles of matter, but it is as many times less
than that distance, as that distance is less than the half diameter of
any wheel whose teeth are thus formed.

I assert therefore that these teeth, placed in proper circumstances, do
work without _sensible friction_ at their pitch lines: as although by
means of mathematical abstraction, it may be possible to _assign_ a
degree of friction between them, that degree cannot be realized on a
material surface: and I fear not the friction on _mathematical
surfaces_, if my material surfaces do not suffer from it. I take leave
then to repeat, that no _friction_ can justly be said to arise from a
motion, too short to carry a _rubbing_ particle from one particle of a
_rubbed_ surface to the next! and this is precisely the case in the
present instance.

Continuing to reflect on this important subject, I soon perceived that
the _screw-formed_ line would give the teeth a tendency to slide out of
each other; and to drive the shafts of the wheels endwise in opposite
directions; but even that evil is not great: for, confining the
obliquity within 15 degrees, that tendency is only about one quarter of
the useful effort; and a _stop_ acting on the central points of the
axes, will annul this tendency _without any sensible loss of power_. We
need not even have recourse to this expedient when any good reason
opposes it: for this tendency can be destroyed altogether by using _two
opposite inclinations_: giving the teeth the form of a V on the surface
of the wheels--a method which I actually followed on the very first pair
I ever executed, which I believe are now in the Conservatory of Arts at
Paris.

A circumstance somewhat remarkable deserves to be here noticed. In the
specification of a Patent which I have seen in a periodical work since
my return from Paris, _for things respecting steam engines_, and dated,
if I recollect right, in 1804 or 5, this V formed tooth is
introduced--as an article of the specification, yet having no connection
whatever with its other subjects; nor being attended with the most
distant allusion to the _principle_ of this _geering_. The fact is that
I had these V wheels in my _Portique_, in 1801, when that exhibition
took place in which my Parallel motion appeared and was rewarded by a
Medal from Bonaparte: so that _two_ of my countrymen at least, engineers
like myself, appear to have taken occasion from that exhibition, to draw
my inventions from France to England--a thing by no means wrong in
itself nor displeasing to me: who was then totally precluded from
holding any communication of that kind with my native country.

It would be repeating the statements contained in the foregoing memoir,
to say more on the general principles of this System. I request
therefore, my readers to give that paper an attentive perusal; and to
accept the following recapitulation of its contents:

1. To cut teeth of this form in any wheel is, virtually, to divide it
into a number of teeth as near to _infinite_, as the smallness of a
material point is to that of a mathematical one.

2. By the use of these teeth, and the _multitude_ of contacts succeeding
each other thence arising, all perceptible noise or commotion is
prevented. (This of course supposes _good execution_, or long-continued
previous working.)

3. For the same reasons, all sensible abrasion is avoided: for we have
proved that the passage of any point of one wheel, over the
corresponding point of another, is indefinitely _less_ than the distance
between the nearest particles of matter. (This supposes the action
confined to the pitch line of the wheel; and this it will be in all
common cases--since the teeth wear each other in preference, within and
without that line; _which therefore must remain prominent_.)

4. From the foregoing it appears that the teeth of two wheels working
together tend constantly to assume a form more and more perfect: as
they abrade each other _while imperfect_, and cannot wear themselves
_beyond perfection_.

5. For a similar reason the division of the teeth cannot remain unequal:
for those that are too far distant from a given tooth will be _attacked
behind_, and those that are too near before; so that the division also
will finally become perfect.

But it must be remembered that these _recoveries_ of form are in their
nature _very slow_; since the nearer the teeth come to perfection the
slower is their approach to it: so that in thus dwelling on these
properties, we do not advise the making of _bad_ wheels that they may
become _good_; but only wish to destroy an _honest prejudice_ that has
already much impeded the progress of the System; namely, that it
requires great nicety to adjust them so as to work together at all:
which is--(to say the least) a very great error.

In Plate 14, fig. 1, I have shewn the apparatus presented at the
Exchange, as mentioned in page 110 preceding. _A B_ is the stand; _C D_
is a disk turning on the centre _E_; _b a_ is the transparent line cut
through the stand, and representing the place of contact of two wheels
geering together. It is there seen, (supposing the disk to turn in the
direction of the arrow) that the action of the teeth, is always
progressive _along_ the transparent line _a b_; whether the single or
double obliquity _G_ or _F_ be used. In reality, the lower end of any
tooth _c_, does not uncover the line _a b_, till the upper point of the
succeeding tooth _d_ has begun to cover it; whereas, observing a few of
the common teeth represented at _H_, as directed to the centre of the
disk, _they_ would be seen to pass the line _a b_ all at once; and thus
to represent, with a certain exaggeration, the transient manner of
acting of the common geering.

Some knowledge of the nature of this geering may be gathered from its
very appearance: see fig. 5 Plate 14. To represent these teeth properly,
no light must appear between them. The tops of the teeth offer a
continued circular line, similar to what it would be if there were no
teeth at all: and the latter are distinguished only by a different
shading of their front and lateral surfaces. The reason (as has been
already observed) is, that they are necessarily so placed, as that the
_last_ end of any tooth shall not quit the plane of the centres, until
the _first_ end of the succeeding tooth arrives at it; which principle
precludes the possibility of any space remaining between the teeth, that
an eye directed _parallelly_ to the axes could penetrate. Such a space
indeed would introduce a portion of the properties of the old geering,
which it is the object of this System to avoid. As this wheel then
_appears_ in fig. 5, _so it acts_: that is equally and perpetually.

It were well also to observe the appearance of these wheels on their
edges; or in the planes which, as wheels they occupy. The 4th. figure
of this Plate is outlined with some care, in order to shew the varying,
and seemingly anomalous form which the teeth assume as they approach the
boundaries of the figure. Although cut as obliquely to the axis there,
as any where else, the receding cylindrical surface, thus seen, appears
to take this obliquity away; and the _very_ outward teeth seem nearly
parallel to the axis of the wheel. But this is only appearance: and we
give here _one_ example of it, that we may not be obliged to lose much
time hereafter, in drawing correctly, wheels on this principle--a
process indeed which in many cases, would be found very difficult, if
not impossible.

We have already adverted to the oblique tendencies of these wheels, when
used with a single inclination of the teeth; from which, among other
things, it follows that, in the act of urging the shafts endwise, they
tend also to bend these shafts: for which reason the shafts require to
be stronger than those of common wheels--that is, when the effort bears
any proportion to their stiffness--a circumstance which, in light rapid
movements, is of small moment. And in heavier works, when it is
desirable to get rid of these tendencies altogether, we have peremptory
means of avoiding the very appearance of this evil.

Suppose then (fig. 2 and 3, plate 14) _a b_ to be a straight rack on
this principle; driven by the wheel or pinion _c_. The motion, backward,
of the pinion, tends, clearly, to urge the pinion endwise towards _d_,
and the rack sideways towards _a b_. But either of these motions is
prevented by fixing to the pinion, or the rack, a _cheek_ _e f_, to
support them against this lateral pressure. But then, exclaims a
doubting friend, you introduce _friction_: and it is true: there is now
a real rubbing of the _ends_ of the teeth against this cheek; but the
pressure there being only one quarter of what it would be on the front
of straight teeth, we avoid (on a rough estimate) three quarters of the
friction; while preserving _all_ the constancy and smoothness of motion
which the system gives; and which after all, is the most important part
of the business.

This idea then applies among other things to the racks of slide-lathes;
giving a regular motion to the _rest and cutting tool_, thereby adding
to the perfection of the turning process: and many other cases might be
adduced.

But instead of using a rack and pinion, as thus described, _two wheels_,
of any desired proportions might have been thus treated, and the result
would have been the same. _They_ would have worked with perfect
smoothness, under about one quarter of the friction attendant upon
common wheels in similar circumstances. There are cases therefore, in
which it would be expedient thus to employ the System. I cannot but
observe likewise, that this method of using _cheeks_ to prevent any side
motion in spur wheels, might also be applied to bevel-wheels, to prevent
the _angular_ tendency which the obliquity of their teeth gives them:
and that I prefer such a method of obviating this evil (where it is
one) to any attempt at using teeth in the V form, on bevel wheels. Still
however, as before observed, this counteraction of the oblique
tendencies is not always necessary. It may be dispensed with in all
light and rapid movements; especially in the use of perpendicular
shafts; and where the _driven_ wheels are small and distributed round a
central wheel in positions nearly opposite each other: of all which
cases we shall see examples in the spinning machinery to be described
hereafter.


  OF
  THE CUTTING ENGINE,
  _To form Spur-wheels, on my late Patent principle_.

The figures of this Engine (see Plates 15 and 16,) are drawn to a scale,
from the Machine itself, now before me. The scale of the objects on
Plate 15, is one inch and three quarters to the foot; and that of the
objects on Plate 16, one inch and one third. These were convenient
proportions for introducing this object into the present work; but the
size itself of the Machine is arbitrary. I did not make it according to
my ideas of the _best_ dimensions: but bought it as a common cutting
Engine, and gave it those other properties that my System required.

The first remarkable deviation from the usual form is in the shaft or
axis of the dividing plate. See fig. 1 and 2 of the Plates 15 and 16.
The dividing plate _a b_, is concentric with, and fixed to an axis _A B_
made as perfectly cylindrical as possible, so as _both to slide and
turn_ in the bars _C D_, and _E F_ composing the frame. These bars are
_bushed_, to fit the axis _A B_, either with a contracting ring of
brass, as usual in some mathematical instruments; or with _type metal_,
cast around the axis into _rough_ holes in those bars:--which metal,
closing upon the axis makes a good centre; and will last a long time. My
Engine is made in this manner; and has been renewed in this part only
twice in several years. This frame _C D E F_ of the Engine, is strongly
connected with the feet _G G H H_, by means of the nuts _E F_ in the
plan: and by these feet it is fixed to its bench or table, as will be
seen in Plate 16.

Figure 2 of the present Plate, represents the plan of the Machine, but
turned upside down; so that the feet _G H_ screwed _under_ the lower
plate _E F_, are wholly visible. In this figure, also, is shewn at _c
d_, the edges (without the bottom) of the horizontal slide which carries
the _stand_ for the cutter frame represented in fig. 4. This stand is
indicated by the dotted lines of this figure 2, as situated _under_ the
arm _D_ of the bar _C D_; but it is better shewn in fig. 5, where _e f_
marks the slide in which the cutter frame (fig. 4) moves up and down, by
means of the screw and handle _e f_. In general I avoid dwelling much on
these smaller parts, because they exist, probably in a more perfect
state, in most other machines. In this fig. 5, _g h_ shews the screw
that moves this stand nearer to, or further from the axis _A B_ of the
Engine, according to the diameter of the wheels: which is also a common
process in Machines of this kind, on which therefore much need not be
said. But a somewhat greater importance attaches to the _cutter frame_
represented in the 4th. figure: which is a kind of small _lathe_ whose
_spindle_ _n o_, carries the cutter _n_, _outside the frame_, for the
purpose of changing the former without displacing the latter. The cutter
(of any proper section) is placed in or near that line which is a
continuation of the centre of the fixing screw _o p_. It is _in_ that
line for wheels whose teeth can be finished with once cutting: but
_near_ it for those whose teeth must be cut at twice. In this same
figure, _i k_ represent the _ends_ of the standards that form the
vertical slide _e f_ of fig. 5; and the separate figure _p q_, shews the
_back_ of the cutter frame _l m_, the flat part of which, _p_, presses
correctly on these uprights _i k_, and thus fixes this instrument at
_any desired height_, and to _any given angle_ with the perpendicular:
the _use_ of which arrangement we shall soon have occasion to exemplify.

Turning now to fig. 3 of this Plate, we there see the main shaft _A B_,
broken off at _B_: and the letters _a b_ again shew the dividing plate
of figs. 1 and 2: under this Plate is seen an _alidade_ or moveable
index, shewn by section only at _c_, and in elevation at _d e_; where it
clips the plate as far as _n_ and carries a boss _between n and e_, on
which the dividing index _e f_, turns; and to which it is strongly fixed
by a nut _o_, when the proper number to be cut is determined. Moreover,
this boss forms, itself, _the nut_ of a thumb-screw _s_, which, carrying
a circular plate at its lower end, clothed with leather or any soft
substance, connects strongly, without injuring the plate, the moveable
index with any point of it, as determined by the dividing index _e f_.
This brings us into the midst of things, as it respects the _use_ of
this Engine; for the former index _c d_, is furnished with a small
roller, _p_, the motion of which all the foregoing objects must obey,
when they have been fastened together by the thumb-screw _s_. We turn
then to the figures 1 and 2 of Plate 16, in order to shew those parts
in action: after remarking only that the form _p q r_ of this fig. 3, is
that of the moveable index shewn before at _c d_; requiring only, to
become complete, that the part _q_ should be sufficiently lengthened to
make the arc _r q_ a complete semi-circle--for purposes that will
shortly be explained.

In the two figures of Plate 16, the Machine is shewn as placed on its
bench or table, accompanied by the parts which give it a distinctive
character, and in fact embody the System. In addition to the parts
already described, we first remark the circular rim _c d_, fixed to the
ends of the bar _E F_; and made perfectly concentric with the main shaft
_A B_, and the dividing plate _a b_. This rim is shewn in section only,
at _v_ fig. 2. Its section resembles an L, and thus forms a basis for
certain _plates_ that will soon appear; and receives the screws by which
these plates are fastened to it. This being sufficiently clear, we now
proceed to describe the table and the connection of its mechanism with
the foregoing.

In Plate 16, _K L_ is the table: to which the Engine is screwed through
its feet _G H_. _I_, is a square bar of wood, sliding in a mortice
through the top of the table; and connected by a joint with the lever _M
N_--itself moving round a pin at _O_, and carrying a friction roller,
_P_, which pressed by the spiral _Q_, as turned by the handle _R_,
raises the bar _I_, and with it the main axis _A B_ of the plate, _and
of course the wheel to be cut, centered as usual on this axis above B_.
Finally, _p q r_, in both figures, is the moveable index first shewn in
fig. 3 of Plate 15; prepared to be _drawn round_ by a weight _W_,
hanging to the cord _x_, passing over the pulley _y_, and tied to the
_right_ end of the arc _q r_, when _this_ is to move to the left; or to
its _left_ end, when the motion is to be toward the right:--these
motions depending on the right or left-handed direction of the _teeth_
which it might be wished to cut on the Machine.

Between the two figures 1 and 2 of this Plate, there appears a diagram,
the base of which is nothing more than a part of the rim _c d_ supposed
straightened, and placed there that its use may be the easier
understood. On the rim is seen a right angled triangle _e g f_, against
which the roller _p_ will lean by the action of the weight _W_ on the
cord _x_, and the arc _q r_ of the moving index _p q r_. So THAT when,
by the handle _R_, the spiral _Q_ depresses the lever _M N_, by means of
its roller _P_, _then the bar I raises the axis A B of the Engine, and
the weight W turns it at the same time_, as much as the small roller _p_
permits by rolling up the side _e f_ of the plate _e g f_. And thus may
a _screw-formed tooth_ be cut in any wheel centered above _B_ in the
usual manner.

Thus then, in describing this Machine, the manner of using it has been
also shewn: for the _cutter_, in this Machine, (to cut spur wheels) is
always _fixed_; and _all_ the motion is composed of the _rotatory and
longitudinal movements of the principal axis, which carries the wheel
along with it_. The cutter I say is fixed, at a proper height just above
the wheel, and at an angle to the perpendicular, equal to that it is
wished the teeth should form at it's pitch line. This inclination as
before observed is 15 degrees; and the tangent of 15° is in round
numbers 268, when the radius is 1000. That is, in our present figure,
the basis _e g_ of the plate _e g f_, occupies 268 divisions of a scale,
of which the height _g f_ contains 1000. It appears then, that to cut a
tooth with 15 degrees inclination, _by this Plate_, the wheel _receiving
that tooth_, must be _just as large as the rim itself_; for the surface
of the wheel would _turn_ more, with a given elevation, if it were
_larger_ than the rim; and would turn _less_, by the same elevation, if
it were smaller. In a word the whole theory of this operation, is now
clearly seen. The smaller the wheel to be cut, the longer, horizontally,
must be the Plate; or in other words, _as the diameter of the wheel is
to that of the rim, (c d) so is the length e g of the Plate to the
length required_. Now this height _f g_, is _always the same_; all
change therefore, in the plates, takes place on the horizontal length:
and this length is most easily found by the foregoing RULE OF THREE. If
then, instead of the triangle _e f g_, I had used the triangle _e´ f´
g´_ it would have followed at once, that to produce an inclination of 15
degrees, I must have taken a wheel of just _half_ the diameter of the
rim; for the plate _e´ f´ g´_ is just _twice_ as long as that _e f g_.
To prove this, let us _suppose_ the diameter of a wheel wanted, to equal
one half that of the rim _c d_: then the _rule_ will stand thus:

1 is to 2, as 268 is to ...536, the length of the plate according to the
theory; which is precisely the length it is drawn to compared with
_that_ _e f g_, namely twice as long. Thus the four triangles, drawn to
the right and left in this diagram, represent the plates for the wheels
of the following diameters respectively:

  No. 1, a wheel _equal to the plate rim_ _c d_;
      2    do.     do.  to 1/2       do.
      3    do.     do.  to 1/3       do.
      4    do.     do.  to 1/4       do.

A small anomaly, _of form_, may be mentioned here to prevent mistakes.
The shaded triangle _e f g_ in the Plate, _looks_ higher than the rest:
but if higher, it is also _longer_ in the same proportion; and the
roller _p_ never reaches the bottom: so that the _effect_ of this Plate
is the same as though it resembled the others in every respect. In
general the effect of the Plates depends on their length _compared with
their height_: and indeed they must be made _higher_ than the thickness
of the wheel to be cut, that the latter may disengage itself from the
(fixed) cutter both above and below.

It is proper to observe, that for every _pair_ of wheels there must be a
_pair_ of plates; one leaning to the right and the other to the left,
(see the diagram) but, as before said, the degree of obliquity _must_ be
different in each pair, except in the case of equal wheels, when the
_same_ plate serves for both; only turning it to the right for one
wheel, and to the left for the other. Nor does this offer any
difficulty, as the plates are made of _common tin plate_: which is
easily brought to fit the rim, whichever way it is applied. I shall now
add another example of the process for finding the length of the plates:
and to that end repeat that the _plate rim_ _c d_, is 22 inches in
diameter, or 11 inches radius. Supposing then that we wished to cut a
pair of wheels, _one_ of them being 1 inch in diameter and the other 12
inches; _both_ to have teeth inclined 15 degrees to the axes; (as
without _that_ they could not work together) to do this we must _effect_
these two proportions:

    (1) 1/2 inch (radius of small wheel) is to 11 inches, (radius of
    plate rim) as 268 parts (of which the height of the plate is 1000)
    to another number, which is the length of the plate sought: measured
    on a scale of parts of the same magnitude.

    (2) 6 inches, radius of the large wheel; is to 11 inches radius of
    plate rim; as 268 parts (as before) is to another number, which is
    the length sought for this second plate.

  Both proportions being effected, the first plate is 5896 parts.
  And the second                                    491.33  do.

The one of course, to be directed toward the right hand, and the other
toward the left, on the plate rim; where note, that if the height (1000
parts) is found so numerous as to create confusion, let 100 parts be
assumed; when the _length_ of the plate will become 26.8 or 26 and 8/10
instead of 268, and the operation will be so much the more simple.

It should be added that this process admits of being further simplified:
since the product of 11 inches, radius of the plate rim, multiplied by
268 (tangent of 15 degrees, or _length of the plate for a wheel equal in
diameter to the plate rim_) since this product, I say, is a _constant
number_, namely: 2948--which, divided by the _half diameter_ of any
wheel, gives, at once the length of the plate adapted to that operation,
in parts of which the height contains 1000; or supposing the height to
be 100 only, this constant number becomes (nearly enough for practice)
295. In a word, on a height of plate of 100 _parts_, when wishing to cut
a wheel of 4 inches in diameter, I merely divide 295 by 2, and get for
_the length of my plate_ 147.5 parts of which the aforesaid height is
100.

It may possibly be suggested that this method of using _plates_ to
determine the obliquity of the teeth is a homely method, giving some
trouble in the execution, and leaving a certain degree of roughness in
that execution. The fact is allowed; but this method has the advantage
of a _very general_ application, which many a better looking apparatus
would not present.

Besides, for _most_ uses, these teeth require chiefly that the obliquity
should be correct, and _not_ that the surface should be licked like
those of a gewgaw. In fine, the principle of this Machine once known,
its best form will occur to the reflecting mechanician according to the
_quality_ of the work he has in view: And in fact, in the hands of a
well known _artist_, this form has been already varied so as to produce
effects much higher wrought than could be drawn from the Machine above
described: which latter however in point of generality, still preserves
the advantage.


  OF
  A DOOR-SPRING,
  _To keep a Door strongly closed, yet suffer it to be opened easily_.

That "necessity is the mother of invention," is a remark none the less
true, for having become a trite proverb; I could mention the time,
place, and circumstance which gave birth to this little Invention: but
such detail would be superfluous. A certain door was, and is still, most
inconvenient, from the stiffness of the spring, and the noise it
occasions in a place where silence ought to prevail: which state of
things suggested to my mind the Machine represented in fig. 5, of plate
17.

_A B C_ in that Plate, is a horizontal section of the door, door jambs,
&c. The door spring now in use, is a barrel-spring, with an arm carrying
a small roller which presses in a gutter-formed plate, screwed to the
door. My door spring is on a different principle. The roller is fastened
in and by a small frame to the door, and the arm is fixed to the axis of
the spring, which passes up through the top of the barrel. This spring
is _much_ weaker than the former, insomuch as only just to close the
door by its elasticity; but when the door is shut, there is a sharp bend
in the arm that wedges itself against the roller, and _decuples_ at
least the force of the spring, as tending to keep the door closed. When
therefore it is desired to open the door, by pressing the door itself,
a good push is necessary, but only for an instant: for as soon as the
bent part of the arm is forced off the roller, there remains only the
small resistance of the spring to be overcome; which latter, when
suffered to act in shutting the door, will _not_ shut it with that noise
a stronger spring would occasion; and yet, when arrived at its first
position, it will keep the door as strongly closed as ever. And should
it be wished to avoid the necessity of pushing hard against the door,
even at first, there is a sliding button and stem _B_ put through it,
which, if pressed from the other side, with the force only of the
spring, will raise the latter beyond the roller, and thus open the door
with perfect facility: and this same process will take place in pulling
the door open by the hook _D_ from the inside: yet still the door when
closed will be as firmly so as before; the spring-bar acting in the
latter position, as much like an invincible _stay_ as the workman shall
have desired--this property depending clearly on the _nearness_ of the
bend to a right angle.

This device may appear to some an object too inconsiderable to be justly
dignified with the name of an invention. But if I should sometimes fall
into such an error as this, I intend to compensate for any thing too
trivial by giving in other cases, Inventions of ample size and number. I
might even mention the Cutting Engine given in this part, where several
Inventions are compressed into one, or rather presented as _one_, of
which several examples will occur.


  OF
  A DRAW-BENCH,
  _For making my twisted Pinions_.

The pinion wire of clock and watch makers is well known. I am not wholly
acquainted with the manner in which it is drawn: but I have made my
pinion wire, of brass, in lengths of about a foot, by the Machine
described below.

A common Draw-bench (not here represented) is worked in the usual
manner: but the instrument which forms the pinion (see Plate 17, fig. 1)
is of a peculiar construction. It consists of a plate _A B_,
containing--1st. a guide tube _a_, (fig. 2) to centre and conduct the
blank wire;--2d. a ring _b c_, with _nine_ grooves cut on one of its
surfaces, directed to the centre, and in which are _well_ fitted the
cutters 1 2 3 4 5 6 7 8 9; and 3d. a ring _d e_, formed into nine
spirals exactly like each other, answering to the cutters, and destined
to urge them _equally_ toward the common centre whenever this circle _d
e_, is turned by the endless screw _C D_, in the direction of the arrow.
In fig. 2, _f g_ is merely a top piece to cover at the same time the
cutters and the ring _d e_; which latter is thus duly centered. The
points of the cutters 1, 2, 3, &c. are formed like the spaces of pinion
teeth; and in the other direction, are sloped 15 degrees to the common
axis, as taken at their pitch line.

The third figure represents the drawing clams, or pinchers, with a piece
of blank wire _d_ in them, tapered off to give easy entrance to the
cutters. These clams have a cylindrical part of about a foot long, in
which is cut a winding groove _a b_, whose use is to _turn_ the wire in
the act of drawing; for which purpose also the _swivel_ _e f_ is
provided. The method I employ to _trace_ this groove to the obliquity
required, is to measure the circumference of the cylinder, and call that
268; and then, to make its length, in the cylindrical part, equal to
1000 of the same divisions. But this is right, _only_ when the _pinion_
to be drawn is of equal diameter with the clam-cylinder _a b_: so that
if it is wished to draw pinions of a smaller diameter, I further say:
diameter of clam-cylinder _is to_ diameter of pinion, at the pitch line;
As 1000 (present length of clam-cylinder) _is to required length of
ditto_. Thus, for example, if the diameter of the pinion were only 1/4
that of the clam-cylinder, the _length_ of the latter would be only 250
of the 1000 divisions, before found: and so in proportion for smaller
diameters.

The figure shews this groove receiving a guide screw or stud _a_, which,
placed in the fixed headstock _a c_, turns the clams _d_, with the wire,
just enough to give the teeth an inclination of 15 degrees, thus
adapting them to the wheels of which the proportions have been already
given; where note, that the real dimensions of this pinion Machine are
_twice_ as large as those of the figures 1 and 2: but the size of every
thing is of course _variable_, according to the pinions required to be
produced.


  OF
  A GEERING CHAIN,
  _Formed to work in the Patent Wheels_.

This Chain is shewn in fig. 4 of Plate 17. The links are formed to an
angle, in the middle, similar to that of the wheels at their pitch line;
of which the obliquity, for the V wheels, is greater than 15 degrees;
since the thickness of the wheel, is necessarily divided between the
right and left handed slope. Be this slope what it may, the chain and
wheels must of course be alike, measured at the pitch line of the
wheels; and _then_, as the chain geers with a straight _line_ of
pinions, they work together without sensible friction on the teeth, and
with nearly the same steadiness of motions as wheels would work
together. Moreover, if the drum be of a pretty large diameter, its
action will likewise be nearly _equable_. The degree of precision
depends, however, on the fineness of the pitch, and the largeness of
diameter in the drum; since every chain bending round a cylinder _must_
form a polygon of a _greater or less_ number of sides, dependent on
these circumstances. I repeat then, that while the chain works on the
pinions in a tangent to them all, there is no necessary friction between
them; nor yet on the pins of the chain, but only at the drums which
actuate and return the latter:--I shall dismiss the subject, by
observing, that I have used the term _drum_, because of the similarity
of this chain-motion to that produced by bands, where drums are
generally the _movers_. But here, this supposed drum is a wheel of
proper diameter, cut into teeth similar to those of the pinions; and
placed at the same height on its spindle. I have reason to think that
this chain, carefully made, would be an useful addition to the _bobbin
and fly frame_, applied both to the bobbins and spindles, instead of the
bands now in use; which, though a convenient resource, give a result
equally uncertain and imperfect.


  OF
  A SERPENTINE BOAT OR VESSEL,
  _To lessen the Expence of Traction, &c._

The present description of this Machine, will consist, chiefly, of a
translation from my own specification, given at Paris with the
application for a _Brevet_, or Patent, obtained in the year 1795, and
which is thus introduced.

"It is a well-known fact, that the longer any Boat or Vessel is, in
proportion to its width, the less power it requires to convey a given
load, from one place to another. But these lengths cannot be extreme,
without introducing a degree of _weakness_, that would offer great
danger in the use of such vessels. If then a Boat of a given volume, be
divided into several long and narrow ones, the head of each adapted with
a certain exactness to the stern of its forerunner, they will (with the
trifling difference arising from the asperities of their surfaces) _all_
move through the water with the same ease as any single one; and carry,
unitedly, the same weight as did the large Boat before it was divided.
This idea constitutes the principle of my Serpentine Vessel."

"This Invention is not to be considered as an imitation of the
well-known man[oe]uvre of towing one vessel in the _wake_ of another:
for the resistance of the vessels thus towed, remains nearly, though not
quite the same as if drawn along separately. But here, by the adaptation
of the _prow_ of one Boat to the _poop_ of another, the first alone
suffers resistance from the water--which, although it enters between the
_joints_, strikes _only_ the first--and from this it follows, that the
_resistance_ of these vessels, in passing from one place to another,
_bears no necessary proportion to the weight they carry_."

"Thus then, I obviate the necessity of having _broad_ vessels to carry
the heaviest burdens; for I disseminate the load over an indefinite
_length_: by which method also, my vessel rides in shallower water, and
depends less for its passage, on the state of the rivers or the seasons.
Besides, they require a much less number of horses, or exertion of
_power_, to transport a given quantity of goods; admitting at the same
time, a greater swiftness of motion. And finally, if these vessels
travel through different towns on the same voyage, the goods of each
town may be lodged in the same _part_, and merely detached in passing,
so as to lose _no_ time in unloading them."

"Fig. 1 of Plate 18, shews the _plan_ of several forms which I give to
the articulations or separate parts of these vessels: so as to connect
them strongly, yet leave them, as a whole, in some degree flexible. The
form _A B_, is, for the first boat, a straight line across to form the
_stern_, and for the second an obtuse angle terminated by a semi-sphere
or vertical semi-cylinder, which enters a hollow and similar figure in
the first Boat--which latter, in this case, forms the _Head_ of the
whole Serpentine Vessel."

"These two parts or joints, of which we have been speaking, are held
together by a rope _c d e f_, which, fastened to the second part at _c_,
passes over two pulleys _e d_, in the head, to the small capstan _f_, by
which, both parts are bound together as tightly as may be judged proper.
If it were thought necessary, the spaces _A B_ might be underlined with
a piece of leather or metal, _not_ to prevent the water from entering
between the Boats, but to prevent its _striking_ those which follow the
others through the water--a precaution less urgent in the other kind of
joint we are about to describe."

"_C D_, in this same figure, presents another form of the head and stern
of two contiguous Boats or _parts_; (which, to save room, are both
supposed to be _broken off_ at some point between their ends:) where as
in the former case, the Boats are connected so as to remain horizontally
flexible. These forms are semi-cylindrical, the stern concave, and the
_head_ convex, to the same radius; and the motion takes place around a
bolt and pulley _p_, reeved with a rope coming from one side of the
first Boat near _C_ and led again to a small windlass or capstan placed
on the other side near _D_. _E F_, is another modification of the same
kind of joint: the centre of which is a bolt or stud _q_, (better seen
at _q_ in the 2d. figure) over which a triangular frame falls from the
preceding Boat, and thus connects them instantaneously; leaving a
certain flexibility in the horizontal direction."

"Finally, _G H_ shews a simple mean of connecting these Boats, on the
supposition that both ends of each are formed alike to an obtuse angle
in the middle of their breadth. It is a kind of hook _r s_, mounted in a
frame turning on centres in the _preceding_ Boat, and reaching over into
the succeeding one; where it finds a hollow _step_ of metal which
receives and fits it, so as to hold these neighbouring Boats with
sufficient tightness, but still with a certain degree of flexibility.
Many other methods might be suggested, by which to form these joints;
and almost _any_ might be made to answer the purpose. I shall therefore
leave this branch of the subject, observing only, that the second figure
of Plate 18, is an _elevation_ of the same things: which, generally, are
marked with the same letters as far as they are visible."

"The third figure presents the same objects in perspective; to which are
now added _two_ masts _I K_, placed obliquely on that Boat which forms
the Head of the whole vessel. This obliquity is useful when the boat is
drawn from one side only; but is injurious where the traction takes
place indifferently on both sides: so that I should not, _now_, advise
the use of this method--which indeed, I have avoided in fig. 4 of this
Plate."

"In every case, each of the masts carries a pulley near _I_ _K_, over
which passes a rope, the ends of which are fastened to the masts by
proper brackets, near the deck: and to the middle of this rope is
fastened the track rope _L_, by which the horses draw the Boat along. By
these means the vessel is _steered_ either to or from the land: for if
the knot of the track rope is brought near the mast _I_, the Boat (which
as before observed is the head of the whole vessel) veers towards the
horses; and the contrary when the knot is drawn towards the mast _K_:
both which effects are rendered the more prompt and decisive, by the use
of the _lee boards_ _K M_, the nature and use of which are already fully
known."

"But there are cases in which, from its great length, this Serpentine
Boat would require a particular direction, for some intermediate point
between its extremities; as although, in theory, every separate part
ought to pass through the same water, yet in canals or rivers much bent,
_this_ may not invariably take place; and _then_ a rudder would be
useful, even in the middle of the vessel. I have therefore placed a pair
at _P R_, fig. 3. Their motion is a vertical revolution, round a
horizontal centre; and as they are formed obliquely to the sides of the
Boat, when one of them is plunged into the water, it tends to drive the
Boat in a sidewise direction: and if at any time it should be desired to
stop the whole vessel, _both rudders_ would be plunged at once into the
water, when they would greatly contribute to that effect."

"The fourth figure in this Plate 18, presents a general view of the
vessel, comprising five articulations, (or Boats) besides the head and
stern--which latter would fit each other without any intermediate parts,
and form a Boat alone. Nor do these five parts by any means limit the
useful number: but the Plate would not have contained more, unless on a
scale too small to be distinctly understood."

"Returning now to fig. 1, we observe the ropes _A D F H_ and _B C E G_,
which are supposed fixed to the stern Boat, and carried to the capstans
represented in the _Head_. These ropes consolidate the whole fabric, and
act, occasionally, as a kind of _muscle_, to govern the larger
evolutions. These ropes pass in the brackets placed near the joints _A
B_ and _C D_, &c. being _under_ the gang ways, of which a portion
appears at _S_ fig. 3, hung upon hinges, that they may be turned up when
the Boat is used in narrow water."

To the above specification were added the following remarks, which still
apply to this kind of vessel, navigating on canals and inland rivers:
"this vessel admits of the use of every kind of _mover_; such as men,
horses, wind, or the steam engine; the latter of which I propose to
apply to it in a manner equally simple and effectual; especially so as
_not_ to injure the banks of any canal, &c. by acting against and
disturbing the water."

I need not repeat that this Invention dates as high as 1795: as the
_Brevet_ was issued in that year. It may be added that four _parts_ of
such a Boat were executed about the same time; namely, the head, the
stern, and two intermediate _pieces_: making together a length of 100
feet; and these, loaded to a certain depth with stones, were drawn _up_
the river Seine by a single horse _on a trot_--which would likewise have
taken place had the Boat been ten times as long; since, as before
mentioned, _the resistance of this kind of vessel bears no given
proportion to the Load it carries_.


  OF
  A MACHINE
  _For destroying, or lessening Friction_.

I think it may be assumed that _friction_ is fully expressed by the word
_rubbing_: and that where rubbing cannot be found, friction does not
exist; especially that _kind_ of friction which opposes the motion of
machinery--in which respect, the subject is chiefly thought interesting
to mechanicians. It would be abandoning my intended plan in this work,
to treat largely of friction, or any other accident in practical
mechanics; but having already declared myself "no believer in several
sorts of friction," I am in a measure bound to introduce my description
of the two following articles, by a short reference to the general
subject. I offer then the following remarks, more as hints for the
consideration of learned experimenters, than as conclusions sufficiently
proved to become rules in practice. What I cannot help urging strongly
is, that _rolling_ is not _rubbing_. If it were, I would ask in what
direction it takes place? Is it in that of the plane rolled over? or in
that of the radii of the rolling body? If in the former, it would indeed
_glide_ over that plane, and occasion or suffer _real_ friction; but
this, I think, is not pretended. If this motion is in the latter
direction, (that of the radii of the rolling body) it is indefinitely
_short_, compared with the progressive motion of the rolling body, so
that the _power_ of the latter, to overcome any resistance in that
direction, is _infinite_. Whenever therefore, in experiments of this
kind, a finite resistance is perceived, it must, I should think, be
ascribed to other causes, and not to _friction_. In my wheels for
example, (see a former article) where there is a real and deep
_penetration_ of the surfaces, I have proved that the friction between
the teeth is _less_ than the distance between two of the last particles
of matter: and surely, when penetratration is purposely made as small as
possible (by the use of _smooth_ rollers) the friction thence arising
must be still more imperceptible. But I hear it answered, that _this_
friction is both known and measured! and certain celebrated experiments
are adduced to prove it. But what I most wonder at is, that a person so
truly learned as the author of those experiments, should have adopted so
remarkable a misnomer; in which to all appearance, indentation has
usurped the name of friction. Nor let this surprise, surprise any body:
nor especially, offend this learned author himself; for I am persuaded
that the sole act of placing these wooden rollers, on these surfaces of
wood, must indent them both sufficiently to account for all the facts
observed; and still more so when loaded with weights of 100, 500, or
1000lbs. No friction, therefore, is requisite in accounting for the
resistance of these rollers to horizontal motion. Nay, I submit, whether
a resistance, arising from indentation alone, would not prove to be
"directly as the pressures and inversely as the diameters of the
rollers?" To me the subject presents itself under three aspects: either
the whole indentation takes place on the rollers, when they are very
soft and the _rulers_ very hard; or the latter, when _they_ are very
soft and the rollers very hard: or, which is most likely, this
indentation takes place on both bodies at once; so as to produce a
_surface of contact_, intermediate between the _straight surface_ of the
_rulers_, and the _cylindrical_ surface of the rollers. But in either
case, the _place_ of resistance to horizontal motion, must be _out of
the line of direction_ of the roller's centre of gravity: and thus would
the roller present more or less resistance, independently of every thing
that can be called friction: and which degree of resistance will
continue to exist as long as the place of contact is made to change on
the rulers--for thus to change this place of contact is to renew this
indentation; which process will elicit a resistance equal to what would
be observed were the roller (without indentation) forced _up_ a plane,
inclined to the horizon in the same angle as a line, drawn from the
centre of the roller to the extreme edge of the _surface of contact_,
makes with the perpendicular.

I cannot possibly enter at length into this subject, as it makes no part
of my engagement to the public: but I would observe that _this_
resistance is, _a fortiori_, something besides friction, since _greasing
the surfaces_ "did not cause any sensible diminution of it;" whereas it
made a difference of _one half!_ in some others of the experiments
alluded to.[4] Were I asked the reason, I should answer, because
friction had little or nothing to do with it; and I would say further,
that greasing or oiling these surfaces would most likely _increase_,
instead of diminishing, their resistance to horizontal motion: namely by
_softening them_, and making them more susceptible of change of figure:
which opinion gathers strength from _another_ fact adduced, viz: that
"rollers of elm produced a friction (or resistance) of about 2/5
_greater_ than those of lignum vitæ:" but why? because elm is relatively
_soft_ and lignum vitæ hard--the only cause that appears sufficient to
account for the facts observed.

[4] See Dr. Gregory's Introduction to his Mechanics. Vol. II.

I must now leave these remarks to persons having more means and leisure
than myself, to pursue the subject; wishing only, that _useful truth_
may result from them: and that this unbelief of mine "in several special
kinds of friction," may at least be found to have _some_ reasonable
ground to rest upon.

But I may be opposed in some of my statements by the fact, that friction
rollers, with centres, have been used with little advantage; and _often_
laid aside. This I acknowledge; and go a step further. Friction is by no
means of so much consequence as it was once thought to be: and is _not_
the source of the greatest defalcations that occur in the use of power.
Yet, to get rid of it, in some cases, would be of considerable
importance; and the subject deserves at least the attention of every
intelligent mechanician.

Those who have used friction rollers, know that it is a thing of great
difficulty, to place their axes exactly parallel to _that_ which they
are intended to support: and even, if rightly placed at first, that a
small degree of abrasion, greater on one pivot than another, will soon
destroy that parallelism; and thus introduce a _growing_ friction,
capable, at length, of rendering the whole completely useless: for
although the original friction is _lessened_ by being transferred to a
slower-moving axis, yet the latter still resists in some degree, say 1/4
of the whole; (its pivots being 1/4 of its whole diameter) so that the
cohesion, or something else, between the main shaft and the friction
roller, (thus resisted) must be sufficient to _drag round_ the latter,
against about 1/4 of the original friction; which in a word it cannot do
without some _relative_ motion between those surfaces, the friction
roller lagging behind the main shaft, until its own friction is overcome
by _another_. And thus it is, that a friction roller of this kind, does
not make so many revolutions on its pivots, as its diameter compared
with that of the main shaft, would imply; for example, if the shaft were
4 inches in diameter and the friction roller 8 inches, the latter would
_not_ complete one revolution against _two_ of the former. There would
thus remain a difference spent in _real_ friction, in addition to that
on the axis of the friction roller. Besides this, we have the want of
parallelism above mentioned; which occasions a rubbing, in the direction
of the shafts, small indeed in quantity, but for that reason very
_powerful_ in bringing on a change of form, and thereby hastening the
common destruction. Both these accidents, therefore, make friction
rollers, in general, an unsatisfactory and perishable expedient: and it
is to make them _less so_, if not entirely to cure these evils, that the
two following articles are designed.

In fig. 6 of Plate 17, _A B_ is an axis which it is desirable to divest
of its _friction_. To do this, as nearly as may be, I connect with it
two rings of hard metal _C D_, formed as truncated cones; and under the
shaft, in the same vertical plane, I place two smaller shafts _E F_,
carrying on their tops, other two cones, similar to the former. The
summits of each pair of cones meet of course in the points _a b_ of the
main shaft; and, on the principle of bevel geer, every contiguous part
of the touching cones moves with the same velocity: so that there is no
sensible _rubbing_ between them--for, 1st. the pivots _c d_, are hard
and pointed, and run on the hardest _steps_ that can be obtained; and,
2ndly. the tendency of the cones _u_ toward each other, is repelled
without friction by the cylinders _e f_, attached to them, and which
_lean_ right and left against each other, turning with the same
velocity, without causing any friction, or any _creeping_, between the
two pairs of cones _e C_, and _f D_. All the weight therefore, of the
shaft _A B_, (which of course is kept in place in the other direction by
proper side cheeks, &c.) rests on the points of the vertical shafts _E
F_, accompanied by no sensible tendency of these points to quit the
places assigned to them.


  OF
  A SECOND MACHINE,
  _To avoid or diminish Friction_.

In Plate 17, figs. 7 and 8, offer a mechanism different from the
preceding, though intended to produce a similar effect. Referring to
_that_ cause of friction which consists in the want of parallelism
between a principal shaft and its friction rollers, I here introduce a
form for the latter, which admits of this consideration being in a
measure neglected. These friction rollers are only portions of
cylinders; and they have _no_ shafts. They turn simply on a sharp edge,
placed in a prismatic box _A B_, in a well formed angle of which, they
move to and fro, without _rubbing_. When at rest, these axes _D C D_,
(fig. 7 and 8) are drawn against the right hand side of the box, by
small weights _E_; and the shaft is carried by one or the other of them,
according as they are, or are not, within reach of its radius. Thus, in
the present position of the shaft, (see fig. 7) the second arc _C_
supports it, the third having fallen behind the first, so as not to be
seen: and the first arc _D_ being on the point of taking up the load. In
short there are _six_ spaces, either _left_ or _cut_ on the shaft,
opposite the three arcs _D C D_. 1st. _one_ space, of 1/3 of the
circumference, left concentric with the real centre of the shaft,
opposite the first arc _D_, followed by 2/3 of a circumference _cut an
eighth of an inch lower_. 2ndly. another third of a circumference
opposite the second arc _C_, beginning where the first ends, and
followed by 2/3 of a circumference cut an eighth of an inch lower: and
3rdly, another space of 1/3 in circumference, opposite the arc _D_,
followed by a similar space of 2/3 cut an eighth of an inch lower. By
these means the shaft is never without _a concentric bearing_: and the
better to secure this property these arcs _left_, may be each of them
_more than one third of a circumference_ in length, so as to avoid the
least _drop_ at each change of roller; and even to give the shaft a
support from two rollers at once, during a good part of its revolution.

In using this mechanism, the vessel _A B_, would be filled, to a certain
level, with oil or water, to prevent any blow from the returning
arcs--which latter might be made to fall on a lining of leather, to
avoid still further all commotion: and thus, even were these rollers not
placed _quite_ parallel to the shaft, this imperfection would be
corrected by the frequent _renewal_ of these movements, and the
consequent absence of _lateral_ friction between the arcs and the shaft.
It may be observed that either of the above methods of destroying
friction is not confined to the vertical direction: but may be so used
as to receive the pressure caused, in any direction, by the action of a
wheel or other agent. And with respect to the best use of each method
respectively, I would propose the former for light and swift motions,
and the latter for slow-going shafts, heavily laden: it being well
understood that the shafts must be kept in their places, in the less
essential directions, by proper steps, at the discretion of the person
who employs these Machines.

Finally, I consider it as a matter of course, that _all_ the surfaces
coming into contact in these operations, should be _as hard and
impenetrable as possible_. For if, by neglecting this precaution, any
_change of form_ occurred, what is said above could not be practically
true: But these properties can be realized, with only those degrees of
hardness that are _often_ employed in the mechanical world. Thus _a die_
of hardened steel, bears almost unimpaired, the strokes and pressure it
suffers in the coining-press. A chisel, _stands_ thousands of blows and
cuts hard metal, without sensibly giving way. The _knife-edges_ which
carry a heavy pendulum, suffer it to vibrate many years without wearing
out; and the fulcrums of scale-beams, bear enormous weights, for almost
an indefinite period, without any injurious effect. I request therefore,
that these facts, may be put into the scale, when my foregoing
statements are _tried_: whether as applied to these anti-attrition
machines, or to my late patent wheel work, _or both combined_: for I
foresee the use of these friction rollers, cut into teeth on that
principle, to insure the proportionality of their respective motions.


  OF
  AN EQUILIBRIUM COCK,
  _To prevent abrasion and leakage_.

In the common form of this useful instrument, no method seems to have
been devised for preventing the _plug_ from being _pressed aside_, by
the weight of the liquid: which provision nevertheless would have
diminished the wear and tear of the touching surfaces, and secured much
longer the perfection of the instrument. This property would be
particularly desirable in cocks which convey a fluid from a great
height; and still more so in those used for containing steam or any
other fluid under a _high_ pressure. I can hardly persuade myself that I
have stood so long alone in my ideas upon this subject; but not having
seen any thing _published_ on the subject, under a name implying the
above mentioned property, I venture to give this as my invention--which
indeed it is, even should other persons have pursued and embodied the
same idea.

Fig. 9, 10 and 11 of Plate 17, represents one of the forms of this
equilibrium Cock. It consists of a square plug case or chamber _a b_,
with a hole _c d_ bored transversely through it, exactly across its
centre: and to this chamber is fixed by the flanches _e f_, the
bifurcated water-passage _g h_, forming one body at _i_. The plug of
this instrument admits of various forms and proportions; of which I
have shewn two in the figures 9 and 11. The first _m n_, receives the
fluid through the two openings _c d_, which correspond, in one position
of the plug, with the double water-passage before mentioned. And
further, the plug itself is bored lengthwise in its under end _n_, so as
to form the spout of the cock: or otherwise (see fig. 9) this spout is
taken in a double form from the _outer_ surface of the plug at _b a_, so
as to present two streams, thus producing, I think, an instrument of
somewhat greater solidity. All that seems important is, that whatever be
the pressure of the fluid from without, it be made _equal_ on both sides
of the plug, so as to occasion no friction between it and the chamber.
The principle is indeed so effectual, that one might distribute steam
pressure of the greatest strength or even gunpowder pressure, without
_much_ resistance to the operator, and without injuring the mechanism by
oft repeated action.


  OF
  A MACHINE
  _To communicate and suspend Motion_.

In Plate 19, figs. 3 and 4, shew this mechanism in two directions. It is
composed of two wheels _C D_, cut (or cast) into teeth of a peculiar
kind, that both _geer_ with one another, and at the same time, include
the chord or round strap _A B_, by which they are driven. These teeth
can be better represented by a figure than in words; and will I suppose
be understood from figures 3 and 4: They are divided, on the rim of each
wheel by a _space_ too small to admit a tooth of the other wheel: but
then, _every-other_ tooth is cut away in a sloping direction on each
side of the wheel, from the bottom of the tooth to its top on the
opposite side: so that while these teeth are working in each other they
offer two grooves, in the form of a V, which coming together surround
the chord and press it in four points, either to drive the wheels by the
cord, or to pull the chord by the wheels, according to the use it may be
wished to make of this mechanism. In fig. 4 the cord is seen at _A B_,
passing among the teeth of the wheels; and in fig. 3 it is shewn at _C_,
as a mere circle, in the centre of a lozenge formed by the teeth whose
points _now_ geer together. Fig. 5 is a sketch belonging to this
subject, which shews something of the manner of using this _round
strap_ as a _mover_: for by carrying it (either in a horizontal or
vertical plane) _by a line slightly curved_, from one machine to
another, it will drive them all and give the means of stopping any _one_
at pleasure. Suppose then, _A B C D_ fig. 5, to be four machines placed
as above mentioned. If I wish to stop the machine _B_, I merely draw
back the pressure wheel _E_, and the cord ceases to lay hold on the
machine as shewn by the dotted line: but when I want to _set it on_
again, I do it by bringing back the wheel _E_ to its present position.
And thus at a small expence, I could _geer_ a considerable factory, in a
way which I think as durable as it appears economical. The principal
objection, perhaps, is that this cord is liable to wear out soon, by
such incessant action; but then the pressure on it needs not be great;
and of friction properly speaking there is _very_ little: Besides which,
the cords would be made of a peculiar texture, perhaps of leather, sewed
edge to edge and covered like a whip, _by one of the machines I shall
bring forward hereafter_.

It so happens that many of my Inventions are of a generic nature, and
thus apply to cases which, appearing different, have nevertheless some
common properties. The _rule of contraries_ especially applies to many
of them,--of which this is an example. It offers a good method of
driving a boat through a tunnel, or other confined space, either by the
force of steam or any convenient power. To this end a rope laid along
the side of such canal, and fixed at each end, or at several
intermediate points, might be led between a pair of wheels like those
above described; which duly turned, would drive the boat the distance
required with the least possible expence of _power_, and _without_ the
defect of agitating the water.--But I must not anticipate too much on my
intended subjects.


  OF
  A MACHINE
  _To set on, and suspend, rapid Motions_.

This Invention is under the protection of a Patent. It is applied to the
spindles of my spinning machinery called Eagles, from their analogy to
the machines named _Throstles_. It is in my opinion an excellent
machine; as it secures a mathematical equality of twist to _any_ number
of spindles from permitting the use of geering to turn them, which could
not have been done without some means of stopping a single spindle. This
mechanism (see Plate 19 fig. 1 and 2) consists of a toothed pinion _A_
soldered to the box _B C_, (partly cut down in the figure to shew its
contents) and with it running loose on the lower part of the spindle _E
D_. In this box are placed two weights _M N_, like that _M_ fig. 2,
which both together, fill the box loosely, and, rising above it, are
pinned at _O P_ through the spindle. They are moreover kept from
quitting the latter by the ring shewn in section at _q q_, which holds
them _loosely_, yet prevents their flying away or hurting any one. When
now the spindle _E D_, turns swiftly, the centrifugal force of the two
weights _M N_, projects them from the centre as far as possible; and
they lay hold, by friction, of the cylindrical surface of the box _B C_,
and thus _keep_ the revolutions of the spindle to the same number of
turns per minute, as the pinion _A_ receives from the driving wheel.
But when the spindle is stopped and held by the fly as usual, then the
centrifugal force ceases to act, and the box _B C_ does _not_ wear out
much, by its further revolutions. And when as before, the spindle is
again let loose, _that_ friction which takes place on the bottom of the
box sets the spindle running again, when the centrifugal force comes to
its aid, so as to unite again the box and the spindle, thus renewing
that valuable property of all spinning machinery, the mathematical
correctness of its movements.


  OF
  A MACHINE
  _For forging Screws, Beads, &c._

The effect which this Machine is intended to produce, is analogous to
several culinary or officinal processes that might be named. It is
called _rolling_: but not in the same sense in which that word is used
in manufactories, where _rollers_ form or modify the body acted on. Here
this body itself _rolls_ between two surfaces moving different ways and
receives from them the desired impressions, and this idea I have
extended to _screws_; proposing to _finish_ them on some metals and in
some dimensions; and to _rough them out_ in others. The Machine is
represented in figs. 6 and 7 of Plate 19, where fig. 7 shews the _faces_
of the arcs _A B_ of fig. 6. By the form and connection of the arms _A
C_ and _B D_, these arcs move opposite ways: and since they are grooved
obliquely as shewn in fig. 7, if a prepared cylinder of soft metal _a_,
be put between them, and the handle _C_ be sharply pressed into the
position _A E_, the cylinder _a_ will be made to _roll_, and the grooves
of fig. 7 be impressed on it so as to meet and form the screw in
question. The only conditions are, that the arc _B A_ be at least equal
in length to the circumference of the screw, when finished; and that the
grooves (fig. 7) be rightly sloped, and have the _form_ intended to be
given to the threads of that screw. It will occur of course, that the
opening between the arcs at the point where the blank cylinder is
introduced, must be larger than the distance between the arcs by the
whole depth of the threads to be impressed: which therefore will begin
to be formed at two opposite points the moment the screw _a_ begins to
roll. This however, might and would be otherwise, if it were thought
best to form the arcs _A B_ spirally; and let the deepening process be
gradual: in which latter case another consideration would occur, namely;
that the grooves themselves (see fig. 7) must diverge a little instead
of being parallel, so as to permit the screw to lengthen as the pressure
should displace a part of the metal. In all cases the upper surface of
the grooves should be _milled_ so as to lay hold of the soft metal, and
insure the rolling motion: and should this material be hot-iron, the
stroke should be taken in an instant, and the machine be kept cool by
every proper method, in the intervals of working.

I need not add that this rolling process would be still easier
performed, if the impressions to be made were circular and _not_
oblique: such as beads, balls, &c. but these considerations I leave to
my readers.


  OF
  A DIFFERENTIAL STEEL-YARD,
  _To weigh vast Weights with short Levers_.

Plate 19, figs. 8 and 9, offers two representations of this Machine--one
intended to shew its manner of acting, and the other _one_ of its
practical forms. By means of the first, (fig. 8) we may compare it with
the common steel-yard; and even shew the latter as a part of the former.
If a weight, or load to be weighed _M_, were suspended to the arm _A B_,
and the counter-weight _W_, placed at the point _C_, of the arm _A C_,
we should have a common steel-yard whose power would be as 5 to 1: for
the arm _A B_ is just 1/5 of the arm _A C_, and this is the principle on
which steel-yards are commonly made. But instead of this, my steel-yard
_G E B D C H_ fig. 8, is now infinitely powerful: so much so indeed, as
to be infinitely useless. If millions of pounds were now to be suspended
at _P_, they would not raise the weight _W_ one tittle, for they hang
_entirely_ on the point of suspension _A_. But although the Machine is
_now_ useless, it can be altered in a moment and made both useful and
commodious; only I thought its principle would be the better understood
from being thus shewn _in excess_. To make it a useful and powerful
Instrument, I only move the hanging bar _D G_, to _a b_; and the bar _E
B_ to _c d_, the lever _b d_ being similar to that _E G_. In this state
of things, the whole load _P_ is found at the point _o_ of the lever _B
H_, (for the lever-arms _c o_ and _d e_, and those _e b_, and _a o_ are
equal) and the power of this steel-yard is as the line _A C_ to the line
_A o_; that is as 20 to 1, instead of being as 5 to 1 which it before
was. But this is not _yet_ a powerful Machine; being chiefly intended to
shew the principle on which it acts--and to prove that however small the
distance _A o_, that distance, dividing the arm _A C_, gives the real
power of the steel-yard. And supposing now the arm _A C_ to be four feet
in length, and the distance _a D_, _B c_, and _A o_, to be 1/10 of an
inch, then the power of the weight _w_ to raise (or weigh) the load _P_
is as 48 inches to 1/10 of an inch, or as 480 to 1: so that if the
weight _w_ were 10lbs. this steel-yard would weigh 4800lbs. or upwards
of two tons; and it is easy to see that this power can be almost
indefinitely extended.

Fig. 9 of this Plate shews a real steel-yard made on this principle; the
power of which, under its present length, is as 40 to 1. In this Machine
all the centres are fixed: and the load is suspended on knife-edges, the
distances of which from each other and from the common centres are
invariable--as they _must_ be in all instruments of this nature.


  OF
  A RETROGRAPH,
  _Or a Machine to write backwards, for Engravers_.

This Machine is exhibited in the two figures 10 and 11 of Plate 19. It
is composed of a straight ruler _A B_, having an exactly dove-tailed
mortice made along it, to receive the rollers, (or slides) by means of
which the parallelogram _C D E_ _F_ slides up and down in this mortice.
This parallelogram is composed of four rulers _C D_, _D E_, _E F_, and
_F C_, connected by cannons or tubes fixed to every-other arm: and on
which the contiguous rulers turn very correctly. Through which moreover,
in two cases, _F D_ the drawing pencils are introduced, and under which
in other two cases, _C_ and _E_, the guide rollers already mentioned are
nicely fixed by the screws on which they turn. This is seen by an
elevation in fig. 10, where _p_ marks one of these rollers, and _o q_
the end of the ruler supposed fixed to the paper by proper blunt points,
&c. At _r_ is seen one of the tubes which form the joints _C_ and _E_:
and _r t_, are, one the writing pen, and one the retrographic style or
pencil. Fig. 11 is a plan of the whole Machine: where if the hand
guiding the pen _D_ goes upward, the tracer _F_ rises too. But if the
pen or hand _D_ moves to the right, the tracer moves to the left at the
same moment. In a word this is to write backward in the sense of
engravers, who thus write that their letters may proceed forward after
_one_ impression.

If it were desirable to give the engraver the same facility he has in
the use of a pen, the tracer _t_, fig. 10, would be terminated above as
a hollow conical cup, into which he would introduce a pointed style held
as a pen. In this case the tracer _t_, would be made as short or _low_
as possible, to bring the style so much the nearer to the paper; and
thus to prevent all anomalous movements.


  OF
  AN EYE MACHINE,
  _Or Machine for making the Eyes of Hooks and Eyes_.

If it were enquired why this Machine is offered to the public without
the Hook Machine; the answer would be, this only is _finished_: and it
is wished to present nothing here that admits even a doubt of its
utility. The drawings given in Plate 20, figs. 1, 2 and 3, are more
intended to be useful in the construction of this Machine than complete
in _appearance_: so that nothing has been done by way of shading, but
what it was thought would the better distinguish the parts from each
other, and facilitate their assemblage in one effective Machine. The
Machine consists first of a slide _A B_, (worked by a lever-handle, a
crank, or any proper first motion.) It glides between two cheeks _C D_,
(see the _end_ view in fig. 1) connected with the several parts about to
be mentioned. This slide is marked _A B_ in all the three figures. It
carries (by means of the screws _a b_, coming through the slits _c d_,
in the main Plate _E F_) a plate _g_, the chief use of which is to
support a tumbler _e_, whose use is to throw the eye, when made, from
the machinery: which tumbler is kept to its work by the spring _i_, as
will be further explained presently. This slide itself has a peculiar
form at the end _B_, (fig. 2) which is shewn by dotted lines at _c d_ in
fig. 1. It is a slit, with the corners rounded off for the purpose of
working the springs _now_ to be described. These springs _m n_, (see
fig. 2) are fixed to a _cock_, itself screwed behind the main plate: and
they come through the latter to the _left-hand-ends_ of the small curved
mortices seen (with the springs) at _m n_ fig. 1. The slide _A B_ then,
with its forked end shewn by the dotted lines at _c d_, is destined to
take the springs _m n_ and carry them to _r s_, where they are _now_
seen surrounded by the eye _almost_ formed: for in this motion these
springs take the wire (shewn by the lines dotted _across_ the Machine
and previously _cut_ by the sheers _u_) and meeting with the obstacles
_t v_, being the thicker parts of the clams _t v w_, they bend it into
the form _r s_--when the screws _a b_ lay hold of the sloping ends of
the clams _c t w v d_, and squeeze them together; by which operation the
hooks _t v_ finish the _eye_, by rolling its two ends round the springs
_m n_ now in the position _r s_. Where note, that the slit _c d_ of the
slide _A B_ is so formed as, when it has carried these springs _m n_ to
_r s_, to slide forward without doing any thing more to them, while
closing the clams. It performs, however, some other less important
operations, to which it is now necessary to allude: among other things
this slide works the sheers _u_ that cut the wire, and _that_, by means
of the doubly wedged hook _x_, which goes back with the plate _G_, doing
nothing: but which by the action of its springs fixed at _a_, falls
_under_ the sloping end of the sheers _u_; and, when the slide, by the
screw _b_, carries it to the right hand, raises the end _x_ of the
sheers _u_, and cuts the wire near _v_, to prepare it for the operations
already described. The part _y_ in the two figs. 1 and 2, is the other
cheek of the sheers fixed by screws to the main plate, and covered by a
small plate _z_, in which a _nick_ is cut to form a passage for the
wire, and present it to the sheers, that they may cut it to the proper
length, after having directed it right across the springs _r s_, then
placed by their elasticity at _m n_. It hardly need be added that a
_stop_ is placed at _o_, to determine the length of the wire so as to
form the eye complete, and not to admit more wire than is sufficient;
all which is regulated between the sheers and the _stop_, by proper
adjusting screws, which it is very easy to suppose or supply.

Fig. 3 is intended chiefly to shew the mechanism by which the eye, when
finished, is thrown off the pin round which it is bent by the springs _m
n_. It consists of a _tumbler_ _e_, placed in a mortice in the end of
the plate _g_, and kept to a given position by the pressure of the
spring _i_. When the slide _A B_ is carried forward, toward _E_, to
perform the operations already noticed, this tumbler _e_, gives way to
the angle _G_ of the _doffing lever_ _m G_, (this lever being shewn also
between _c m_ & _d n_ in fig. 1) and rides towards _m_ without producing
any effect either on the plate _G_ or the lever _m G_: but when it has
once passed the said angle _G_, it cannot go again toward _F_ without
depressing smartly the end _G_ of that lever, and thereby raising the
end _m_, thus starting the eye from the stud _m_, round which it had
been bent by the processes above described.

At the right of fig. 1 near _F_, is an object, the use of which is too
evident to need description. It is a double spring for the purpose of
keeping the _hooks_ _c t w v d_ pressed against the pins, near _t v_,
which determine the position of the said hooks; and the degree of _bend_
first given to the wire by passing the points _t v_.

There are some less important parts and operations left undrawn, in
order to prevent confusion in the figures: but they are such as would
strike any person having the above under his eye. In a word I have done
what I thought best to aid the construction of this Instrument:--which
is represented at two thirds of its natural size--but whose dimensions,
of course, would vary with that of the objects to be produced by it.


  OF
  A VENTILATOR,
  _Rotatory yet by pressure_.

By this title I wish to distinguish this Ventilator from all such as act
by the mere centrifugal force of the air: and to make this distinction
the more palpable, I would add that _this_ Machine acts like a pump,
that is by means of a space alternately contracted and expanded, into
which the air enters, and from which it is expelled _by force_ as water
is from a pump. The means are the following: _A B_ (fig. 4 of Plate 20)
is a hollow cylinder, of a diameter proportioned to the effect wanted to
be produced. _C_ is a cylinder closed at both ends, which fills that
just mentioned as far as the length goes, excepting _a play_ of about
1/8 of an inch. This interior cylinder revolves in the former; but _not_
on its own centre. It revolves on an axis _E_ eccentric to itself, but
exactly concentric with the outer cylinder _A B_. The centre therefore,
of the inner cylinder _C_, describes a circle within the outer one,
which is always parallel to its circumference. On the axis _of motion_
of this cylinder _C_, and outside of that _A B_, are fixed two cranks _E
F_ fig. 5, which exactly reach from its centre of motion to its centre
of figure: so that whatever circle the latter describes _in_ the large
cylinder, the former describe the same line _without it_. And hence any
slide or valve _D_, driven by these cranks, will always touch, or be
equally near, the circumference of that interior cylinder _C_. The valve
_D_ then, worked by the bars _G_ from without, forms a constant
separation between the right and left hand parts of the _lunular_ space
left between the fixed and moveable cylinders; and if the latter turns
from _C_ by _B_ to _D_, the right hand space _C B G_ is the _plenum_,
and the left hand space _C A D_ is the vacuum of this Instrument; or in
other words the air will flow _in_, through the passage _H_, and flow
_out_ through the passage _I_: and by a contrary motion of _C_, it would
do the contrary--but I prefer the first process because any pressure
within the valve _D_ is not liable, then, to press the valve upon the
drum _C_, and produce contact and friction; which in the second case it
might do. Suffice it to add, that the quantity of air displaced at each
revolution of _C_ round its centre of motion, is the difference between
the area of the drum _C_ and that of the cylinder _A B_: and that its
quantity at each part of the revolution is proportionate to the
curvilinear triangle _G B_, multiplied by the length of either cylinder.

In the prospectus, this Machine was said to be good as "a gas meter,"
which I still think it is. For such a purpose however, _friction and
eccentricity of weight_ should be obviated, by placing the axis _E_, _in
a perpendicular position_: when I doubt not it would measure flowing gas
better than many of the machines that have been proposed for that
purpose.


  OF
  A COMBINATION OF WHEELS
  _To raise Water_.

This _mode_ of raising water in its simplicity, is I think called the
Persian wheel. The buckets hang upon centres, dip in the _under_ water,
fill themselves there, and by meeting an obstacle above which turns the
buckets aside, they empty themselves into the upper _back_, from which
the water is conveyed to the general reservoir prepared for it. This
present Machine is such an extension of the above principle as to make
it applicable to considerable degrees of elevation, and to many
situations where a single wheel would be of no service. Having observed
that in every _train of wheels_, the circumferences of any two wheels,
have motions _towards_ each other, as well as _from_ each other; I
perceived that, in a vertical train, this circumstance might be laid
hold of to compose a machine for raising water. Be therefore, (Plate 21,
fig. 1) _A B C D_ four of a set of wheels thus intended: on the left of
the lowest wheel the buckets move _upward_, as indicated by the arrow;
while those at _B_ move downward, coming thus to meet the former. The
buckets _A_ are full, and those _B_ are empty; and as the latter, by the
motions of the _equal_ toothed wheels on which they are hung will
infallibly meet the former, and even plunge into them at _I K_ and _L_,
it is only to put a _clack_ of leather or a valve, in the bottom of
_all_ the buckets, and we have a machine that will raise water to the
top-most wheel, be it ever so high, and there the water will be poured
out into the vessel _M_, as in the common Persian wheel above alluded
to. On this principle the first change of buckets will take place at
_I_; where the lower bucket belonging to the wheel _B G_ will take the
water from the upper bucket of the wheel _A H_; when the bucket _I_ will
go down, nearly empty, by _H_ and fill itself again in the under water;
But the bucket of the wheel _B G_ having now _got_ the water, will rise
by _G_ to _K_, where another bucket belonging to the wheel _C F_ will
come empty, and plunging itself into _that_, take its water and go
upward by way of _C_ to _L_, where a similar change will take place and
the water from _L_ will rise by _E_ to _M_, into which vessel it will be
poured by the _canting_ of the bucket as seen in the figure. Thus it
appears that any number of toothed wheels geering together, surrounded
with buckets _valved_ at bottom, and receiving power from any one of
their number, will raise simply and effectually a quantity of water _not
small_ in proportion to the power employed, and by means that promise
great durability to the Machine.


  OF
  AN ECCENTRIC BAR PRESS,
  _For clearing wetted goods of Water_.

This press (see Plate 21, fig. 2) is indefinitely powerful. It was
invented for the use of my late beloved brother, then contractor with
government for cleansing the sea bedding. It is composed of a centre
piece _A_, strongly fixed to a post in the ground, the bars _A B_ _A C_
being suspended above it, so as to remain horizontally moveable, while
describing 1/4 of a revolution round the general centre _A_. The
blankets (or other goods) are put into the space _s_, (on a net nailed
_under_ the bars) while in the position _A B_; and the whole is then
thrown with force towards _B C_; the length _A C_ being so calculated as
to cease pressing at the desired moment: for such is the _power_ of this
Machine, even without this projectile force, that were the stress not
moderated, nothing could remain whole under its operation. It is clear
however, that, when this operation _begins_ at _s_, the relative motion
of the jaws _s_ and _B_ is assignable, and even visible, as shewn by the
dotted circles; but as the whole approaches toward _B C_ that relative
motion becomes insensible, the circles parallel, and consequently the
power infinite: which is all I shall say on the theory of this Machine.


  OF
  A COLOUR MILL,
  _For Calico Printers_.

This Machine is delineated in fig. 3 of Plate 21. It has several
properties which I think important in the process of grinding colours,
either in a wet state or a dry. It consists of a frame _A B_, which has
a hollow centre, through which the axis of the bevel wheel _C D_ is
brought in such manner as to geer with the bevel pinion _P_, in whatever
position the frame _A B_ may be placed. The axis of the pinion _P_
carries a vessel _of which_ _E F G_ _is a section_, and in which rolls a
well turned and heavy ball _H_, _upon_ the colour to be ground: which it
crushes in the line of direction of its centre, and to a greater or
lesser _width_ according to the diameter of the ball, as compared with
the section of the groove _E G_, in which it rolls. Now as the motion of
the vessel _E G F_, is oblique to the perpendicular, the contact between
it and the ball does _not_ take place in any great circle of the latter:
but is constantly varying by a twist in its motion dependent upon the
angle of the vessel's inclination to the horizon. From hence arises the
_impossibility_ of any colour remaining on the ball unground: and in
order likewise, that none may remain uncrushed in any part of the vessel
_E F G_, the frame _A B_ gives it constantly new positions, _one_ of
which is represented by the dotted lines _I K_: where it is seen that
the ball bears on a different line of the vessel's bottom than it did
before. This also adds still greater change of action to the ball
itself, and occasions (taking both these properties together) an
unbounded variety of effect, which necessarily brings every particle of
colour under the ball by the mere continuance of motion: and thus grinds
it all without any care on the part of the attendants. It may be added,
that this vibrating motion of the frame _A B_, is easily made to result
from an eccentric stud and proper connecting rods behind the frame; all
which is too easy to require further description.


  OF
  A DYNAMOMETER,
  _Or a second Machine to measure power & resistance in motion_.

In Plate 21 fig. 4, there is a representation of this Instrument. It is
composed of a frame _A B_, containing a strong shaft _C D_, on which are
placed the three following objects. First, a fixed pulley _E_, working
by a strap, the Machine whose resistance is to be measured. 2ndly, a
loose pulley _F_, receiving the power from the _mover_ whatever it be.
And 3rdly, a barrel _G_, which is the acting pulley, when the strap is
put on it from _F_ in the common method. But this barrel _G_ acts by
means of a barrel-spring within it, which is hooked by one end to the
boss of the shaft, and the other to the rim of the barrel, as is usual
for barrel-springs in general. Now the power produces the desired motion
by coiling this spring to the necessary degree: and to make that degree
_visible_, there is fixed to this barrel _G_ a spiral _s_, which as the
spring bends, drives _outward_ the stud _t_, and with it the _finger_
_v_, which, pointing to the graduated scale, shews at once the number of
pounds with which the spring acts on the shaft _C D_ to turn it. By
these means the stress on the straps and on the Machine turned is known;
of which also the velocity is easily determined by counting the number
of revolutions performed by either of the pulleys _E F G_, which are
alike in diameter.

       *       *       *       *       *

In ending the first part of this work, I gave my readers room to expect
_this part_ "within three months," and am happy now to fulfil that
engagement. Although these pages contain fewer errors than the
former--an apology is due for those that have crept in: to which I add
the promise that every thing shall be done to lessen them further in the
future parts, and wholly to correct them before the work closes.

  Page 100, line   2,  for ":",                read ::;
   "   126,   "    4,   "  "on its surface"    read at its pitch line.
   "   126,   "   17,   "  "its height _f g_," read the length required.
   "   129,   "   16,   "  "2,"                read 4,
   "    "     "   20,   "  "imperfect,"        read homely.
   "   144,   "    7,  take away  "_alone_."
   "    "     "    8,  for "usually"           read chiefly.
   "   146,   "   23,  for "the friction,"     read it.
   "   147,   "    1,  for "nothing,"          read little or nothing.
  In fig. 7 of Plate 19, slope the groove of both _faces_ the same way.

       *       *       *       *       *

A few words seem wanting to complete the description of the Cutting
Engine above given. They relate principally to the cutter-frame and
cutters. Although, with a view to celerity, I have shewn the cutter
_out_ of the frame (fig. 4) yet a common frame, carrying the arbor on
points, may be used with propriety; and would often be an eligible
substitute for the frame above described. In cutting bevel wheels
however, either on this Machine or that to be described, there is a form
of the cutter frame which leaves less freedom of choice, as the cutter
itself _must_ have a peculiar form and position. To return to the cutter
for spur wheels, their form (or section) depends on the degree of
_finish_ which the wheels require. For _rough_ work they may be
cylindrical on the face, the sides being _under cut_, so as to leave
them thickest at the circumference--whence a certain coarseness of cut
ensues, but without _any injury_ to the spiral form. But, generally
speaking, the cutters are best, when made a little tapering towards the
edge, and toothed on both sides as well as on the circumference. The
teeth should be tolerably fine, but not very so, unless great
_smoothness_ of surface were required: and we have seen above that, in
this System, great smoothness is very seldom necessary, _provided the
obliquities be correct_. I may add, that those cutters used on common
engines, whose great rapidity compensates for the small number of their
teeth, would not answer here, on account of the twisting motion in the
wheel. But nothing prevents using cutters, so formed on the sides, as to
round off the teeth in the act of cutting--only the cutter must be so
thin as that its thickness, added to the aforesaid twist, may not make
the _spaces_ too wide. A little observation will render these things
familiar to an attentive observer: nor shall this work conclude before
all that I have gathered from long observation on this subject, be fully
known to my readers.

  J. W.

  _5, Bedford-street, Chorlton Row,_

  _20th. November, 1822._




  PART THIRD.
  A NEW CENTURY OF
  Inventions.


It has been observed and regretted by a well-known writer, that "a
periodical work resembles a public carriage--which _must_ depart at the
usual hour, whether full or empty;"--and having undertaken to deliver
_this_ work at stated periods, I have found myself in a situation not
unsimilar: the consequence of which has been a too cursory view of some
of the subjects. I feel however, that _this_ is not a sufficient apology
for any essential defect: nor would it be more so to say that, although
verging to old age, I am still a young author. Yet I may claim the
privilege of supplying, in the latter parts of the work, what is most
deficient in the former; and thus of proving that I do not intentionally
neglect any thing that might make it practically useful.

With these views I commence this third _part_: intending first to
continue the description of the Cutting Engine given at page 121, _and
here applied to Bevil Wheels_; and then to re-consider, shortly, one or
two other objects, that were too rapidly passed over in their proper
places.

Plate 22, repeats at fig. 1, the first figure of Plate 15; by way of
shewing the additions required to extend this method of cutting teeth,
to Bevil Wheels. These additions are _first_, a disk _n n_,
concentrically fixed to the main axis _A B_ of the engine. And,
_second_, an inclined plane _o_, of _variable_ obliquity, connected by
a joint with the _forked_ sliding bar _p q_, by which the plane _o_ is
put in contact with the disk, at whatever distance the cutter-stand _e
f_ may be from the common centre, _which distance_ depends, of course,
on the diameter of the wheel to be cut; and to secure which is the
office of the fixing screw _r_, in the figure.

It is now evident that for the disk _n n_, and the shaft _A B_ to rise,
the slide _p q_ and the cutter-stand _e f_ must recede: and _this_ more
or less according to the degree of obliquity of the inclined plane _o_,
that is according to the slope of the _bottom_ of the teeth in the wheel
_w_: see the dotted line _w p_.

A circumstance presents itself, that should be here explained: when the
bevil of the wheel _w_, or the cone of which the wheel is a part, is
very obtuse, the cutter-stand _e f_, can not be driven back by the
action of the disk _n n_ on the plane _o_, without too great a stress
being applied from below, to the axis _A B_. (See the apparatus _I M O
N_, Plate 16, fig. 2.) In this case therefore, the handle _R_ is not
used: but a weight is suspended to the end _N_ of the lever _M N_,
sufficient to give the whole System _A B_, a tendency _to rise_; and the
operator now acts on the screw _g_, so as to draw back the plane _o_; by
which motion the disk _m n_ with it's axis _A B_ is _suffered_ to move
upward, and the wheel is cut, as desired. But on the other hand when the
wheels are portions of _acute_ cones, they are cut by means of the
aforesaid handle; by which the plane _o_ and the cutter-stand are
_forced_ backward as before intimated.

We proceed now to describe the perpendicular part of the cutter stand _e
f_; which is made double, as shewn at _i k_ in fig. 4 of Plate 15; and
is also perforated at various heights to receive the bolt which forms
the centre of motion of the arm _m u_, the latter having a cylindrical
boss _u_, fitted into the _fork_ of the stand _e f_, and so graduated as
to determine the angle of it's obliquity to the horizon, or it's
parallelism to the dotted line _w p_, which indicates the slope of the
bottom of the teeth on the wheel. Finally, the cutter-frame _x_ is
fastened to this arm at right angles to it, and thus forms a right angle
(or nearly so) with the surface of the wheel: and is, moreover, directed
to the centre, produced, of the shaft _A B_. This latter fact is
strictly true, only when the teeth required are of so common a kind as
_not_ to require greater exactness: for in theory the sides of the
cutter (supposed cylindrical) must alternately direct to that
centre--namely, _that_ side which is actually cutting: so that a
provision must be made to shift the cutter spindle sideways, a distance
equal to it's diameter; this being no more than what is necessary in
every system of wheel cutting.

We may also consider here, the form of the cutter itself, _v_, fig. 1.
It is slightly conical, (more or less so according to it's use) and of
no greater diameter than the smallest width of the _spaces_ between the
teeth of the wheel. A common disk-like cutter would not produce perfect,
nor even tolerable teeth on a bevil wheel. The reason of this will
appear by considering that a spiral line, either on a cone or it's base,
_turns_ more the further it is from the centre, and less the nearer it
comes to it. So that a _flat_ cutter placed at _any_ angle, is parallel
to the curve at _one_ place only; whence the propriety of using a cutter
of the kind represented in this figure. It is however true, that the
first opening of the spaces may be made with a common cutter; but it
should be very thin comparatively with the spaces required: and it's cut
would serve only as a _sketch_ of such space, serving principally to
permit the metal to escape while finishing the teeth with the cutter
just described.

I proceed now to the examination of _the plates_, and the manner of
adapting their length to the process of cutting _spiral teeth on bevil
wheels_. But before entering on this subject, I would explain a kind of
inadvertency into which I fell at the close of my former description of
this Engine (see page 129). In my zeal to be candid in stating the
properties of my Machines, I have suffered it to _appear_ that I thought
this an "imperfect" one:--an expression which, although modified among
the errata, may still cause it to be looked upon as radically defective;
than which nothing could be further from the idea I wished to convey. I
intended merely to express the want of _absolute_ connection between the
two movements of the shaft--the rotatory and longitudinal motions. I
meant that the process by this Machine was not theoretically _certain_,
because dependent on the action of a weight (Plate 16, fig. 1 and 2) and
an _unforced obedience_ to the direction of the plates. But this small
remove from rigourous principle is in my opinion _much_ overballanced by
the facility of cutting _good wheels of all diameters_, by the sole
change of a morsel of tin, which leaves untouched every other part of
the Engine.

Entering then on this branch of the subject, I first observe that if we
chuse for the teeth an inclination of 15 degrees (in imitation of the
cylindrical wheels) it can only be for one point of such wheels--as
observed above. This point therefore I have placed at _r_ in the middle
of the face. And supposing now that at this point the wheel _O_ were 4
inches in diameter and the wheel _S_ two inches, these plates would be
found as before by these analogies:

(1) _wr_, or 2 inches : 11 inches (rad. of plate rim) :: 26.8 : 294.8/2
= 147.4 plate required.

(2) _vr_, or 1 inch : 11 inches (rad. of plate rim) :: 26.8 : 294.8/1 =
294.8 2d. plate required.

But it is plain that the conical face, _b C_, (common to both wheels) is
_broader_ than the supposed cylindrical ones _b e_ and _b d_: and
therefore that the above plates must be made longer (to furnish the said
obliquity) in the following proportions, namely: for the wheel _O_ in
the ratio of _b e_ to _b C_; and for the wheel _s_ in that of _b d_ to
_b C_: that is, these plates should be lengthened as the tabular
cosines of the angles _B A C_ and _D A C_ to radius (for _b e_ : _b C_ ::
_A B_ : _A C_; and _b d_ : _b C_ :: _A D_ : _A C_.) Thus then,

(1) Cos. 63°27´ : radius :: 147.4 (present plate) : required plate _x_, =
147.4 r/Cos. 63°27´; and

(2) Cos. 26°33´ : radius :: 294.8 (present plate) : required plate _y_, =
294.8 r/Cos. 26°33´.

Now, by the tables, cosine 26°33´ = 894, and cosine 63°27´ (it's
complement) = 447, when radius is 1000: whence dividing the two
equations by _r_, and substituting these values of cosines 63°27´ and
26°33´ we shall find the two quantities _x_ and _y_, _equal_. Whence it
appears that for every _pair_ of bevil wheels, whose shafts lie at right
angles, _the same plate serves for both wheels_: only turning it once to
the right, and once to the left hand on the plate rim.

And if now we _measure_ on a scale of _equal_ parts, the line _A r_ and
call it 100, we shall find the line _w r_ (near enough for practice) to
be 90, and the line _v r_ to be 45, and these numbers respectively, put
for rad. for cos. 26°33´, and for cos. 63°27´, will make the first
equation _x_ = 147.4 × 100/45 and _y_ = 294.8 × 100/90 or _x_ = 327.55
and _y_ = 327.55, &c. confirming the above deduction that the _same
plate_ serves for both wheels; and giving, withal, the length of the
plate required.

In performing this operation by actual measurement of the lines, I have
had in view to trace a path for those of my readers who may not have
the tables, or may be unaccustomed to use them. The process, generally,
is to take the diameter of any bevil wheel _O_ fig. 4, in the middle of
it's face; and _supposing_ it a spur wheel, to find it's plate by the
method above given: and then to multiply the length of that plate by the
line _A r_ and divide the product by the line _A w_, both measured on
the same scale of equal parts.

It may be well to observe, likewise, that the same method of finding the
plates, applies to bevil wheels of every description or angle: but that
it does not give equal plates for every _pair_, except in the above case
of wheels placed at right angles to each other.

I would just remark that by the figure near _B_, is shewn a _section_ of
the Machine on which I centre the wheels to be cut on this Engine. It is
an inverted cup _s t_, into which the _arbor_ is screwed in a _true_
position; and this cup is fixed on the top of the shaft _A B_, by the
_three_ pressure screws near _s t_, which enter a triangular neck made
round the shaft, against the _upper_ slope of which, the screws press so
as to draw the cup downward in the act of centering it. This I say is my
present method; but it is in a measure accidental, the shaft not having
been perforated to receive arbors of the usual kind. Mine, however, have
their utility in the ease with which they are varied in size, and
changed on the Machine: but on their _comparative_ usefulness I give no
opinion. The other is the most solid method.

In the description of my differential Steel-yard, (see page 163) I
stated that the load _P_ was wholly collected in the point _o_; and that
dividing the line _A C_ by the line _A o_, the power of the Machine was
known. But I should have shewn that this line (_A o_) is _equal to one
half the difference between the arms_ _A D_ _and_ _A E_. To do this,
here, (see Plate 23, fig. 4) I take the Machine in the state of infinite
power, before mentioned; and observe, that in moving the point of
suspension from _o_ towards _A_, I at once _lengthen_ the arm _A E_, and
_shorten_ the arm _A D_: by which process, (supposing each arm to have
been called _a_) that which I lengthen by any quantity _d_ becomes _a_ +
_d_, and that which I shorten by the same quantity becomes _a_ - _d_,
and the difference of these quantities, is 2_d_: so that the line _A o_
is in reality one half the difference between the two arms _A D_ and _A
E_ as was required to be shewn.

But we may go a step further: The two arms of the equibrachial lever _x
y_ may likewise be made _unequal_: and the line _s a_ be subdivided in
any ratio: which division will augment still more the power of this
Machine. If for example, we hang the load on the point _v_, halfway
between _a_ and _s_, that power will be doubled; for the line _c v_
(representing the space moved through by the load in this case) is only
one half of _that_ _w s_, or _o q_, and might be still less at pleasure.
Thus the whole power of the Machine is _now_ found by dividing the
length of the long arm, beyond _D_, by the line _a v_, instead of the
former line _A o_, or dividing the _motion_ of it's extremity upward, by
the line _c v_, the motion downward, of the load _P_.

It has been further suggested, that the description of my excentric Bar
Press was not sufficiently explicit. I have therefore added the figure 2
of Plate 22, to assist in elucidating that description. I had, perhaps
made an undue use of the principle of virtual velocities by saying, too
concisely, (page 174) that "as the whole approaches toward _B C_, the
relative motion (of the cheeks _s_ and _B_) becomes insensible, the
circles parallel, and consequently, the power infinite." It is however
_vulgarly_ said that _power_ cannot be gained without losing
_time_--which implies that if time _is_ lost, power will be gained: and
the principle of virtual velocities says the same thing, though in more
appropriate terms--that if a small movement be given to a system of
bodies actually counterpoising each other, the quantity of motion with
which one body ascends, and the other descends perpendicularly, will be
equal: so that, as remarked in page 50, by "whatever means a slow motion
is obtained, dependent on that of a moving force, the power is great in
the same proportion." Now, in the eccentric Bar Press, (see fig. 2) this
is so in an eminent degree: for when the bars are in the position _A B_,
the distance of the cheeks is equal to _B s_; and they must move,
circularly, as far as _A f_, to bring them closer to each other by the
quantity _s a_: dividing therefore, the distance _B g_ by the line _s
a_, we find (near enough for practice) the power of the Machine within
the limits _A g B_. It is nearly as 10 to 1. In like manner this power
at _A e g_, is equal to the arc _e g_ divided by the line _f b_; and at
_A l n_ to the arc _l n_ divided by the line _d k_, namely by the
difference of the lines _k l_ and _m n_. From the above it appears that
the _nearing_ motion of the cheeks of the press, becomes slower and
slower as the bars _A_ and _C_ come nearer to the point _C_: insomuch
that the difference between the lines _m n_ and _o p_ is nearly
imperceptible, and _that_ between the lines _o p_ and _C q_ entirely so.
But according to the above process, the distance _p C_ should be divided
by this _imperceptible line_, to find the power of the press at the
point _C_; which therefore is _immense_. Another proof of this may be
drawn from the supposition (see fig. 3) that the small lever _a d_ is
turned round the centre _o_ by a bar _o C_ fixed to it, and of equal
length with the line _A C_ fig. 2. Fig. 3 shews that the lines or bars
_C d_, and _a C_ are moved endwise by the _circular_ action of the
points _a_ and _d_; and therefore (by statics) their motion is the same
as though caused by the perpendiculars _b o_ and _o c_ let down from the
centre _o_, on each of them. Hence the power of this Machine is found by
dividing the distance _o C_ by the sum of the lines _b o_ and _o c_;
which sum (when these lines _vanish_ by the union of the bars over the
centre) becomes infinitely small: the quotient of which division
therefore is infinitely great--as was to be shewn.


  OF
  A PUNCH MACHINE,
  _For Engravers to Calico Printers_.

The usual method of making Punches for engraving Copper Cylinders,
(otherwise than by the _milling_ system) is to _cut_ the desired pattern
on _a die_, and then to transfer that pattern by blows or pressure to
the punch, from which it is again transferred to the cylinder. My
Machine in this operation, unites motion to the needful pressure; and
thus renders the result more easy and complete. This effect I could the
better ensure, because the surfaces of _my_ punches are essentially
convex, or rather cylindrical; as will appear when my engraving Machine
comes to be described. Their convexity however, can be diminished at
pleasure--whence this Machine is capable of offering useful assistance
to a maker of flat punches.

In Plate 23, _A B_ fig. 1 and 2, is the body of the Machine, with the
vibrating bar _C D_ laid upon it; reposing especially on the correct and
level parts of the body at _a b_; this bar contains the _die_ _c_, with
which it vibrates between the cheeks _B R_, as impelled by the screws _E
F_, it's centre of motion being the pin _P_, duly supported by the
strong shoulder _A_. In a line with the bar _C D_, is placed a second
_vibrator_ _G_, containing the steel _d_, that is to become a punch,
already rounded into the cylindrical shape it must have when finished.
This vibrator has it's centre of motion at _e_ fig. 1, and it need not
be added that the curvature of the punch depends on it's distance _e d_
from that centre: for the centre of the long bar _C D_ is _so_ distant
as to have little influence on it's formation. Further, the cap or
bridge _H I_, which furnishes a centre for the smaller vibrator _G_, can
be brought forward to any useful position by the nuts _K L_: that cap
sliding horizontally between the cheeks _M N_ as directed by the small
_arms_ _m n_. This motion, then, taken from the nuts _K L_, serves to
impress the _work_ of the die on the steel prepared for the punch; and
this being done to a _first_ degree, both the handles _O Q_, are laid
hold of: and by turning the screws the same way one of them goes forward
and the other recedes, until the punch and die have been in contact over
half their surface. At this moment both screws are turned backward, and
the motions of the two vibrators reversed: by the repetition of which
alternate motions accompanied by the needful pressure, the whole pattern
is transferred from the _die_ to the punch--when the latter is taken out
of the Machine, and _filed up_ in the usual method.

It should be observed, that the smaller vibrator _G_ can be displaced
with ease when the nuts _K L_ are withdrawn: and this should be
frequently done to examine the progress of the impression. Nor is there
any difficulty in re-entering the figures. In a word, the perfection of
this process depends more on _much_ motion than on violent pressure:
whence this facility of re-entering is a desirable property. This
Machine is usually laid on a bench or tressel, with a long mortice in
it, into which the feather _x_ of this Machine enters so as to be firmly
fixed.


  OF
  A DIFFERENTIAL PUNCH MACHINE
  _For Engravers_.

I was the rather induced to attend a second time to the differential
Steel-yard, because I had it in contemplation to apply that principle to
the present purpose; since, to make flat punches, is to some engravers a
more desirable thing than to make cylindrical ones. I am not fully
persuaded that it is even possible to transfer a large pattern, from a
flat die to a flat punch, by _any_ pressure acting simultaneously on the
whole surface. In those cases, if there is much _work_, the whole
surface _goes_ _down_; and the parts that form the pattern do not
_rise_. But, all that can be done in this case, is, I believe, feasible
by the Machine now to be described.

Plate 23, gives in fig. 3 and 4, a representation of this Machine; _A B_
and _C D_, are two _slides_, having wedge-formed ends above _A_ and
below _D_, well made, well steeled, and well tempered. One of these
slides contains the _die_ and the other the steel prepared for the punch
(see _B C_). These wedge-ended slides are _embraced_ by two levers _E
F_, _G H_, which are themselves connected by two stirrups _I K_ and _L
M_, better shewn at fig. 3. These latter are supposed in fig. 4 to be
broken at _L M_, to leave the levers _E F_ and _G H_ more visible. They
are formed, at the turning below, into wedge-like edges _a b_; well
hardened, that clip the _nicks_ _c d_ of the lower lever: and at the top
of the Machine their arms _e f_, pass through the caps _m n_, above
which they are _nutted_ like a common bolt, and made to press strongly
on the main lever _E F_. The stirrup placed to the right hand, presses
in particular, by it's cap _n_, on the moveable _step_ _o_, exactly in
the notch _q_: this step having a backward and forward motion
communicated by the regulating screw _p_. Before beginning to use this
Machine, I make all it's arms _A E_, _A g_, _D e_, _D d_, equal, when
it's power (see page 162) is infinite; and to put it in a working state,
I turn the screw _p_ backward, say one half round: which motion (if the
screw has 20 threads to the inch) makes a difference in the two arms _A
r_ and _A q_ of 1/40 of an inch, and the virtual centre of the Machine
is therefore 1/80 of an inch from the former point _A_, that is from the
_edge_ of the slide _A_ in this fig. 3. Supposing now, the whole working
lever _E F_ to be 3 feet, and the workman's force to be 100lbs. in each
arm, then by displacing the lever to any proper distance from _F_
towards _f_, he will produce a pressure between the die and the punch of
200lbs. multiplied by 1440, the number of times that 1/80 of an inch is
contained in 18 inches.--That is, a pressure of two hundred and
eighty-eight thousand pounds!

I have been seduced, by the anticipated brilliancy of this result, from
the regular course of description,--and the plate _w x_, _y z_, which
forms the base or frame of this whole Machine has not yet been spoken
of. But that plate is supposed screwed down to a horizontal bench, at or
near the height of a man's breast; the slides or cases are fastened to
it, and the man is supposed to _work_ the Machine nearly as he would a
die-stock in tapping a screw. This however is not indispensable; the
Machine might be placed vertically, and these motions given by any
proper mover; or a weight may be suspended to the arm _F_, so as to add
continuity to pressure. It is however important, that the position
should comport with the frequent extraction of the punch in order to
examine the progress of the work, or cut away any redundant metal. I
have before given it as my opinion that _much_ could not be expected
from mere pressure: but _this_ is a pressure of a peculiar kind,
consisting of immense powers with _very_ short motions. In this respect
it is _just_ what was wanted, as it can be renewed and repeated
frequently, without loss of time. And the more to facilitate this
delicate operation, the hollow slides or cases _B C_, are made slightly
pyramidical, to be furnished with _set-screws_ on the four sides, by
which to change the place of bearing; and thus to meet the case of a
flat punch with the advantage of impressing it by _portions_, so as to
have only to _finish_ it by brute pressure.

The foregoing application of the principle of the differential
Steel-yard, is, I think, important, and founded on unobjectionable
principles; for although by changing alone the place of the step _o_,
we disturb a _little_ the parallelism of the stirrups _I K_, and _L M_;
we do it not enough to produce, any material change in the theoretical
result. With respect then to the lesser properties of this Machine, I
leave them with confidence in the hands of those whom they most
concern--who doubtless, will treat them with greater practical utility
than I could myself hope to do.


  OF
  A MACHINE
  _For Moulding Nails._

This Machine offers, I think, a valuable application of a well known
Instrument: or rather of the principle on which it is founded. I allude
to _that_ parallel ruler which, by means of an additional joint, keeps
it's members not only parallel, but directly opposite each other. In my
Machine for moulding Nails, I wanted to give motions to the two plates
different, yet dependent on each other. Supposing then, (Plate 24 fig.
1, 2, 3, 4,) the upper plate _a b_, to be moved up and down by a lever,
a screw-press, or any other _first mover_, I connect the under plate _c
d_, with it by two (or four) _strong_ parallel rulers _e f_, in such a
manner, that when the plate _a b_ is drawn upward it shall extend the
arms of the ruler _almost_ to a straight line, as represented in fig. 4;
and then carry the under plate with it: and when it comes down again
(see fig. 3) it shall _not_ carry down the said under plate, until the
same arms are bent into the position _f g_; that is, till the two plates
touch each other: the use of which arrangement I will now explain.

The under side of the upper plate _a b_, is _ground_ perfectly flat, and
bored at proper distances with holes to receive and hold the punches
which represent the shanks of the nails that are to be moulded. The
lower plate _c d_ is ground _true_ both on it's upper and under
surfaces; the first to fit the under surface of the upper plate, and the
under surface to impress a perfect plane on the sand below it. This
under surface, shewn in an inverted position at fig. 2, is moreover
covered with proper _prints_ 1, 2, 3, &c. to form the heads of the nails
in question, and with proper _gets_ (jets?) 3, 5, 6, &c. for conducting
the metal to every part of the surface. I mean models in relief of those
gets; and the under plate is further pierced with holes, placed exactly
like those in the upper plate, bored indeed from that (and through the
aforesaid _prints_ of the nail-heads) _after_ the parallel joints _e f_
have been affixed. Now on another level plate with proper ledges, the
sand boxes or flasks, fig. 5 and 6, have been prepared; and have
received an obtuse pyramidical form at one stroke from a competent
press, the construction of which is easily conceived: or this might be
done by hand, if preferred. These boxes, in-fine, are successively
brought under the before described mechanism while in the state
represented in fig. 3, in which all the nail models are protruded
through the under plate as at 1, 2, 3. The moulder now gives a stroke
under the following circumstances:--Both the plates drop together and
the nail models pierce the sand while the under plate makes it's surface
perfectly level: but when _that_ motion is reversed, it is _not_ the
under plate which first rises, but the upper--by which the nail models
are drawn out of their holes _without disturbing the sand_, for this is
kept to it's place by the under plate: and when, by the continued motion
upward of the upper plate, the parallel joints are duly extended, and
the nail models quite extracted; then, and not till then, the under
plate leaves the compressed sand, in which are moulded as many _scores_
of nails as the mould has been made for--and that, in a space of time
almost imperceptible.

I shall conclude the subject by observing, that the counter flask or box
for closing this mould is made in the same way, by a smooth plate
prepared in the same manner; and which _must_ fit the former, because
they are both perfectly level surfaces.


  OF
  A FIRE ENGINE
  _Giving_ POWER, _while heating Rooms, Liquids, &c._

This Machine, though conceived many years ago, can hardly yet be called
an invention--if material existence is necessary to justify that
appellation: _for I have never seen it in action_. It _may_ possibly be
one of those fascinating conceptions of which my noble friend the late
Earl Stanhope used to say--"'tis a _beautiful_ invention--but 'twill not
do;" yet I give it with some confidence, because of the great utility it
_would_ present, if it's chief properties should fulfil my expectations.

The principal idea on which it is founded, is this: _to use, as power,
the expansion of that air which feeds the fire_; and _again_ to employ
it's heat heating liquids or rooms, or any similar purpose. The form I
have given to the Machine is by no means the only one it admits; nor
perhaps the best: but it was indispensable to give the idea (which I
hope is not an "airy nothing") "a local habitation and a name."

It consists, then, of two cylinders, lying horizontally, of nearly equal
length, but of unequal capacity:--one of which _A B_, (Plate 24, fig. 7)
is an air pump with a valve in it's end _a_, and another in it's piston,
both opening _to the left_. The second cylinder _C D_, is the working
cylinder, as much larger than the former, as may belong to the principle
of motion already announced. This cylinder receives the piston _E_,
which fits it nicely, but is not stuffed in the present case. (It may
perhaps be made tight by some of the methods, used to _close_ metallic
pistons.) At all events, this piston is connected with that _c_, by a
frame _F G H I_, which embraces the whole Machine, in a horizontal
position, though here shewn in a vertical. These two cylinders are cast
in one piece, together with an upright cylinder, not bored _K_; the use
of which is to receive the _earthen_ chafing dish _L M_, with it's fire,
made (according to my present views) with _coak or charcoal_, and
lighted before it is introduced. It is needless to say, that this vessel
is let down into the cylinder _K_, by a kind of bucket handle entering
any _pair_ of holes in the dish. The top of this latter cylinder is
_ground_ to fit the flanch _A N_: It swings open on one of the bolts and
falls to again in a moment, to prevent loss of time in _firing_. The
_means_ of doing this I do not much insist on, from their extreme
facility. Nor do I make it a _condition_ to use this method at all. The
coak, (or perhaps the coal, or the wood) _might_ be introduced through
an upright tube furnished with two slides, one placed close above the
top _A N_, and the other at a proper distance above; so as for _one_ to
be always shut. This is nothing more than the System used for feeding
high pressure Steam Engines--only _this_ application is to dry
substances, which forms no insuperable obstacle.

When now the Machine is _fired_, the pistons _E_, and _c_, are pushed
towards _b_ and _B_ respectively; the valve _d_ having been previously
opened, and the valve _c_ opening by this very motion--which thus clears
the large cylinder of it's included air, while the air in the pump _A
B_, is brought into contact with the fire; whence a _considerable
expansion_ ensues, and a _pressure_ is created tending at the same time
to drive the piston _c_ to the _right hand_, and that _E_ to the _left_:
but acting in the latter case on a larger area, the whole system moves
that way, and _all_ the air in the pump _A B_ is driven through the
fire: where, being much heated, it acquires great elasticity and
developes considerable _power_--which, by any of the known methods, may
be applied to any of the known purposes.

I hope my readers will conclude here, that I allow for the disappearance
of the oxigen in this conflagration: but I expect the expansion of the
residue (together with what _new_ vapour may be developed) will more
than compensate for that loss of volume. By this motion then, the pump
_A B_ is again filled with cold air through the valve _a_; and the
piston _E_ flying _out_ of the cylinder _C D_, the hot air it contained
_rushes_ into the pipe _o_, and thence goes to perform _any heating
operation_ that may be desired. But further, this same recession of the
piston _E_ strikes the stem of the valve _d_ against the cover _e_, and
opens that valve; by which means the large piston is at liberty to reach
again it's _inner_ position _b_: where the bar _b_ closes it's valve _d_
and prepares the Machine for a new stroke. For, as before, the pump or
cylinder _A B_, is full of cold air, and by the backward motion of it's
piston exposes that air to the fire in _K_: whence arises the renewal of
all the former phenomena.

Many ideas, and doubtless some objections, will present themselves to
the readers of these pages; of which I shall probably anticipate _some_,
by noticing a few less important particulars.

And first, is it not to be feared that the vertical cylinder _K_, and
the whole system _K C D E_ will become too hot--nay acquire a red heat,
and thus introduce danger? The answer, I think, is that the fire must be
_lessened_, or the Machine enlarged, until this danger disappears: for
by heating _air_ to any thing like a _red_ heat (without attaining it)
the expansion will be _immense_: and probably beyond our wants or
wishes. The chaffing dish then (if that is used) must be lessened, that
the air from _A B_ may partly circulate _round_ it, instead of going
wholly through the fire: thus cooling the vertical cylinder _K_, and
diminishing the intensity of the heat in the working cylinder. Further,
the two cylinders _C D_ and _K_, might be inserted in the bottom of a
boiler, and surrounded with water; through which also, may be conducted
the pipe _O_, so as to concur in the same effect of heating _that_
water, while the steam thus accruing from the _double use_ of this heat,
may be made to drive an engine, heat a room, or fulfil any common
purpose.

In a word, all our difficulties on this branch of the subject, seem to
lie in _excess of action_: and we need only mitigate the general effect,
to render this Machine useful, safe, and commodious.

There is another objection that must be met, on pain of direct censure,
which is this: what will become of the ashes? (for _smoke_ is as yet out
of the question) my answer is--a recess, or several, must be found for
them beyond _o_; to do which will not be more difficult than to lodge
any other residue. But if this Machine fulfils my views in respect of
_power_, _this_ residue will be no burden. For example, if ever a farmer
should hereafter drive his _plough_ by such an engine as this, he will
manure his land furrow by furrow with the ashes--an idea which I must
not yet indulge, lest I should be thought fanciful beyond the due
proportion.

But my mechanical impetus is not to be thus instantly checked. If what I
_hope_, can be realized, there are properties in this invention, for
locomotive engines, superior to any the steam engine itself can boast. A
light Machine: a light combustible: no water to carry; no steam to
condense, &c. &c. As however I have never _tried_ this felicitous
creation, I assert nothing.

But again, this seems to be a really good method of distributing heat in
any useful direction: for there is an _impulsive force_ which not only
requires no _draught_ to make the fire burn, but will drive heat to
_any_ distance through pipes of _any_ form, and placed in _any_
position. There is therefore, a certain utility attached to this
Machine, whatever may be it's merits as a _power engine_. Our present
methods--of destroying coals--are excellent! but our methods of making
them useful are defective in the extreme. If you have no draught in your
chimneys you are stifled with smoke. If you have much draught, you have
_little_ heat--for the chimney swallows it, and half your room is _in
Norway_. Use then an impulsive system, (of some kind) and you may _send_
your caloric down into the cellar to be _drawn_ from thence as wanted,
for the upper apartments.

But my subject pullulates as I proceed. This idea is by no means
exhausted. It is _not_ an indispensable feature of it, to heat rooms
with _the same air_ that fed the fire. For instance, if a fire were made
_under_ the vertical cylinder _K_, and led into and through it by a
proper pipe, _almost_ filling it--then the cold air of the pump _A B_
would _pass round that pipe_ to the working cylinder _C D_, and there
impel it's piston _E_ as before. Not perhaps so strongly; but with an
air uncontaminated by burning, or by ashes--and therefore more congenial
with some uses of the Machine. In fact, air thus introduced might be
_perfectly fit for breathing_, and still get elasticity enough from this
passage, to _force_ heat to the bottom of any room we wished to have
warmed; whereas, by using only the levity of heated air to give it
motion, we scorch the tops of rooms and factories, and unmercifully
freeze the bottoms. I must beg leave to be a _little_ severe on this
point:--since for a thinking people, as strangers call us, we have been
extremely thoughtless in this respect: so that as much seems now to do
by way of introducing _comfort_ into our saloons, as was done about the
year 1200, when those chimneys were introduced that are now become a
kind of nuisance. In a word, and I am serious when I say it, the present
arrangement of our chimneys, is in my humble opinion, essentially
unphilosophical; and as such ought to be speedily discontinued or
greatly modified.

In the above pages I have laid myself open to much animadversion, by a
kind of _cast_ for much honest fame. I have let the public into my
secret--_I have thought aloud_: And if the greater part of these
cogitations should prove to be imaginary, I shall only plead, that they
are drawn from the same source as the many useful Machines I am known to
have devoted to public utility.


  OF
  A ROTATO-GYRATORY CHURN.

This title I confess, seems very ambitious, as applied to an utensil for
the dairy: but I had to express the combination of it's own axis, and
those of the leaves or wings about their respective axes, while gyrating
round the common centre.

The principal shaft _A B_, fig. 8 and 9 of Plate 24, is the general
centre of rotation; and _a b_ are two lighter shafts carried round that
centre, and turning at the same time on their own centres by means of
the wheels _e f_ geering in the fixed wheel _c d_, (of which one half
only is drawn) and which forms part of the top of the churn. Each of the
shafts _a b_, carries four leaves or wings (better seen in fig. 9)
reaching from the top, nearly to the bottom of the vessel; and they run
in proper steps in the cross piece _m_, and also in proper collars in
the upper cross piece _g h_. In fine their wheels _e f_, and the fixed
wheel _c d_, which turns them, are furnished with teeth on my patent
principle; and therefore work without noise or commotion. Now, the
principal shaft _A B_, rests on the step _B_ at the bottom of the
vessel; and runs, at top, in a collar formed in the metallic bridge _i
k_, which, fixed to the outside rim of the cover, passes directly over
the centre of the Machine. When therefore, the cream is put into the
churn, (to do which the above mechanism is taken out) the mechanism is
re-placed as now represented; and the main shaft set in motion by _any
convenient power_: when the side shafts _a b_, turned by the fixed wheel
_c d_, give a backward motion to the wings _a b_, and create a great
agitation of the cream--for, it should be remarked, that this is not a
circular motion: but each fly produces a kind of vortex round it's own
centre, while progressing round the common centre. The consequence of
which, as above intimated, is, an unceasing agitation of the liquid,
and, I believe, the best of churning. This however, I state as a
mechanician, not having been initiated into the secrets of the dairy
properly so called.

It may finally be observed, that the leaves or partitions _l n_, _fixed_
to the sides of the churn, (beyond the reach of the moveable wings _a
b_) are destined to prevent still further any _general_ motion of the
butyraceous matter; and thus to accelerate the churning process: and
further these leaves, both fixed and moveable may be pierced with holes,
like the analogous parts of other utensils of this nature.


  OF
  A HELICO-CENTRIFUGAL MACHINE,
  _For raising Water in great quantities_.

The screw of Archimedes, is well known. When used to raise water it is
placed obliquely, in such a position as that it's _hollow threads_
become _more_ oblique to the horizon than the axis of the screw itself:
observing which practice, some have said of this Machine, that it raises
water by letting it run down: But this cannot be true. The threads of
the screw merely _wedge_ themselves under the water, and make it _rise_
in a direction parallel to the axis of the screw; at the highest end of
which it falls into the upper reservoir.

I once placed a screw of this kind _upright_, and said (in thought) is
it then impossible to raise water by means of this screw thus placed?
The answer in a few minutes was--"not at all; there is a force would
make it easy: namely, the centrifugal force:" and this mental soliloquy
was the origin of this Invention, which, some thirty years ago, I shewed
to a public man, whom the lovers of the mechanical arts will long
remember.

In Plate 25 fig. 1, _A B_ are two screws, perfectly like those used in
exhausting watery foundations; and named of Archimedes. They are placed
perpendicularly in the frame _C D_, so as to turn in the cross bars _a
b_, _c d_, fixed horizontally on the main shaft _E F_ of the Machine. At
the bottom of this shaft, _E F_, (which turns in a step on the _sill_ _G
D_) is a low cylindrical vessel, shewn by a section only at _e f_, which
dips into the under water nearly to the brim. It is used to carry, in
proper _steps_, the centres of the screws _A B_, and, being pierced with
many holes, to feed them amply, without exposing their motion to any
resistance from the stagnant water. These cylinders _A B_ are merely
indicated as screws by the _threads_, dotted between _h_ and _d_ and _e_
and _g_, and their upper mouths are seen near _a b_, just under the
cross piece marked with these letters. These screws then, are turned by
the wheels _i k_, as actuated by the fixed wheel _m n_, in the same
manner as those of the churn before described; which in fact, is a
corollary from _this_ Machine, but of much later date. To return to the
Helico-centrifugal Machine--the screws _A B_ are terminated above by
circular plates _o p_ (marked with the same letters in fig. 2 and 3)
intended to receive the water from the mouths of the screw-threads _a
b_, and carry it _on_ to the plate _q q_, which insures it's further
progress into the _ring canal_ _r s_, also shewn by a section only, to
prevent confusion in the figure. Now what raises the water in these
upright screws, is, it's own _centrifugal force_, combined with the
revolution of the screws: for while this central force is urging the
water outward, the screws are bringing their sloping threads like
_wedges_, _against_ that tendency; and the consequence is, that the
water actually rises perpendicularly till it flows over the ledges or
rings _o p_, _on_ the plate _q q_, and thence into the ring canal _r s_,
from which it is conveyed to any place desired.

If this Machine is well made and proportioned, I think it is one of the
best that can be used, to do much work by a given _power_: It gives no
_shock_ to the water; which, when once in motion, continues to rise, and
escapes when arrived at it's proper height: and, being spread over a
large surface, no part of it is raised higher than enough. The
perfection of the Machine depends on a due relation between the
centrifugal force, and the sine of the angle, which the threads of the
screw make with the horizon; and this may be modified by the diameter of
the wheels _i k_, as compared with that of the screws _A B_.

The figures 2 and 3, are two views of the upper part of the Machine.
They shew, and mark with the same letters, the cross bar _a b_, the
inside of the screws, and the circular plates _o p_, together with the
circular conducting plate of which _q q_, fig. 1, is the section. Fig. 3
shews the fixed wheel _m n_, the two screw-wheels _i k_, the cross piece
_a b_, and under them the plates _o p_ of the 1st. and 2d. figure.

One other object claims our attention: The threads of the screws
(whether more or less numerous) should each be furnished with a valve at
bottom: that the water may _not_ run out when the Machine ceases
working.


  OF
  A FORGING MACHINE,
  _For Bar Iron, Steel, &c. square or figured_.

This Machine acts by pressure instead of percussion. But this pressure
is so instantaneous as to resemble a blow, and so often repeated as to
produce a considerable effect in a short time. The means are represented
in fig. 4 of Plate 25.

There, _A_ is a mass of metal answering the purpose of an anvil, but
having two surfaces, situated at or nearly at right angles to each
other, on which the metal is alternately struck or compressed. The two
sides of this mass _A_, are perforated by two holes, properly _bushed_,
in which turn the crank shafts _B_, _C_: the latter furnished with the
bevil wheels _D_, _E_, which geer into and receive motion from two
_equal_ bevil wheels _F_, _G_, fixed on the main shaft _H I_, and to
which the power is applied. It is thus evident that the two crank shafts
_B_, _C_, will make the same number of revolutions; and that if one of
the rollers _K_, _L_, is placed on the excentric arm of one shaft, and
the other roller on the other (their position being as in the figure)
that then the rollers _K L_ will impinge alternately on any bar, held in
the angle _M_, and forge or extend it, and finally leave it reduced to
the same dimensions, in it's whole length, if, by hand or proper
machinery, the bar has been drawn or pushed along the angle _M_, in a
manner analogous to this motion at the tilt hammer. It is also clear,
that the size of the bar will be determined on a given Machine, by the
diameters of the rollers _K L_, compared with the distance of the shafts
from the angle _M_ of the anvil.

It may be of use to observe, that the effect of this Machine is not
confined to square bars: since with unequal rollers _K L_, it will
produce flat bars; and with rollers properly grooved, (the piece _M_
being formed accordingly) it will produce round iron or steel of better
texture (I presume) than when taken from the slitting-mill, and merely
passed through grooved rollers. I expect, at all events, a _rapid_
effect, from four or five hundred turns of the cranks per minute.

It will occur to every mechanical reader, that the mass _M_, which is
tempered and adjusted to the principal anvil _A_, may be still more
varied in form, so as to give other results besides those above
anticipated. Nor need it be said, that the shafts _B C_ might run in
steps capable of being _screwed up to their work_, even during the
process, should any such motion be expedient. These are details I do not
wish to dwell on in these descriptions--where I endeavour to make known
general and essential properties, leaving particular views and cases to
my reflecting readers.


  OF
  A RECIPROCATING HORSE WHEEL,
  _For Mines, Mangles, &c._

I believe there is no better floor for a working horse to tread on, than
a plane of wood--on condition, of the horse being rough shod: I speak
however, on recollection of many years' standing. I then felt persuaded
that a horse wastes less effort by travelling on _this_ floor than on
any other; which is one of my reasons for the adoption of the present
Machine. It consists (Plate 26, fig. 1,) of a wheel _A B_, on which the
horse walks, as indicated by the sketch of him given in the figure.
Besides this, he is placed between two shafts _C D_, affixed to the
lever _E F_, the latter carrying round with it, at intervals, the drum
_G_, whose office it is to raise the weight _I_, whatever kind of
resistance that weight represents. This lever runs by means of it's
_cannon_ _L_, on a round part of the shaft common to it and to the drum
_G_. Moreover, there is a second drum _H_, destined to raise the weight
_K_, whatever kind of resistance _that_ represents. Both the drums, _G_
and _H_, turn on round parts of the main shaft _M_, but are alternately
connected with it--first, the drum _G_, by the rising of the bolt _a_
into it; and secondly, the drum _H_, by the falling of the cross piece
_b c_, between the studs _e d_ affixed to it. Now, this cross piece _b
c_, is part of a T-formed bar, that penetrates the centre of the shaft
as low as _f_, where it rests on a transverse lever _f g_, connected _to
the right_ with the bolt _a_ above mentioned, and forming a branch of
the bent lever _f g h_, which works the bolt _h i_ under the wheel. In
the present state of things, if the horse steps forward, he draws the
shafts _C D_, round the common centre; for the wheel is immoveable by
means of the bolt _i_, which _takes_ against some fixed object at _k_:
and thus will the weight _I_ be raised. And when this motion is
achieved, the handle _o_ is raised a few inches, which brings it into
contact with the obstacle _p_, and puts a stop to that motion of the
lever _E F_. At the same time the bolt _a_, is drawn out of the drum
_G_, and the cross piece _b c_ is let down between the studs of the drum
_H_, while, by the bent lever _f g h_, the bolt _h i_, which held the
wheel, is drawn back, and _then_ the horse, instead of progressing round
the centre of the wheel, is himself brought locally, to a stand; and
without even knowing it, (for he is blinded) he now treads round the
wheel in a backward direction, and raises the weight _K_, while the drum
_G_ permits the weight _I_ to descend by the uncoiling of the rope, till
_this_ operation has likewise produced the desired effect--when things
are again placed in the state first observed. One thing remains to be
noticed: It is, that both these motions _might_ have been produced by
acting from a fixed point on the central bar _b c f_, through the upper
gudgeon of the shaft, _instead_ of using the handle _o_, as before
directed. It is even easy to conceive how the Machine may itself be made
to perform these changes, and thus to produce the whole effect without
any personal care or attendance.


  OF
  AN EXPANDING VESSEL,
  _For Steam Engines, Pumps, Blowing Machines, &c._

It is one of the simplest and most perfect operations of the mechanic
art, to form a _flat surface_: witness the process of grinding looking
glasses, and forming one plane from another. Nor is it, necessarily,
more difficult to place two surfaces parallel to each other, by means of
three or more _pillars_ with proper shoulders, or counternuts against
which to screw the plates from behind. It is therefore easy to compose
an expanding and contracting vessel, that shall become _a mover_ by the
force of any fluid, elastic or not, or shall act as a water or air pump,
when driven by a convenient power; or both together, when this
combination may be desirable. Thus, in Plate 26, fig. 2 and 3, _A B C D_
is a box with four sides and four _jointed angles_--which, if one of
it's sides, _D A_, be fixed to a given position in the cage or frame _E
F G H_, will expand or contract according as the sides _A B_ and _D C_
shall rise toward the perpendicular, or fall toward the horizontal
position. The dotted lines _A_ 2, _A_ 4, _A_ 6, &c. shew that the
successive capacities included in the vessel, are respectively as the
sines of the angles which those sides _A B_ and _D C_ make with the
horizon; so that, although this device furnishes an _unequable_ power,
yet it is equable enough for many purposes in the first few divisions
_D_ 3, _D_ 5, &c. and might be altogether _equalized_ in it's effect if
necessary. Let us suppose then, that the aperture 8, brings steam into
this vessel: The _lid_ _B C_ will rise to 6, 7, when, if the pipe 9,
communicating with a condenser, be opened, the steam in the vessel will
rush thither and be destroyed: when the atmosphere will press on the lid
_B C_, and cause the vessel to collapse with a power proportionate to
that area; for the sloping and parallel sides _A B_ and _C D_
counterpoise each other; where note, on occasion of the _pressure_ which
I am now speaking of, that the ribs or bars _L M_, are used to
strengthen the sides of the vessel, and thus prevent it's fracture under
this pressure.

From this manner of making these expanding vessels, it follows among
other things, that if the frame _E F G H_ were surrounded with wood or
any non-conducting substance, and made to communicate with a warm close
room, the atmosphere thus acting on the vessel would _not_ cool it, and
that therefore, an atmospheric engine, would, in this respect, be as
good as a steam-acting one. But steam might be introduced into this
outer case, and act as a spring to reciprocate the internal effect of
the same agent.

The third figure of Plate 26, offers an end view of this cage or frame,
shewing the expanding vessel at _B C A D_, where the strengthening ribs
of fig. 2 are seen _endwise_ at 1, 3, 5, 7, &c. and moreover, _F G_ and
_H_ are the pillars or cross bars by which the parallelism of the two
end plates is effected and secured.

There remains an important subject to be considered: How to make the
corner joints _D C_, and the end joints steam or water-tight as
required. The small figure 4 answers the question as far as _water_ is
concerned. _A_ is a strip of leather screwed more or less near to the
_edges_ of two contiguous sides of the vessel, so as to cover the joint
or hinge, and make it water tight whether the pressure come from within
or without. This figure also shews the grooves which receive the
stuffing to close the _ends_ of the vessel, by sliding against the
plates or cheeks _E F_, &c. fig. 2. The several members of the corner
joints themselves should be well fitted into each other: so indeed as
almost to close the vessel without _any_ stuffing. Nor need we in all
cases be anxious about this stuffing; for I think it very possible to
make this joint close enough for pumping or blowing without any such
provision. I observe, however, that the leather _A_, fig. 4, might give
place to a strip of thin metal, bent into the same form, (or nearly so)
the elasticity of which would leave play enough for the joints, on the
supposition of working only with a moderate degree of motion in the said
joints.

I should not have given this idea so much attention, had I merely wished
to use it where the cylinder-motion now applies: But my present views go
further. I foresee the use of this Machine for _very low_
pressures--and in _very large_ dimensions; and I can conceive a
proportion between it's length and height, that shall as it were annul
the effects of friction and leakage, compared with those of the
cylinder-formed piston. But I do not undertake, or hardly wish _now_, to
exhaust this subject: being more anxious to _deliver_ the idea to my
readers, than to announce all I intend to undertake by it's means. I
shall, therefore, merely finish the description of the other figures 5
and 6 of this Plate. The first, is a small hand pump on this principle,
having a suction pipe _A_, and a rising pipe _B_, both having proper
valves and opening into the expanding vessel, as _worked_ by the handle
_C_, much in the manner of a common pump. It will therefore act by it's
expansive and contractile properties; and have one good quality we
should seek in vain elsewhere--It will _begin_ the motion of the water
with a _softness_ unknown in the use of pumps in general.

In fine, the sixth figure shews a System of this kind applied to the two
objects, of _giving_ power, and _using_ it. The vessel _A B_, receives
the power from steam or any other agent; and the vessel _C_ blows a
fire, raises water, or does any analogous work, without requiring any
other _parts_ than those here displayed.


  OF
  A GOVERNOR, OR REGULATOR,
  _For Wind-Mills, Water Mills, Steam Engines, &c._

This Instrument was first intended to regulate the grinding of a
wind-mill; and was used for that purpose in Kent, some time before my
departure for France, in 1792. It is founded on the doctrine of opposite
qualities--and is a practical combat between equal and unequal motions.
In wind-mills, the mechanism is exposed to all the variations of a
capricious element: and the common way of preventing these convulsive
motions from injuring the _flour_, was for a man to attend a lever
connected with the _bridge tree_, (which carries the upper stone) and by
it to bring the stones nearer together when the wind was strong--and
nearer still, when it was violent: and, contrariwise, to lift again the
upper stone when the wind assumed a milder movement. A process this,
which _nearly_ equalizes the degree of grinding, but not so nearly the
quality of the meal--for this is found to be more heated by great, than
by moderate velocities. At all events I thought a Machine like the
present, would regulate this process, as well as a man; and it was found
to do so--except, perhaps, in very extreme cases.

This Governor, is represented in fig. 1 of Plate 27--the ground work of
which is the same as that of the third figure in Plate 3: for in reality
the present Machine claims the precedence of the Dynamometer; and may
therefore, well borrow a figure from it's description. _A_ is the
power-axis, receiving motion from any proper shaft of the mill. It is
turned _backward_ by that shaft, and therefore tends to raise the ball
_B_--an operation equivalent to bringing the mill-stones nearer
together. At the same time, the axis of resistance _C_, carries round a
pallet-wheel _D E_, and by the pallet _D_, sets the pendulum _F G_ a
vibrating, which therefore, by every stroke, _lets down_ the ball _B_,
and thus _raises_ the upper mill-stone. A _proper_ position of the
latter depends on the similarity of the motion of the power-axis _A_,
which winds up the ball _B_, and that of the axis _C_, which _lets it
down_. While these are equal, the weight _B_ remains stationary, and the
work goes on well. But if a gust of wind increases the speed of the
mover _A_, (the pendulum _F G_ confining the axis _C_ to it's usual
speed) the ball _B_ is immediately raised and the stones brought
closer--which is what the grinding process requires: And should that
gust increase in violence and become a hurricane, the intermediate
cylinder _M_, while producing _that_ effect, carries also with it the
cord _H I_, and thereby raises the bob _G_ of the pendulum, and thus
fits this movement to the increased speed of the mill: raising,
sometimes, the bob to the very centre _F_ of it's vibration, where it's
oscillations become rapid enough to _unwind_ all the excess of motion
which the hurricane had occasioned; until, the wind subsiding, the
pendulum acquires a medium length, and things go on moderately as
before.

It may be observed, that the _present_ form of this Machine is not quite
so simple as it might have been made; nor is it so simple as it first
was. The required motions being much shorter than those of a
Dynamometer, the cylinder _M_, among other things, might be dispensed
with; and one of the intermediate wheels be likewise suppressed. And if
we advert to the retarding principle which resides in the pendulum, the
well known conical pendulum might be substituted for the present one;
since from it would arise a regular or equable resistance, opposed to an
equable effort. Some however, might _then_ consider the conical pendulum
as an ordinary centrifugal governor; and, as a mere retarding principle,
it may be thought too complex for the occasion: but I think on the
contrary, that it's use in this connection, would make this Machine one
of the best of regulators, as well for steam engines as for water and
wind-mills of every description: especially if fitted up with my Patent
Geering.


  OF
  A MACHINE
  _For Forging Nails_.

There is a strong analogy between this Instrument for forging Nails, and
the Machine heretofore given for forging Bar Iron, Steel, &c. The
process of _kneading_ the softened metal, by means of a pair of
alternating cranks, is the very same: but the acting bars or stampers
_A_, _B_, are an addition to the former method. Plate 27, at figs. 2 and
3, gives a representation of the present Machine; which forms the nail
almost instantaneously, by _many_ contacts of the stampers _a b_, (fig.
3) on one of which the figure of the nail is engraven--or rather _filed_
across that stamper, for no _hollow_ figure is required by this System.

The second stamper _c d_ fig. 3, whose place is at _A_ fig. 2, is quite
plain on it's face; being destined merely to keep the metal to it's
thickness--as the particular nail here intended, is a floor nail,
requiring a head on two sides only. As to the figured stamper _b a_,
fig. 3, it meets a similar form in the anvil, as at _e_: and it is by
the pressure of these _half matrices_, that the head is formed and the
bar separated from the nail. It may be noticed that the stampers _a b_,
_c d_, are shewn in the figures, as perfectly straight on the face: but
the kind of motion resulting from that of the cranks, would require a
gentle curve here, which a _first_ experiment will sufficiently
indicate.

Some skill would doubtless be necessary in presenting the nail bar to
this Machine; but to make this operation the easier, there should be a
guage, moving toward the working point _e_, by a given quantity for each
nail: say that this guage comes forward at each time a distance equal to
half the length of a nail; and that the thickness of the nail bar is so
proportioned as to contain in that length, enough of metal for the nail
when finished.

It remains to be observed, that the stampers or bars _A_, _B_, fig. 2,
are contained, in the direction of their width; by two plates like _f_,
connected with the anvil _e_, and leaving near _e_, an opening large
enough for the nail-bar to pass easily.


  OF
  A MECHANICAL ASSISTANT
  _For the Tea Table_.

I shall, perhaps, be laughed at by some unfeeling censor, for including
the tea table in the field of my mechanical speculations. But, in so
doing, I seriously mean to be not only attentive, but useful to the
ladies--who, I am _old_ enough to believe, deserve this service at my
hands. My object is to obviate for them the necessity of tediously
wielding a ponderous tea-pot, until real and painful fatigue ensues:
thus emphatically making a _toil_ of that pleasure they had hoped for in
administering comfort to others.

This new method of tea-making admits the use of the common tea
urn--which is placed on the table near the left hand of the fair
distributor. This arrangement is given at figs. 4 and 5 of Plate 27.
There, _A_ is the Urn; and _B_ any common tea-pot, for whose spout, the
cock _a_, has been substituted; and the handle of which has been
slightly modified, so as to make it a proper centre of rotation. This
tea-pot is, of course, _opened_ before it is brought into the position
shewn in the figures. At _C b c_, is placed, first of all, on the table,
_a stand_ of metal, terminated upward by the stem _C D_ which forms a
vertical centre to the whole apparatus: and which is sufficiently fixed
to the table by standing on _three_ feet, _b c_, &c. under which are
stretched small pieces of Caoutchouc (or India rubber), which, by their
adherence to the table, make the whole steady. By these means, the
tea-pot can be turned round, by a gentle effort, till it comes under the
cock of the urn, from which it receives the boiling water. And, finally,
the tea-board, which is itself circular, revolves on the same axle _C
D_, supported by the casters or rollers _e f_, and bringing successively
_all_ the tea-cups _m_, _n_, _o_, &c., to the spout of the tea-pot,
where they are filled without the smallest difficulty, as will appear by
a further inspection of the figures, and especially by an appeal to
experience.

The above, I should presume, is all that need be _said_ upon the
subject. It remains for some rationally zealous friend of this social
repast, to put these (or other analogous) ideas in practice: in which
enterprize, should he succeed in pleasing the _ladies_, he may depend on
the approbation of every _lord_ who deserves the name.


  OF
  A COPPER-PLATE PRESS,
  _With curious and useful Properties_.

This Machine, as intimated in the Synopsis, was invented expressly for
the use of the lithographic art, as an improvement on the _roller press_
used in Paris when that process was first introduced there. I have,
however, seen in England the description of a Machine which takes the
desired impression _without_ any rolling motion. This Machine, in that
description, carries a kind of scraper, or, as the calico printers would
say, a Doctor, which, pressing on a line only (while drawn over the
paper, or the paper under it), acts successively on every part of the
sheet, and, no doubt, gives a good impression. Of the relative
perfection of these methods, I do not presume to judge, as it is a
technical question; and _both_ Systems are, or have been, used. But,
when intense pressure, joined to much precision, and great economy of
power, are desirable, _this_ Invention appears to me superior to any
thing I have seen used for these purposes.

In fig. 1 and 2, (see Plate 28), _A B_ are two horizontal planes of hard
wood or metal, connected, at a proper distance, by the pillars _C D_,
shewn in fig. 1 _only_. _E F_ are two _Sectors_ of a large cylinder,
united at the point _a_, either by a _good_ hinge or by a joint
composed of a _hollow_ prism fixed to the upper sector _E_, and of a
_solid_ one, more acute, fixed to the lower sector _F_; so that, in the
latter case, this joint works with an insensible degree of friction, and
thus occasions a great saving of power.

In the working of this Press, the joint just mentioned, however made,
describes a straight line, parallel both to the floor _B G_ and the
ceiling _H A_, which have been already shewn to be parallel to each
other: and thus are the joint _a_ and the sectors _E F_ suspended to the
cap or ceiling _A H_ by a pair of triangular braces _I a K_, which slide
smoothly in two dove-tailed grooves _A m_. Moreover, to the lower sector
_F_ are fixed two working arcs _b c_, one on each side of the Press, and
whose radii are exactly equal to that of the upper sector _E_ (whose
circumference, therefore, is invisible in fig. 1.) Further, just above
these arcs, and in the middle of the slide _I K_, are placed, on proper
centres, a pair of grooved pulleys _P_, destined to _work_ the under
sector, without disturbing the motion of the upper one, which latter is
a rolling motion under the aforesaid ceiling _A H_. For the said
purpose, a metallic cord or chain is fixed at _m_ (fig. 1), which,
passing round _one_ of the pulleys _P_, is led to the end _n_ of the arc
_b c_, _n o_; and near _A_ is fixed a similar cord, which, carried round
the other pulley at _P_, is led to the angle _o_ of the same arc _b c_,
_n o_. By these means, the sector _F_ is fixed both in place and
position, as long as the slide _I K_ retains it's present position and
state. But, again, a system of similar cords, placed _under_ the
ceiling _A H_, near the edges of the upper sector _E_, determines the
place of that sector, in every case, _except_ a change of _position_;
for a _rolling_ motion can still have place, without occasioning any
other change.

When, therefore, a pulling bar, a crank and fly, or any other prime
mover, applied at the joint _a_, carries that joint (say) toward the
pillar _D_, that motion takes place without any _rubbing_ of surface
either above or below; for, when the upper section has rolled under the
ceiling _A H_, into the position _n p q_, the lower section has rolled
upon the plate _s t_, into the position _q r s_: in such sort that the
analogous angles _o t_, _p r_ of both sectors are always found in the
same perpendicular line--or plane--_o t_, _p r_; the cause of which I
shall now endeavour to unfold.

When a wheel, in general, _rolls_ on or against any fixed plane (and the
cords _m P_, _A P_, now act the part of a fixed plane), the point of
it's circumference the most distant from that plane, moves, in a
direction parallel to it, just _twice_ as fast as the centre of such
wheel, because it is twice as far from that plane, the virtual centre of
its motion: (an example of which is found in the wheel of a carriage,
whose top moves forward just twice as fast as it's axle-tree.)
Supposing, then, in the present case, the frame _I a K_, with the
pulleys _P_ to glide toward the right hand, the cord _A o_ fixed near
_A_, will turn the arc _b c_ to the right, twice as fast as the centre
of the pulley _P_ moves in that direction: and if this impulse had
acted on the joint _a_, _while fixed_ in position, the arc _b c_ would
have turned _too much by half_. But it so happens (if this expression
may be used), that the joint _a_ itself moves in that direction _once_
as fast as the pulley-pin; so, that the motion remaining to the sector
_F_ is a _single_ motion, merely sufficient to keep the two sectors _E_
and _F_ directly under each other, or within the same perpendicular
lines _p r_, _n q s_, &c.

Thus, it appears, that the turning motion of the two sectors is the
same; and that a given point of the lower one will always _visit_ the
same point of the corresponding plane _s t_, independently of contact
with any substance lying on it; and that, therefore, the pressure,
though successive, is perpendicular, having _no_ tendency to displace or
_pucker_ the paper laid on it; besides which, it may be observed, that
the _power_ of this Press is immense, from the length of the radii of
the sectors _E F_, and the absence of any _rubbing_ motion.

I observe, further, that _racks_, made with teeth on my principle,
either singly inclined with cheeks, as in Plate 14, or with teeth in the
V form, will produce a more certain effect than the cords and pulleys
above described, provided the arcs _b c_, and the upper sector _E_, be
prepared and toothed accordingly.


  OF
  A REFLECTOR
  _For Lighthouses, &c._

The object of this Invention is to join economy of light with splendour
of effect. The means are the following:--

From the nature of reflecting curves, it follows that the smaller a
luminous point is, the more perfectly will its emanations be reflected;
for a _focus_ is a point of the smallest magnitude, if, indeed, it has
any dimensions. My idea, then, is to make a focus of a _line of light_
very minute in it's _section_, but as large, in it's contents, as may be
desired: thus securing a considerable _fasces_ of luminous particles
while using them in an economical manner. To this end (see Plate 28,
figs. 3 and 4), I form my reflecting surface of two distinct parts,
having a section common to both, viz.--1st. a concave-parabolic-spindle,
represented at _A B C_, as cut by a vertical plane passing through it's
centre; and 2ndly, a parabolical bason _E D F G_ (represented in the
same manner) surrounding the former, and so placed as that these
surfaces have a common focus--namely, the _circular line_ of which _a b_
is the section; the line itself being shewn by an elevation passing
behind the aforesaid _spindle_ _A B C_. This _linear_ focus, therefore,
may be two or three feet in diameter; thus imitating the tenuity of a
_punctual_ focus, while emitting a large quantity of rays.

This LAMP, then, consists of an oil vessel, which is formed by the
outside of the parabolical bowl before-mentioned, surrounded, in it's
turn, by the cylindrical surface _P H_, _I Q_, this vessel communicating
with the wick-ring _a N_, _b O_, by a passage, _H I_, made as thin as
possible, in order to leave the light at greater liberty to pass
downward after reflection. (Where it is proper to add that the
_wick-ring_ is drawn too thick in the figure.) Now, it is well known
that all rays of light issuing from a point, and falling on the concave
surface of paraboloid belonging to that point as a focus, are reflected
from it in lines parallel to each other; and, therefore, a great part of
the particles emanating from the linear (or circular) focus _a b_, and
impinging on the surfaces _F G A B_, and _B C D E_, will be reflected
perpendicularly downward, as at _a_, 1 3; _b_, 2 4, &c. and this being
the case all round the common centre _B_, there will be formed a
cylinder of light of the diameter _H I_, diminished only by the shadows
of the wick-ring, the passage _H N O I_, and the pillar _B L_, when
_that_ is used, which is not indispensable.

If this cylinder of light strikes on the plane mirror _K H_, placed at
an angle of 45° from their direction, these rays will be reflected
horizontally, and, preserving their cylindrical form, may serve as a
powerful _beacon_ to the benighted mariner; the more useful, because
susceptible of those temporary variations of direction and aspect, long
since employed to distinguish one station from another.

But, if it were desired to illuminate a large space at sea, or
elsewhere, the aforesaid cylinder of rays would be received on a conical
surface _K L M_, which would give it the form of an immense sheet of
light, of a thickness (allowing for aberration) equal to the height of
_P L M_, of the same conical surface.

I shall add only one idea--namely, that to light any round space,
building, theatre, &c., this system might be made very efficient by
throwing the sheet of light _M P_ higher or lower on the walls, &c. or
(altering the angle of the cone _K L M_) by bringing it down to any
position in or below the horizon, as circumstances may direct.

It would be superfluous to say that this Lamp might be furnished with
_all_ the advantages of the argand principle; or, the whole
_wick-apparatus_ might be superseded by a circle of _minute_, and very
numerous gas lights, forming, sensibly, the same linear focus; or a thin
circular _slit_ might produce a real ring of light, strengthened by all
the resources of this new and splendid discovery.


  OF
  A LONG PARALLEL MOTION,
  _For Mangles, and other Reciprocating Machines_.

In the year 1793 or 4, I received _a written problem_, desiring me to
give a plan of a _long_ Reciprocating Motion, that should be driven by
the pit-wheel of a common water-wheel, of given dimensions, and placed
in a given position. In a few days, I produced the drawing now
represented in Plate 29. Its object, as required, was to move the
cylinders _L M_, figs. 1, 2, 3, backwards and forwards, in the _long_
grooves or gutters _N O_, for the purpose of crushing or bruising their
contents: but what those contents were I never knew. I, however,
produced this Machine, considering it as a general thing, and of a
nature to perform most operations of a similar kind. The Machine
consists--first, of a long rack _I K_, much like a narrow ladder placed
on it's edge, and in the teeth of which work those of a pinion _p_,
whose axis _q_ is connected with the wheel _r_, which receives it's
motion from the vertical wheel _s t_, which is the _pit-wheel_ in
question. This communication takes place by means of an universal joint
_x_, being a mean of permitting the pinion _p_ to vibrate from side to
side of the rack _I K_, when arrived at either end of it. For example,
the pinion _p_ now turns from left to right, and, being on the other
side of the rack, and _held_ by the chain _v_, it drives the slide _P Q_
in the same right-handed direction, and, with the slide, the two heavy
cylinders _L M_ before-mentioned;--for, the said slide _P Q_ carries
across it's middle the axle-tree _S T_, which is the centre of both
these cylinders, and connects their motion with that of the slide now in
question. Further, there are rollers placed between the cheeks _V V_,
_on_ which the slide moves horizontally, as guided by other rollers,
placed at the points 1, 2, 3, 4, &c. Again, the ends of the axle-tree _S
T_ are furnished with two bow-like bridles, which, connected with the
pulling bars _Y_, are again fastened to the slide _P Q_, at the two ends
of the present figure.

When, now, the pinion _p_ turns (see fig. 1 and 3), the rack, slide, and
cylinders roll in the grooves, till the end of the rack comes to that
pinion; which, finding no more teeth, swings round the _last_, and
taking a new position, reverts the motion, till the other end of the
rack comes to it, and occasions another return: _ad inf._ This will be
better seen at the third figure, which is an end elevation of a part of
the Machine.--There, _P_ shews the slide and _one_ of the teeth of the
rack (which teeth are longer than the rest, as seen near _L M_, in fig.
1.) In this figure, we see at _A_, a mass of brick-work, covered by the
_sleepers_ 5, 6, 7, &c., on which the long cheeks _V V_ repose. There,
also, the chains _v z_ are seen, connected with ring-bolts, which go
_through_ the bars _a b_, and are _nutted_ on the other side of the
spring-beams _c d_, in order to avoid the commotion which would
otherwise attend every change of motion in the slide and cylinders. For
this purpose, also, and especially to prevent any waste of power at
these moments, there are _mixti-linear_ wedges laid in the gutters, such
as are shewn at 6, which are formed so as to absorb the momentum of the
cylinders, in exact conformity to the time employed by the pinion _p_,
in swinging round the end tooth of the rack; and thus to save all the
power and time possible.


  OF
  A MECHANICAL SYPHON:
  _Which expels Part of it's Water at the upper Level_.

An ordinary Syphon acts by the pressure of the air on the _upper_ water,
which drives it into the ascending pipe, _because_ there is a (partial)
vacuum made there by the weight of the falling water in the descending
pipe; this being always longer than the first. Thus, in Plate 29, fig.
5, _A B_ shews the rising pipe of a Syphon, and _C D_ the falling pipe,
which is longer, and sinks to a lower level _D_, than that _A_ of the
water, which feeds the machine. _E_, in this figure, represents the
vessel containing the mechanism on which the new effect depends: and
which I shall now describe.

_B_ and _C_, fig. 4, are, one the ascending pipe _A B_ of fig. 5, and
the other the descending pipe _C D_. They are surmounted by two
cylinders, of unequal capacities--this inequality bearing a given
proportion to the difference in the heights of the rising and falling
branches of the Syphon. In each of the cylinders works a piston _a_,
_b_, which, I think, need not be stuffed, but _well_ fitted. The large
piston has proper valves in it, to let the water pass upwards, at all
times; and the small piston has a valve _i_, opening upwards, by means
of the mechanism we are now describing; and closing itself merely by
the arrival of the piston into it's present position; for the screw _c_
prevents the valve from rising higher: _e_, _f_, are two arcs belonging
to the lever _E_, and being circles round it's centre of motion. They
are cut into teeth, on my Patent principle, and work in the racks
similarly _toothed_, which give motion to the pistons _a b_, or receive
it from them. Further, behind the stand _F_, common to both levers,
vibrates, on a pin, another lever _g h_, the use of which is to _work_
the aforesaid valve _i_ in the small piston; and this it does, by means
of the weight _h_, in the following manner:--The machine being supposed
in the present state, the Syphon will act, as usual, through the valves
of the large piston; and the water pressing on the small one, with a
power proportionate to the excess of it's column over that of the other
piston (_a_), will raise the latter as fast as the piston _b_ descends;
but the area of the piston _a_ being _larger_ than that of the piston
_b_, there will be a pressure within the vessel _b c d a_, that _must_
expel (through any prepared aperture at the top) a quantity of water
equal to the difference of area between the two pistons, multiplied by
the stroke of both: the real quantity of which will ultimately depend on
the difference of level between the higher and lower water; or between
the lengths of the rising and falling branches of the Syphon, _B_ and
_C_. When, therefore, this stroke is made, the end _h_ of the lever _g
h_, which carries the ball, will touch the screw _d_, and stop the
descent of the valve _i_, which will thus be opened; when the water will
have free egress through the descending pipe _C_, and the piston _b_
will then rise through that water by the weight of the piston _a_, the
valve _i_ being _kept open_ by the action of the weight _h_, until the
piston _b_ has risen to it's present position, when a new stroke is
prepared, for the same reason as before: and thus may water be carried
over a hill of (about) 30 feet above the level of any stream or pond,
and dropped into a _lower_ canal on the other side, with the condition
of leaving a part of that water upon the hill, proportionate to the
difference between the level from which the water is brought, and _that_
to which it is carried.


  OF
  A FORCING MACHINE,
  _For taking on and off the Cylinders of Calico Printers_.

The two figures, 1 and 2, of Plate 30, are intended to make this Machine
known, assisted by the following description:--The first is a front view
of it, and the other a partial view from above. In the former, _A B_ is
the frame formed of, and firmly connected with the two columns _C D_,
which are fixed strongly to the ground, at such a distance below the
ends _C D_, as to place the aforesaid frame at the height of about two
feet, or higher, if convenient.

In the two cheeks of the frame _A B_, are cast or bored two round holes
for receiving the gudgeons of the _swivel_ _E_, one of which gudgeons is
also seen at _E_, in fig. 2. This swivel turns in these holes; and it is
itself perforated with a round hole just large enough to receive freely
the body of the mandrel _F G_. This mandrel has now on it the cylinder,
which is to be taken off. _I K_ are, moreover, two ears or studs cast or
welded on to the top and bottom of the said frame _A B_, and at exactly
the same distance from the centres of the swivel _E_ before-mentioned.
These _ears_ receive the ring-formed ends of the bars _L M_; see also
the bar _L_, in fig. 2. To these bars is firmly fixed the cross-bar _N
O_, which forms the _nut_ of the screw _P_, by means of which the
operation of the machine is duly _prepared_; for, now the cup _Q_ (in
the centre of which the screw _P_ revolves against a proper shoulder)
receives the end _G_ of the mandrel, which it presses forcibly, while
the whole is in the position _E L_, of fig. 2; that is, when the two
centres _E_ and _R_ form one right line with the bar _L_, figs. 1 and 2.
To complete, then, the process of driving out the mandrel, the bars,
mandrel and cylinder are, at once, strongly made to describe the arcs _a
M b_, _a c_; the mandrel revolving round the centre _E_, which is that
of the swivel and the bars round the stud _R_. But, in thus revolving, a
given point of the mandrel describes the _quadrant_ _a M B_, and a
contiguous point of the bars _L M_ describes the quadrant _a c_;
insomuch, that the mandrel _must_ have been forced out of the cylinder
in direction _G F_ by the distance _c b_; where we observe that, at the
beginning of this motion, the two curves _a b_ and _a c_ coincide in
their movements, and only begin greatly to diverge from each other in
the latter parts of these motions (see _M b c_.) The power, then, of
this machine, when the cylinder sticks fastest to the mandrel, _is
infinite_: and this power becomes weaker, and the velocity greater
toward the end of the operation; that is, when the cylinder has
slackened on the mandrel, and no longer requires to be driven with the
same force as at the beginning. It may finally be observed, that the
bars _L M_ are suspended by an oblique bar or chain _S N_ to the ceiling
of the room just over the stud _R_ or _I_, which is their real centre of
motion, in the above-described process.


  OF
  A SYSTEM OF MACHINERY,
  _For cutting and trying Tallow by Power_.

The wheel _A B_, Plate 30, fig. 3, _was_ a horse-wheel, but may be a
_first motion_ of any given kind. It is placed on the ground-floor; and
over it's centre is another shaft, having on it's upper end a chopping
block _C_, which revolves with the wheel _A B_, as turned from below. In
this wheel, _A B_ geers a pinion _D_, driving the lateral shaft _D E_,
which has two functions: the first to work the lying shaft _F_, and by
means of the cams _G H_, to lift the contiguous stampers; and, by means
of the knives _I K_, to cut the tallow on the revolving block
before-mentioned. Over this block is fixed an oblique scraper, which
takes the tallow as soon as it is cut, and pushes it down an inclined
channel, placed at _C x_, into the boiler. The second use of the shaft
_E_ is to turn the _mill_ _M_, (better shewn at fig. 4), which is let
down into the boiler, in one stage of the process, and drawn out by the
tackle _N_, when not wanted. The use of this mill is to tear the fleshy
parts of the substance, while in the act of boiling, and thus to
disengage the tallow with so much the less heat, in order that it may be
so much the less coloured. Besides this machine, there is a grapple _L_
to be first used, which stirs the tallow in the boiler by the rotatory
motion of the arm _x_. This position of the grapple would alone
indicate what I have yet to observe--namely, that the boiler is a kind
of ring, the section of which is the line 1, 2, 3, 4, and it's depth 1,
2, or 3, 4. To prevent, still further, the fat from being burnt or
coloured, the flue for the fire is conducted solely under the bottom of
the boiler, as shewn by the dotted lines in fig. 5: the smoke or heated
air being forced to make two revolutions under it, as indicated by the
arrows in this figure, where we see more particularly the fire-place _F_
in close connection with the rising shaft of the chimney at _G_; and
this is so, because, with so great a length of horizontal flue, the fire
would not enter the chimney till it had been heated to a first degree.
There is, therefore, an opening into the chimney at _a_, and the fire,
in lighting, is suffered to escape directly from the fire-place into the
chimney; by which means, continued a few minutes, there is draught
enough created to make the fire take its useful course through the flue
afore-mentioned. I may just observe, reverting to fig. 3, that _O_ shews
the fire-place _in elevation_, and _p_ the entrance into the flue, which
last is double under the boiler, as shewn in fig. 5. Finally, the 4th
fig. shews an end view of the _tearing-mill_, before-mentioned; but here
on a larger scale, _A B_ being a part of the side of the boiler.


  OF
  A WASHING MACHINE, FOR HOSPITALS,
  _Which confines the offensive Matter till cleansed away_.

Doubtless, the salubrity of every place, where _many_ people are
collected, would be much increased, if all impure exhalations were
expelled as soon as formed; and this is especially true of those awful
but sublime receptacles, provided by Philanthropy, for the sick, the
wounded, and the dying! To assist in the work of purifying the
atmosphere of these doleful abodes, was the object (30 years ago) of the
VENTILATOR, presented in page 170 of this work. But, I conceive, that a
share of evil, quite as great, resides in the putrescent qualities
contained in or connected with the clothes, the bed-linen, the
dressings, &c., of the inmates of an hospital; to whose sacred claims on
the efforts of every good citizen, the present article is devoted.

This Washing Machine (see Plate 31, figs. 1 and 2) is a triangular (or
square) box _A B_, furnished with a lid _a b_, so fitted, as, when
screwed down, to be hermetically closed.--And, N. B., to facilitate
_this_ operation, I use in it a particular kind of screw (invented for
the _hose_ of fire-engines), which I shall now describe. I take a common
screw, with it's nut, and cut away the threads of both, at two opposite
_quarters_ of their respective circumferences, so that the screw can
_enter the nut to the bottom without turning_; and the stuffing between
the shoulders is so well fitted, in thickness, as to secure the
penetration of the threads of the nut and screw the moment the latter
_begins_ to turn. There is thus a full quarter of a turn, in which the
nut and screw will press as strongly as though the threads had not been
cut away; and thus are _nine tenths_ of the time required to use a
common screw _saved by this simple process_: and thus, then, I close the
lid afore-mentioned.

This Machine is further composed of a wheel _C D_, and a pinion _E_, to
turn it with, either by hand, or by any proper application of power. The
wheel turns the box _A B_, and thus agitates the contents in a way not
dissimilar to the operation of the dash-wheels of calico printers. But,
again, this wheel and vessel turn upon _two hollow gudgeons_ _c d_; one
of which is destined to convey cold water into the wheel from the
reservoir _F G_, to regulate which is the use of the cock _f_: the
stuffing box _e_ being made as _good_ as possible, in order to prevent
all leakage, either of air or water. The second hollow axis _d_ serves
two purposes: it gives a passage to the fetid matter of which the
expulsion is desired, and conveys it through the cock _g_ to the _sink_
or _sough_ below _h_, _without any communication with the surrounding
atmosphere_.

But we said this hollow gudgeon had a second use: it is to bring steam
into the revolving vessel _A B_, from any proper boiler beyond _K_,
when that part of the process requires it.--There are, moreover, two
partitions _C D_, _l m_, made near the ends of the vessel, and pierced
with many holes, in order to suffer the cold water to flow in, and the
dirty water to escape, without choking up the respective passages: and,
finally, at the eduction end of the Machine (see _n_, _o_, _p_, fig. 2),
there are placed three pipes, reaching from the angles of the box to the
hollow centre, and furnished, at those angles, with valves, opening
outwards; which thus form a kind of hydraulic machine to raise this
matter from those places to the hollow centre, and thus, after a certain
number of revolutions, to expel it entirely.

The process, then, for cleansing the objects contained in the vessel _A
B_ (including the condition of cutting off all communication with the
ambient space,) is as follows:--

1st.--These objects are dropped into the vessel as soon as produced, and
the vessel is filled, one half or more, with cold water from the
reservoir _F G_. The things are then left to _steep_ in this bath for a
day or two, or what space of time the periodical mutations of the house
permit. By which operation _alone_, the miasmata are already much
confined by the water, even though the lid of the vessel should be but
partially shut: after which, this steeping operation may be continued,
with the accompaniment of a few turns of the handle (_E_) to fully
saturate every part of the mass. In the second place, a small stream of
water is let through the cock _f_, and the wheel _C D_ is kept turning
for a few hours, to discharge the cold water and the most offensive
matter, through the cock _g_, into the sink: and, thirdly, the
steam-cock _K_ is opened (that _g_ being shut), by which means steam is
brought into the vessel _A B_, and the whole soon raised to the boiling
temperature. This state of things is continued, as long as it is found
necessary; the motion, of course, being also continued, and even
accelerated, that the mass of objects may _fall_ from angle to angle,
and be thus _well washed_--that is, well _finished_, if _plain_ things;
and fully prepared for finishing, by hand, if of a nature to require
close attention. And, finally, in many cases, the warm process may now
be abandoned, and a new stream of cold water be injected, accompanied by
a due motion in the vessel, so as to _rince_ the contents; and thus
leave nothing to do for the laundresses, but to dry and mangle, or
_iron_ them; where, it is plain, that no inconvenience can have arisen
from this process, either to these persons, or to the other inmates of
the house.--Hence, then, this Machine _has the properties announced--of
confining the offensive matter until cleansed away_.


  OF
  A MACHINE,
  _For propelling Boats, on narrow Canals, without disturbing the
  Water_.

The application of steam-power, to the motion of boats on narrow canals,
is, I believe, much impeded by the consideration that the agitation of
the water injures their banks, and would finally destroy them. On the
other hand, it is known, that to drive a vessel, by acting on a fleeting
medium, such as water, we must, at once, submit to lose about one half
of the whole power employed--that is, the power, armed with energy
enough to produce the required velocity, must go through twice the space
that constitutes the _way_ or progress of the vessel. This depends,
however, on the size of the floats or paddles employed, compared with
the section of the boat, as modified by the form of the prow; but it is
difficult to employ a paddle so large as to suffer more resistance from
the water than the boat itself; and, if they are found _just_ equal, the
_loss_ of power is exactly one half of the whole. These, then, are the
two difficulties which I hoped to avoid, by the method now to be
exhibited.

The idea is this--To have a large and heavy wheel _A_ connected with a
_long_ shaft _B_, reaching from the boat to the shore, and, turning that
wheel _in_ the boat, to propel the latter, by means of it's rolling
motion, on the bank or track-way; or, in some cases, on a proper rack,
placed there for that purpose.

The Machine itself is represented in figs. 3 and 4, of Plate 31; fig. 3
being a stern-view, and fig. 4 a side-view, both of the machine and the
vessel. _C_ is an axis, placed along the vessel, and turned by _any_
convenient power--as a horse, a steam-engine, &c. On this axis,
considered as the _first motion_, are fixed the two bevil wheels _b c_,
from which the long shaft _B A_ of the rolling wheel takes it's motion.
The use of the two wheels _b c_, is to drive the boat in the same
direction on whichever side of the boat the wheel _A_ may be placed; for
this, of course, must follow the track-way, which is sometimes to the
right and sometimes to the left of the vessel.--Between the two wheels
_c b_, is a sliding block (or catch-box) _d_, in which the shaft _A B_
of the large wheel has it's lower pivot, and by which it's wheel _B_ is
almost instantaneously shifted from one to the other of the vertical
wheels _b c_: the catch-box _d_ being itself _worked_ by a lever, of
which the end only is seen at _e_, fig. 4. In fig. 3, there is further
shewn a rope or _stay_ _f_, which, fastened to the socket _s_, of the
rolling wheel _A_, and fixed in the middle of the boat, at the greatest
possible distance from it, serves to keep that shaft at or near an angle
of 90 degrees with the boat's side: so that (the vessel being _long_) it
becomes easy by means of the rudder, assisted, perhaps, by _lee-boards_
to keep the _way_ of the boat in a line parallel to the shore,
notwithstanding the tendency to veer outward, given by the wheel _A_,
while acting on a point so far from the body of the vessel.

I further observe, that, in order to shift the apparatus, with a certain
facility, from one side of the boat to the other, there is a mast _M_
placed ahead of the mechanism just described, which rises as high as the
length of the main-shaft (but can be _lowered_ to pass a bridge, &c.),
and to the top of which is fixed the block _g_, through which a rope
passes from the foot of the mast to the above-mentioned socket of the
wheel _A_. By this rope the wheel is hauled up till nearly ready to fall
over the centre; when a push from below will complete that passage; and
the wheel _A_, being afterwards _lowered_ by the rope _h i_, will soon
find it's proper position on the other side of the boat, as before
anticipated. Where, it should also be remembered, that this shaft must
have a joint and socket, to permit it's being bent, to pass a bridge,
&c.

Hitherto we have supposed this rolling wheel to act on the bank or
track-way solely by it's weight; but this is not our only resource; for
this wheel might be made of a moderate weight, and be pressed down by a
brace reaching along the boat, toward the head and stern (see _k l_,
fig. 3.), and _hauled taught_ through an eye of the socket _s_; by which
_man[oe]uvre_ (the points _k l_ being lower than the centre _A_ of the
wheel) the latter will be pressed forcibly downward, and cause that
cohesion there, from which the boat is ultimately to take her motion.

And, as to the wheel _A_ itself, I have _not_ represented it in the very
form I should wish it to have, because it can be sufficiently described
in words. I should cast this wheel (if made at all in metal) as a
_shell_, the outside of which would be what is really seen in the figure
(at _A_), and the rim would have in it mortices, like those which are
made for iron wheels destined to receive wooden cogs, and geer with cogs
of iron. In fact, this would become a wooden-toothed-wheel, with its
teeth roughly formed and placed, so as to occasion a small expence, and
to be easily changed, when worn away by the friction on the track-way.
Thus would, I am persuaded, a very moderate weight in the wheel, and as
moderate a pressure from the braces _k l_, connect the wheel with the
road enough to produce the desired effect, with a trifling _loss_ of the
power employed. And thus might we navigate a narrow canal, with a great
saving of expence; not to mention that other advantage of avoiding
entirely that injury to the banks, which must attend every system of
propelling the boats, founded on the agitation of it's waters.


  OF
  A MACHINE,
  _For working, swiftly, the Slide-valves of Steam-engines_.

The Slide-valve is an excellent substitute for the _hand-geering_ of
steam-engines, from the simplicity of form which it introduces, and the
certainty of it's recurring effects. But it is, I believe deservedly,
reproached with being too sluggish in it's operation, at the very moment
when _activity_ would be most desirable--namely, at the beginning of the
strokes; insomuch, say some, that the _power_ of the engine is
materially lessened by it. The fact is, that the _excentric_ (usually
placed on the crank-shaft) is almost always moving, and with it the
slide-valves also; which thus open by _slow_ degrees, when they should
open by _rapid_ ones.

Without discussing the question further, I cannot refrain from
introducing this application of the principle of my Parallel Motion,
given in page 237; which appears to me greatly calculated to obviate
these difficulties; and thus to leave the slide-valve in possession of
all it's own advantages, with the addition of those which have hitherto
belonged exclusively to the Hand-geering System.

I have represented this Mechanism in figs. 5 and 6, Plate 31: where _A
B_ shew the crank-shaft of a steam-engine, working by means of
slide-valves, the place of the _excentric_ being at _a b_, in a line
with the pulling-bar _e f_. Instead, then, of the usual connecting
_frame_ between the excentric at _a b_, and the valve-lever at _g_, I
use for the above purpose, a lever _e f_ terminated by an arc _o_,
furnished (in the present instance) with _five_ teeth, and connected by
the joint _e_ with the valve-lever _g_, in the usual manner. In the arc,
which terminates this lever _to the right_, are the five teeth
above-mentioned; and, they geer in the _ten_ teeth of the wheel _c d_,
which will be seen (in fig. 6) to be on the same shaft with the
spur-wheel _m_, itself driven by the spur-wheel _n_, of twice the
diameter. This wheel _c d_, therefore, makes two revolutions for one of
the crank-shaft: and, supposing it to turn in the direction of the
arrow, it will first of all draw _upward_ the arc _o_, producing no
effect on the valve-lever at _g_; but, when the tooth _r_ is arrived at
_p_ (the tooth _p_ being then arrived at the entrance of the curve _q_),
the wheel _c d_ will begin to draw the arc _o_ along with it, round it's
own centre; and, the teeth of the arc being kept in it's teeth by the
similar curve _q_, the valve-bar will be drawn from _g_ to _h_, in the
course of _one quarter_ of a revolution of the crank-shaft _A B_. But,
now, the tooth _r_ of the arc _o_ will be found at _s_: and, therefore,
the further revolution of the wheel _c d_ will carry the arc _o_
downward toward _t_, until the tooth _r_ has reached the point _t_; that
is, until the wheel _c d_ has made another half-revolution, and the
shaft _A B_ another quarter; when, as before, the arc _o_, conducted by
the curve _t r_, will again drive back the lever _e f_, till it comes
into it's present position: after which, their motions will be regularly
continued. It is, then, evident, that the slide-valves are thus opened
and shut, each during one _quarter_ of a turn of the crank-shaft _A B_;
and thus they remain stationary during another quarter, and that, in two
positions of said shaft diametrically opposite to each other. And thus
have we a simple mean, adaptable to every engine, of giving it much of
the advantage of the hand-geering system, while preserving _all_ that of
the slide-valve principle. And, were it desired to lengthen the
_interregnum_ of the opening motion, it would be done by making the
wheel _c d_ smaller, and the ratio of _n_ to _m_ (see fig. 6) larger in
the same proportion.

I observe here, however, that care should be taken not to make the valve
motions _too_ rapid, nor the intervals between them too long; for, I
consider one of the best properties of this motion to be, that it acts
_like an excentric_; that is, slowly at first, most rapidly afterwards,
and finishes as slowly as it began; which is a _precious_ quality in all
reciprocating machines.

Finally, I would remark, that the two last _rounds_ in the rack of the
arc _o_ might be rather larger than the intermediate ones, and turn,
moreover, on pins, so as to suffer less friction when rolling on the
conducting curves _q_ and _t_. There might also be a plate or cap
rivetted or screwed over all the teeth, so as to strengthen each one, by
the force of the whole, as is shewn in fig. 1, Plate 29; from which, as
before observed, this Mechanism is deduced.

       *       *       *       *       *

The foregoing completes the Third Section of my work: and gives an
article beyond the twenty, first intended:--which I thought important
enough to claim this distinction. I now beg leave to add a remark or two
on the text and plates of this, and the Second Part, by way of clearing
up some obscurities, that might otherwise embarrass my readers.

And, first, in fig. 1, of Plate 21, the receiving vessel _M_,
erroneously _appears_ to form part of the wheel _D E_; but is, in
reality, placed _before_ it, as in all similar cases.--And, further, a
small deviation of the circular lines, in Plate 22, has set the plate
and it's description, in page 192, _at variance_; the difference between
the lines _o p_ and _C q_ being _not_ "imperceptible," as there stated.
I wish, then, that the dotted radius _A o p_, in the said fig. 2, may be
carried (or supposed) halfway between _p_ and _C_. Finally, in page 200,
line 8, the 24th Plate is incorrectly called the 25th.

I shall conclude this Part, by an observation or two on the reception my
System of Toothed Wheels, as described in this work, has met with--not
intending to speak of the local difficulties I experienced at a former
period. But, _here_, the interests of truth force me to break silence.
The necessity I stood under of bringing out this work in Parts, has, at
least, had one advantage: it has given me an opportunity of watching the
workings of prejudice--not to say of envy,--and thus of neutralizing, in
some degree, the effects of either: from which, however, I claim nothing
but the _right_ of making my labours the more extensively useful, by
making them better known. I have, then, to say that, among _a few_ other
objections to the System, _this error_ has come from so respectable a
quarter, that it would be unjust to Science, and injurious to truth, to
let it pass unrefuted. It has been said, that "my wheels are a Chinese
Invention;" and _this_ proof has been adduced of it--namely, a
sugar-mill, from China, having it's cylinders _fluted in a spiral
direction_. Now, the fact is, it would have been difficult to give a
better proof that the wheels are NOT a "Chinese Invention;" for two
inventions are then only alike when they produce the same effect, by
similar means. But here the effects intended are totally different. A
sugar-mill acts in or near the plane of the centres; and one of it's
cylinders is not intended to drive the other independently of pressure
between them. This is so true, that the rollers of many sugar-mills are
not fluted at all. Besides this, my wheels exert no pressure in that
direction; and if they did, they would not be cog-wheels. In a word,
their action is _at right angles to the former_, and has an object of
quite a distinct nature. These, then, are by no means the same machine;
and, therefore, mine is not a "Chinese Invention."

Here, however, I _beg_ not to be misunderstood! I should feel no regret
at appearing on the mechanical stage, a few hundred years after so
ancient and astonishing a nation as the Chinese! But, in this case,
truth did not permit me to sanction, by my silence, this flagrant
error.

Finally, an opinion exists, _somewhere_, that these wheels _will_ never
be generally used, from the difficulty of making them; and this opinion
has been expressed, apparently, with no very amiable feeling. But,
amiable or hateful, the opinion is highly erroneous! It is so far from
fact, that, in a competent manufactory, they can be made more cheaply
than others now are; and _many_ persons are already calling for them
from every quarter; nor is any thing wanted to insure their immediate
prevalence but a _common_ degree of commercial energy.




  PART FOURTH.
  A NEW CENTURY OF
  Inventions.


  OF
  A CUTTING ENGINE,
  _For large Bevil Wheels and Models, on the Patent Principle_.

One of the most prominent subjects of this essay, if not the most
important, is the System of Toothed Wheels, with which the second and
third Parts were introduced, and which still claims a share of my
readers' attention. As hinted a few pages backward, it seems not enough
for me to exhibit and describe the System, but I must defend it against
repeated objections, on pain of seeing it's utility delayed, and the
public deprived of it's real and solid advantages. I am _far_ from
wishing to impeach the _motives_ of those who still nourish or express
dissent, when they deign to bring reasons for so doing; but the mere
opinion--"it won't do"--expressed by a man of reputation, may impede,
for a time, the progress of an useful discovery, and thus produce a
public evil. This, then, is a result I am anxious to avert; as the
present System _has_ many points of excellence, against which no
insuperable objection _can_ be brought. Had I not declined, already, to
name either the friends or enemies of the System, I might here appeal to
persons who highly approve of it; and, indeed, who use it daily with
manifest advantage. But, I forbear. If, by means of the Engines already
given, and _that_ I am going to offer, it is proved, that the difficulty
of making these wheels is _trifling_, compared with their utility, one
important point will be gained: I shall not hear it repeated, "that the
System cannot succeed, _because of the difficulties of it's execution_."

The present Cutting Engine is shewn in figs. 1, 2, 3, of Plate 32. It's
immediate use is to form the teeth of _wooden models_, for casting.
These are previously _built_ as usual, and _lagged_ with _bay-wood_, of
sufficient thickness to furnish the teeth, and leave a small thickness
of _that_ wood behind or under them.--_A B_, in fig. 2, represents a
wheel of this kind, ready for cutting;--mounted correctly on the centre
pin _C D_, which latter is so formed as to be _fixable_ in any position
on the table or bench _E F_. Under the wheel _A B_, there is a kind of
_index_ _a b_, put upon the said centre pin _C D_, which, by means of
the clamp and screw _b c d_, can be occasionally connected with the
wheel _A B_ so as to turn it, when it is itself turned by the means
hereafter to be mentioned. To proceed with the description: _G_ is a
slide, moving horizontally on the bench _E F_, as seen at _f e_ fig. 3;
this slide being the basis of the headstock _G H_, which contains the
_perpendicular_ slide _H I_, itself the support of the cutter-frame _K
L_, so constructed as to turn on it's bolt above _I_, and take any
proper position over the edge of the wheel or model _A B_. This slide,
then, with it's appurtenances _H I K L_, moves along the bench _E F_, as
seen in fig. 3 at _f e_: and what gives it this motion, is, the screw
_g_, furnished, purposely, with a left-handed thread, working in the
_half-nut_ contained in the small frame _h_, which contains also a
jointed _cap_, that can be lifted off in an instant, and the screw set
at liberty. Moreover, the second use of this screw _g_, is to _be_ thus
disengaged from it's nut, and lifted up to about _i_, where it serves to
push back the slide _G_ towards the wheel, without that loss of time it
would occasion if pushed back by the working of the screw. The letters
_M N_, shew another important part of the Machine, applying to the
cutting-process. It is an inclined plane, sloped to the same degree as
the bottom of the teeth of the wheel. (See the line _a k_.) This
inclined plane, then, is fastened, in any proper place, on the bench _E
F_, by the wedge _N_, _just_ like the puppet of a common turning lathe;
and it passes through an opening in the slide _G I_, or rather suffers
this to pass _over it_, as better seen at _M_, fig. 3. Furthermore, the
slide _I_ (fig. 2), after gliding down this inclined plane _M G_, will
have to be raised between each cutting: and that is the office of the
workman's hand acting on the lever _O P_, through the iron frame _Q M_,
which is shewn at fig. 3, in another direction; and marked with the
letters _Q l m_. In fine, the slide _G_ carries on each side of the
Machine a pulling bar _n_, connected with the said slide, and with a
smaller sliding piece _o_, the use of which is to hold a pin (seen in
the figure, but leaving no room for a letter of indication), which
_turns_ the wheel _A B_, by the plate _p_, as the slide _G_ recedes, and
the cutter-system _I K L_ descends on the inclined plane
before-mentioned. Having thus adverted to all the important parts of the
Machine, we turn to fig. 1, for the purpose of shewing _what_ the plate
(whose edge is seen at _o p_) means; and the effect it is intended to
produce.

In that figure, let _B A c_ be the section of any wheel it is desired to
cut on this principle. The width of the face of such wheel is shewn by
the line _a b_; and _a c_ is called the _projection_ of that face, on
the base of the cone of which the wheel _A B_ is a portion; it's summit
being at _C_. The line _e d_, shews _one_ of the spiral teeth with which
the wheel is to be furnished; and I make it by this uniform process: The
pitch of the wheel, whatever it be, is set off from _e_ to _f_: and that
pitch is divided into _eight_ parts, (shewn here as _four_ on account of
their smallness) while the width of the face _f d_, is divided into
_nine_ parts, shewn here (for the same reason) by _four and a half_
divisions. This latter division is more numerous than the former, that
the principle may be a little _overdone_; or that the teeth may overlap
each other by 1/9 of the pitch: To which purpose, beginning the spiral
line _e d_ at _e_, I move in the second circular line from _e_ to the
second radial line _C i_, and draw _that diagonal_ which forms the first
part of the curved line _e d_. From this second point, I go to the third
circular line, taking also the third radial line, and drawing the
diagonal. This I do until arrived at the fifth circular line, when I
find myself likewise at the fifth radial line _C d f_. These four spaces
thus gone over, represent the eight parts into which this part of the
face _a b_ _would have been_ divided, had the figure been larger: and
there remains a small division near _d_, equal to one half the others,
through which the curve _e d_ is prolonged by a similar process; and
this latter portion is what the successive teeth _overlap_ each other,
as before stated.

Now, it will be seen below, that the needful _circular_ motion is given
to this wheel, by a movement that takes place in a direction parallel to
the base _a c B_ of this figure. The curve _e d_, must, therefore, be
transferred from the surface of the cone, to this base _a c B_. To do
this, I place a point of the compasses at _A_, and trace, with the
openings _A a_, _A c_, &c., the six _quadrants_ included in the space _a
c g h_, which are now the projections, on the base, of the circular
lines _a b f d_ on the surface of the said cone. Here, a slight
difficulty should be obviated: strictly speaking, this _projection_
would be horizontal, and, of course, invisible in this position of the
wheel. But I have supposed the figure _a c g h_, turned ninety degrees
downward, round the horizontal line _a B_, so as to make one
representation suffice; and also to shew the connection of the lines _a
b g h_, with those _f d a b_. The curve _k l_, is thus a _copy_ of that
_e d_, only _shortened_ in the proportion of _a b_ to _a c_--that is, of
the side of the cone _a C_, to the half-base _a A_.

To secure, then, the coincidence of the pitch, as set off on the
circumferences _a f_ and _a g_, we must divide a similar portion of both
into an equal number of parts, _e f_; and treat them, on the lines _a c
g h_, as we did on those _a b d f_; by which means we shall get the
curve _k l_, _the projection of that_ _e d_. And this curve _k l_, must
be made part of a _plate_ _k l m n_ (about 1/10 of an inch in
thickness), the use of which is as follows:

This Plate _k l m n_, is no other than that marked _o p_ in fig. 2; and
it is there fixed to the index _a b_, directed to the central pin _C D_,
as it is in fig. 1 to the centre _A_--insomuch, that the _pin_ shewn in
fig. 2 near _o_, acting on the _sloping_ curve _k l_, will turn that
index (and with it the wheel) by the very motion which draws back the
slide _G_ (fig. 2), and lets down the slide _I_ on it's inclined plane
_G M_.

We may remark, lastly, that as the present Machine is adapted to _large_
models, it is not, now, provided with a dividing-plate, although the
means of so doing are self-evident. On the contrary, the division dots
are seen on the edge of the wheel _A B_, as is likewise one dot, near
_b_, on the clamp _b c_, from which a given distance is set off to each
of the dots on the wheel, so as to give the pitch required. By these
means, then, the wheel is divided and cut, in _good_, if not in
exquisite divisions; and all the teeth take their shape from the Plate
_o p_ (or _k l m n_ of fig. 1), and are thus good, in that respect also.

To recapitulate the steps of this process--The workman stands behind the
Machine, near _E_; and, working the screw with his right hand, draws
back the slide _G_, (the _power_ then turning the cutter _r_ very
swiftly) by which means, the slide _I_ glides down the inclined plane
_M_, and the cutter, impinging on the sloping face of the wheel, cuts it
to the depth _r a_; the shape of the tooth (by the turning of the wheel)
being the spiral form _e d_ of fig. 1. It may be added, that the lifting
lever _O_ permits this descent of the bar _Q M_, because it is suffered
to fall lower than _now_ represented. Thus, when the slide _G_ is
arrived near _h_, the tooth is finished; and the cutter leaves the wheel
at _a_: after which, the cutter-frame and slide _I K L_ are raised by
means of the lever _O_--the screw _g_ taken out of it's _steps_, and the
slide _G_ pushed back by it, until the vertical slide _I_ rests again on
the inclined plane _M_, as it at first did. Nothing, now, remains to
prepare for cutting a new tooth, but to change the division-dot, by the
application of the gauge or compasses, from _b_ to the next point on the
wheel; to do which, of course, the clamp _b c_ must be loosened and
refastened by the thumb-screw _d_. I would just notice the 4th
figure--to say, it is a sketch of one quarter of a bevil wheel; intended
merely to shew the form and position of these teeth, and the general
appearance of the System.

Finally, my readers will please to advert to what has been already said
on the _forms_ of these teeth, and their uses: and recollect especially
what was observed on the epicycloid, as applied to them. It will easily
be perceived, that to _put_ that form on one of these teeth would be an
almost hopeless attempt!--and, happily, it is not necessary. We can,
however, by using the cutter _r_ with various slopes, and going several
times through each _space_, cut _facets_ on the teeth, quite near enough
to the theoretical form to make them work _well_ together; and, as
before observed, nothing is wanting to make the teeth _perfect_, but to
run them together with the wheels placed in due position.


  OF
  A CENTRIFUGAL DASH-WHEEL,
  _For Bleachers, Dyers, &c._

To form a true estimate of the value of any new machine, it is necessary
to examine the nature and operation of those that have been used before
for similar purposes. And this is the more needful here, because the
present _Dash-wheel_ is essentially good, both in it's properties and
effects. The only room left for improvement, seemed to respect the
_quantity_ of work done by it: and this is, the chief point of
comparison we shall establish in what follows:--

The third figure, in Plate 33, is a sketch of the common Wash or
Dash-wheel. The pieces of calico (or other goods) are put into it
through the round holes, dotted in the figure; and, by the revolution of
the wheel from right to left, are carried up from _a_ to _b_, or nearly
so; from whence they drop by their weight to _about_ the point _c_,
where they meet the angle formed by the circumference of the wheel and
one of the four arms or partitions, by which it is divided. If the wheel
go too fast, the line of falling becomes more like the curve _b d_, and
the goods strike the circumference too high, and in an oblique
direction;--whence the blow is reduced, and the washing becomes
imperfect. If, on the other hand, the wheel move too slowly, the pieces
_slide_ down the ascending partition (_a_) before it comes to the
vertex, and thus only fall from the axis to the lowest point of the
wheel;--whence, also, an inefficient stroke. Thus, do these wheels
require a moderate velocity: and they are reckoned to do their work best
when making from 22 to 24 turns, and giving, of course, four times that
number of strokes per minute.

The produce of these wheels is thus circumscribed by a _natural_ cause
that cannot be altered--namely, by the law of falling bodies; and my
Invention has in view to _elude_ the shackles which confine this
process, and to produce a much greater effect in the same space,--the
same time,--and with the same expence of workmanship.

To this end (see figs. 2 and 4, of the same Plate) I place two, four, or
more boxes _a_, _b_, _c_, _d_, on as many wheels _e f_, toothed on my
Patent principle; the latter, in the present case, being about two feet
in diameter, and the boxes, in length, three quarters of that diameter:
and of _any_ convenient _width_, according to the size of the pieces.
The wheels _e f_ are mounted on the strong shafts _C D_, which run,
below, in the wheel _E_; and by which, also, they are turned round the
common centre, by means of the vertical wheel _F_. Further, in the
centre, and between the wheels _e f_, I place the bevil wheel _i_, of
half the diameter, in which the main shaft runs loosely, and which is
itself fixed to the upper frame work, so as not to turn at all. The
three _Patent_ teeth at _e i f_ shew that these wheels are to geer into
each other on that principle: and it is likewise seen that this whole
mechanism is included in a set of rails, of an octagonal form, for the
purpose of preserving the men from danger, while in the act of charging
and discharging the boxes. And here it is worthy of _some_ remark, that
this process must be _easier_, and more quickly performed, with these
_open_ boxes, than through holes made in the _vertical_ side of a
Dash-wheel, on the usual principle.

To account, now, for the sloping position of the shafts _C D_, and the
consequent slope of the boxes, they are thus placed, in order that the
goods may not drag too much on the bottoms of the boxes, when passing
from one end of them to the other. Instead of this, they are, in fact,
_thrown_, by the centrifugal force, from the inner angle _h_ (fig. 2) to
some point _k_ up that side of the box which is then outwards; where
they strike, and then _fall_ into the contiguous angle under _k_, to be
again projected thence, after one revolution round the common centre;
for, it should here be remembered, that, by the given proportion of the
wheels, the circulating wheels _e f_ turn on their own axes exactly one
half round, for every whole revolution round the common centre _A B_.

To elucidate this still further, I have outlined, at _A_ fig. 1, the
central wheel _i_, of fig. 2, together with _one_ of the excentric
wheels _B_, and the lines _a b_, _a b_, &c., representing the boxes,
are _supposed_ to be wires with the balls _b b_, &c. sliding on them, as
is usual in some experiments on the _Whirling Machine_--(See "FERGUSON'S
LECTURES,") Of these _wires_, I have given the true directions in 12
positions of the wheel _B_: the epicycloid _b b b_, &c., shewing the
steps by which the ball _b_ is brought _toward_ the common centre,
during _three quarters_ of the revolution; and also the position of the
wire on which it slides: where it is evident that the ball _b_ has a
tendency to preserve it's station, at the _first_ end of the wire, until
the latter takes the position _b b c_, when it forms (or nearly) a
tangent to the curve, and is, at the same time, at right angles to the
_radius of motion_, _A b d_. From this moment, then, the ball is free to
leave the centre, and to fly off in a tangent with the velocity with
which the curve itself is generated at that point. We might, thus,
during the rest of it's flight, seek it somewhere in the line _b f g_;
but, as the wire _continues_ to change it's position, and _must_ turn
half round on it's own axis, by the time it arrives at _B b_, or
describes a quarter-circle on the common centre, it will again overtake
the ball--and, giving it a curvilinear direction, will finally carry it
to it's other extremity, at or near the point _B_--where it's motion
first began: and thus shall we give as many strokes to the ball, as
_half turns_ to the wheel _B_; or, in other words, as many _dashes_ to
the cloth, as we give turns to the boxes, round the common centre.

By this process, then, substituted for that of the common Dash-wheel, we
can increase almost indefinitely, the number of passages of the cloth
from one end of the boxes to the other; and the force of the _dash_ will
be as the squares of those numbers; since (as FERGUSON expresses it) "a
double centrifugal force balances a quadruple power of gravity." If,
then, with four boxes we turn this machine 60 times in a minute, we
shall have 240 strokes in that time, instead of about 90 given by a
common Dash-wheel; and this difference might be more than doubled, if so
desired: for should, then, the stroke be found too severe, the boxes
might be shortened, so as to lessen it's violence, though preserving all
it's frequency.

There are _two_ other objects that present enough analogy to this
_Washing_ process, to be here mentioned. The first is the operation of
_Fulling_, as applied to woollen cloths in general. That process, I
fear, is not performed at present in the best manner possible; and I
feel persuaded that the centrifugal motion might be applied to it with
advantage--whether as to quantity of produce, or perfection of effect:
and having thus said, I shall leave the idea to the riper judgment of my
manufacturing readers.

The second object I shall just introduce is, that of _Kneading Dough_,
for bread, by the same centrifugal agency. It is well known, that an
ingenious _baker_, of Paris, invented, some time ago, a method of
_kneading_; which consists in letting the lump of dough fall
successively from the four sides of a square box, revolving on a
horizontal centre. As this idea seems to have succeeded _perfectly_, I
offer the Centrifugal System, as tending to quicken, almost
indefinitely, such a process; and I particularly recommend it to the
attention of Government, and of all _large_ establishments as a mean of
doing well and rapidly, _by power_, what is frequently done slowly and
ineffectually, by the usual methods. _Verbum sat._


  OF
  AN HYDRAULIC LAMP
  _For the Table_.

I call this an Hydraulic Lamp, to distinguish it from the Hydrostatic
Lamps, commonly so named: and I think the distinction proper, because
this Machine acts in a different manner. It's principle will be seen in
a moment, by turning to the 5th figure, of Plate 33. If, there, we pour
oil (or any liquid) into the bent tube _A D G_ at _A_, the first effect
will be to raise it to _C_, in the rising branch _B C_; and from _C_ it
will trickle down the branch _C D_, leaving _the air, there, to occupy
it's own place_. Continuing to pour, slowly, more oil into _A_ the
trickling oil in _C D_ will ultimately fill the rising tube _E D_,
expelling the air before it; and, now, the weight to balance the column
in _A B_ will be _both_ the columns _B C_ and _E D_; whence, of course,
that column will rise as far above _C_ as _C_ is above _B_; that is,
half-way between _C_ and _A_. Here, _there would be_ a small deduction
to be made, if the height _B C_ were considerable; but, as it is only
supposed to be about a foot, the compression of the air in _C D_, &c.,
(being about 1/3 of a foot or 1/90 of an atmosphere) may be neglected.
Continuing, then, to pour oil into _A_, we shall again fill, _not_ the
descending tube _E F_, but the rising tube _F G_; whose column will thus
be to be added to those _B C_ and _E D_; so that now the column _A B_
will rise to _A_, and _there abide_, as long as the mouth _G_ is kept
full, or nearly so.

The above is the principle of the Lamp announced in the title; whose
effect depends, then, on the number of _bends_ made in the tube _A D G_,
which number (whatever be the _form_) it would be well to make rather
greater than smaller, as the height _B C_, &c., might be so much the
less, compared with the whole height of the column _A B_; by which
means, also, a smaller difference in the level of the column _below_,
would _return_ the oil necessary for the consumption of the wick
_above_.

I have given this idea what I think a better form in fig. 6. Instead of
the bent tube _A G_, of fig. 5, _this_ form supposes a series of
_air-tight cups_, embracing each other; one half of them with their
mouths opening _upwards_, and the other half with _theirs_ opening
_downwards_. They are shewn, by a section only, in this fig. 6; where _a
b c_, _c b a_, present the under cups, forming one piece with the outer
surface of the bottom vessel _d a c_, _c a e_: and, while speaking of
this part of the Machine, I would just indicate it's cover _d e f g_ put
on like the lid of a snuff-box, and carrying a case or tube _f g_, the
use of which will be mentioned in a moment. To proceed, then, the upper
vessel is shewn by the edges of it's cups seen immediately over the
_figures_ 1 2 3, 4 5 6, placed between the _letters_ _a b c_, &c.--These
inverted cups make also _one body_ with the moveable cover shewn between
_d_ and _e_, and to which is soldered the tube _h i_--which, sliding in
the case _f g_, keeps this inverted vessel steady. Where note: that
there is an _inner_ tube soldered into the tube _h i_, through which
alone the oil rises, and which can hardly be made too small, since it
has only to supply the consumption of a lamp--namely, a few ounces of
oil in a whole evening. We may, finally, take notice of the weight
placed _under_ _f g_, upon the said inverted vessel, and which helps to
counterpoise the oil in the rising tube _h i_; which tube, as before
observed, may be as many times _higher_ than the distance _a d_ or _e
a_, as there are rising columns between the cups _a b c_ and those 1 2
3, &c.

I am not wholly prepared to say what portion of the oil it might be best
to re-elevate by the pressure of the aforesaid weight _f g_; but, if it
were a considerable part of that contained in the central compartment _c
c_, _that_ column would be shortened in proportion; and the reservoir at
_i_ would, doubtless, feel the want of it to preserve it's level. I
think, therefore, it might be well to use, below, a _cup_ or two more
than sufficient, so as to raise the main column higher than actually
wanted; and to coerce this rising tendency, by a small stop-cock in the
rising branch, to be _gently_ opened at the will of the person using the
lamp. I cannot say I have exhausted this subject; either in these
respects, or as to it's technical capabilities. But I have fully _tried_
this method of raising oil above it's level; and used, for some time, a
lamp made on this principle, and which is still in my possession: and,
at some future time, I intend to bring forward an Hydraulic Machine,
founded on the same principles.


  OF
  A MECHANICAL ESSAY,
  _To derive Power from expanding Metals_.

It is not supposed that this Essay can lead, immediately, to any result
of magnitude; but it is thought to be a subject capable of further
extension, and thus, finally, of future usefulness. Were this process
only sufficient to supply a single house with water, at a small expence,
the labour bestowed on it would not be altogether in vain.

By General Roy's experiments, cast iron (and steel) expanded by 180° of
heat (or, by passing from the freezing to the boiling point of
FAHRENHEIT) 0.013 of an inch per foot.

Supposing, then (Plate 34, fig. 1), the tubes _A B C_ to be 20 feet
long, their whole expansion will be 0.26 hundredths of an inch. But, as
the tubes are placed in the figure, the _half_ tubes _A D B D_ act
together on the sphere _D_, and, both together, drive it in the
direction _E D_, _more_ than as the above expansion, in the proportion
of the line _E D_ to that _A D_. Taking, then, one half only of the
above expansion = 0.13 hundredths of an inch, _that_ must be augmented
in the ratio of the sine of 60 degrees to radius, or in that of _A D_ to
_E D_. I, therefore, multiply this decimal 0.13 by the fraction
1000/866, which gives 1300 to be divided by 866, or very nearly 0.15
for the expansion, in the direction _E D_, occasioned by the two half
bars _A D B D_: and the same is true at the other angles _F_ and _G_.

Again, to find the expansion (and _contraction_) of the bars _a b c_, we
must compute their length as compared with the half tubes
above-mentioned; and that length is to 10 feet (the half tube _A D_ or
_B D_) as 866 is to 1000 = 11.54 nearly: the expansion of which is thus
found:--if 10 feet expand 0.13, what will 11.54?--Answer, 0.15. Now, as
the machine acts by the _heating_ of the pipes _A B C_ simultaneously
with the _cooling_ of the bars _a b c_, we must add the former expansion
to this _contraction_, which gives us 0.30, or _three tenths_ of an inch
for this combined effect at the three angles of the Machine. And,
_supposing_, now, any pair of bars to act directly against each other,
as at _H I K_; and that, further, the bars be stretched until the angle
with the horizon be only 2 degrees, then the vertical motion at _I_ will
be to the horizontal (arising from the expansion aforesaid) as 1000 to
35, the sine of 2; that will be, in round numbers, 28 times as great, or
28 _times three tenths of an inch_ = 8.4 inches, which is the _stroke_
of this Machine in these dimensions.

In this calculation, I have not forgotten that the vertical and
horizontal motions are _nearer alike_, when the bars are not drawn so
tight at _K H_; that is, when the joint _I_ is lowered. But it is
equally true that, when the joint _I_ rises still more, the difference
between these motions is _still greater_; so that, as a medium effect, I
think we may reckon on an _eight-inch stroke_ in the present case.

The question now recurs, of what _strength_ are these strokes? Are they
sufficiently powerful to produce a useful effect with so _short_ a
motion? This I cannot say from experience; but, from the known strength
of iron and steel, their power, in these dimensions, must be _very
great_. A few more observations may occur in the course of the enlarged
description we shall give of the Machine itself.

_A B C_ are three pipes of cast iron, well turned at the end, and having
conical points of iron, well steeled, let into them, so as to have no
tendency to _bend_. _a b c_ are three steel bars, placed in troughs, so
as to be heated or cooled by water poured into the latter. Or, these
troughs _may_ be exchanged for tubes, to admit heated or cooled air,
according to the means used to cause these mutations. In a word,
although I have represented these bars as contained in troughs, I intend
to finish my description, on the supposition that they are _tubes_,
because I intend to suppose the Machine worked by _air_ instead of
water.

To proceed: at _d_ is an opening _under_ the tube _B_, into which air
enters, and _C_ is an opening _on_ the top of the tube which emits the
same air, the three pipes being made to communicate by means of a short
junction-pipe at each of the angles _D_ and _G_. Here, then, the
fire-place _f g_, fig. 2, must be noticed: the use of which is both to
heat and cool the Machine; and the following are the means:--This little
instrument contains fire in it's middle compartment, and that fire draws
_air_ into the part _f_, and drives it out of the part _g_. It also
_turns_ on a centre-pin, seen in the figure. This chaffing-dish, then,
is placed at _i d_, and there serves a double purpose. When it's pipe
_g_ conveys heated air into the pipes _B A C_ (and _out_ at _C_), it
heats those pipes and expands them; but, at the same time, the pipe _f_
of this instrument draws cold air through the three tubes _a b c_, in
which are the steel bars that require to be _contracted_: both which
operations conduce alike to the above-described effect. By these means,
the weight _w_ is raised, and (for example) water sucked into the pump
_X_. But, turning the fire-place half round, we reverse this effect. The
_hot_ air is now drawn, out of the pipes _A B C_, and _cold_ air drawn
through them, by which they are _cooled_; while the hot air, from the
fire, is thrown through the pipe _g_ into the tubes _a b c_, and passing
through the chimneys _k l_, there heat the bars and expand them,--both
which operations concur in _letting down_ the weight _E_, and thus, in
forcing the water of the pump to whatever destination was previously
assigned it.


  OF
  A MACHINE,
  _For Making Laces, Covering Whips, &c._

Many people, in these parts, have seen a certain machine, said to have
been invented by an inmate of that laudable institution the Liverpool
Asylum for Blind People; for the purpose of making laces, covering
whips, &c. I hope the similarity of name will not induce any reader to
suppose that I have had that machine in view, and am endeavouring to
cast it into the shade, or purposely to supersede it. If any person
should thus think, I have a _safe_ reply at hand. My own invention
(somewhat less perfect than it now is) was made, many years ago, on
purpose to serve _an Asylum for the Blind in Paris!_--a reflection with
which I shall, at once, close this, perhaps, unnecessary apology.

This Machine is represented in Plate 34, at figs. 3 and 4. It consists
of a frame of wood or metal _A B_, on which are _mounted_ the following
objects:--1st, on the traverse _B_, a fixed tube, having for it's base
the horizontal plate _a b_, and rising perpendicularly to _near_ _c d_;
where it unites with a conical or trumpet-like vessel _c d_, _f e_; the
left side of which is shewn in perspective, and the right side in a
section only. To this _fixture_ is adjusted the spherical portion _g h_,
_h_, prepared to receive several cuts or slits 1 2 3 for the
bobbin-slides hereafter-mentioned, to slide up and down in. This leads
us to observe the upper fixture _C_, which is a cylinder, terminated
downward by a spherical _dome_ _i k_, _k_; also receiving the several
cuts 4, 5, 6, into which the aforesaid bobbin-slides pass from the
former slits 1, 2, 3, &c. Now it will be seen that the two spherical
parts thus fixed, are separated from each other by the circular and
horizontal slit _l m_, whose use is to permit the _pipes_ shewn in the
section at _n o_, to circulate _all round the machine_, while the
bobbin-slides and bobbins _k p_ are sometimes _above_ and sometimes
_under_ the said slit _l m_.

Now, then, it becomes necessary to speak of the _cause_ of this passage
of the bobbin-slides from the under to the upper parts of the slits 1,
4, 2, 5, and _vice versa_. That cause is in the second dome _q r_, which
covers, as far as it rises, the inner dome _f i_, _k h_; and it consists
in a serpentine canal, of which a section is given to the left of _q_,
and at _s_, _in the section of the principal figure_.

But to make this important piece of the Machine better known, I have
drawn it apart, in figure 4, on the _supposition_--that it is a portion
of _a cone instead of a sphere_: I say a cone drawn with the radii _t
q_, _t r_, according to the dotted line _t r_. The surface then of this
cone, is supposed straightened in the lateral figure; and the aforesaid
serpentine canal is shewn at _a b c d e_, having the rollers of the
bobbin-slides placed in that canal, at the same points _a b c_, &c.
Here also, certain dotted lines _f g_, _h i_, &c. shew the _relative_
positions of the slits 1 4, 2 5, &c. of the principal figure, and also
of the horizontal slit _l m_: whence it appears, that the revolution of
the bent canal, _a b c_, &c. must some times drive the rollers towards
_g i_, &c. and sometimes towards _f h_, &c. while the _pipes_ _n o_ pass
undisturbedly round the Machine, in the horizontal slit _l m_ of both
figures.

The question now arises, _how_ is the circular motion given to the outer
dome _q r_ of the principal figure? that dome is _screwed_ to the cone
_r v w r_, being itself of one piece with the hollow tube _v w_, on
which the wheel _x y_ is fixed. Now, this wheel _x y_, is driven by a
vertical wheel _z_, of _twice_ the diameter, for a reason we shall soon
disclose.

It remains now, principally, to speak of the drawing-system of this
Machine, shewn, in small, at _c_, and of a natural size in fig. 5 of
this Plate. That Machine has also it's own tube _c x´_, working inside
of the fixed tube _a b_, &c. and terminated, at bottom, by the wheel
_x´_, which turns it by means of the second vertical wheel _x´ z_, fixed
on the same axis as the wheel _z_ before-mentioned, and of half it's
diameter.

Supposing then, for the moment, that the mechanism _c_ derives from it's
circular motion, the property of drawing downward the threads from the
pipe _n o_, and the bobbin _p_; (being one of the _twelve pair_
distributed round the Machine) we shall now set the Machine at work, for
the purpose of viewing it's operation a little more narrowly. Looking at
the two kinds of texture, indicated in the figure below the traverse
_B_, we see that on the left composed (in weavers' language) of a
straight _warp_, crossed by an oblique _weft_; and this I believe, is
the common texture of _round, small ware_, as usually woven: the slope
of the weft being less and less as the number of shuttles diminishes,
insomuch that with one shuttle that slope, _might_ become almost
invisible. But in the work made on this Machine, where, virtually, there
are as many shuttles as threads in the chain, the slope would become
very perceptible, too much so, perhaps, to give a desirable appearance
to the work; although the rapidity of execution, from the multitude of
crossings, would compensate for some imperfection of that kind. But, in
fact, this Machine is intended to make a diagonal or diamond texture, as
in the specimen to the right hand: and _that_ is the object of the _two_
pair of wheels _x y_, with _z_; and _x´_ with _x´ z_ before mentioned.
Their effect is this: when the large vertical wheel _z_, has turned the
outer dome and the pins _n o_, once round the common centre, the smaller
vertical wheel _x´ z_, has turned the drawing-system _c_, just one half
as much round that centre, and thus sloped the threads coming from the
fixed slits in which the bobbins move, as much, in one direction, as the
_whole_ turn given to the pins _n o_, has sloped the other half of the
threads in the other direction, and the result has been the aforesaid
diagonal texture.

There are a few other things to be observed by way of closing this
article. As the Lace, or Cord is made on the Machine by a turning
motion, it must be received below into a turning vessel, or it will be
twisted, and thus injured. The vessel _D_, is provided for that purpose;
and is turned by a cord from a pulley on the axis of the wheel _z_,
coming under two vertical pullies, and acting on an horizontal pulley _F
E_, connected with the said vessel; and if preferred, the draught itself
might be placed in, or above, the vessel _D_, but it would not, I think,
produce so perfect an article.

With respect to the drawing Machinery _in_ the Machine at _c_, there is
shewn, a flat surface just under that Machinery. It's purpose is to
serve as a _mover_ for that System: To shew which, in a clearer manner,
is the use of the fifth figure. In this figure, the drawing rollers turn
in a frame _a b b_, and carry on one of their shafts a cog-wheel _c_
_or_ _d_, by which they receive this motion from the pinion _e_; this
pinion being connected with the rowel _f g_, and running with it on a
stud _h_, more or less removed from the centre, as circumstances may
require. This rowel then, (for it's edge, formed as in the figure, is
_indented_ with sharp teeth across it's face) runs on the _flat surface_
before indicated, at or near _e_, (fig. 3) and by the rotatory motion
received from the wheel _x´_, gives a drawing motion to the rollers, the
use of which has already been explained; namely, to draw down the
_goods_ as they are formed. It need hardly be observed further, that
_any kind of filling_ may be brought down twisted from _C_, to the
entrance of these rollers at _c_, and thus be included in the plaited
texture; and in fact, the rollers in fig. 5, are shewn (by the dotted
lines) as formed to receive an object of considerable diameter, as a
whip, &c. that it may be wished to cover. Where I remark, that this
lozenge form of the grooves _O_, is not given without a motive: the
grooves are thus formed (the cylinders being supposed capable of opening
by a springy movement) in order that, if desired, they may draw the body
downward, so much the faster, as it's diameter increases--and thus keep
the covering threads at the same angle in every case. I shall only add,
that these movements can be permanently determined by wheels, when the
rowel _f g_, acting on the horizontal surface _c_, has fixed the real
velocities of draught required for a given purpose.

This Machine then, is capable of excellent results, and of a speed
almost inconceivable: since at every turn, if there are _twelve_ bobbins
_p_, and twelve pipes _n o_, it makes twenty-four passages of the
threads among each other, answering, in some cases, to an _inch_ in
length of the fabricated texture; so that, counting 120 turns per
minute, (which is moderate) we have 2880 passages, and 120 inches of
work in a minute; equal to 200 yards per hour--a quantity which does not
yet limit the produce of this Machine.


  OF
  A BATTING MACHINE,
  _For Cotton, or_ FINE _Filaments in general_.

This Machine is represented in figs. 1 2 3 of Plate 35. It is composed
of a frame _A B_, on which are placed two sets of rollers _a b_, _c d_,
round which is stretched an endless feeding cloth, on the upper surface
of which the Cotton is laid by the attendant. Across this frame _A B_,
is fixed a strong board _C D_, having a ledge or _bridge_ at each end,
over which are tightened the cat-gut strings 1 2, 3 4, &c. Moreover,
across this board, is fixed on proper bearings, (placed either straight
or diagonally) the axis _e f_, furnished with any proper number of _iron
fingers_ 7 8, &c. which _spring_ the cords 1 2, 3 4, &c. every time they
pass by them: where it may be observed, that by the varied _forms_ of
the ends of those fingers, the vibrations are made to be vertical,
horizontal, or oblique, at pleasure. In fig. 2, these fingers are seen
from one end of their axis _e f_--and in figs. 1 and 3, they are shewn
sideways: and in the latter figure, the strings are shewn as small
circles between _e_ and _f_, with the feeding cloth _a c_, stretched
under them.

The following then, describes the effect of this Machine: The Cotton
being laid on this feeding cloth near _B_, is gently drawn under the
vibrating cords at _g h_: for while _this_ takes place by the action of
the handle at _e_, the pulley _f_ by the cord _i_, gives a slow motion
to the cylinder _B_, and by it to the feeding cloth _B A g h_. The
Cotton then passes under the strings toward _B A_, and is greatly
agitated in the passage; and when arrived at _A_, it falls into any
proper receptacle--whence it is taken to undergo the succeeding
operations of the factory. I would just mention, finally, that the axis
_e f_, though here supposed to be turned by the handle _e_, would, _of
course_, receive it's motion from a proper _power_; set on, or stopped
by the usual methods.


  OF
  A HORIZONTAL WIND MACHINE,
  _For raising Water in large quantities_.

This Invention has for it's object, to make a more abundant use of the
wind's agency, _at a given expence_, than is usually done: and the
means, generally, are to avoid a part of the expence lavished on the
foundations or fixtures of wind-mills, and _yet_ to carry _more sail_
than that system admits of. Machines of this nature, are chiefly used in
low marshy countries, where there is much water to be raised, and little
solid ground to build on. My idea here, is to found the whole on the
water, and to make that element the medium, and as it were the _centre_
of every motion.

Let us then suppose already constructed, the _long_ and narrow boat _A
B_, figs. 4 and 5 of Plate 35:--and that there is contained in the
middle of it's width, a cylindrical _pipe_ of iron, (or a square wooden
box) of equal length, serving as a pump, by means of a spherical or
square piston _a_ or _b_, drawn from end to end by the means soon to be
described. The cost of such a pump-barrel would not be _great_, though
it should be of considerable length--(even 300 feet would not cost so
many pounds). Now, at each end of this vessel _A B_, there would be
raised a vertical part of equal size _C D_, surmounted by a caster, (_E
F_) turning, horizontally, on a hollow centre, _through_ which a rope
would pass from the aforesaid piston, (_a_ or _b_) to the boat or ship
_S_, which is the _primum mobile_ of the System. This boat would further
be made to carry as much sail as possible, and to encounter as little
resistance as possible from the water. It's properties of carrying sail,
might even be enlarged, by the use of one or more _out-riggers_, as is
done in various eastern countries.

It would be proper, likewise, to give the vessel a rudder at each end,
and to reverse her motion by changing the sails, _without tacking_. This
is also represented in the two figures 4 and 5: and, in the present
case, the vessel is rigged with three masts, and three large sails
nearly square, yet somewhat _deeper_ on the lee side than to windward,
to make the sails the more governable, though as large as possible.
Supposing now, all these things arranged, and the rope _N O_ fastened to
or near the middle of the vessel, and to the aforesaid piston over the
pullies of the casters _E F_; _then_, if the vessel sails in the _long
ellipsis_ 1, 2, 3, 4, the _sum_ of the two portions of rope _N, O_, will
be always the same; and, the wind coming from _a_, in the direction of
the arrow, she will sail advantageously from 1 to 4, or the contrary,
carrying the piston from end to end of the pump; and thus exhausting it
at every passage; and filling it again from the _lower_ water.

To recapitulate--and bring the several parts again to view; _S_, in
both figures, is the vessel, supposed of the best form for carrying
_much_ sail: _E F_ are two casters with their pullies; _p q_ are two
pullies at the bottom of the vertical barrels _C D_, _under_ which the
rope passes to the piston at _a_ or _b_, &c. In fine, _q r s_ are the
three sails, and _t v_ the two rudders, by which the vessel is steered
in either direction, so as to keep it's wind without causing _too much
stress_ on the rope _N O_. This consideration involves another, which
must now be cleared up: namely, _how_ can this mechanism be made to
produce the same effect in every direction of the wind? I answer, the
whole System must be _moored_ at one end _A_, in the strongest manner;
while the opposite extremity _B_, shall have liberty to veer round that
point, as a centre, through 90 degrees of a circle; _some one position_,
between which extremes, will suit every wind, _on this condition_, that
the vessel by it's rudders, keel, &c. be able to keep her ground,
although the wind should come from the _convex_ side of the ellipsis; a
thing by no means impossible, though less desirable than the state first
represented.

Thus it appears, that I expect the favourable result of this System from
two sources: the first, (but _least_) from the length of this pump,
which permits much water to be raised without much agitation; and
second, from the _quantity of sail_ it is possible to carry by this
method, compared with the sails of a wind-mill. My idea is, indeed, that
since the power of the wind is so boundless, we ought to use it more
liberally than we do: and I am persuaded, that _ten times_ as much work
might be done _at a given expense_, by such means as these, as can be
done by the usual methods.

Before I quit this subject, I would just observe, that there are _many_
situations in which this powerful agent might be made useful, in
conjunction with water power, as applied, perhaps, to encreasing works,
and being itself incapable of proportionate extension. Thus, there are
_many_ water mills (used for various purposes) that are obliged to
_wait_ the re-filling of the mill pond; and which, therefore, lose much
time, although the _wheel_ would be capable of doing even more work than
is actually wanted. In fact, it _often_ happens, that the worse the
supply of water, the better is the wheel: for _this_ has been sometimes
thought a mean of making up the deficiency. In such a case then, a cheap
wind apparatus might double or triple the effect of the wheel, and the
produce of a given establishment. But it will be objected, that the wind
is an uncertain helper! and thus less fit to be resorted to. This I
acknowledge; but still say, that could it be used when only a _breeze or
a zephyr_, it's utility would be much extended; and _this_ is another
consequence of a system founded on the application of _much sail_ to a
given purpose. Still however, as nothing absolutely conclusive can be
said on so _variable_ a subject, I shall not now lengthen this
discussion.


  OF
  A FLAX-BREAKING MACHINE.

It is important, in _most_ machines, to avoid oscillatory
motions:--which uniformly protract _the time_ of an operation, or
require a greater _power_ to perform it. This consideration has given
rise to the form and properties of the Machine I am about to describe.

In Plate 36, figs. 1, 2 and 3, represent this production. The first is
an elevation; and the second is a plan, serving to shew the manner of
_feeding_ the Machine. To speak first of the second figure--_A B_ is a
pulley, (shewn at large in fig. 1, and marked with the same letters;)
it's use is to receive the endless cord _C D E_, which is composed of
three strands, like the apparatus of a peruke-maker; these strands being
divided at _F_, and passing there over three pullies placed at a proper
distance on the same shaft _F_. These pullies are gently turned by that
shaft, and carry with them the afore-mentioned triple cord, _to_ which,
in the passage _toward_ the Machine, have been _woven_ small handfuls of
flax, by the same process as the barber uses to fasten the hair of a
wig; one difference however obtains: the flax is knit to the cords at
it's _small_ end, and within a few inches of it, so that the root-ends
hang pendent, and when that part of the cord enters beyond the pulley
_E_, those ends hang round the large pulley _A B_, against the grooved
surface of the outer rim: The method of grooving this drum is better
shewn in fig. 3: and it should be noted, that the smaller drums _C D_,
are grooved in a similar form, their diameters being such as to divide
exactly, in _some_ ratio, the outer cylinder _E F_. In fig. 1, two
_portions_ of these handfulls of flax are represented by the waved lines
_m n_, drawn between the cylinders _C D_, and the section _E F_ of the
said outer cylinder; where it is evident, that if these cylinders had,
in that place, teeth like those of fig. 3, these handfulls of flax would
appear _bent_--which is indeed the process by which the wood is broken,
and the filament divested of it. It appears also by the figure 1, that
the cylinders _C D_, run on centres, fastened _only_ to the pins of the
cross piece _o p_, (shewn by dotted lines in fig. 2.) These cylinders I
say, are thus mounted, that there may be _no centres below_, to gather
up the flax or wood, and thus embarrass the motion of the Machine.

Adverting then, a second time, to the second figure, the flax is
fastened in small handfulls, to that part of the endless cord that goes
_toward_ the Machine; namely, _F E_, and taken off from that part which
_comes from_ the Machine behind the pulley _A B_: so that the triple
cord before mentioned, there consists of _three cords_, and passes round
the separate pullies at _F_. The flax being thus taken off at _M_, is
handed to the charger at _N_, and _re-fixed_ to that cord by it's other
end--so as to be finished by a second passage. It would be superfluous
to add, that the waved form of the grooves in the cylinders, is intended
to break the flax at _every_ point of it's passage before those grooves
as conducted by the large pulley _A B_, (in the centre of which the main
shaft _turns_ without giving _it_ any of it's own motion) the said
pulley _A B_, being turned, as before stated, by the triple cord from
the _slow_ motion of the pullies _F_ in the figure.


  OF
  A BOWKING MACHINE,
  _To accelerate and equalize that process_.

Having heard it observed by some Calico Printers, that there is more or
less of _inequality_ in this process as usually performed; and that some
parts of the goods are exposed to be more acted on than the _inner_
parts, I have thought the following Machine would be useful, both to
equalize and accelerate that operation.

In figs. 4 and 5 of Plate 36, _A B_ is a hollow cylinder, running on two
gudgeons _C D_, with a very slow motion, and thus, requiring _very
little power_. One of these gudgeons _C_, is hollow, for the purpose of
receiving steam from a boiler, like those at present used. The cylinder
_A B_, is double, both around it's circumference, and at it's ends, (see
_a b_, _c d_, figs. 4 and 5). It is also furnished with one or more
doors _E_, through which to introduce the goods; and which doors are
afterwards closed with screws, like those mentioned in the article
"Washing Machine," of the third Part. The goods being put in, with the
usual doses of alkaline liquor, &c. the steam is introduced through the
gudgeon into the interstice _a b_, and thence through proper openings
into the body of the wheel, and between the cylindrical partitions _a
b_, _c d_, &c. By the steam, the water acquires a boiling heat; and by
the motion of the wheel, is carried up in the boxes _a b_, &c. to the
top, whence it falls through proper holes upon the goods; thus keeping
them _wet_, and steaming them at the same time. The figures shew the
division of the liquor into several jets 1, 2, 3, &c. which are
constantly falling on the goods, as the process requires. The 4th.
figure shews further, the effect of the turning motion of the cylinder
_A B_; namely, that of changing the position of the articles; and
offering, successively, every part thereof to the steam and flowing
liquid: and thus, I presume, must the Bowking process become more rapid
and equal, than that which takes place in a Bowking-keer, unaccompanied
with such a motion.


  OF
  A PRINTING MACHINE,
  _For two Colours_.

This Machine occupies a great part of Plate 37. It is represented in
figs. 1 and 2; the first being an inside view of one of the cheeks; and
the second, a view endwise--represented as broken in the middle, to gain
space in the Plate. As far as possible, both the parts are marked with
the same letters.

To begin with fig. 1, _A B C_ is the cheek: being a kind of shallow
_box_ with edges to strengthen it and give it thickness for the _steps_
_a b_, &c. These steps are strongly fixed to the screws that slide in
the boxes _A B_, and the nuts of which, are seen at _c d_. The screws
enter, besides, into the heads of the perpendicular levers _D F_, _E G_,
against which these nuts press to _set_ the cylinders, by their steps _a
b_, against the _bowl_ _H_. This pressure of those cylinders _a b_ is a
_modified_ effect: for the levers _D F_, _E G_, are drawn inward by the
pulling bars _I K_; which, meeting in the centre of the Machine, are
pressed downward by the hanging bar _L_, to which are suspended the
scales and weights _M_, these being more or less heavy according to the
wish of the _Printer_. It were well to mention a circumstance of some
importance connected with this subject:--If the bars _I K_ form
together an angle _very_ obtuse, the power of pressure is immense; and
the weights at _M_ might be the lighter: But, then, the _degrees_ of
pressure at different angles of the bars _I K_ would vary too much, if
any excentricity of the cylinders _a b_, occasioned any motion. It is
therefore best to use a sensible angle between the bars _I K_, together
with a weight at _M_, so much the heavier; by which means these motions
will be the more mild and manageable. Proceeding with the description:
_e f_ are two hooked screws, by which the pulling bars _I K_ are raised,
when necessary, so as to increase the _nip_ in any corner of the
Machine, without affecting the rest. It should be observed also, that
the steps _a b_, have dove-tailed slides screwed to them from under the
rim, and in it's thickness, to make them move more correctly, when
pressed horizontally by the nuts _c d_. The upper works of this Printing
Machine are not greatly different from those of the common one. In one
respect, however, I think them superior. The roller, prepared for the
returning blanket, is mounted in a frame _g_, (fig. 2) which moves on a
pin in the centre of the Machine, insomuch that _one_ screw and nut _h_,
suffices to regulate this return. This then, is an improvement, as the
printer has but one operation to perform instead of two. The use of the
piece-roller is the same as usual; and the goods are carried down on
stretching bars, &c. exactly in the same manner.

But a more important property of this Machine remains to be noticed, The
two cylinders _a b_, are made to press diametrically across the centre
of the bowl _H_; so that it's shaft suffers no friction from that
pressure. And hence, this _two_-coloured Machine requires no more power
to work it, than a common machine for _one_ colour.

A further property of this Machine deserves attention; but for want of
room on the Plate, we are obliged to describe it by means of _dotted_
lines on the face of the present figure. At _a b_, and at _H_, we have
dotted _three_ toothed wheels, of which one is keyed on each of the
mandrels, while the central one is placed in a frame, forming part of _a
slide_ _N_, (fixed on the plate _N_ of fig. 2) and by which this wheel
is moved up and down at pleasure. Here it is evident, (see again fig. 1)
that if this central wheel rises, it will turn the mandrel _a_,
backward; and the mandrel _b_, forward: and this is a peremptory method
of increasing or lessening the distance between any two points on the
cylinders; or in other words, of fitting the colours of one cylinder
into those of the other--an operation which is thus performed by a
single movement; while in other machines it is necessary to go on both
sides of the machine to produce the same effect. In a word, this process
is completed in a few moments, by turning backward or forward a _nut_
like that _h_, applied to the screw placed against the side of the
Machine, as at _P Q_.

But we have another important property to speak of. The colours on the
two cylinders must be _fitted in_, laterally, as well as
longitudinally: and the Machine performs this by an easy method. At each
side of the Machine (see figs. 1 and 2) is fixed on a centre _i_, a
short lever _k l_, the bent end of which (_l_) rises just to the brass
step which carries the mandrel of the cylinder _a_, and is formed so as
to push that step _inward_, when it's end _k_ is pressed _outward_;
which latter motion is occasioned by the screw _m n_, which goes all
across the Machine, and performs the same office on either side as
wanted. This then, is another economy of time and pains; this setting
being usually done by passing round the Machine, from one side to the
other.

Finally, _R S_ shews one of the cross-bars by which the two cheeks are
connected. They are formed as portions of a hollow cylinder, and screwed
to the cheeks through flanches, the breadth and form of which give
considerable strength to the Machine; which is further strengthened by
the bars _T V_ and _W X_, in it's upper parts.

In the above description of this Machine, (in which the parts common to
other machines are omitted) I have endeavoured to avoid all invidious
comparison: and have only said what my additions appear to warrant, and
what, I am persuaded they will justify, when this Machine shall be
compared with others, placed in the same circumstances _for the sake of
liberal comparison_.


  OF
  A MACHINE
  _For clearing turbid Liquors_.

I confess, I again stand on a kind of forbidden ground; and am uncertain
to what _degree_ this Invention will justify it's title. Yet I think
myself safe in expecting it will produce an useful effect. But the fact
is, I never _fully_ proved it: the apparatus with which, more than
twenty years ago, I was trying the System, having broken in the
experiment--which I then had no opportunity of resuming.

I had then, as formerly, asked myself a question, viz: "will not the
centrifugal force of a _heavier_ body, suspended (without chemical
action) in a _lighter_ fluid, increase the subsiding tendency, and
_quicken the clearing process_?". I then thought "yes," and do not yet
see why it should not. But not having any absolute _fact_ to build my
conclusions on, I must leave the whole matter to time and experience;
and crave the candour of my readers in favour of my somewhat bold
assumption.

This Machine then, which _is to_ purify muddy liquors by motion, is thus
composed: a perpendicular axis _A_, (Plate 37, figs. 3 and 4) turns very
swiftly, surmounted by a conical cap _B C_, so formed, as to receive and
_lodge_ in it's thickness, four or more vessels _a b_, _f e_, which hang
on pins _c d_, near that centre and have the liberty of leaving it by
the centrifugal force, round the said pins, until lost in the thickness
of the cap above mentioned; where they turn on the common centre,
without suffering any resistance from the surrounding atmosphere. This
conical cap _B C_, &c. is made as light as possible, by protuberant
ledges, but it's solid _form_ would be restored by lighter substances
fixed between the arms, so as to add _little_ to the friction or
resistance of the whole mass. Any turbid liquor then, being introduced
into any pair of these vessels while in the position _g h_, fig. 3, and
put into swift motion, will have it's muddy particles thrown from the
centre, and (I presume) soon deposited at the greatest possible distance
from that centre: since, although the centrifugal force will add, in the
same degree, to the tendency outwards of the particles of the _liquid_,
and make them _gravitate_ more towards the circumference; _that_ force
will _not_ render the liquid less _fluid_--which, therefore, will suffer
the _clearing_ process to take place _sooner with motion than without
it_; and this is all I dare advance in the present state of my knowledge
on this subject. Thus have I again reckoned on the kind forbearance of
my readers, and risqued a little more of "the bubble reputation."

My readers will supply one remark I had omitted--which is, that if
bodies heavier than the fluid, recede faster from the centre _by_ this
motion, than without it, _lighter_ bodies will approach toward the
centre, and be there collected for the same reason--another cause for
which, will doubtless be the pressure occasioned by this centrifugal
force in the revolving fluid.


  OF
  OPEN CANALS,
  _As Hydraulic Machines_.

I have said, and shall still say, much on the desirableness of making
use of a greater portion of that gigantic agent--WIND, than has yet been
customary. This article is another attempt to urge it's propriety. But
it will be of no use to those who cannot extend their views beyond the
present state of things, to that possible state which every successive
mechanical improvement appears to anticipate or promise. These
speculations of mine, suppose extensive means and extensive necessities:
and they promise results still more extensive. In a neighbouring
kingdom, where the country is, as it were, redeemed yearly from the
ocean's grasp, what would not it's inhabitants give for a security
against the encroaching tide? or the means of saving several months to
agriculture, by the speedy disembarrassment of it's fields from the
common destroyer of health and produce? It is even said, that in the
last winter, some _dykes_ in Holland were broken, and many lives lost by
inundation: and in our own country there is many a submerged spot, over
which there blows wind enough to drink up, or throw out, it's last
particle. I submit then, the present means, as capable, with proper
modifications, of forwarding every analogous purpose; and thus as
worthy to occupy the attention of every friend to rational improvement.

If my 38th. Plate were considered as a _corner_ of any inundated
country, whose boundary were a dyke contiguous to this chosen spot, I
would propose building a long curvilinear canal _A B_, of which the
middle space should receive and contain the lower water; and the two
outside spaces the upper: especially the outer circle, which should
communicate with a few branches _C D_, leading to and through the dyke
before mentioned. In the two outside canals should float a pair of boats
(long and light) _E F_, joined together by one or more cross-beams _G_,
which would produce the double effect of connecting the boats so as to
make them _bear much sail, without oversetting_; and of carrying along
in the middle or lower canal a kind of _water-drag_ _H_, that should
take with it the under water, and raise it's level nearly to that of the
upper canals--into one of which it would enter through it's lateral
valves, and thence flow into the eduction canals _C D_ as before stated.
My idea will be better understood by referring to the small figs. 2 and
3, at the bottom of the Plate: for they are, _one_, the transverse
section of the canals with the boats, and the other a longitudinal view
of one of the vessels in it's canal, with the water-drag _H_ in the act
of making (what is technically called) a _boar_, of the lower water; and
raising it above the level of the valves _I K_, which open into the
canal.

To recapitulate, _E F_ in fig. 2, are the two vessels seen sternwise,
with their sails _supposed_ very large: _G_ the beam that connects them;
_H_ the water-drag; and _O_ one of several valves which open _from_ the
lower water, and close when the drag is going over them. In fig. 3, _H_
is the same water-drag, whose distance from the bottom is regulated by
the brace _b_: it's beam or shaft, being fixed to the crossbeam _G_, of
figs. 1, 2, and 3.

Thus then, at _one_ passage of this double vessel along the curved canal
_A B_, all the water in it's middle compartment will be raised into it's
outer one: and be thrown into _the sea_ through the canals _C D_, &c. It
appears, near _E F_ in this fig. 1, that the vessels _E F_, have
friction pullies or wheels placed horizontally on their decks, to act
against the sides of the canal and prevent the lee-way: thus converting
the whole effort of the wind to a useful purpose. And here I observe,
that if the wind blows in, or nearly in the direction of the diagonal,
then, the vessel would go almost from one end to the other of the main
canal without tacking, and thus do an abundance of _work_ at each
return: for it is a common thing for ships to sail nine or ten knots an
hour! And here note, that the present curvilinear form is given to the
canal in order to take all winds, (tacking more or less often) whether
coming from the inside of the curve or from the outside. I cannot but
add that in this Machine--in that I have already given--or in those I
may yet give, there is much to be found that promises useful
application in many an important position. An example now strikes me.
The reservoir at the Manchester Water Works might furnish room for a
floating Machine, capable, on windy days, to do all the work of the
steam engine, and thus economize a good portion of the fuel it
consumes.


  OF
  A PORTABLE ENGINE,
  _For extinguishing Fires_.

This Machine (see Plate 38, fig. 4) is intended to be carried or
conveyed in a small cart, to the place where an incipient _fire_ may be
preluding to it's fearful horrors! It is, as to form, a common lifting
pump, inclosed in a vessel of air, whose spring perpetuates the _jet_ in
the usual manner. When used, it is held on two men's shoulders, by means
of a bar going through the ring _A_. Further, a rope is fastened to each
of the extreme rings _B C_: and a stick put through each of the second
rings _b c_. Two rows of men are then marshalled along the ropes; one
set to _hold-on_, and the other to pull in regular time, the piston _c_
along it's pump, thereby sucking water through the pipe _D_, and forcing
it through the valve _v_ into the air vessel: from which it is forcibly
expelled through the directing pipe _E F_. Here it is clear, that this
small Machine is capable of an effect almost indefinite: since the rows
of men may be very numerous; there being always people enough at a fire.
To work the Engine by pulling, is nothing more than to repeat many a
nautical man[oe]uvre: and if only one man in the company should have
learn't to _sing the sailors' song_, they would soon produce--"a long
pull, a strong pull, and a pull altogether." To be serious, a hundred
men may as well work at this Machine, as ten; and the effect will keep
pace with the cause. In a word, there is scarcely any limit to the
abundance of water, that might be thrown on a fire by such an Engine as
this; of which I shall say nothing more, save that the bar of the piston
rod at _c_, is intended to be used for drawing it inward, by the efforts
of two men, at each interval in the effort of the working-men. A mere
inspection of fig. 4 will fully shew what here remains unsaid.


  OF
  A WIND MILL,
  _With double Power_.

This Mill produces a double power, merely because it uses two pair of
_sweeps_ or sails, both of which (though turning opposite ways) concur
in giving the same motion to the vertical shaft of the mill. _A B_ fig.
5, (Plate 38) is the shaft in question. It has on it two bevil wheels or
pinions _o_, _b_; bearing the same proportion to their respective
wheels: one of which (_o_) works in the wheel _C_, fixed to the _outer_
shaft _a c_, and the other (_b_) in the second wheel _D_, which takes
it's motion from the inner shaft _E D_. This latter, then, is turned by
the front sweeps _F G_; which revolve, as usual, "_against the sun_,"
while the other sweeps _H I_, are braced round the large shaft _a c_,
and turn _with the sun_--being sloped and _clothed_ for that purpose.
Now, lest any doubt should arise, whether these two sets of sails would
not injure each other's motion--I would remark, that one principal
effect of the front sail _on the wind_ would only be to turn it aside,
and _thus_ make it the _more fit_ to turn the other sails, which
_require_ to go the other way; and which, therefore, will rather be
favoured than otherwise, by the aforesaid effect on the direction of the
airy current. It may be useful to observe, that the two sets of arms can
be put, circularly, into any given position, by means of the wheels _C
D_, and will _retain_ that position if the proportions of the wheels to
the pinions _o b_, are the same for each pair--a result which it is easy
to insure.

I shall dwell no longer on this subject, convinced as I am that nobody
will question the propriety of enlarging the scope of these operations.
It is a subject I especially recommend to our Batavian neighbours--the
more, as, without presuming to dictate on a subject they may think I
have not experience enough to judge of--I have only a hint to give to
their _Moolen Maakers_, to insure their attention to a subject so
intimately connected with the welfare of their never-forgotten
_Vaderland_.


  OF
  A WATCH ENGINE,
  _To extinguish incipient Fires_.

It is well known, that many ruinous _fires_ have originated so _slowly_,
that they might have been put out in a minute, had a _little_ water been
at hand--especially with the power of _throwing_ it to a short distance.
This fact makes it more desirable than it would at first appear, to have
small vessels full of water, furnished, in themselves, with the power of
forming _a jet_, without a moment's delay! and this is the purpose of
the _Watch Engine_, represented in fig. 6 of Plate 39.

In that figure, _A B_ is a cylindrical vessel, with spherical ends, made
strong enough to bear (without danger) a pressure of several
atmospheres: and into which is introduced, by a _condenser_, (which
might be the very system _C p r_) a quantity of water sufficient to
occasion the aforesaid pressure. The valve _C_ being water-tight,
retains entirely this water; and the Machine is placed on it's three
feet, in a corner of the apartment it is wished to secure. It is seen in
the figure, that the valve-pipe _C p_, opens into the ejection pipe _p
q_, while the valve stem _p_ passes through a collar of leather, and
comes in contact with the lever _p R_ while in it's present position.
If, now, any part of the house or apartment should be found to be on
fire, this Instrument can be carried there instantaneously, by the pipe
_p q_, _as a handle_; and the jet be levelled at the point desired:
when, by taking the lever _p R_ in his hand, _with_ the pipe _p q_, the
bearer will open the valve _C_, and thus have an immediate supply of
water, in a state of impulse sufficient to quell a fire that might else
have become so violent as to mock every attempt to extinguish it! This,
then, is the object of the present simple tribute to public safety.


  OF
  A MACHINE
  _For Engraving the Cylinders of Calico Printers by_ POWER.

The principle of this Machine is as follows: When two equal toothed
wheels _a b_ (see Plate 39, fig. 1,) geer together, a given tooth of
either wheel _visits_ a given tooth of the other, once every revolution:
and will continue to do so as long as the wheels continue to revolve.
But, when the wheels are _unequal_, as _A B_ fig. 2, then _different_
teeth in one wheel, visit the same tooth in the other, until, after a
certain number of turns, the revolutions of both wheels have a common
divisor. My System of equable Geering (see Part 2d. of this Work,)
justified me in applying this principle to Engraving; and is the chief
foundation of the Machine now to be described: for this System, as we
have seen, communicates the very same kind of motion that two touching
cylindrical surfaces would impart to each other by mere contact. The
punch, therefore, will not _scrape_ the cylinder, when brought into the
desired places of contact by the aforesaid process. Let us suppose then,
(fig. 2) that the wheels _A B_, are to each other in diameter and teeth,
as the numbers 2 to 3; and that a given tooth in the wheel _A_, (which
we have pointed out by a dot) now touches a certain spot on the wheel
_B_, marked by a dot like the former. When, now, this spot on the wheel
_B_ has made _one_ revolution, the wheel _A_ will have made 3/2, or
1-1/2 revolution: and the tooth first mentioned, will be found
diametrically opposite to the place where it touched the spot first
adverted to. And if, further, we give the wheel _B_ another turn, the
wheel _A_ will again have made 1-1/2 turn; and the tooth first mentioned
will again visit the spot with which it coincided at the beginning.

  To recapitulate--The 1st. turn of _B_ gave 1.5 turns of _A_, and
                   The 2d.  turn of _B_ gave 1.5 turns of _A_:
                                             ---
                   Sum. 2  turns of _B_ &    3.0 turns of _A_:--

which numbers are thus in the inverse ratio of the number of teeth in
the wheels respectively.

Referring again to fig. 3, there we see a cylinder to be engraven, (_M_)
and a _porte-outil_ (or tool-bearer) _N_, connected by the wheels _A B_;
whose teeth are singly inclined, like those that were considered in Part
2d. It can hardly ever occur, that the circumference of a cylinder can
require to be divided into two parts only: but most often into a greater
number, as 9, 11, &c. and it so happens, (from these initial diameters 2
and 3) that we must take _uneven_ numbers for our basis, in order to
reduce the System to any thing like regularity. And, this admitted, the
theory of this division will be as follows:

Let the chosen (uneven) number of figures required round the cylinder be
called _m_: then must the number of teeth in the small wheel _A_, be
likewise _m_: when the number in the wheel _B_, will come out uniformly
_m_ + (_m_ ± 1)/2; in which formula every case of practice is included.
For suppose, any uneven number to be required, say 11: Then will the
cylinder-wheel _A_, have 11 teeth; and that of the _porte-outil_ (_B_)
11 + 12/2 = 17, or 11 + 10/2 = 16: either of which numbers, working with
the 11 teeth of the cylinder-wheel _A_, will divide the latter into 11
parts, as was before stated.

It must, however, be observed, that, as expressing a set of teeth
actually working, these numbers are fictitious; because the teeth would
be too coarse to work well. The numbers thus found, must, therefore, be
multiplied by 2, 3, or more, so as to bring the teeth to a _reasonable_
size, say 1/8 of an inch thick, according to circumstances.

As another example, take the following: suppose it were required to
engrave a cylinder of 4 inches diameter--or 12.56 in circumference, and
to put twenty-five figures round it, giving very nearly half an inch for
each figure. Then the cylinder wheel (_A_) must have 25 teeth; and the
porte-outil wheel 25 + 26/2 = 38: or, doubling both numbers to give the
teeth a proper strength, the cylinder-wheel would have 50 teeth, and the
porte-outil wheel 76.

To proceed now, in stating the principles of this Machine, it is evident
(in this System of geering) that the diameters of the wheels must be in
exact proportion with the number of their teeth, _taken at the pitch
lines_; and that these pitch lines must be of the same diameters,
respectively, as the cylinder to be engraven, and the porte-outil taken
at the surface of the punch: which is saying, in other words, that the
length of the punch must be regulated _after_ the diameter of the
porte-outil wheel has been determined from it's number of teeth,
compared with those of the cylinder-wheel. But we shall return to this
topic after having described more fully the principal parts of the
Machine.

In fig. 5, (which is a kind of transparent view of one end of the
Machine), _A B C_ is one of the stands or legs on which it rests; _a b_
is a section of the frame or bench, which supports the _headstock_ _C
D_, one of which is bolted down at each end of the frame, (see also _C
D_ in fig. 3.) This figure shews the transverse form of the headstock,
with the centre (_c_) of the porte-outil; and _e d_ are the _two_ wedges
that go through the headstock to support the step of the cylinder, of
which the mandrel appears at _f_. This mandrel-centre is also covered
with a second step, over _f_, by which it is kept down by means of a
regulating screw _A_, (fig. 3) which finally determines the degree of
nearness of the cylinder to the porte-outil, and thus the depth of the
engraving:--that is to say, this regulating screw influences this depth
as far as the wedges (_e d_) permit: for by the screw _d_, these wedges
slide on each other so as to raise or let fall the steps _f_, by small
degrees; the position thus given being _confirmed_ by the said
regulating screw. It is needless to say that this operation takes place
at both ends of the Machine, (_C_ and _D_) and thus places the surface
of the cylinder in a line exactly parallel to the slide _n q_ of the
porte-outil.

In fig. 3, all the parts thus adverted to, are given in a front
view--where we may observe, that the rope marked by dots at _R_, is a
loaded friction-drag, used to prevent the porte-outil from
_over-running_ the cylinder, when the punch is just emerging from
between them.

The same figure 3, shews also the position of the frog _x_, in the
triangular slide of the porte-outil; the latter, as well as the
cylinder, borne by the headstocks _C D_. Moreover, the rack _w_, which
gives the end-motion to the punch, is here shewn, as going through the
frog, and connected with it in one direction by the catch _o_: and at
_n_, there is a spring, formed like a horse-shoe, the use of which is to
push the frog, by the catch _o_, _to the right_, whenever the rack is
_suffered_ to go that way, by the mechanism hereafter to be described.

The _frog_, then, (so called because it seems to leap when the Machine
works) must now be adverted to: it consists of an under mass, formed
prismatically to fit exactly the slide _n q_, cut out of the porte-outil
_N_. This mass is capped by a thickness of steel, which completes the
passage for the rack _n w_, and offers, besides, a compartment for the
punch-clams _o_, and another (_x_) for a wooden or steel _bridge_,
being a portion of a cylinder, so formed, as to support the engraved
cylinder after the stress of the impression is passed, and thus to
equalize the depth of the engraving. The compartment for the punch-clams
at _o_, is terminated to the right hand by an obtuse angle near _x_,
which serves as a centre, when, by proper fixing screws in the rim near
_o_, it is found necessary to place the punch a little awry. The other
properties of this _frog_ will easily be supposed by my mechanical
readers.

We come, then, to it's motion in the slide. _p r_ shews a wheel, running
loosely on the axis of the porte-outil; and having fixed to it a
concentric rim _r_, with _three or four waves_ in it's circumference.
Further, above _s_, is seen a lever, turning on a pin in the stud _s_,
and pressing against the right-hand end of the rack _w_, when driven to
the left by the waves _p r_, &c. This rack is cut into ratchet teeth as
at _w_, in which enters the catch _o_, as impelled by a proper spring
acting on it, (but not seen in the figure.) As long then, as the waved
wheel _p r_ can _turn_, with the porte-outil _N_, this last described
mechanism does nothing: but when _p r_ is _stopped_, it begins to work
usefully; for the lever _s_ then rides on the waves _p r_, and presses
the rack _w_ against the spring _n_, so that the catch _o_, takes into
some new tooth; by which means, when the spring _n_ unbends (by the
sinking of the lever _s_ into any wave _p_) the frog is itself carried
_toward the right hand_--which is the effect intended. But, in fine,
_how_ is this wheel _p r_ stopped and set agoing _a propos?_ Fig. 5
will shew this, with the aid of a little imagination--since our fig. 5
is a kind of transparency rather than a regular view. The wheel _m_, is
a crown wheel, near which the wheel _p r_ (fig. 3) turns, having a
spiral _g_ on it's hither surface, which runs between the teeth of the
wheel _m_ and turns it one tooth, in each of it's own revolutions: But
when, after a given number of these turns, the end of the spiral _g_
meets with a _large_ tooth on _m_, it _lodges_ on it, and stops the
motion of the wheel _p_, and then the aforesaid waves _r_ perform the
task of driving the rack _w_ _backward_; after which the spring _n_
changes the place of the frog, so as to make another line of impressions
round the cylinder. It remains then, only to be explained, how this
stoppage is itself stopped; which is thus: to the porte-outil is
fastened, near _g_, a small arm, which turns with it, and which in fig.
5 the dot _t_ represents. This arm, therefore, drives back the beak _t_,
(connected with the spring _v_) at every revolution of the porte-outil,
thereby working the small catch that hangs to that beak. This catch,
therefore, _slides_ on the edge of the crown wheel _m_, _but produces no
effect_, until it finds there, one small notch, so placed as to be acted
on by the catch _when this disengagement is wanted_--and, _then_, this
motion jogs forward the crown wheel _m_ just enough to take the large
tooth out of the way--when the spiral _g_ begins to move through the
common teeth of _m_, and thus ceases to act on the rack till the large
tooth again comes to stop the wheel _p_, and recommence the rack's
motions. And thus is the place of action of the punch changed after
_any_ number of it's contacts with the cylinder--that number being
doubled or trebled--or more--when necessary, by increasing accordingly
the number of _common_ teeth in the crown wheel _m_, before a _large_
tooth occurs.

A few practical remarks on this mode of engraving may here be added with
advantage. Theoretically speaking, the _punch_ should form a portion of
a cylinder, of equal radius with the porte-outil wheel, taken at it's
pitch line. But through the _relative_ weakness of some mandrels, a
certain spring takes place, which requires the punches to be more curved
than that wheel, and even considerably so. This also depends on the size
of the punch, and the fullness of the pattern. In a word, it depends
likewise on the method of employing the Machine--whether with _few_
passages, and _considerable_ pressure, or with _light_ pressure, and
_many_ swift passages:--The latter System is in my opinion much the
best; since it brings the practice nearer to the theory of this Machine.
If, indeed, the cylinders and mandrels of Calico Printers, had been
originally made _thicker_, and thus strong enough to bear the pressure
without sensible deflexion, this would have been, from the first, a
perfect process: and the nearer these objects are brought to this state
of inflexibility, the nearer will it's effects approach to perfection;
for in all other respects it works with admirable precision.

I may just add, that the facility with which the revolutions of this
Machine are _counted_, has induced some persons to dispense with the
rack movement: but for small patterns with numerous impressions, it is
doubtless better to use it--especially when employing the rapid and
light pressures just alluded to; and these will become additionally
interesting when the punches themselves acquire a more exact form--which
is the object of the _third_ Punch Machine, still remaining to be
described.

It is not superfluous to add, that this Engraving Machine is dangerous
to the persons employed--and should therefore be guarded behind, _by a
fence-bar_, to prevent the hands or clothes from being drawn in.


  OF
  A HORIZONTAL WATER WHEEL,
  _Probably the best of the impulsive kind_.

In this title, I have repeated _that_ given in the prospectus: nor do I
think I have assumed too much in so doing. It will be seen in the course
of this description, on _what_ I found my opinion; which indeed, was
substantiated by the fact as soon as formed: the execution having
speedily followed the invention. The Machine, in it's different parts,
is represented in figs. 1, 2, 3, and 4 of Plate 40. Fig. 1 is a plan of
the floor, _on_ which the upper water flows, to it's whole depth, when
the flood gates are opened: this floor being close over the wheel, as
seen in fig. 4, at _c d_. Further, _a b_, in both figures, is a circular
slit of the whole diameter, through which the water rushes at once on
_all_ the floats of the wheel; whose axis goes up into the building
through a kind of barrel, that prevents the water from escaping in any
other part than the aforesaid circular aperture. The wheel itself is
represented at _e f_, fig. 2; and fig. 4 is an elevation of it, with
it's shaft, and a few of the _floats_, to shew the manner of their
receiving the stroke of the water. A section of the ring-formed slit is
also given at _a b_, with two floats receiving the flowing water: and in
that elevation is also shewn two of the _swan-necks_ by which the
central part of the floor is supported on the framing, _without_
stopping the watercourse.

Finally, the slit or aperture _a b_, figs. 1 and 4, is fitted with a set
of cast iron curves, of which _six_ are shewn in the Plate, between _c_
and _d_, and whose use is to turn aside the falling water to any desired
inclination; these instruments being moved at will by a proper chain of
bars, reaching from one to the other, and connected with eight or more
levers at proper intervals on the floor of the water chamber.

Thus then, it appears that this Machine has two or three very important
properties: 1st. _all_ the water escapes in the _same_ direction,
(relatively to the motion of these wheels) and that direction concurs
with _that_ in which the wheel is made to turn. 2d. Every one of those
fluid prisms into which the stream is divided, is urged with the _same_
velocity, because impelled by the same _head of water_. 3d. The velocity
of these jets is the greatest possible, because the water is carried as
low as possible before it is emitted; and falls as little as possible
after it has struck the wheel. 4th. In fine, the inclination of the
floats _may_ be made most perfect; and their form, being that of a
_boat_ slightly curved, is among the best forms possible for receiving
the utmost impulse from flowing water.

Although by these means much is done in favour of the impulsive system,
it is allowed, that, in general, a wheel acting by impulse, is less
effective than a bucket-wheel acting by the weight of the water. But the
higher the fall is made, the more similar these effects become. Hence, a
_very_ high fall may be made to produce, by impulse, an effect equal to
that of the bucket-wheel. To meet, therefore, such a contingency as
this, I have given, in fig. 3, a cover to the water chamber of fig. 4,
intended to close it upward, and thus adapt it to a fall of _any_
height; the water entering into this chamber from a large pipe _A_, of
the required length: and being compressed accordingly, the result is
forcible in proportion.

A few _facts_ on the above subject will not be uninteresting. When this
wheel, fifteen or sixteen years _ago_, (for I have forgotten it's exact
date) was about to be put in motion at La Ferté in France, several
knowing ones took upon them to say "that it would not turn at all." But
who so astonished as they, when, at twelve feet diameter, and with less
than five feet fall, they saw it make fifty-four turns in the first
minute! I acknowledge, with pleasure, that these men soon expressed
their approbation with unsophisticated candour; for although an honest
prejudice had beset them, it was un-poisoned by that envy, I have more
than once had to deal with in a country we are accustomed to call
_better_! I therefore take leave, on this occasion, to say to my beloved
countrymen, "Go and do likewise."


  OF
  A NEW SPINNING MACHINE,
  _Called, and being the_ PATENT _Eagle_.

The Machine commonly used for continued Spinning, in low numbers, is
named a Throstle: and as my Invention acts in a similar manner, I have
presumed to call it an _Eagle_. My motive is no mystery. The Machine
spins more and better than a throstle: and reaches, especially, to a
fineness unknown in throstle spinning. It could not, therefore, justly
receive a meaner name, nor even an equal one.

The present Machine then, is a superior kind of throstle, the
construction of which will be understood, by spinners, from the annexed
figures, 5 and 6 of Plate 40. As the principal difference between the
former machines and this, resides in the toothed wheel by which it's
spindles are turned, we shall begin this description by adverting to it:
_A B_ is that wheel, cut, at present, into 800 inclined teeth, and
working with pinions of 11 teeth, one of which, with it's spindle, is
shewn at _a b_, fig. 6. The revolutions, therefore, of these spindles to
_one_ of the wheel, are 72.7272, &c. and since the latter, in spinning,
makes from 60 to 70 turns per minute, the spindles run at the rate of
5000 turns in that time, and _might_ do more if desired by the spinner.
In a word, the useful speed depends on the size and weight of the
spindles, the flyers, &c.

Immediately above and below the wheel _A B_, are two rings of cast iron,
to which are screwed rims, either of wood or metal, destined to hold the
steps and bolsters of the spindles, as is usual in a throstle, with the
difference of the circular form, which the wheel of course requires; and
the relation of which, to the rollers, is shewn at _a b_, fig. 5, being
a plan of this Machine. Returning to fig. 6, the next object upward is
the _roller-beam_, (cast hollow for lightness) the form of which is that
of an octagon, with two brackets _c d_, by which it is fastened to the
pillars _E F_: these, in their turn, being connected with the top and
bottom cross-pieces (_G H_, _I K_) so as to make up the frame, properly
so called. All these parts are placed (in section) similarly to those
usually composing the throstle; and the copping motion is produced by
the curve _f_, driven by an endless screw on the shaft _h f_, and acting
on the slide _f g_, and through it on the ring of which the square _i_
is a section: and on whose iron plate, in fine, the bobbins _drag_, as
they do in the throstle. In the Machine before us, the rollers are
driven by _two_ side-shafts _h f_, which take their motion either from a
train of spur wheels placed above the traverse _G H_, or by bevil wheels
from two small shafts, coming under that traverse from the central shaft
_L M_, to those _h f_, and acting on the rollers by means of the bevil
wheels _f m_, seen in the figures. Now, the rollers are contained in
eight heads--1, 2, 3, 4, 5, 6, 7, 8, each of which has it's _speed
wheels_ in the angles _n o_, &c. and receive their motion from six sets
of bevil wheels _q_, &c. which propagate the motion round each _half_ of
the Machine, from the points _m_ and _p_ respectively.

Above this roller-beam, is the creel-ring _N O_, which (either in one or
_two_ rows) receives the sixty roving bobbins that supply the sixty
spindles, of which the Machine is composed: and whose threads pass under
the eight sets of rollers--one thread being suppressed in each of the
heads--1, 4, 5, 8, on account of the columns. (This, at least, is the
arrangement I prefer; but some of the Machines have been made with eight
threads in _all_ the compartments.) Finally, in this frame _G H_, _I K_,
is placed a ring _P Q_, (of glass or bright metal) over which the
rovings are thrown before they are put in the guides behind the rollers;
so that the _route_ of a thread in the act of being spun, is shewn in
fig. 5, by the line _P R_, _S b_, where it meets the bobbin on the
spindle _a b_, before mentioned.

It may be observed here, to prevent ambiguity, that the guide-boards,
with their hooks, are placed below the octagon roller-beam _q n o_, &c.
_as they are in the common throstle_; being, each, 1/8 of the whole
circumference, and of a circular form on the outside, reaching, by these
hooks, to the point _S_, so as to hold the thread just over the centre
of the spindles as at _a b_, fig. 6. Considering this as a commonplace
subject, I have not attempted to _draw_ these boards, since their form
and position would occur to every constructor: and this is the reason
also, why I have given only the section of the copping ring _i_, fig. 6:
nor at all shewn the _top rollers_--nor the detail of the creel--on all
which topics, opinions vary considerably, while the things themselves
are really of minor importance.

There is, however, in my Patent System, something which I think
important, and which, therefore, I have sketched near _Q_, fig. 6. If _w
x_ be there considered as _the second_ communication shaft, a wheel _z_
is put on it, of that kind which is calculated to work in a certain
geering chain, called in French _chaine de Vaucanson_, (from the name of
it's inventor); and further, similar wheels (_y_) are connected with
_all_ the pins on the creel, round which the chain is carried from the
wheel _z_, till it comes to it again. The consequence is, that all the
wheels (_y_) are turned by that chain, so as to _untwist the roving_
while the spinning rollers draw it off the bobbins: and this is so,
because, in my Patent System, the rovings are _over-twisted_, in order
to admit their being made _very fast_, without the danger of breaking.
This then, completes my Patent Eagle, formed, on the _right hand of the
figure_ so as to use _over-twisted roving_; and _on the left hand_, so
as to spin common roving in the usual manner. In both cases, the motion
of the spindles by geering, ensures a mathematical twist, and thus
produces yarn better than common; whence also it's fineness can be
carried _much_ farther than on a common throstle. It need hardly be
added, that these spindles are stopped and set in motion by the
mechanism described in my second Part, at fig. 1, Plate 19: and there
mentioned as "a Machine to set-on and suspend rapid motions."


  OF
  A SECOND SPINNING MACHINE,
  _Adapted principally to Wool_.

This Machine, represented in Plate 41, figures 1 and 2, may be called a
Spinning-card: whose use, however, I shall now suppose confined to
spinning coarse yarn, or rather rovings, to be re-spun on the common
machines, or on machines similar to my Eagle just described. It
consists, in reality, of an horizontal card _A B_, having it's flyer,
&c. adapted to perform, in a perpendicular position, what those several
parts do, in an horizontal one, on the common carding engine. All this
is so well known, that I have not thought it necessary to draw it in
these figures; but merely to say, that in this Machine, those operations
are performed on the left hand, as at _A_, where is introduced a broad
flat ribbon of wool, duly made on a preparing card, and laid on edge in
a box at _C_, from whence it is drawn by the feeding rollers, &c. _so as
to cover the whole of the central card_ _A B_. Now, round this central
card, are placed, _ten_ or more small fillet cards, 1, 2, 3, 4, &c.
being at different heights on the central one; by which arrangement, the
whole surface of the latter is stripped by these cards, and as much
filament collected on each, as is sufficient to form a thread or roving,
as before mentioned. But, further, these small cards have to be stripped
in their turn: and that is done by the circular combs _a b_, which
being placed _obliquely_ to the cards, receive motion from them, and
gather a regular mass of filament of a size fitted to become the yarn or
roving in question. Nor need this roving be re-drawn, by rollers, before
it is twisted: for it is the property of the bobbins _D E_, fig. 2, to
_draw mathematically_: and with _any_ speed that shall have been
determined. If we examine how this is done, we shall see at bottom,
_two_ wheels _F G_, (toothed on the patent principle) one of which
drives the spindles and flies, and the other the bobbins _D E_: the
wheel that drives the bobbin having a few teeth _more_ than that which
drives the spindles--whose pinion is the same in number as that of the
bobbin. Thus, therefore, the bobbin goes as much faster than the spindle
as is necessary to _take up_ all the wool furnished by the comb, and
_to_ the comb by the small card, which receives it from the central card
_A B_; where note--that the draught, by this difference of motion is
_not_ variable, but determined: since the heads of the bobbins _E D_,
are a hollow inverted truncated cone, on which the yarn cannot
remain--for in _winding_, it drives downward that which is already
wound, so as to fill the whole bobbin _from the head_--a reason for the
conical shape of the latter object.

It will appear by the upper figure, (which is a plan of the central
card, and the small cards, 1 2, &c.) that the latter receive their
motion from the chain _H I_, by means of the train of wheels _K L_,
turning on studs in the upper cross-piece. Suffice it to add, that the
centres of these cards, of the combs, &c. are fixed to the rings by
proper cramps, as will be easily conceived. I have offered to sight,
_only_ the essential parts, to avoid confusion: and I presume to hope
every thing important will be thus seen without difficulty.

In my present view of this Invention as a _preparing Machine_, I would
observe, that the central card is only considered as a _distributor_,
and that I should, _now_, add to it a System of machinery to make it a
_forced_ distributor. I had, indeed, prepared this very System to be
patentized many years ago: but the delays that occurred then, followed
by the _Restoration_, (which gave me an opportunity of coming to
England;) made me suspend this intention--respecting a method, perhaps,
the only thing wanted to make this Machine in all respects excellent.

In the small figure 5, (Plate 41) _x y_ is supposed to be the section of
a central card, such as _A B_, fig. 2; and the horizontal lines between
_x_ and _y_, shew the height of the card teeth. Of these, I take out a
portion in several perpendicular lines round the card--say, at an inch
distance from each other: the intervals thus stripped, being about 1/16
of an inch in width: and in all these upright slits, I introduce a blade
_x y_, (whose transverse section is like that of a card wire) and whose
edge is undulated as at _a b_. Finally, to these blades is given, (by a
proper Machine) a slow up-and-down motion, which makes them push off
the filament from the card wires at the highest points of the waves, and
suffer the wires to retain these filaments at the lowest points; whence
it follows, from the motion just mentioned, that these points of
reception and exclusion of filament, are constantly changing on the
surface of the whole card, and that, therefore, the card will never be
totally clogged with wool--as it is in the common process. It will be
seen that the use of this System need not interrupt _that_ of the common
_flyer_, (or stripping card) whose use is to keep the teeth in working
order, and to discharge a part of the obtruding filament.

In terminating this article, I cannot resist the desire of recommending
this whole subject to any opulent English Manufacturer, whose zeal and
public spirit, are commensurate with the scope which these hints
embrace, and to which they tend, if duly appreciated.


  OF
  MY PARALLEL MOTION,
  _As applied to_ HEAVY _Steam Engines._

While this Invention, as described in page 30 of the first Part, is
allowed to possess curious properties, and to be a _pretty_ thing,
opinions do not all concur in declaring it, essentially and generally, a
_good_ thing. Nor could I be unjust enough to insist that it is so, in
every kind and magnitude of application. I have, however, convinced
myself that it is susceptible of practical excellence, as a _first
motion_ to steam engines, whatever be their dimensions; and have,
therefore, presumed to re-produce it, with those modifications which are
required to make it so. In thus acting, I have again preferred the
_useful_ to the _agreeable_, and in some measure inverted the order of
my subjects. But I trust this deviation will be excused, in favour of
the motive and the result; on both which I feel a good degree of
confidence.

To obviate the point of mechanical _weakness_ in this Parallel Motion,
(see Plate 41, fig. 3,) I have _doubled_ it's parts; and brought the
piston rod _a b_, to act, at once, on _two_ of the circulating wheels _c
d_, placed exactly opposite each other, and rolling, as before, on the
inside of the fixed wheels _f e_, so as to produce the rectilinear
motion, by the action of the piston rod _on them both_. And to make
their respective motions one, (as connected with the fly _B A_) this
latter is fixed to a shaft common to the two wheels _g h_, and by which,
therefore, the two other wheels _i k_, fixed to the crank shafts _m n_,
are kept in due position. Thus, then, is all winding or twisting motion
done away: and, therefore, can this System be employed in engines of
every required power. Nor need I add, (what will be generally allowed)
that much of the expence, and of the retardation, which a given engine
suffers from the beam, the connecting rod, &c. will thus be completely
obviated.

I must, however, stop every gainsaying mouth, on the circumstance of
using _geering_ between the engine and the fly--a system which I
acknowledge to have been hitherto an evil; though, perhaps, a
_necessary_ evil--as giving (by a simple method) a _double_ speed to the
fly from a _single_ motion of the piston. At all events, in this shape,
I submit only to a very common difficulty--and might there rest my
apology.

But I should have hesitated to go thus far, had I not foreseen that
_all_ the evil arising from _this_ use of wheels, can easily be avoided
by my geering:--by means of which I am bold to say, every vestige of
shake or _backlash_ may be destroyed; and this method of working a steam
engine be made as _silent_ as when a beam is used: in which case,
considerable advantages must accrue from this method.

To come to the point:--the small figure 4, in Plate 41, relates to this
subject. My geering is there seen in three forms or applications--each
one intended to bring the above property into play. The part _n o_,
represents the manner in which two wheels with singly-inclined teeth,
work together when one of them is furnished with a cheek, as directed
in fig. 3 of Plate 14. But here, in addition to that, the teeth of both
wheels are sloped _more_ on one side than on the other, so as to assume
_a wedge-like form_: insomuch, that in beginning to work, (if not
_perfectly_ formed) the wheels would not occupy the same plane. For, in
fact, the _cheek screws_ press home the cheek _o_ against a number of
thin washers all round the wheel, and thus only draw the wedge-formed
teeth into each other as they become _bedded_, and successive
washers are taken away. Hence, a good degree of precision is
obtained--accompanied with little friction, and thus with great
durability.

But we stop not here. The part _p q_ of this figure, shews a pair of
wheels doubly inclined--one of them only, being made in two halves,
which are connected together by screws and washers, like that just
described. Here then, _another_ degree of friction is got rid
of--namely, that of the cheek _o_: but still, a small degree remains,
(dependent on the double versed sine of the angle formed on the wheel's
circumference, by the _thickness_ of a tooth). This quantity, is indeed,
very minute; and brings, perhaps, the whole near enough to perfection.
To do, however, completely away with all _friction_, (see my preceding
statement)--as well in the wheel acting _backward_, as in that acting
_forward_, we must do what is shewn in the parts _r_ or _s_ of fig. 4:
we must have a _pair_ of V wheels on the same shaft, with the power of
turning one of them in reference to the other; and then connecting them
by proper screws, &c. to preserve the position thus given: by which
means, in a word, all shake or _backlash_ will be completely annulled.




  PART FIFTH.
  A NEW CENTURY OF
  Inventions.


  OF
  AN ADDING MACHINE,
  _Or Machine to Cast up large Columns of Figures_.

This Machine is not, generally, an _arithmetical Machine_. It points
_lower_: and therefore promises more general utility. Though less
comprehensive than machines which perform all the _rules_ of arithmetic,
it is thought capable of taking a prominent place in the counting-house,
and there of effecting two useful purposes--to secure correctness; and
thus, in many cases, to banish contention. It is represented in figs. 1,
2, 3, and 4 of Plate 42, and in figs. 3 and 4 of Plate 43.

There are two distinct classes of operations which may be noticed in
this Machine: the one that does the _addition_, properly speaking; and
the other that records it by figures, in the very terms of common
arithmetic. The first operation is the adding: which is performed by
means of an endless geering chain, stretched round the wheels _A B C D_,
(fig. 1) and _over_ the two rows of smaller pulleys _a b c d e f g h i_;
where, observe, that the chain is bent round the pulley _A_, merely to
shorten the Machine, as otherwise the keys 1 2 3, &c. to 9, might have
been placed in a straight line, and thus the bending of the chain have
been avoided.

The chain, as before observed, _geers_ in the wheels _B_ and _D_, which
both have ratchets to make them turn one way only. Now, the keys 1 2,
&c. have pulleys at their lower ends, which press on the aforesaid chain
more or less according to the _number it is to produce_, and the depth
to which it is suffered to go by the bed on which the keys rest, when
pressed down with the fingers. Thus, if the _key_ 1 be pressed, as low
as it can go, it will bend the chain enough to draw the wheel _B_ round
_one tooth_--which the catch _E_ will _secure_, and which the wheel _C_
will permit it to do by the spring _F_ giving way. But when the key 1 is
suffered to rise again, this spring _F_ will tighten the chain by
drawing it round the pulleys _A_ and _D_, thus giving it a circulating
motion, more or less rapid, according to the number of the _key_
pressed. Thus, the key 5 would carry _five_ teeth of the wheel _B_ to
the left; and the catch _E_ would fix the wheel _B_ in this new
position: after which the spring _T_ would tighten the chain in the same
direction and manner as before. It is thus evident, that which-ever key
is pressed down, a given number of teeth in the wheel _B_, will be
_taken_ and secured by the catch _E_; and, afterwards, the chain be
again stretched by the spring _F_. It may be remarked, that, in the
figure, _all_ the keys are supposed _pressed down_: so as to turn the
wheel _B_, a number of teeth equal to the sum of the digits 1, 2, 3--to
9. But this is merely supposed to shew the increasing deflexion of the
chain, as the digits increase: for the fact can hardly ever occur. We
draw from it, however, one piece of knowledge--which is, that should the
eye, in computing, catch several numbers at once on the page, the
fingers may impress them at once on the keys and chain; when the result
will be the same as though performed in due succession.

Thus then, the process of _adding_, is reduced to that of touching (and
pressing as low as possible) a series of keys, which are _marked_ with
the names of the several digits, and each of which is sure to affect the
result according to it's real value: And this seems all that need be
observed in the description of this process. It remains, however, to
describe the 5th. figure, which is an elevation of the _edge_ of the
keyboard, intended to shew the manner in which the two rows of keys are
combined and brought to a convenient distance, for the purpose of being
easily _fingered_.

We now come to the other part of the subject--that of recording the
several effects before-mentioned. The principle feature in this part, is
the System of _carrying_, or transferring to a new _place of figures_,
the results obtained at any given one. This operation depends on the
effect we can produce by one wheel on another, placed near it, on the
same pin; and on the possibility of affecting the second, _much_ less
than the first is affected: Thus, in fig. 3 and 4, (Plate 42,) if _A_ be
any tooth of one such wheel, placed _out_ of the plane of the pinion
_B_, it will, in turning, produce no effect upon that pinion: but if we
drive a pin (_a_) into the tooth _A_, that pin will move the pinion _B_
one tooth (and no more) every time this pin passes from _a_ to _b_. And
if we now place a second wheel (_F_) similar to _A_, at a small distance
from it, so as to _geer_ in _all_ the teeth of the pinion _B_, this
latter wheel will be turned a space equal to _one_ tooth, every time
the pin _a_ passes the line of the centres of the wheel and pinion _A
B_, (say from _a_ to _b_.) It may be added, likewise, that this motion,
_of one tooth_, is assured by the instrument shewn at _E D_, which is
called in French _a tout ou rien_, (signifying all or nothing) and
which, as soon as the given motion is _half_ performed, is sure to
effect the rest: and thus does this part of the process acquire,
likewise, a great degree of certainty--if indeed, certainty admits of
comparison.

It is then, easy to perceive, how this effect on the different _places_
of figures is produced: and it is clear, that with the chain motion just
described, it forms the basis of the whole Machine. There is, however,
one other process to be mentioned, and as the 2d. figure is before us,
we shall now advert to it. In adding up large sums, we have sometimes to
_work_ on the _tens_, sometimes on the _hundreds_; which mutations are
thus performed: The wheel _B_, (fig. 2) is the same as that _B_, fig. 1;
and it turns the square shaft _B G_, on which the wheels _k l_ slide.
The wheel _l_ is to our present purpose. It is _now_ opposite the place
of shillings; but by the slide _m_, it can be successively placed
opposite _pounds_, tens, hundreds, &c. at pleasure: on either of which
columns, therefore, we can operate by the chain first described--the
wheel _B_ being the common mover.

We shall now turn to figs. 3 and 4 of Plate 43, which give another
representation of the carrying-mechanism, adapted especially to the
anomalous _carriages_ of 4, 12, and 20, in reference to farthings,
pence, shillings, and pounds, and _then_ following the decuple ratio.

In fig. 3, _k l_ represent the two acting wheels of the shaft _B G_,
fig. 2; the latter _dotted_, as being placed _behind_ the former; these
wheels, however, are not our present object, but rather the carrying
system before alluded to; and described separately, in fig. 3 of Plate
42. _A_, in figures 3 and 4 (of Plate 43) is the first wheel of this
series. It has 12 teeth with _three_ carriage-pins (or plates) _a_,
which jog the carrying-pinion _B_, at every passage of 4 teeth; thus
shewing every _penny_ that is accumulated by the _farthings_. This is
so, because the farthings are marked on the teeth of this first wheel in
this order--1, 2, 3, 0; 1, 2, 3, &c. and it is in passing from 3 to 0,
that this wheel, by the carriage-pinion _B_, jogs forward the _pence
wheel_ _C_ one tooth: But this pence wheel is divided into 12 numbers,
from 0 to 11; and has on it only _one_ carrying-pin (or plate) _b_; so
that, here, there is no effect produced on the third wheel _D_, until 12
pence have been brought to this second wheel _C_, by the first, or
farthing wheel _A_. Now, this third wheel _D_, is marked, on it's
_twenty_ teeth, with the figures 0 to 19, and makes, therefore, one
revolution, then only, when there have been twenty shillings impressed
upon it by twenty jogs of the carriage-pin _b_, in the second wheel _C_.
But when this wheel _D_ has made one whole revolution, it's single
_carriage-pin_ _c_, acting on the small _carriage-pinion_, like that _c
d_, (but not shewn) jogs forward, by one tooth, the wheel _E_, which
expresses _pounds_; and having _two_ carriage-pins _e f_, turns the
wheel called _tens of pounds_, one tooth for every half turn of this
wheel _E_: and as, on all the succeeding wheels, to the left from
_E_--(see fig. 2, Plate 42) there are two sets of digits up to 10, and
two carriage-pins; the decuple ratio now continues without any change:
and thus can we cast up sums consisting of pounds, shillings, pence, and
farthings, expressing the results, in a row of figures, exactly as they
would be written by an accountant. The opening, through which they would
appear, being shewn in fig. 1, at the point _w_, corresponding with the
line _x y_ of fig. 2 in the same Plate.

I shall only remark, further, that the figures 3 and 4 in Plate 43, are
of the natural size, founded, indeed, on the use of a chain that I think
_too large_; being, in a word, the real chain _de Vaucanson_, mentioned
in a former article: and that the figures of Plate 42 are made to half
these dimensions, in order to bring them into a convenient compass on
the Plate.

I would just repeat, that I have not attempted here an arithmetical
machine in general; but a Machine fit for the daily operations of the
counting-house; by which to favour the thinking faculty, by easing it of
this ungrateful and uncertain labour. Had I been thus minded, I could
have gone further, in a road which has been already _travelled_ by my
noble friend the late Earl Stanhope, (then Lord Mahon) but I took a
lower aim; intending in the words of Bacon--"to come home to men's
business and bosoms."


  OF
  A ROTATORY PUNCH MACHINE
  _Adapted to my own Engraving Machine_.

It is highly desirable, (not to say indispensable) in the use of my
engraving Machine, to have punches not only of the true cylindrical
form, but exactly of the proper length. (See the remarks on this
subject, in the description of that Machine). It is, therefore, a matter
of consequence, to be assured that both these circumstances unite; and
to unite them _without_ depending on personal skill, whenever the work
can be accomplished without such dependence: and this is the object of
the present rotatory Punch Machine. Adverting first to the length of the
punch: _that_ is insured by having a kind of slide on the Punch Machine,
formed like the _frog_ spoken of in the above article--Engraving
Machine. In the 5th. figure of Plate 43, this slide is shewn at _a_, and
it is at exactly the same distance from the centre of motion _A_, as the
bottom of the frog-plate fig. 3 Plate 39 is from _it's_ centre of
motion. Thus, the bottom of the punch is filed straight, once for all,
and being fixed in proper clams, as in the figures, the shaft _A_ is set
a-turning, by power--from which motion two uses are derived: first, the
cylindrical form is given to the punch by presenting to it, in it's
revolution, a _file_ duly wedged on the (now fixed) slide of the Machine
_B B_; against which it is kept turning, till, by a due depression of
the centre _A_, the radius is brought to the length required, and the
surface perfectly formed and smoothed. This being achieved, the cams _c
d_, are fixed to the slide _B B_, and to the turning body _A d_, so that
when the die _f_ is moved toward the left hand by the said cams, the
prepared punch gently presses on it, and begins to receive it's
impressions; which are gradually deepened by the set screws _g h_, fig.
6; till, at once, the proper radius is given, and the engraving
sufficiently transferred from the die to the punch--an operation which
this process is calculated to perform, rather by means of frequent and
gentle contacts, than by slow and heavy pressure. It need not be added,
that the motion of the slide _B B_ is reciprocated by the spring _C_,
against that _D_, after each forward motion given to it--as _begun_ by
the _cams_ _c d_, and continued by the contact of the die and punch, all
which a mere inspection of the figures will sufficiently explain. It is
likewise evident, that the figs. 5 and 6, shew, both, the same objects,
namely:--the regulating wedges _i k_, the upper set screws _g h_, and
the rollers _E_, on which the slide vibrates during the operation of the
Machine.


  OF
  A PORTABLE PUMP,
  _To be worked by the Feet_.

It is not solely because, to work with the feet is a good method of
employing the strength of men, that this device is presented to the
mechanical public; but it is with the view of _so_ employing the feet
and hands, that they may occasion a constant and _equable_ flow of
water. The means, (see Plate 44, fig. 1) are, to provide the man with
two supports _a b_ for his hands, and two pedals _c d_ for his feet, by
which the two rods _e f_ are worked; and by them, through the cords or
chains _g h_, the piston rods _i_ and _k_. Of the latter, the one which
answers to the lower pump _l_, goes through the upper piston, whose rod
is _i_: and the pistons are both constructed in the manner shewn in fig.
2; that is to say, the piston has no _body_, fitting the pump barrel:
but a triangular bar _x_, going diagonally across the pump barrel,
(which is square) and carrying two wings or valves _y z_; which, both
together, fill the barrel _when down_, and leave it as empty as possible
when up, by which motion the chains _a e_ are slackened. Further, these
pistons, with their rods, are heavy enough to raise the pedals, the
instant the man raises his feet in any degree: so that, by a proper
combination of the motions of his hands and feet, he can let down a
given piston, and begin again it's ascending motion before his effort
has wholly ceased on the other pedal. A mean this, of producing a
constant and equable rising motion in the column of water through the
pumps _k l_; and a mean also, of doing more work with a given fatigue,
than would be _possible_ in a pump whose motions were merely reciprocal,
and the water of which, in rising, would be subject to any unequable or
convulsive motions.

In general, this portable pump was made (many years ago) with a view to
being easily carried to any field or garden, bordering on a river, and
worked on it's bank; the flexible suction pipe _p_ being thrown into the
river, or a well, as occasion might require. To this end, the whole
frame (as is evident from the figure) can be folded up into a kind of
_faggot_: and thus it's transport from place to place, be made perfectly
commodious.


  OF
  THE BISECTING COMPASSES.

It _often_ happens, that from a central line, (in drawing for example)
we want to set off, quickly, many equal distances on each side; or
between two given lines we want a central line; to perform either of
which operations, is the use of the Instrument just mentioned.

It is represented in Plate 44. figs. 3 and 4, where _A B_ is the central
_point_, being cylindrical in the greatest part of it's length, and
conical at _E B_. It slides correctly in two _cannons_ or swivels _E_ &
_A_, which also have two short axes or trunnions, on which _first_, the
double compass joints _C D_ turn; and second, the _two_ pairs of arms _F
G_. I have called these cannons, _swivels_, that I may shew their
construction, by referring to figure 1 in Plate 30--which describes the
swivel of the _forcing Machine_; and which will give a complete idea of
what is here intended. From this construction it will appear evident,
that the point _A B_, (Plate 44) will be always found in the middle,
between the two points, of the outer legs of the compasses; and _that_
whether the question is to take two equal distances from a central
point, or to _bisect_ a given line or distance at one operation. The
point or style now _slides_ in the two swivels _A_ and _E_; but the
Instrument might be so constructed, as for it to follow the rising
motion of the middle joint (_E_), and thus to keep the three joints in
the same horizontal line: but I think a small perpendicular motion of
the said _style_, would be always desirable in the Machine, as a drawing
Instrument.


  OF
  A MUSICIAN'S PITCH-FORK,
  _With variable Tones_.

This device is shewn, in two positions, at figs. 1 and 2 of Plate 45. In
it's present application, it is intended to produce a whole octave on
the diatonic scale: and therefore, the unsupported ends of the fork are
just half as long as they would become if the sliding handle _A_, were
drawn to the bottom end of the branches _c d_. For, again, the fixing
screw _C_, and it's box _D_ are fastened to this sliding handle by one
or two screws, (_s_) so as to be always ready to press the branches
against the enclosed slide _A B_, at whatever place the intended tone
may be found. Now, the branches _a c_, _b d_, spring out of a common
trunk _c d_, which is pierced with a square hole, exactly fitting this
sliding handle _A B_; and the latter is marked, at proper distances,
with lines across it, each of which (placed opposite the mark _c d_)
gives such a length to the remaining branches _a b_, as to make them
sound the note desired. Thus, the line l, brought to _c d_, lengthens
the branches _a b_, to (nearly) 53 parts, from 50 at which they are
_now_ fixed; the whole length _a c_, being 100. This, and the following
divisions would, of course, follow any desired _temperament_, according
to the will of the tuner: but I have supposed them founded on the
equi-harmonic scale; and thus will the successive intervals to be set
off on the slide _B A_, be as follows: (while the corresponding notes
will be those expressed in the table.)

In the state represented by the figures 1 and 2, the line a _B_, is
5000; being one half of the whole length _a b_, _c d_.

  To form the Sharp   7th. it becomes 5297 the distance _c d_ 1, being  297.
        "     greater 6th.      "     5946       "       1-2,      "    649.
        "        "    5th.      "     6674       "       2-3,      "    728.
        "        "    4th.      "     7491       "       3-4,      "    817.
        "        "    3rd.      "     7937       "       4-5,      "    446.
        "        "    2nd.      "     8909       "       5-6,      "    972.
        " the fundamental note       10000       "       6-7,      "   1091.

The above lengths 1 2, 2 3, &c. have been measured off on the slide _A
B_, as nearly as possible, or at least with precision enough to give the
idea: and the rest I must leave the detail of, to those musical readers
who may feel interested in the subject.


  OF
  AN ESSAY,
  _To obtain a Level at Sea_.

I have done right in calling these attempts "essays": and if I had said
"immature attempts," they would have been better designated. Yet, having
promised them to my readers, I cannot now withhold them, although, from
want of opportunity of trial, I can do little more than _talk_ of their
supposed properties.

The first essay, as shewn in fig. 3 of Plate 45, is a _mental deduction_
from a device which I executed in 1801, and brought before the public at
the exhibition then given, by the French government, of the produce of
national _industrie_. It was, nothing more than a _pendulum_, made with
a view to lengthen, considerably, the going of a given clock, without
altering the wheels. To that end, the weight or bob, was a heavy bar _C
D_, suspended diagonally on two points _A B_, placed at a distance from
each other, exactly equal to the length of the said bar: and _that_ by
the double cross-bars _B C_ and _A D_, of a length sufficient to make
the whole assume a form exactly square: where it may be noted--that were
this figure _longer_ than high, the curve of vibration would have two
points of inflexion, and the bar _would not_ place itself horizontally
at last; and that were it narrower and _higher_, that curve would
assume a form more like, though still distant from, the arc of a circle.
In the present case, such was the effect of this disposition of things,
that the centre of gravity of the bar described, in vibrating, a curve
_E C D F_, the lower form of which, was so near to a _horizontal line_,
that the _times_ of vibration were immensely prolonged; so much indeed,
as to represent a common pendulum of several thousand feet in height;
and to give a proportionate slowness to any mechanism with which it
should have been connected. In fact, this line is so minutely different
from such horizontal line, that it is wholly included in the thickness
of the _drawn-line_ _C D_: nor becomes visible but near it's two ends _C
D_, when it begins to rise, and _then_ rises faster than that described
by a _short_ common pendulum.

In fine, this curve itself is formed by continually bisecting the line
or bar _C D_, and drawing lines from it's centre of gravity, thus found
in one of it's positions, to the same in another position, till the
curve _E C D_, &c. arises from this process.

It follows, then, from the nature of this curve, (or pair of curves)
that the time of vibration of this pendulum is the _longer_, the
_shorter_ the arcs are, in which it vibrates; and that, when the
vibrations have attained a certain _length_, compared with the height to
which the centre of gravity rises, the _time_ becomes considerably
shorter. I shall not now pursue this idea, because it is at once an
abstruse question, and at the same time one of uncertain utility--I
mean that it's use is problematical as a pendulum: since the _time_ of a
vibration depends on it's _length_, which cannot _easily_ be determined
by any invariable method. I shall, however, add two things on this
subject, by way of land mark; the one, that the balance-wheel of a watch
has power enough to drive this pendulum, heavy as it is;--and the other,
that I have _seen_ it make (for many hours together) vibrations of _half
a minute's duration!_ In a word, this is one of the subjects, which
untoward circumstances have prevented me from bringing to maturity--but
which I owe to my subscribers, and the public, in any, or every state,
to which I have brought them.

I therefore, say nothing more of this Instrument as a pendulum: but an
inspection of the figure will shew, that it will not be useless as an
ELIPSOGRAPH--which it clearly is, since the intersection of the bars _A
D_ & _B C_; describes a true Ellipsis. It may be further shewn, that the
ends of the moveable bar _C D_, are the vibrating _foci_ of a second
ellipsis, like the first, which rolls under the other, so that the curve
itself is _that_ which the centre of one ellipsis _a b c_ would
describe, by rolling on the surface of another _e b d_. But, into these
considerations I cannot now enter, as my "Century of Inventions" is fast
becoming due, and time commands dispatch; I beg leave, therefore, to
pass to the relation this subject seems to bear to a "Marine Level."

It must, however, be premised, that I scarcely expect either of these
methods to be correct enough for astronomical observations; as among
other things, they have the _nautical top_ to contend with: but if I am
fortunate enough to have suggested useful methods of procuring
_relative_ stability on board a rolling ship, so as to suspend the
better, a _nice_ instrument of astronomy; or so to counteract the
restless ocean, as to assist the victims of sea-sickness, I shall not
entirely have lost my labour.

My first idea on this subject, is the following: If we had on
ship-board, a simple pendulum of several thousand feet high, it appears
_certain_ that the oscillations of the ship would be begun and ended,
before any single vibration could have been given to such a length of
pendulum--which therefore, would scarcely vibrate at all: and if the
natural _time_ of this compound pendulum (for we are not confined to
these small dimensions) were made to be much longer than those of the
ship _on it's meta-centre_, this pendulum would scarcely vibrate at all:
because it's several tendencies to take motion from the ship, would
extinguish each other before they had had time to produce any common
effect.

Further, this result would probably be assisted by another property
belonging to this mechanism: see fig. 4. This diagonal suspension, as
repeated at _a b c d_, fig. 4, is of such a nature, that when it's
centres _a b_, are placed in any oblique position _e f_, (say by the
rolling of a ship) the suspended bar _c d_, immediately takes a position
of opposite obliquity _g h_, pointing _upward_ towards _i_, just as much
as the line _e b_ points _downward_; while the middle line _k l_ remains
level--whether caused by the slides _k l_, or the single slide _m_.

I dare not assert any thing respecting the form this principle should
assume, in order to produce the most useful effects; but it appears that
the principal _weight_ of the apparatus should be placed in the centre
of gravity of the under bar _c d_. It would occur, of course, to every
mechanician applying this System to real use, that in this fig. 4, we
have only provided for one motion of the ship, the _rolling_ motion: and
that, in consequence, this System should be suspended _in_ another
similar one, acting longitudinally, so as to provide for the _pitching_
motions of the vessel. In a word, I confess, with regret, that I leave
much _to do_, by way of bringing this idea to maturity--it being at this
late hour, more than doubtful, whether I shall myself ever be able to
resume the subject _at sea_, where alone it can be duly tried.


  OF
  A SECOND ESSAY,
  _To procure a Marine Level_.

This would seem to be a simpler process than the former: but how far it
may go beyond it in effect, I cannot say--having never had it in my
power to _try_ either of these ideas on ship-board. I therefore merely
present them to my readers, as themes for future thought and experiment.

Plate 45, fig. 5 represents this System--which is founded on the idea of
deadening oscillatory motions at sea, by connecting the bodies to be
thus _guarded_, with _a stream of flowing liquid_, the horizontal
motions of which _must be_ subject to laws very different from those
which rule vibrating bodies merely suspended.

The fluid used in this Machine (as oil, water, mercury, &c.) is to be
pumped up by appropriate mechanism, from the vessel into which it flows
at _x_, into a vessel placed a little above _z_; and to be let out by
the cock _y_, through a kind of strainer _s_, of sufficient collective
area to supply, with ease, the descending column _C_. The vessel and
tube _C D_ are made as thin and light as possible: and the upper part,
which is spherical, is inclosed in and suspended by the universal joint
_a b c_, like those used to suspend other bodies, as a compass, &c.
Moreover, the areas, at different heights, of the tube _C D_, are made
in the inverse ratio of the velocities of the spouting fluid, at each
given depth--so as to leave it but little tendency to press either
outward or inward, while thus obeying the law of gravity. By these
means, then, I think no vibrating motion will be excited in the falling
column: but that the liquid will continue to flow perpendicularly, so as
to preserve (nearly) the quietude of the vessel _C D_, and of any mirror
or instrument it may be wished to keep in a given position, by
connecting it with the perpendicular line thus obtained.

I repeat, however, that I know not how far these methods may go towards
obtaining an artificial horizon, for astronomical uses. Indeed, I fear
they will fall short in this respect--but I think them still worth
trying, even for these--but especially for the purposes to which I have
already alluded. And, if success crowns _this publication_, to the
degree I am led to anticipate, I will not always leave so rich a
question, in this doubtful predicament.


  OF
  A FIRE-ESCAPE,
  _On a retarding Principle_.

This is a recollection from the specification of a Patent which I took
out above thirty years ago, and in which I huddled together as many
objects as a child would like to see in a box of play things. I perhaps
acted, then, according to the _words_ of a French proverb--"abondance de
bien ne nuit pas;" but in so doing, I fell into the charybdis of
_another_ French proverb--"qui trop embrasse, mal étreint," (a wide
embrace cannot be a strong one) and in so doing, paved the way to much
litigation--which happily did not occur.

The intention of this Machine, as represented in Plate 46, fig. 2, was
to retard the fall of any _body_, or person, suspended to it, so as to
prevent any concussion on reaching the ground. The means are brought to
view in the perspective sketch given of the Machine. It is a kind of
_jack_, inclosed in a case, and supposed to be laid carefully aside in
the house represented in fig. 1 of this Plate. The Machine has a barrel,
much like that of the jacks used for roasting; round which a rope is
coiled, of sufficient length to reach the ground: and a wheel, connected
with this barrel, works in an endless screw, which turns a shaft also
like that of a common jack, but somewhat stronger; and finally, to this
shaft is fixed a small cross piece, carrying, on pins, two weights _y
z_, inclosed in the _fixed_ barrel _x_; by the centrifugal force of
which enough friction is created, to prevent the acceleration of the
falling body--whether a person or weight of any kind.

There is, moreover, a jib _a_, fig. 1, fixed between some, or all, the
windows of the house whose inhabitants it is wished to guard from the
danger of fire; this jib having the property, from the form of it's
foot, of taking by the suspension of any weight to it, a position
perpendicular to the wall: Insomuch, that by the act of suspending the
Machine to the jib--engaging the wrist in the noose _n_, and perhaps the
foot in another loop of the same cord; a person may safely flee those
dangers from fire, of which so many persons become the unhappy victims.

Since the 46th. Plate was engraved, it has occurred to me, that a method
should have been shewn for raising the cord _n_, (fig. 2) after each
descent. This operation might be performed by a handle put on the axis
of the Machine, accompanied by a ratchet on the wheel, just like the
similar parts of a jack for roasting. But, lest the inmates of a house
on fire, should not have presence of mind enough to perform this
operation, it might be better to have a spiral spring _in_ the Machine,
to be _wound up_ by the descending body, and of force sufficient to
raise again the cord after such descent.


  OF
  A SECOND FIRE-ESCAPE,
  _By breaking the Fall_.

This Machine is also shewn in Plate 46, at fig. 1. It consists of a
large truck, _A_, to be drawn rapidly to any _house on fire_, by one or
more horses. The carriage or frame part _B B_, is an _open_ square frame
_subtended_ by a first sheet of sack cloth, similar to the sacking of a
bed: and on this are laid five, or more, _air mattrasses_ made of sack
cloth, and varnished on the inside so as to be nearly air-tight; I say
_nearly_ so, for it is _not_ intended they should form a spring capable
of _returning_ any object thrown on them. On the contrary, each of the
mattrasses has, at one or both ends, a valve 1, 2, &c. opening
_outwards_, but kept closed by proper springs, so as to determine the
pressure at which the air shall escape; that pressure being carefully
graduated, so that the upper mattrass shall give way with ease, the
second with greater effort, and the successive ones with progressive
difficulty, until the under one remains totally closed, and stops the
falling body altogether. By these means, if enough mattrasses are used,
and they are _duly_ regulated, a person may jump from a house of three
or four stories without incurring any danger. As to the length and
breadth of this fire-escape, it should be ample enough to give the
sufferers confidence to take the leap, and as small as an easy passage
in the principal streets would require.

One thing must be described in _words_--as the mechanism to which it
relates is fixed under the truck; and could not be seen in this
perspective figure. These mattrasses are filled with air by an
_horizontal air pump_, worked by a _crank_, which the axle itself of the
hind wheels of the truck forms: whence, by pinning this axle to either
of the hind wheels, the very motion of the carriage, as drawn by the
horses, would distend the mattrasses--which would thus be ready for use
the moment they arrived on the spot; and moreover, when there, this air
could be replenished, after using, by turning this axle, through the
wheels, _by hand cranks slipped on it's ends_ at the place of the
linch-pins. Or, in fine, this operation might be performed by an air
pump prepared for it alone, and placed in any convenient part of the
Machine.


  OF
  A ROTATORY CHOCOLATE MILL.

Figures 1 & 2 of Plate 47, exhibit this Machine. It is, merely, an
attempt to effect, by power and a rotatory motion, what is done by hand
and a vibrating one. To understand this latter, my readers (who have not
seen chocolate made) will suppose a metallic rolling-pin, but
cylindrical held in both hands, and moved parallel to itself, over a
slab of marble, to and from the person employed; who holds the
instrument _fast_ when pushing it from him, and suffers it to turn _a
little_ every time he draws it towards him. He thus presents, sometime
or other, every particle of the chocolate to every part of the slab and
the roller: and this is also done by the Machine shewn in Plate 47. In
figs. 1 and 2, _A_ represents a cylinder of stone or metal, used instead
of the aforesaid slab; and _B_ a cylinder answering to the roller in
question. The latter is placed, by it's axis, on two forks _a b_, so as
to lean, by it's weight, obliquely against the cylinder _A_, which it
does less or more heavily as the forks, or stands _a b_, are placed
nearer or farther off from the general centre. Further, the motions of
these two rollers _A_ and _B_, are connected by two equal (or nearly
equal) wheels _c d_, by which, when _A_ is turned, _B_ turns also; but
so as to give the surface of the latter _much less_ velocity than that
of _A_, though in the same direction. By these means, all the matter
adhering to both cylinders (for chocolate is made in an unctuous state)
is at one time or another, brought into intimate union, and ground
together; and thus is the usual problem resolved, on rotatory
principles: nor need we mention the several scrapers, &c. that would be
applied to gather up the paste to the middle of the rollers, when spread
abroad by the grinding process.

It may not be useless, just to say here, that this is likewise a good
mill for grinding paint or oil colours.


  OF
  A ROTATORY MANGLE.

I have insisted, often, on the propriety, mechanically speaking, of
doing every thing by rotatory motion; and thus of avoiding oscillation
wherever it is possible. The present Mangle is another attempt to employ
that principle. In Plate 47, figs. 3 and 4, is an under cylinder, turned
as usual by any convenient _power_. _B_ is a small cylinder not
connected with it, nor touching it, being intended merely to receive the
weight of the mangle-cylinder _D_, with the _goods_ rolled on it. _C_ is
an upper cylinder as heavy as necessary, or loaden through it's
_journals_ or centres, with sufficient weights to make it so. Again, the
motions of the two cylinders _A_ and _C_, take place in such a
direction, that any round body placed and pressed between them, would
receive from them the same motion; and thus, a roller of goods, there
introduced, will be _mangled_. This process is so performed, because the
cylinders have toothed wheels _a_, _b_, on their axes, but which do
_not_ geer together: These wheels being connected by an intermediate
wheel _c_, which makes them concur in producing the rolling effect above
mentioned. But, one thing remains to be observed: the wheels _a b_,
though drawn apparently equal, are not equal. The upper one _a_, has a
tooth or two _more_ than the under--so that the motion to the right hand
of the under surface of that cylinder, is not equal to the opposite
motion of the cylinder _A_. And hence, the cloth roller _D_, progresses
from _D_ towards _x_, between the cylinders _A C_, and finally falls out
at _x_, after as many turns of the whole, as the wheels _A C_ have been
calculated to give; and this, is according to the degree of mangling
required.


  OF
  A MACHINE,
  _For driving the_ SHUTTLE _of_ POWER LOOMS.

It is too late to bring this Machine into what might almost be called an
overstocked market of ingenuity--since many power Looms exist, work, and
seem to want nothing to make them perfect. But an idea of _forty years_
standing, founded on a principle worthy of attention then, may perhaps
not be altogether vain at present: Besides--I have engaged in my
prospectus to present it to the public. I could, indeed, enter into
other parts of the Power Loom--which I had then begun to execute; but
such is the rapidity with which that Machine is now _striding_ to
perfection, that it would be superfluous. I merely then, fulfil my
promise.

On the afore-mentioned occasion, I thought it of importance, that the
force employed to throw the shuttle, should be capable of being
regulated to any and every degree: and especially should be fully
_prepared_ to act, _before_ it's action began: and should, then, act
independently of every other impulse.

In fig. 1 of Plate 48, _A_ is a wheel or pulley of about six inches in
diameter, from which two cords proceed in opposite directions (_B C_)
to the _pickers_, which drive the shuttles _D E_ in the usual method.
This pulley runs on an axis going through the bottom of the lathe, (or
beater) and it _might_ have a crank, behind, of a radius equal to _a b_:
but to shew the whole in one figure, I suppose the following mechanism
to be placed in the front of the lathe, and just _before_ the face of
this wheel or pulley _A_. _c d_ is a bar turning on the centre _c_, and
receiving at it's other end the pressure of a spring _e d_, which in
it's turn, is susceptible of different degrees of springiness, as
regulated by the screw _f_. On a stud _i_ in the wheel _A_, is put the
small bar _i d_, which forms also a turning joint in the bar _c d_: and
thus communicates the effort of the spring to the stud _i_, and thence
to the wheel _A_. Finally, this wheel has either under it, on the front
side of the lathe, or on it's axis, at the back, a pulley, by which it
can be turned, by means of one or other of the cords brought from the
_breast beam_ of the loom, round the pullies _x_ and _y_, to this wheel
_a b i_, according to the dotted lines. Supposing then, _one_ of these
cords to be tightened by the backward motion of the lathe, it will draw
the wheel _A_ about half round: when the stud _i_ will rise to the point
_b_, straining the spring to get over the centre: and as soon as it _is_
over, the spring will _act_, and drive the picker and the shuttle with
the desired speed, independently of any other _mover_. And it is
evident, that now the opposite cord _x_ or _y_, will be tightened so
that when the lathe shall be again pushed backward to form the opening
for the shuttle the slide will be carried back over the centre _a_, and
re-produce another impulse in a contrary direction.


  OF
  AN AIR PUMP,
  _Or_ ESSAY _towards completing the Vacuum_.

The rapidity with which a vacuum is formed by an Air Pump, depends on
the _ratio_ between the contents of the receiver and those of the pump
barrels. If the latter be just equal to the contents of the former,
(which is a _very_ large proportion) the exhaustion will follow this
series:--there will _remain_ in the receiver after each stroke, the
first contents being 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256,
&c. But if the pump barrel contains _twice_ the volume of the
receiver--then the remaining air, after the strokes, will be 1/3, 1/9,
1/27, 1/81, 1/243, 1/729, 1/2187, 1/6561, &c. being much nearer to a
vacuum than on the former supposition.

To meet this case, then, I have thought a water pump might be used: that
is, a barrel or vessel, _much_ larger than the receiver; and which by
the action of a smaller pump, placed on a lower level, might be
alternately filled with water and emptied so as in a few operations to
complete the exhaustion, very nearly.

Thus, in fig. 2 of Plate 48, _A_ is a receiver, _B_ is a large vessel
that can be filled with water from the tub _C_ below; and _D_ is the
pump, worked by the handle _E_. It is a common water pump, (so much the
readier adopted, as requiring _little_ care in the execution.) The
question was to make this pump alternately _fill_ and _empty_ the vessel
_B_. Adverting first to the _filling_, _a c_ are two cocks, having each
a side-passage for the water; and these passages are _now_ so placed, as
by working the pump we suck water out of the tub _C_, and throw it into
the vessel _B_, through the valve _b_;--by which means all its air is
driven out through the lateral valve _e_. When this is done, the cocks
_c d_ (which are so made as to be worked by the same _mover_) are turned
into a new position, which opens the pipe _p_ to the pump _D_, and
_that_ _q_ to the returning spout _r_; by which means the water is drawn
_from_ the vessel _B_, and thrown into the tub _C_: so that the air is
again drawn out of the receiver _A_, through the inverted valve _s_,
into the vessel _B_, and another degree of exhaustion occasioned. This
being done, the cocks are again put into their present position; the air
expelled by the water through the valve _e_ as before, and a new stroke
prepared. It is scarcely needful to add, that if the vessel _B_
contained ten times as much volume as the receiver _A_, the exhaustion
of the latter at each emptying of the vessel _B_ would follow this
ratio--1/11, 1/121, 1/1331, &c. thus approaching by rapid degrees to a
perfect vacuum. The water, or liquid, used for this purpose would of
course be as perfectly purged of air, as possible.


  OF
  AN INCLINED WATER WHEEL.

The principal mechanical merit I conceive this Machine to possess, lies
in the facility it gives of taking a stream of water as _high_, and
discharging it as _low_ as possible: and both nearly in the direction in
which it naturally flows. Of the advantage it possesses in keeping the
water a long time from falling, I shall not now speak, as it would
require more discussion than this work comports; and, moreover, the
Plate confines us to a somewhat contracted representation, which I hope
my readers will excuse.

Plate 48 fig. 3, _A B_ is the section of the wheel, and _C D_ a small
portion of it's circumference--which shews the form and position of the
floats _a b c_, &c. _E_ is a floor on which the upper water flows, and
from which it falls thinly on to the wheel--whose motion is purposely
made as slow as possible. The water then, occupies one half of the
wheel's circumference, falls by a gentle slope and finally leaves the
wheel at _d_, whether it there touches the lower water, or not. This
wheel is allowed to be incapable of _using_ to advantage a large stream
of water--but is doubtless fit to employ a small stream, _in the best
manner_.


  OF
  A VESSEL,
  _To assist in taking Medicine, &c._

I have hesitated a moment to describe this method of helping the weak,
in body or mind, to conquer their aversion to medicine--several persons
having threatened me with a larger dose of ridicule than I am prepared
to swallow. But surely, if we can only conquer a child's timidity, so as
to induce him to take, speedily, what his health requires, we shall not
do a thing altogether laughable. We shall, perhaps, preserve a beloved
child to the solicitude of a mother! and perhaps--a citizen to his
country! If then, some laugh, _more_ will approve; and I therefore
continue the promised article.

Fig. 4 of Plate 48, shews this cup, composed of an inner and an outer
vessel: the first to hold the medicine, and the latter a little tea, or
other proper liquid to wash it down. The cups have a spout common to
both; but the outer cup retains it's contents as long as the small
funnel _a_, is stopped with the thumb or finger. Thus then, the medicine
is first taken, while the liquid is retained in the outer vessel--but
the thumb being removed, the liquid also flows into the mouth, and in a
good measure removes the taste it was wished to disguise.


  OF
  AN AERO-HYDRAULIC MACHINE,
  _For raising Water in large quantities_.

The art of constructing Mills, or Machines to be driven by the wind, is
so well known, that the results are considered as being, very nearly,
what a perfect theory would require. It is, therefore, no part of my
purpose to discuss either the theory or practice of that art. But I
think _that a still wider grasp may be taken of this powerful agent_, so
as to secure a further degree of utility, even while following less
closely the abstract principles of mechanical philosophy. I enter then,
directly, on the description of another of my _wind Machines_, in order
to give an idea of the means I contemplate for _losing_ the importance
of those details in the magnitude of the general effect.

This Machine (see Plate 49, fig. 1,) is capable of great results
_merely because it employs, at a small expence, a great mass of air in
motion_; whether _ill_ or _well_, is not the question: for as this
source of _power_ is almost indefinite, methinks we may draw from it
without reserve. The present method of so doing, consists in using _a
very large sail_, (_A B_) both to receive the impulse of the wind, and
to raise the water. This figure is _a section_ of the Machine _in it's
length_:--and it's _width_ (not represented) is as great as the occasion
may require. The sail is here shewn as placed over a lake or other sheet
of water which it might be wished to drain, (or which may serve as a
mill pond to drive any required Machines, by the water thus raised.) _C
D_ is the water in it's lower bed: and _E_, is a canal on a higher
level, into which a large quantity is thrown at each _man[oe]uvre_ of
the Machine, _a_ is the bank of the upper canal, to which is affixed the
_edge_ of the canvass, of which _a B A d_, is a section; and which
_might be_ large to immensity. At 1 2 3, &c. is a row of stakes as long
as the Machine; and they are capped transversely with round poles, on
which the sail rests when in it's lowest position. In this state, also,
the part _b_ of the sail, plunges into the water, which rises above it
in the prismatic form, _b r s_; a row of valves or clacks, (_b_)
permitting it to rise through them, but preventing it from again falling
that way. Thus, at every change, this prism of water, is sure to be
replenished; and if we suppose the triangle _b r s_ to have an area of
ten square feet, and the prism to be one hundred feet long, the water
there contained will be a thousand cubic feet--capable, however, of
being augmented or diminished at pleasure, by slackening or tightening
_the sail_ towards _A_. At _d_, is the weather-end of this sail, which
is supported when at rest, on the surface of the water, by the posts and
caps before mentioned. This end _d_, of the sail is connected with a row
of posts _C F_, placed more or less closely, as the prevailing strength
of the wind and the _size_ of the sail may require. The sail is held to
these posts by rolling pulley frames, of which _one_ is seen at _g_, and
is drawn up and down by the rope _g h_, acting at one end directly on
the rolling pulley-frame _g_, and the other on the sail _d_, after
having passed over a pulley (_F_) in the post itself: where note, that
this effect can be communicated by proper machinery, from any _one_ of
these posts (_C F_) to all collateral ones; so as to make the
man[oe]uvres general, _across the sail_, whatever be it's magnitude.

The following then, is the operation. The wind blows (by supposition) in
the direction of the arrows in the figure: and the rolling pulley-frame
_g_ is quickly drawn up to _g_, where the hook _i_ holds it fast. By a
necessary consequence the wind fills the sail _d c r_, and stretches it
into the figure _d A B a_: in doing which it lifts the water _r s_, and
_pours_ it, in all the width of the sail, into the canal _E_; thus
raising a thousand cubic feet of water at each stroke. As soon as the
water is turned into the canal _E_, the hook _i_ is pulled outward, and
the rolling pulley _g_ is forced down, by the wind itself, to the
position k, when the wind blowing _over_ the sail, will give it a bent
form, (_k c a_) and soon bring the sail into it's present position on
the posts 1 2, &c.--when water will be again admitted by the valves at
_b_, and another stroke of the Machine be prepared.

The above contains the basis of this idea. I do not expect it will
obtain at once universal assent: But if I knew the several grounds of
objection, I am persuaded the greatest number of them could be removed.
The first I anticipate, is the difficulty of turning this Machine to the
several winds that may blow over it. To this objection I would reply,
that in such a case, the canal _E_, should surround an area made large
enough for the sail, of some polygonal form, say an octagon, to
different sides of which the stretching cords of the sail should be
carried, so as to catch the prevailing winds--but the direction of which
need not be followed to a nicety; since an obliquity of a few degrees
would not prevent the effect.

It might be added, that it is not indispensable that the canal _E_
should be stationary. Made of wood, or metal, it _might_ turn round a
fixed centre, and be braced into the necessary positions with
ropes--when the posts only (_C F_) would have to be removed, or quitted
for others duly placed. These ideas are connected with immense effects;
and cannot, therefore, be lightly disposed of: they both deserve and
require serious attention.


  OF
  ANOTHER WIND MACHINE,
  _Furnishing immense Powers_.

This is the last of those conceptions I shall now bring forward, for
making _more_ than a common use of the WIND as a first-mover of
Machinery. Horizontal windmills are well known; and this is a horizontal
windmill--yet not like those already in use: for, here, the sails, very
large and numerous, are placed on a boat in the form of _a ring_, which
thus moves through the water without any other resistance than that
arising from the asperities of it's surface.

In Plate 49, fig. 3, _B B_ is a section of the Vessel, placed in a
circular canal _D_, into which the lower water flows through proper
arches (_C C_) in the banks. The vessel is rigged with several narrow
horizontal sails, stretched on ropes between the oblique masts _a b_, _c
d_; and so placed, that the sails (being a little wider than the
interval between the ropes) can _open_ in one direction, but not in the
other; and they are shewn open at _c d_, and shut at _a b_, in the
figure. This, therefore, is a mill, that takes all winds; and although
it's uses might be various, we shall finish it's description as adapted
to raise water _by the centrifugal force_. As before hinted, the canal
_D D_ is circular; and has a bank, sloping outward, with a canal (_E_)
on it's top. When, therefore, the wind blows, the ring boat _B_ (held to
the centre by the ropes _f g_) revolves around it; and by one or more
water drags (_h_) which it carries, collects the water on and up the
bank, and finally drives it into the canal _E_, from which it flows in
_any_ destined direction. If for draining watery lands, it will be done
rapidly; if for irrigating, it will be done abundantly: if, in fine, for
driving any mill with the water thus raised, the machinery will be very
efficient, as working with ten or twenty times as much _sail_, as any
other windmill can carry. I add, merely on this occasion, that the sails
here mentioned, might be placed _obliquely_, instead of straight across
the ring vessel; (see the plan in fig. 2 of this Plate at _E F_) from
which disposition, nearly all the advantages of the _vertical_ mill
might be transferred to the horizontal; and with this remark I leave the
present interesting subject to the studious and candid reader.


  OF
  A CENTRIFUGAL MIRROR,
  _To collect Solar heat_.

My fiftieth and last Plate contains this idea: It is _not_ intended to
vie with the usual mirror, in correctness of form, or intensity of local
effect--but to offer, by the largeness of it's dimensions, some
properties which _better_ mirrors cannot present. It is _intended_ to
pave the way for the use of the Sun's rays in _Engines of Power_. For
this purpose, however, it must probably be transported to some tropical
climate, where "a cloudless sun" diffuses it's rays more constantly, and
less obliquely, than in our northern climes.

This is the more necessary here, because this Mirror can only be used in
a horizontal position, and is in fact a fluid Mirror. Fig. 1, shews it
mounted on a steady frame _A B_, and having a strong axis on which it
can be turned, faster or slower, according to it's dimensions; and it
may or may not be floated on water, to lessen the stress on the axis.
The Mirror, properly speaking, is composed of mercury--contained in the
revolving vessel _C D_, whose motion should be given by proper machinery
in the most uniform manner possible. The mercury, thus turned, acquires
a concave surface, _a_, _b_, _c_; and receiving the parallel rays _d c_,
_e b_, and, _f a_, collects them into the focus _F_; in, or near which,
is placed the vessel where the effect is to become useful, and which of
course is _moveable_ so as to follow the sun's motion. Those of my
readers who have seen the machines used for fixing the sun's image in
the solar microscope, will be at no loss to conceive how our present
focal station must be _moved_ to adapt it to a _fixed_ mirror. I shall
only add further, that it is not necessarily an _exact_ movement that is
here wanted; since the vessel to be heated would have dimensions
somewhat large, and the focus itself be only brought to a moderate
degree of precision. In a word, the utmost heat wanted would be, what
could be usefully employed in heating water. It remains then to be
observed, that the source of power, in this Machine, is _magnitude of
parts_, more than precision of form: yet it may be mentioned, that the
form we thus procure in the revolving mercury, is a solid of revolution,
having the _logarithmic curve_ (_a_, _b c_) for it's section--a curve,
which in fact, comes indefinitely near to the parabolic figure which
_would be_ required, if greater precision were attempted. We finish
then, by observing, that the bottom itself of the revolving vessel might
be made concave, (like the dotted line under _that a b c_) in order to
avoid the necessity of using a large quantity of mercury, to form the
reflecting surface.


  OF
  A SECOND MIRROR,
  _For collecting the Sun's rays_.

This Mirror seems superior to the former, as depending on _fixed_
materials. It likewise, produces the desired effect, by offering a _very
large surface_ to the sun, and directing the rays to a focus, nearly
enough to give the heat required for water, as before mentioned.

To do this, a frame _A_ (Plate 50, fig. 2) holds the Mirror; and this
frame has a horizontal motion round the _post_ _B_, something like a
common windmill. In this frame and on two horizontal trunnions, turns
the Mirror _C D_: and one or both these trunnions are hollow, to admit
of a process we shall shortly mention. This Mirror itself is composed of
an air-tight ring _C D_, of a width proportionate to the diameter
adopted; and on which are fixed two _heads_, much like those of a
_tambourine_, (or the _under_ head might be made of some metallic
substance). The head _a b c_, is made of a fine texture, duly prepared
and varnished till it becomes air tight, and then there are stuck to it,
a number of small _hexagonal_ looking-glasses or mirrors of any kind,
(see fig. 7) which thus fill up the whole space, and prepare the Mirror
for the intended change of form. The method of giving this form,
consists in exhausting, more or less, this _tambourine_ of air, when, by
the pressure of the atmosphere, the heads will take the form _a b c_,
that is a _spherically concave form_--fit to reflect the sun's rays _as
correctly_ as this our object requires; and thus may some thousand small
images of the sun be brought to fall on the same spot, and an immense
heat be occasioned. The accounts we have of the destruction of the Roman
fleet by the _united_ mirrors of Archimedes, make this process appear
the more feasible--as whatever were the methods of uniting the _foci_ of
his mirrors, a similar effect _may be expected_ from this simple
process.

My readers will perceive that this Machine has the advantages of the
universal joint, by which it can be directed to the sun in every
position; and even made to fix his ardours on any immoveable spot for a
good length of time. The persons to whom I particularly address these
ideas, will require no further details to conceive the less obvious
circumstances of this Invention. In general, we want no effect that
requires _optical precision_: but if we did, it could be obtained to a
good degree, by methods similar to these.

I shall only add here, that this fig. 2 is given _as a section_--because
intended to represent a parallelogram, as well as a solid of revolution:
and thus (with proper mirrors) to make what now appears a spherical
focus, _a linear one_--fit to heat a cylindrical vessel with it's
contents; and thereby draw _power_ from the sun's heat, _without_
running expense. I am serious when I say, that we can thus, practically,
collect the solar rays which fall on many hundred square feet of
surface; and produce by them, at any desired distance, effects to which
those obtained from _modern_ burning mirrors, are but as sparks to a
blaze.


  OF
  AN ENGRAVING MACHINE,
  _For large Patterns_.

This Machine supposes at once a _new kind_ of engraving, and admits of
patterns of _very large_ dimensions. This kind of engraving will be best
understood by persons acquainted with figure-weaving; and especially
with the manner of _mounting_ the looms for that purpose. In that
System, (see Plate 50, fig. 8) the patterns are drawn on ruled paper
divided into squares; and each of these squares represents a point in
the texture, composed of one or more threads each way; insomuch that
whenever that _square_ has any desired colour in it on the pattern, it's
threads are _taken_ by the person who prepares the loom; and they are
_missed_ in every case where nothing appears in that square, or a colour
not then wanted. Now, whatever be the dimensions of these elementary
points on the loom, they may be represented by squares of any convenient
size on the pattern: only remembering that the smaller they are, in
reality, the better will be the delineation. Thus in carpeting, for
example, an element of this kind may be a square of one tenth of an inch
and more; while one on a ribbon or a piece of silk, is often not the
hundredth part. And therefore, the perfection of this engraving depends
on the fineness of the points of which the figures are composed. For, in
a word, this System proceeds on the same principle. When any part of a
line requires a dot or mark to be made, the Machine strikes a blow
_there_; and when no impression is to be made, the Machine (by means
that will be shewn) suffers the cylinder to pass that place without
striking. The means of regulating this is committed to workmen who
merely know how to _read_ off the pattern _in it's length_, as it is now
read off _in it's width_ by the weaver. To describe the construction of
the Machine, (as exhibited in figs. 3 and 4 of Plate 50) _A_ is the
cylinder to be engraved; and _B_ is a worm-wheel _fixed_ to it's
mandril, and destined to turn it. This it does, slowly, by the endless
screw _a_, as turned by proper straps on the fast and loose pullies _b
c_, (figs. 3 and 4). _C_ shews a second wheel, concentric with that _B_,
but running loose on it's axis, which is a pin fitted into the end of
the mandril. This wheel, when the threads of the screw _a_ are _fine_,
requires a motion more rapid than the wheel _B_--to give which motion by
means of the latter, we use a pair of multiplying wheels _d_, which
geer, one in the larger bevil wheel cut near the edge of the wheel _B_;
and the other in a smaller bevil wheel cut or fixed on the inner face of
the wheel _C_--and whence this latter wheel receives a velocity of about
ten times the speed of _B_. The use of this wheel _C_, is to carry,
across the Machine, certain bars, of wood or metal, shewn in figs. 5 and
6, whose function is to carry short pins or studs 1, 2, 3, 4, &c. for
the purpose of determining the places _where_ the punch is to act, and
where it is not. To this end, _g h_ is a frame, which is raised by a
_cam_ or tappet _i_, fixed in the endless screw _a_, once every turn;
and _that_ through the medium of the little tumbler _i e f_, by which is
finally determined whether the stroke shall take place or not--for _m_
being a section of the stud bar of figs. 5 and 6, it's pins, _when they
occur_, raise the end _f_ of the bent lever _f e i_; and when there is
no pin or stud in _m_, this lever is not raised, and the point _i_, does
_not_ come near enough to the cam to be laid hold of, in which case no
stroke is given. This then, is so whenever the studs fail in the bar
_m_; and these fail whenever the _pattern-reader_ has said to the
stud-setter, _miss_: and they occur whenever he has said _take_--both
which cases happen more or less often according to the state of the
squares in the pattern.

To be a little more particular: in fig. 5 we see a part of the wheel _C_
of fig. 3, and also a part of the stud bars _m m_, which _geer_ in the
wheel _C_, and which being conducted by the guides _n_, follow the
motion of that wheel, presenting at _f_, (fig. 3) a stud to raise the
lever _f e_, whenever the pattern requires it. It may be mentioned, that
these studs act _obliquely_ on the wing _f_ of this lever, and thus
_raise_ it as they pass under it. And further, these stud bars are made
and fitted to each other in the manner shewn at fig. 6. There is a
geering tooth under every stud hole, and the last stud hole of a given
bar has, fixed in it, a thin tube _a_, into which the stud enters the
same way as in any other place: but this tube whether studded or not
serves to lay hold of the succeeding bar _b_, by it's first hole--so, in
fine, as to make the bars endless; the attendant having nothing else to
do than to hook them to each other as the wheel _C_ draws them in.

Thus then, are the strokes of the _hammer frame_, _g h_, conformed to
the pattern: for these bars have been studded before hand by one or more
readers and setters; and it is a merely mechanical process to put them
in while the Machine moves: from which, by the bye, they _fall out_
after the passage into a proper box, and the studs out of them, to be
_composed_ again from the succeeding figures of the pattern. A dozen or
two of these bars might be prepared at _any_ time and place, and to
_any_ pattern, which they will thus transfer to a cylinder at _any_
desired moment, without the further preparation of dies, punches, mills,
&c.--as used in other Machines. N. B. The strength of the blows thus
given by the hammer frame _g h_, is lessened or augmented by the
position of the point _i_ fixed to the bent lever _i e f_, and which
makes that lift higher or lower as required--which is a mean of
_shading_ offered by this Machine. But to mention it's other properties,
the endless screw _a_, (figs. 3 and 4) carries another endless screw
_o_, _more or less fine_, which turns at the same time the wheel _p_,
and, by that, the long screw _s s_, whose office it is to shift, slowly,
the punch carriers _k l_, along the Machine, from _k_ by _l_, towards
_s_. And here an observation occurs: this can only be so, when the
pattern permits the action of the punches _k_ or _l_, to take place
_spirally_ on the cylinder; that is, when the _sketches_ are distinct
enough _not_ to shew the anomaly that would occur were a _straight_
pattern thus transferred to a set of spiral lines. But should it be
desirable to engrave patterns so correct as to require an exact parallel
motion round the cylinder, _then_ the motion of this screw must _not_ be
continual--but must intermit and be resumed, at every beginning of a new
line round the cylinder. I hope, I make myself understood: a pattern
drawn on _squares_, produces lines all parallel to the first; while the
spiral motion of the punch causes a slight deviation--which, in a word,
can either be suffered or avoided. At all events, this deviation is so
much the smaller as the punch motion is slower in both directions; and,
in _fine_ patterns, must be _very small_. One remark will close this
part of the subject: although a fine pattern, requires a great number of
blows, and thus a certain expence of time, each blow can be so much the
lighter and more frequent; so as to compensate, in some degree, for this
cause of delay. I add, that the levers shewn above and around fig. 6,
are intended to lift the hammer frame _g h_, equally at both ends: while
the screw _Z_ regulates the _depth_ to which it is permitted to fall.

I observe, finally, that, according to the size of the intended pattern,
there are more or fewer of the punch bearers _k l_, connected, by their
nuts, with the screw _s s_; each of which thus engraves it's sketch,
similar to the collateral ones; and that were it wished to make _one_
pattern of the whole length and circumference of the cylinder, a single
punch bearer would be required--since nothing else limits the extent of
a pattern engraved by this Machine.

       *       *       *       *       *

Thus have I gone through my proposed "Century of Inventions," for every
imperfection in which I beg the indulgence of my numerous readers. And
here I can truly say I have _neglected_ nothing--although the precarious
state of my health may have sometimes veiled the evidence of my
descriptions. On the other hand, I did not even attempt many of the
lesser details of execution; as I wrote for those to whom they would
have been superfluous: but as to the objects themselves, I believe there
is not one that is without the pale of practical utility. In a word,
many of the subjects have been frequently executed, and _are in daily
use_: and as to those which remain to be tried, I engage, if called on,
to give them useful existence. And the better to convince candid minds
of the serious attention I have paid to these subjects, I shall add _the
scales_ on which they have been executed, or to which they are
drawn--those scales expressed by a fraction, shewing what proportion the
figures bear to the reality. Thus the scale of one inch to a foot will
be expressed by the fraction 1/12; that of two inches to a foot, by 1/6,
&c. that is, the figures, in these cases, will be (nearly) 1/12 or 1/6
of the size of the Machines. This premised--and also that we shall
observe the alphabetical order, the following is the


TABLE OF CONTENTS.

  No.                                                    Scale     Page.

    1 ADDING MACHINE; or Machine to cast up large    ||           |
      Sums                                           || 1/2 and 1 | 343
    2 Air Pump: Essay to complete the Vacuum         || 1/10      | 374
    3 Barrel Spring, to lengthen the going of        ||           |
      Clocks, &c.                                    || 1         |  26
    4 Boats (serpentine) for lessening the expence of||           |
      traction, &c.                                  || 1/75      | 137
    5 Bobbin or Laces, (Machine for making) covering ||           |
      Whips, &c.                                     || circa. 1/5| 284
    6 Bowking Machine, for Bleachers                 || 1/24      | 299
    7 Bucket or Persian Wheels, (a combination of)   ||           |
      to raise Water                                 || 1/24      | 172
    8 Canals (open) as hydraulic Machines            || circa.    | 307
                                                     || 1/200     |
    9 Canter, or inclined plane for Draymen          || 1/24      |  72
   10 Chain to act equably on my Wheels              || circa. 1  | 135
   11 Chocolate Mill (rotatory)                      || 1/12      | 368
   12 Cocks (equilibrium) to avoid leakage, &c.      || ad. lib.  | 153
   13 Colour Mill, for Calico Printers               || 1/12      | 175
   14 Compasses (bisecting)                          || 1/2       | 353
   15 Cotton-Machine for batting or _bowing_         || circa.    | 290
                                                     || 1/12      |
   16 Crane (rewarded by the Society of Arts)        || 1/60      |  57
   17 Crank, epicycloidal; or parallel motion        ||           |
      (rewarded by Bonaparte)                        || 1/8 1/12  |  30
   18 Dash, or Wash Wheel, acting with greater       ||           |
      rapidity than usual                            || 1/24      | 271
   19 Differential Wheels, for gaining great power   || 1/4       |  54
   20 Doffing Machine, to take cylinders from their  ||           |
      mandrels                                       || 1/9       | 243
   21 Draw Bench, for my twisted Pinions             || 1/2 1/6   | 133
   22 Dynamometer, for measuring power _in motion_   || 1/4       |  15
   23 ------------ a second kind for do.             || 1/3       | 177
   24 Engine, for cutting my Patent Wheels           || V. text   |{121
                                                     ||           |{183
   25 Engine, for cutting large bevil Wheels and     ||           |
      Models                                         || 1/12      | 263
   26 Engraving Machine, being an important          || 1/12 and  | 317
      application of my Cog or Toothed Wheels        || 1/14      |
   27 Engraving Machine, of a new kind, for large    ||           |
      patterns                                       || 1/14      | 389
   28 Essay to derive _power_ from expanding solids  || 1/20      | 280
   29 Evaporation (Machine to promote)               || ad. lib.  |  78
   30 Eyes (Machine for making rapidly)              || 1/2       | 166
   31 Fire-Escape, on a retarding principle          || 1/2       | 364
   32 ------------ by breaking the fall              || ad. lib.  | 366
   33 Fires (portable Engine to extinguish)          || 1/24      | 311
   34 ----- (watch Engine always ready for)          || 1/6       | 315
   35 Flax (Machine for breaking rapidly)            || 1/24      | 296
   36 Forging bar iron and steel (Machine for)       || ad. lib.  | 215
   37 Friction (Machine to prevent)                  || ad. lib.  | 144
   38 ----------------- of another kind              || ad. lib.  | 150
   39 Grating or cutting Green Roots, &c. (Machine   ||           |
      for)                                           || circa. 1/6|  79
   40 Helico-centrifugal Machine, for raising water  || ad. lib.  | 212
   41 Horse Wheel, (inclined) to save room and gain  ||           |
      speed                                          || 1/60      |  53
   42 ------------ (reciprocating) for Mangles, &c.  || 1/30      | 217
   43 Hot Air as _power_, while heating rooms, &c.   || ad. lib.  | 203
   44 Lamp (hydraulic) for the table                 || 1/6       | 277
   45 Lithographic, or Copper-plate Press, with      ||           |
      curious and useful properties                  || 1/12      | 230
   46 Machine to communicate and suspend Motion      || ad. lib.  | 155
   47 ------- to set-on and suspend rapid Motions    || 1/2       | 158
   48 ------- for clearing turbid Liquors            || ad. lib.  | 305
   49 ------- for driving Boats, without disturbing  ||           |
              the Water                              || ad. lib.  | 251
   50 ------- to assist in taking Medicine           || 1/3       | 377
   51 Mangle, perpetual or rotatory                  || 1/16      | 370
   52 Marine Level (essay on a)                      || circa.    | 357
                                                     || 1/18      |
   53 ------------ (other essay on a)                || ad. lib.  | 362
   54 Micrometer, to measure minute spaces           || 1         |  83
   55 Mirror, (centrifugal) to collect the Solar rays|| ad. lib.  | 384
   56 -----------------------------------------------||           |
      of a different kind                            || ad. lib.  | 386
   57 Mover, by dropping weights                     || ad. lib.  |  76
   58 Nails (Machine for moulding)                   || 1/12      | 200
   59 ----- (Machine for forging)                    || 1/10      | 226
   60 Parallel Motion (double) for heavy Steam       ||           |
      Engines                                        || ad. lib.  | 338
   61 Pencyclograph; or instrument for drawing       ||           |
      portions of large circles, and finding their   ||           |
      centres by inspection                          || ad. lib.  |  51
   62 Peristaltic Machine, for raising water         ||           |  69
   63 Pitch Fork for Musicians, with variable tones  || circa. 1  | 355
   64 Power Wheel, by heated Air, &c.                || ad. lib.  |  43
   65 Press, direct and differential (power as 52000 ||           |
      to 1)                                          || ad. lib.  |  66
   66 Press (excentric bar)--power indefinite        || ad. lib.  | 174
   67 Printing Machine (two coloured)                || 1/12      | 301
   68 Protracting Motion (Machine for)               || 1/4       |  49
   69 Pullies (my Patent) much improved              || 1/6  1/12 |  33
   70 Pump (equable) proposed 1794, for the Machine  ||           |
           of Marly                                  || 1/24      |  45
   71 ---- portable, worked by the hands and feet    || 1/24      | 351
   72 Punch Machine, for Engravers                   || 1/4       | 193
   73 ----- Machine (differential) for ditto         || circa. 1/7| 196
   74 ------------- rotatory, for my Engraving       ||           |
                    Machine                          || 1/6       | 349
   75 Reciprocating or long Parallel Motion          || ad. lib.  | 237
   76 Reflector, for Light Houses, &c.               || ad. lib.  | 234
   77 Regulator (not centrifugal) for Wind and Water ||           |
      Mills, Steam Engines, &c.                      || 1/4       | 223
   78 Retrographic Machine, for Engravers            || ad. lib.  | 164
   79 Rotato-gyratory Churn                          || 1/10      | 210
   80 Screw, with greatly diminished friction        || ad. lib.  |  81
   81 Screws (Machine for forging)                   || 1/3       | 160
   82 Spinning Machines (my Patent)                  || circa.    | 329
                                                     || 1/17      |
   83 ----------------- adapted chiefly to Wool      || 1/12      | 334
   84 Spring, to keep a door closed yet open easily  || ad. lib.  | 131
   85 Steelyard (differential) of great power        || 1/8       | 162
   86 Syphon (mechanical) to expel part of the Water ||           |
      at the highest point                           || ad. lib.  | 240
   87 Tallow (Machine for cutting and _trying_)      || 1/80      | 245
   88 Tea Table (mechanical assistant for)           || 1/8       | 228
   89 Valves (slide) Machine for working             || ad. lib.  | 255
   90 Ventilator, rotatory, yet by pressure          || 1/12      | 170
   91 Vessel (expanding) for Pumps, Steam Engines,   ||           |
      &c.                                            || ad. lib.  | 219
   92 Washing Apparatus, for Hospitals, &c.          || ad. lib.  | 247
   93 Water Wheel (horizontal) probably the best of  ||           |
      the impulsive kind                             || 1/52      | 326
   94 The same, for high falls                       || ib.       | 326
   95 Water Wheel (inclined) using the weight of the ||           |
      water                                          || ad. lib.  | 376
   96 Water (aero-hydraulic Machine for raising)     || 1/200 or  | 292
                                                     || 1/300     |
   97 Weaving by Power (manner of driving the        ||           |
      shuttle, executed A. D. 1780)                  || 1/12      | 372
   98 Wedge Machine (perpetual)                      || 1/12      |  74
   99 WHEELS (my System of Cog or Toothed)           || all       |  90
                                                     || dimensions|
  100 Windmill of _double power_                     || 1/220     | 313


ERRATA.

  Page.
    1, line 27, after System, read of.
    4,   "  27, for them, read it.
   10,   "  16, for vestuble, read vestibule.
   15,   "  10, for parralel, read parallel.
   15,   "  13, after centre, read of.
   42,   "   7, after was, _dele_ on.
   43,   "   1, for Plate 2, read Plate 8.
   49,   "   1, after _A_, read Fig. 4.
   70,   "   7, for ionical, read conical.
  100,   "   2, after _A C_ for :, read ::.
  102,   "  16, for _z_/_a_, read _z_²/_a_.
  126,   "   4, for on it's surface, read on it's pitch line.
  126,   "  17, for it's height _f g_, read the length required.
  129,   "  16, for 2 inches, read 4 inches.
  164,   "  10, for other two cases in _C_ & _E_, read in other two
                cases _C_ & _E_.
  188,   "  17, after _b C_ twice, for :, read ::.
  196,   "  20, for fig. 2, read Fig. 4.
  200,   "   8, for Plate 25, read Plate 24.
  203,   "  11, after heat, read for.
  208,   "   6, for is, read are.
  209,   "   8, for arrangements, read arrangement.
  246,   "  19, after which, read last.
  272,   "  23, for wheel, read bevil wheel.
  273,   "  21, for axis, read axes.
  287,   "  19, for _z´_, read _z_.
  289,   "   1, after down, read twisted.
  294,   "   7, for two, read too.
  311,   "   8, for carried, read used.
  335,   "  10, for bobbin, read bobbins.
  340,   "   8, for edged formed, read wedge formed.
  350,   "   8, for Fig. 3, read Fig. 6.
  357,   "  18, for light, read double.
  374,   "  12, after 1/27 read, 1/81, 1/243, 1/729, &c.
  375,   "  20, for 1/14641 read 1/1331.
  387,   "   9, for makes, read make.


    [***] If, in the following List of Names, it has been thought just
    to mark those of the _first_ promoters of this Work, it has not been
    to lessen the Author's obligations to the rest--who, almost
    uniformly, have given him their Names with the same spontaneous
    kindness, and thus ensured his lasting gratitude.


ALPHABETICAL LIST OF SUBSCRIBERS.

  Abel, S. _Bury_
  Addison, G. W. _Huddersfield_
  Adshead, James, _Stayley Bridge_
  Agnew, Robert M. D. _Manchester_
  Ainger, A. _London._
  Ainsworth, G. Stayley Bridge
  Ainsworth. Richard _Bolton_
  Akroyd, James _Halifax_
  Akroyd, Jonathan _Do._
  Allen, T. & Sons, _Huddersfield_
  Andrew, James _Manchester_
  Andrew, Thomas _Do._
  Antrobus, P. & Nephew, _Bollington_
  Appleton, Ogden & Co. _Manchester_
  Appleton, Plant & Co. _Do._
  Armistead, J. & J. _Leeds_
  Armitage, Cyrus _Ashton_
  Ashton, Benjamin _Hyde_
  Ashton, George _Manchester_
  Ashton, James _Hyde._
  Ashton, John Junr. _Do._
  Ashton, Joseph _Do._
  Ashton, Robert _Do._
  Ashton, Samuel Jun. _Do._
  Ashwell, James _Nottingham_
  Aston, William _Birmingham_
  Atkinson, George _Burnley_
  Atkinson, Joseph _Manchester_
  Atkinson, Thomas _Do._
  Axon, Charles _Stockport_
  Aydon, Isaac _Wakefield_

  Babbage, ---- F. R. S. _London._
  Bailey, ---- _Halifax_
  Bailey, William _Holborn, London._
  Baird, J. & R. _Glasgow._
  Baldwin, J. & J. _Halifax._
  Barclay, John & Co. _Paisley._
  Barge, John & Co. _Manchester._
  Barker, ---- _Do._
  Barnes, John _London._
  Bartholomew, J. & Co. _Glasgow._
  Barton, H. _Manchester_
  Bassett, Thomas _Bury_
  Bates, John _Bradford_
  Bayley, Abel Stayley _Bridge_
  Beaumont, Thomas _Huddersfield_
  Beckton, Joseph _Manchester_
  Beecroft, Heath & Co. _Kirkstall_
  Beeston, Thomas _Leeds_
  Beilby & Knotts, _Birmingham_, 3 Copies
  Bellhouse, David _Manchester_
  Bennet, ---- H. M. Dock Yard, _Chatham_
  Bentley, Richard _Bolton_
  Berthonneau, ---- _Paris_
  Bevan, R. _Wigan_
  Bewley, ---- _Manchester_
  Binns, A. _Stockport_
  Binyon, A. _Manchester_
  Birley, Captain H. H. _Do._
  Birley, Richard _Do._
  Birtles, ---- _Do._
  Blackie and Pollock, _Glasgow_
  Bonsall, Thomas _London_
  Booth and Co. _Park Iron Works, Sheffield_
  Booth, John _Manchester_
  Booth, George _Stockport_
  Bowes and Kilham, _Leeds_
  Bowler, James _Manchester_
  Bowman, James _Do._
  Bradbury, J. L. _Do._
  Bradley, J. _Warwick_
  Branthwaite, F. and J. _London_
  Bramah, Francis _Do._
  Bramley, R. _Leeds_
  Bransome, ---- _Manchester_
  Branthwaite, James _Do._
  Brearley, James _Bolton_
  Briarley, Benj. _Blackburn_
  Briden, John _Birmingham_
  Bridson, Ridgway _Bolton_
  Brindley, ---- _Rochester_
  Brook, Jonas and Brothers _Meltham_
  Brooke, John _Shepley Hall_
  Brooke, John and Sons _Huddersfield_
  Brooke, ---- _Dewsbury_
  Brooks, S. R. _American Consul, Manchester_
  Broom, Sons and Home, _Kidderminster_
  Brotherton, J. _Salford_
  Brown, Baldwin L.L.D. _London_
  Brown, S. H. Halifax
  Brown, Thomas _Barnsley_
  Brown, Thomas _Manchester_
  Buchan, Laurence _Do._
  Buchanan, A. _Glasgow_
  Buckley, John _Todmorden_
  Burford, D. and Co. _London_
  Burn, John _Manchester_
  Burton, George _Middleton_
  Burton, John _Warwick_
  Bury, James _Manchester_
  Bury, John _Pendle-hill_
  Bury, Thomas _London_
  Bury, Thomas _Salford_
  Busk, R. _Leeds_
  Butterworth, Thomas _Oldham_

  Carruthers, John _Manchester_
  Carter, Benjamin _Huddersfield_
  Carter, John _Elland_
  Cartledge, Joseph and Sons _Halifax_
  Casey, Thomas _London_
  Cawood, John _Leeds_
  Chadwick, William _Oldham_
  Challinor, Thomas _Manchester_
  Chapman, Samuel _Ashton_
  Chappé, Paul _Manchester_
  Cheetham, Daniel _Stockport_
  Cheetham, John _Ditto_
  Cheetham, Joseph _Ditto_
  Cheetham, Josiah _Ditto_
  Church, William L. L. D. _London_
  Clare, Peter _Manchester_
  Clark, John Jun. and Co. _Glasgow_
  Clark, Richard Shalford, _Surrey_
  Clayton, D. _Poynton_
  Clement, ---- _Paris_
  Clogg, R. _Manchester_
  Clunie, John L. L. D. _Pendleton_
  Clymer, George _London_
  Cocker, Jonathan _Salford_
  Cogger, Thomas _London_
  Colden, D. C. _New York_
  Collinge, Charles _London_
  Colman, J. M. _Norwich_
  Colquhoun, James _Sheffield_
  Compton, Joseph _Manchester_
  Cook, James _Glasgow_
  Cooke, Thomas _Dewsbury_
  Cooper, Thomas Willis _London_
  Copley, Barrow & Co. _Manchester_
  Cort, & Co. _Leicester_
  Cottam, George _London_
  Coupland, R. & F. _Leeds_
  Cousen, James & Sons _Bradford_
  Cowan, John _Bolton_
  Cox, James _Manchester_
  Cox, Robert _Do._
  Craig, William _Do._
  Crawshaw, Jonathan _Wakefield_
  Crighton, J. & T. _Manchester_
  Crossley, John & Sons, _Do._
  Cryer, Jonathan _Bolton_
  Cussons, Thomas _Oldham_
  Cutfield, ---- H. M. Dock Yard, _Chatham_

  Dacca Twist Company, _Manchester_
  Daglish, John Orrell, _near Wigan_
  Daglish, Robert _Do._
  Dalton, John F. R. S. _President of the Manchester Philosophical
    Society._
  Darwell, ---- _Wigan_
  Darwin, ---- _Soho Rolling Mills, Sheffield_
  Day, George _Wandsworth_
  Dean, John _Bolton_
  Denison, Samuel _Leeds_
  De Volvic Comte Chabrol, _Paris_
  Dewer, Robert _London_
  Dewhirst, William _Halifax_
  Dickinson, ---- _New York_, 3 Copies
  Dickson, Jonathan _London_
  Dimbleby, William _Liverpool_
  Dobson, J. & B. _Bolton_
  Dockray, David _Manchester_
  Dollond, G. _London_
  Donkin, Bryan _London_
  Douglas, John _Manchester_
  Drew, James _Do._
  Dugdale, A. _Do._
  Dunlop, James & Sons, _Glasgow_
  Dunn, William _Do._
  Dutfoy, ---- _Paris_
  *Dyer, I. C. _Manchester_, 2 Copies
  Dyson, Joseph _Halifax_
  Dyson, William _Leeds_

  Eccles, Bannister & Co. _Blackburn_
  Eckersley, J. & W. _Wigan_
  Edge, Thomas _London_
  Edington, James _Glasgow_
  Edwards, John _Manchester_
  Elliot, Thomas _Do._
  Elsworth, William _Preston_
  Embden, S. _London_
  Escher, ---- _Switzerland_
  Evans, John _London_
  *Ewart, Peter _Manchester_
  Ewing, John _Glasgow_

  Fairbairn, ---- _Manchester._
  Fairweather, John _Do._
  Farey, Joseph, jun. _London._
  Farrer, John _Halifax_
  Fauld & Woodiwiss, _Barnsley_
  Faulkner, John _Manchester_
  Fawcett, Richard _Bradford_
  Fawcett, William _Liverpool_
  Fenton & Murray, _Leeds._
  Fielden, Brothers, _Todmorden_
  Fielding, H. & Brothers, _Manchester_
  Fishwick and Sons _Burnley_
  Flackton, Joseph _Do._
  Fletcher, Benjamin _Wigan._
  Fort, Richard _London._
  Fowden, William _Manchester._
  Fraser, James _London._
  Frost, John _Manchester._
  Furniss, P. _Halifax._

  Gallemore, Jesse _Manchester._
  Gallemore, William _Sheffield_
  Galloway, A. _London_
  Galloway, William _Manchester_
  Garnett, John _Liverpool_
  Garnett, John _Oldham_
  Garnett, W. & S. _Bradford_
  Garside, John _Stockport_
  German, William _Wigan_
  Gill, ---- _London_
  Gillett, John _Pendleton_
  Girdwood. C. & Co. _Glasgow_
  Goldie, James _London_
  Goodier, John _Manchester_
  Gore, Henry _Do._
  Gott, B. _Leeds_
  Gough, N. _Manchester_
  Goulding, & Son _London_
  *Grant, William _Manchester_
  *Grant, John _Do._
  *Grant, Daniel _Do._
  *Grant, Charles _Do._
  Gray, Benjamin _Do._
  Green, John _Do._
  Greenway, Charles _Do._
  Greenup, W & G _Halifax_
  Greenwood, Luke _Huddersfield_
  Greg, John _Manchester_
  Grimshaw, John Jun. _Belfast_
  Grimshaw, Brothers _Belfast_

  Hadwen, John & Co. _Halifax_
  Hall, John _Dartford_
  Hancorne, Edward _London_
  Handiside, N. _Glasgow_
  Hansard, T C _London_
  Hardie, D _Liverpool_
  Hardy & Andrew _Stockport_
  Harding, Maver and Leopard, _London_
  Harrison, Abel Stayley Bridge
  Harrison, John _Manchester_
  Harrison, John and Co. _Chorley_
  Haslam, S. H. _Manchester_
  Heath, George, _London_
  Heath, Robert _Manchester_
  Henwood, W. _H.M. Dock Yard, Portsmouth_
  Heron, I. H. _Manchester_, 2 Copies
  *Hewes, Thomas _Do._
  Heywood, John _Stockport_
  Hibbert, J. _Godley_
  Hick, Benjamin _Bolton_
  Hickling, Thomas _Birmingham_
  Higgins, Wm. _Salford_
  Hill, Edwin _Birmingham_
  Hilton, Samuel and Co. _Chorley_
  Hind, Roger _Preston_
  Hindley, Charles _Dukenfield_
  Hirst, John jun. _Halifax_
  Hirst, ---- _Marsden_
  Hodgson, Henry _Burnley_
  Hodgson, William _Birmingham_
  Holdbrook, B. _Warwick_
  Holgate, Massey and Co. _Burnley_
  Holmes, James _Kidderminster_
  Holmes, John _Paisley_
  Holt, Birch and Co. _Manchester_
  Holt, David _Manchester_
  Holt, Luke _Halifax_
  Holtzapffell, Deyerlein and Co. _London_
  Hoomans, Pardoe and Co. _Kidderminster_
  Hope, William _Liverpool_
  Hopwood and Pollard, _Burnley_
  Hopwood, William _Stockport_
  Hordern, Rev. P. M. A. _Cheetham Library_
  Horton, Thomas _Tipton_
  Horrocks, G. _Manchester_
  Horrocks, Miller and Co. _Preston_
  Horrox and Son, _Manchester_
  Horsfield, Thomas _Hyde_
  Hough, William _Manchester_
  Houlden, John _Leicester_
  Houldsworth, Henry _Glasgow_
  Houldsworth, Thos. Esq. M. P. _Manchester_
  Houtson, James _Do._
  Howard, Apelles _Stockport_
  Howard, Daniel _Stayley Bridge_
  Howard, John _Leeds_
  Howard, John _Stockport_
  Howard, John _Warrington_
  Howard, J. and N. _Ashton_
  Howard, Thomas _Hyde_
  Howard, William _London_
  *Hoyle, Thomas _Manchester_
  Hughes, William _Salford_
  Hull, John _Manchester_
  Hulse, Joseph _Alfreton_
  Humphries, Robert _Glasgow_
  Hutchinson, John _Manchester_
  Hutton, James _Leeds_
  Huzzie, William _Glasgow_
  Hyde, John _Manchester_

  Jackson, M. _London_
  Jackson, William _Oldham_
  James, James _Birmingham_
  Jenkinson and Bow, _Salford_
  Jones, George _Birmingham_
  Jones, James _Do._
  Jones, John _Bolton_
  Jones, Joseph, jun. _Oldham_
  Jones, William _Manchester_
  Johnson, G. _London_
  Johnson, Owen _Birmingham_
  Jordon, Francis _Liverpool_
  Joule, Benjamin _Salford_

  Kay, Alexander _Manchester_
  Kelly, W. and S. _Leicester_
  Kennedy, James _Manchester_
  *Kennedy, John _Do._
  Kenworthy, John _Ashton_
  Kilburn, James _Leeds_
  King, ---- _Manchester_
  Kirk, Benjamin _Do._
  Kirkland, Thomas _Mansfield_
  Knight, Samuel _Manchester_

  Lane, ---- _Manchester_
  Lane, Joseph _Stockport_
  Lane, William and Sons _Manchester_
  Landless, William _Burnley_
  Latham, John _Manchester_
  Lawson and Walker, _Leeds_
  Lee, G. A. _Salford_
  Lees, Henry _Ashton_
  Lees, Jerry _Manchester_
  Lees, Jonathan _Do._
  Lees, Samuel _Oldham_
  Leese, Joseph _Manchester_
  Lewis, F. _Do._
  Lightoller, T. _Charley_
  Lillie, ---- _Manchester_
  Lloyd, Lionel _Do._
  Lobley, Matthew _Leeds_
  Lockett, Garnett and Co. _Manchester_
  Lockwood, Joseph _Huddersfield_
  Lockwood, ---- _Leeds_
  *Lomas, William Strangeways, 2 Copies
  Lomas, George _Bolton_
  Longman and Co. _London_
  Longsden, P. and J. _Manchester_
  Longworth, N. _Bolton_
  Lonsdale, Daniel _Manchester_
  Lowe, John _Shepley Hall_
  Lowe, George _London_
  Lucas, Jonathan _Charleston_
  Lumb, Joseph _Leeds_
  Lupton, Jonathan _Leeds_

  M'Andrew, William _Glasgow_
  M'Arthur, Duncan _Do._
  M'Connell, James _Manchester_
  Machan, Luke _Sheffield_
  M'Murdo, G. Soho, _Manchester_
  M'Naught, John _Glasgow_
  M'Naught, Patrick _Do._
  Macray, James _Manchester_
  Malum, George _London_
  Malam, J. _Do._
  Manchester Exchange Library
  ---- New Library
  Manwaring, George _London_
  Marriott, Christopher _Manchester_
  Marsden, William _Salford_
  Marsland, Henry _Manchester_
  Marsland, James _Burnley_
  Marshall, James _Stockport_
  Marshall, Isaac _Birmingham_
  Marshall, W. and T. _Bradford_
  Maskray, James _Manchester_
  Mason, John _Bradford_
  Mattinson, J. _Huddersfield_
  Matterface, A. _London_
  Maudsley, Henry _London_
  Mawson and Bown, _Bradford_
  Mayer, Joseph _Stockport_
  Melling, John _Bolton_
  Mellor, James _Manchester_
  Mellor, Thomas _Ashton_
  Middleton, John _London_
  Miller, John _London_
  Millington, John F. R. S. _Do._
  Milne, William _Edinbro_
  Milne, E. _Manchester_
  Milne, W. _Do._
  Milne and Turner, _Halifax_
  Monks, Samuel _Bolton_
  Monteith, H. and Co. _Glasgow_
  Montgomery, Robert _Johnston_
  Moore, Daniel _Birmingham_
  Moore, Joseph _Leeds_
  Moore, S. M. _Manchester_
  Mosedale, William _Do._
  Moss, Thomas _Wigan_
  Mottershead, Samuel _Manchester_
  Munday, Thomas _Preston_
  Muntz, G. F. _Birmingham_
  Murdock, Wm. Soho, _Do._
  Murdock, William _Manchester_
  Murgatroyd, John _Halifax_
  Murray, George _Manchester_
  Napier, David _Glasgow_
  Naylor, Benjamin _Manchester_
  Neild, William _Do._
  Neilson, John _Glasgow_
  Nelson, William _Manchester_
  Newton, Samuel _London_
  Newton, Scott, Chambers and Co. _Thorncliffe Iron Works_
  Nichols, Benjamin _Manchester_
  Norris, H. _Bolton_

  Occleshaw, William _Manchester_
  Ogden, John _Do._
  Olliver, G. _Do._
  Ormrod, Richard _Do._
  Orrell, John _Stayley Bridge_
  Oswald, James and Co. _Glasgow_
  Ousey, Judson _Stayley Bridge_
  Outram, G. for _Glasgow Foundry Co._

  Paget, J. and W. _Loughborough_
  Paley, John _Preston_
  Palmer, R. _London_
  Park and Sons, _Wigan_
  Parker, F. _Sheffield_
  Parker, Samuel _London_
  Parkes, Josiah _Manchester_
  Parkin, Jonathan _Leeds_
  Parkinson, Adam _Manchester_
  Park Mills Co. _Stockport_
  Parry, Thomas _Manchester_
  Patten, Thomas and Co. _Cheadle_
  Pearson, Barwise _Chester_
  Peel and Co. _Manchester_
  Peel, G. Soho, _Do._
  Penn, John _Deptford_
  Pennington, Richard _Manchester_
  Percival, William _Stockport_
  Perkins, Jacob _London_
  Perrier, George _Do._
  Petrie, A. and Co. _Rochdale_
  Phillips, Nathaniel _Manchester_
  Phipson, J. W. _Birmingham_
  Pollard, Jonathan _Manchester_
  Poole, M. _London_
  Pooley, John _Manchester_
  Pope, Henry _Do._
  Pope, Henry, jun. _Do._
  Potter, John _Do._
  Powell, John _Do._
  Proctor, James and Sons _Leeds_
  Proctor, John _Do._
  Pullan and Sons _Do._

  Raby, Richard _Leicester._
  Radcliffe, James _Stockport._
  Radford, Joseph _Manchester._
  Railton, Robert _Blackburn._
  Ramsbotham, Henry _Todmorden._
  Ramsden, John _Halifax._
  Ransome, James _Manchester._
  Rathbone, R. _Liverpool._
  Rawson & Saltmarshes, _Halifax._
  Ready, Thomas _Peckham Academy._
  Reid, John & Co. _Manchester._
  Rennie, George _London_
  Richardson, ---- _Wigan._
  Rickards, Charles _Manchester._
  Roberts, Brother & Co. _Burnley._
  Roberts, Richard _Manchester._
  Rose, John _Leeds._
  Rothwell, P. jun. _Bolton._
  Rothwell, Richard _Manchester._
  Roughton and Woodhouse, _Coventry_
  Rowlands, R. _Glasgow_
  Royston, Charles _Halifax_
  Rushforth, Joseph _Elland_
  Rushton, J. _Liverpool_
  Rushton, William jun. _Do._
  Ruth ---- _Patricroft_

  Sadler, James _Mansfield_
  Samuels, John _Manchester_
  Sandford, Benjamin _Do._
  Sandford, William _Leeds_
  Sandiford, James _Manchester_
  Satterthwaite, E. _Belfast_
  Sells, John _Manchester_
  Sells, Henry _Do._
  Schlumberger, Grosjean & Co. _Muhlhausen_
  Schofield, Joseph _Manchester._
  Scholes, Varley & Co. _Do._
  Sharp, William _Salford._
  Sharp, James _Paisley._
  Shaw, Joseph _Sheffield._
  Shaw, Joseph and Sons, _Leeds._
  Sheffield Coal Co. _Park._
  Sherbrook, T. _Leeds._
  Sherratt, John _Salford._
  Sherriff, ---- _London._
  Shuttleworth, J. _Manchester_
  Sidebotham, John _Hyde_
  Sidebotham, Samuel _Stockport_
  Simpson, Richard _Manchester_
  Sinclair, John _Atherstone_
  Sior, ---- _Somers Town_
  Slater, Thomas _Salford_
  Sleddon, Francis _Preston_
  Smith, Alexander _Birmingham Gasworks_
  Smith, Alexander _Manchester_
  Smith, Benjamin _Do._
  Smith, E. & C. _Chesterfield_
  Smith, Henry _Birmingham_
  Smith, Joseph _Manchester_
  Smith, O. H. _Chelsea_
  Smith, Thomas _Burnley_
  Smith, Thomas _Leeds_
  Snodgrass, Niel _Glasgow_
  Solly, R. H. _London_
  Spencer, John _Burnley_
  Spooner, Ralph _Bolton_
  Stables, W. W., and H. H. _Huddersfield_
  Stamtin, H. _Carron Wharf London_
  Stansfield, Briggs and Co. _Halifax_
  Stansfield, John _Todmorden_
  Starkey, Buckley and Co. _Huddersfield_
  Steel, Thomas and Son, _Stockport_
  Stirk and Horsfield _Leeds_
  Stock, Aaron _Wigan_
  Stocks, Benjamin _Manchester_
  Stockton, Joseph _Do._
  Stone, James _London_
  Strutt, A. R. _Derby_
  Strutt, William _Do._
  Stuart, John _Manchester_
  Sturges, John and Co. _Bowling Iron Works_
  Sutcliffe, John and Nephews _Halifax_
  Swindells, John _Manchester_
  Swire, Samuel _Ashton_
  Sykes, Richard _Edgely_

  Tattersall and Crooke _Burnley_
  Taylor, Josiah Holborn, _London_
  Taylor, Benjamin _Glasgow_
  Taylor, J. and J. _Manchester_
  Taylor, Phillip _London_
  Taylor and Shatwell _Manchester_
  Taylor, William _Preston_
  Taylor, W. G. _Bolton_
  Taylor and Wordsworth _Leeds_
  Taylor, Edward _Warwick_
  Telford, Thomas F. R. S. _London_
  Tennant, C. and Co. _Glasgow_
  Thackray, Jonathan _Sheffield_
  Thomson, R. jun. _Glasgow_
  Thompson, M. _Bradford_
  Thompson, Samuel _Bolton_
  Thompson, Thomas _Do._
  Thompson, Thomas _Newcastle_
  Throp, William _Blackburn_
  Tilley, J. _London_
  Tipping, G. _Manchester_
  Tomlinson and Co. _Oldham_
  Tongue, William _Birmingham_
  Townend, G. and W. _Manchester_
  Townend, William _Do_
  Travis, James _Halifax_
  Turner, Thomas _Nottingham_
  Twigg, Joseph jun. _Paisley_

  Unwin, Samuel and Co. _Mansfield_

  Vanhouse, James _Peckham_
  Varley, John _Manchester_
  Vaudrey, John _Stayley-bridge_
  Vickers, William _Manchester_

  Wade, Joseph _Bradford_
  Waddington, David _Manchester_
  Wainwright, Benjamin _Stayley-bridge_
  Wakefield, John _Manchester_
  Walker, Benjamin _Leeds_
  Walker, Henry, _Salford_
  Wareing, J. and W. _Stayleybridge_
  Watson, Peter _Manchester_
  Watson, William _Glasgow_
  Weight, Joseph _Manchester_
  Weight, Hezekiah _Do._
  Weir, Edward _London_
  Weir, Charles Alexander _Kent Water works_
  Welch, Thomas _Manchester_
  Wentworth, H. _Wandsworth_
  Wentworth, James _Deptford_
  Westley, W. K. _Leeds_
  Wharton, Joseph _Manchester_
  Wharton, William _Do._
  Whitacre, John _Huddersfield_
  White, John _Glasgow_
  Whitehead, John _Halifax_
  Whitfield, William _Birmingham_
  Whyatt, George _Manchester_
  Wigan, R. _Do._
  Wilder, O. _London_
  Willans, Thomas _Leeds_
  Williams, John _London_
  Willoughby, J. _Birmingham_
  Wilkinson, James _Leeds_
  Wilkinson, James _Stayleybridge_
  Wilkinson, George _Middleton_
  Wilson, George _London_
  Wilson, William jun. _Nottingham_
  Wilson and Co. _Leicester_
  Wolfenden, Richard _Manchester_
  Wolfenden, Stones and Kirkham _Manchester_
  Wood, Alexander _Do._
  Wood, John _Huddersfield_
  Wood, John _Manchester_
  Wood, John _Stockport_
  Wood, George _Manchester_
  Wood and Harrop _Ashton_
  Wood, Robert _Leeds_
  Woodcock and Harrison _Leeds_
  Worswick, John _Manchester_
  Wright, John _Oldham_
  Wright, Joseph _Ashton_

  Yates, Thomas _Manchester_
  Young, Joseph _Do._
  Young and Smith, _Sheffield_


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Transcriber's Notes:

This text follows the text of the orignal work as much as possible.
Inconsistencies in grammar, punctuation, capitalisation, hyphenation,
etc. have been retained, except as mentioned below. Where the author
consistently or regularly uses unusual spelling of words, this has been
retained. Examples are it's for its, wave for waive, guage for gauge,
scapement for escapement, enterprize, rince for rinse, boar for bore, a
mean for a means, absciss for abscissa, keer for keir or kier, mattrass
for mattress, oxigen, vaneer, etc.

The author uses both comma and period as decimal point and thousand
separator. Despite the confusion this might cause, this has not been
changed.

Changes made to the text:
Minor punctuation errors (mainly missing periods) have been corrected
silently.

The errata have already been changed in the text. The following
corrections have been made to the corrections in the errata:

  - plate has been changed to Plate for consistency;
  - ,99990 has been changed to 99990;
  - on page 374 the entire series has been corrected in addition to the
    corrections given in the errata;
  - the correction to page 188 line 17 should be made to page 188 line
    2;
  - some corrections are listed more than once;
  - some errors mentioned in the errata were not present in the text.

Footnotes have been moved to directly under the text they refer to.

Some tables have been re-arranged.

In some formulas, brackets have been added for better readability and to
avoid ambiguity.

Corrections made (apart from the errata):

Page vi: befal changed to befall

Page 24: dfficulty changed to difficulty; clylinder changed to cylinder;
equallized changed to equalized as elsewhere

Page 26: consitute changed to constitute

Page 33: philosohpy changed to philosophy

Page 36: as to the the time changed to as to the time; thepocket changed
to the pocket

Page 38: Lieutenat changed to Lieutenant

Page 39: pasing changed to passing

Page 51/52: proporportions changed to proportions

Page 56: 2,020000 changed to 2020000 (cf. correction of other numbers
page 55, and written-out number in text next paragraph)

Page 58-59: '" changed to "'

Page 61: unweildy changed to unwieldy; shut of changed to shut off

Page 63: difinitive changed to definitive

Page 73: as we llto changed to as well to; theplane changed to the plane

Synopsis: parobolico changed to parabolico

Page 90: Opening quotes added before The subject of this paper ... to
match closing quotes on page 108

Page 96: indispensible changed to indispensable as elsewhere; whould
changed to would; circumferencies changed to circumferences

Page 101: circumferencies changed to circumferences

Page 102: arces changed to arcs; quantites changed to quantities

Page 118: side ways changed to sideways as elsewhere

Page 123: once cutting changed to one cutting

Page 134: circumferenceof changed to circumference of; inproportion
changed to in proportion

Page 138: passsing changed to passing; staight changed to straight

Page 139: beween changed to between

Page 145: penetratration changed to penetration

Page 152: reallized changed to realized as elsewhere

Page 155: representented changed to represented

Page 161: intead changed to instead

Page 170: prouced changed to produced

Page 187: opinon changed to opinion; chuse changed to choose; 174.4
changed to 147.4

Page 188: 63 27´ changed to 63°27´; y changed to y =

Page 191: closing quote added after ... same proportion.

Page 200: dependant changed to dependent as elsewhere

Page 203: "tis ... changed to "'tis ...

Page 286 some times changed to sometimes

Page 289 (if changed to if

Page 307: analagous changed to analogous; disembarassment changed to
disembarrassment

Page 311: mens' changed to men's

Page 337: cloged changed to clogged

Page 339: ackowledge changed to acknowledge

Page 340: preceeding changed to preceding; a pair of of changed to a
pair of

Page 353: contruction changed to construction

Page 357: withold changed to withhold

Page 372: esspecially changed to especially

Page 387: sherical changed to spherical

List of subscribers: De Volvic Comte Chabrol changed to De Volvic, Comte
Chabrol; Edward Hancome/Hancorne: the source was not clear, it could be
either, but Hancorne looks more likely

Plate 36, 43: Engraver added as with other plates.





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