The Project Gutenberg eBook of A Preliminary Dissertation on the Mechanisms of the Heavens
    
This ebook is for the use of anyone anywhere in the United States and
most other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms
of the Project Gutenberg License included with this ebook or online
at www.gutenberg.org. If you are not located in the United States,
you will have to check the laws of the country where you are located
before using this eBook.

Title: A Preliminary Dissertation on the Mechanisms of the Heavens

Author: Mary Somerville

Release date: February 12, 2022 [eBook #67386]

Language: English

Original publication: United States: Carey & Lea

Credits: Laura Natal Rodrigues (Images generously made available by Hathi Trust Digital Library.)


*** START OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON THE MECHANISMS OF THE HEAVENS ***


A

PRELIMINARY DISSERTATION

ON THE

MECHANISM OF THE HEAVENS.



BY

MRS. SOMMERVILLE




PHILADELPHIA:
CAREY & LEA

1832




In order to convey some idea of the object of this work, it may be
useful to offer a few preliminary observations on the nature of the
subject which it is intended to investigate, and of the means that have
already been adopted with so much success to bring within the reach of
our faculties, those truths which might seem to be placed so far beyond
them.

All the knowledge we possess of external objects is founded upon
experience, which furnishes a knowledge of facts, and the comparison of
these facts establishes relations, from which, induction, the intuitive
belief that like causes will produce like effects, leads us to general
laws. Thus, experience teaches that bodies fall at the surface of the
earth with an accelerated velocity, and proportional to their masses.
Newton proved, by comparison, that the force which occasions the fall of
bodies at the earth's surface, is identical with that which retains the
moon in her orbit; and induction led him to conclude that as the moon is
kept in her orbit by the attraction of the earth, so the planets might
be retained in their orbits by the attraction of the sun. By such steps
he was led to the discovery of one of those powers with which the
Creator has ordained that matter should reciprocally act upon matter.

Physical astronomy is the science which compares and identifies the laws
of motion observed on earth with the motions that take place in the
heavens, and which traces, by an uninterrupted chain of deduction from
the great principle that governs the universe, the revolutions and
rotations of the planets, and the oscillations of the fluids at their
surfaces, and which estimates the changes the system has hitherto
undergone or may hereafter experience, changes which require millions of
years for their accomplishment.

The combined efforts of astronomers, from the earliest dawn of
civilization, have been requisite to establish the mechanical theory of
astronomy: the courses of the planets have been observed for ages with a
degree of perseverance that is astonishing, if we consider the
imperfection, and even the want of instruments. The real motions of the
earth have been separated from the apparent motions of the planets; the
laws of the planetary revolutions have been discovered; and the
discovery of these laws has led to the knowledge of the gravitation of
matter. On the other hand, descending from the principle of gravitation,
every motion in the system of the world has been so completely
explained, that no astronomical phenomenon can now be transmitted to
posterity of which the laws have not been determined.

Science, regarded as the pursuit of truth, which can only be attained by
patient and unprejudiced investigation, wherein nothing is too great to
be attempted, nothing so minute as to be justly disregarded, must ever
afford occupation of consummate interest and of elevated meditation. The
contemplation of the works of creation elevates the mind to the
admiration of whatever is great and noble, accomplishing the object of
all study, which in the elegant language of Sir James Mackintosh is to
inspire the love of truth, of wisdom, of beauty, especially of goodness,
the highest beauty, and of that supreme and eternal mind, which contains
all truth and wisdom, all beauty and goodness. By the love or delightful
contemplation and pursuit of these transcendent aims for their own sake
only, the mind of man is raised from low and perishable objects, and
prepared for those high destinies which are appointed for all those who
are capable of them.

The heavens afford the most sublime subject of study which can be
derived from science: the magnitude and splendour of the objects, the
inconceivable rapidity with which they move, and the enormous distances
between them, impress the mind with some notion of the energy that
maintains them in their motions with a durability to which we can see no
limits. Equally conspicuous is the goodness of the great First Cause in
having endowed man with faculties by which he can not only appreciate
the magnificence of his works, but trace, with precision, the operation
of his laws, use the globe he inhabits us a base wherewith to measure
the magnitude and distance of the sun and planets, and make the diameter
of the earth's orbit the first step of a scale by which he may ascend to
the starry firmament. Such pursuits, while they ennoble the mind, at the
same time inculcate humility, by showing that there is a barrier, which
no energy, mental or physical, can ever enable us to pass: that however
profoundly we may penetrate the depths of space, there still remain
innumerable systems compared with which those which seem so mighty to us
must dwindle into insignificance, or even become invisible; and that not
only man, but the globe he inhabits, nay the whole system of which it
forms so small a part, might be annihilated, and its extinction be
unperceived in the immensity or creation.

A complete acquaintance with Physical Astronomy can only be attained by
those who are well versed in the higher branches of mathematical and
mechanical science: such alone can appreciate the extreme beauty of
the results, and of the means by which these results are obtained.
Nevertheless a sufficient skill in analysis to follow the general
outline, to see the mutual dependence of the different parts of the
system, and to comprehend by what means some of the most extraordinary
conclusions have been arrived at, is within the reach of many who shrink
from the task, appalled by difficulties, which perhaps are not more
formidable than those incident to the study of the elements of every
branch of knowledge, and possibly overrating them by not making a
sufficient distinction between the degree of mathematical acquirement
necessary for making discoveries, and that which is requisite for
understanding what others have done. That the study of mathematics and
their application to astronomy are full of interest will be allowed by
all who have devoted their time and attention to these pursuits, and
they only can estimate the delight of arriving at truth, whether it be
in the discovery of a world, or of a new property of numbers.

It has been proved by Newton that a particle of matter placed without
the surface of a hollow sphere is attracted by it in the name manner as
if its mass, or the whole matter it contains, were collected in its
centre. The same is therefore true of a solid sphere which may be
supposed to consist of an infinite number of concentric hollow spheres.
This however is not the case with a spheroid, but the celestial bodies
are so nearly spherical, and at such remote distances from each other,
that they attract and are attracted as if each were a dense point
situate in its centre of gravity, a circumstance which greatly
facilitates the investigation of their motions.

The attraction of the earth on bodies at its surface in that latitude,
the square of whose sine is ⅓, is the same as if it were a sphere; and
experience shows that bodies there fall through 16.0697 feet in a
second. The mean distance of the moon from the earth is about sixty
times the mean radius of the earth. When the number 16.0697 is
diminished in the ratio of 1 to 3600, which is the square of the moon's
distance from the earth, it is found to be exactly the space the moon
would fall through in the first second of her descent to the earth, were
she not prevented by her centrifugal force, arising from the velocity
with which she moves in her orbit. So that the moon is retained in her
orbit by a force having the same origin and regulated by the same law
with that which causes a stone to fall at the earth's surface. The earth
may therefore be regarded as the centre of a force which extends to the
moon; but as experience shows that the action and reaction of matter are
equal and contrary, the moon must attract the earth with an equal and
contrary force.

Newton proved that a body projected in space will move in a conic
section, if it be attracted by a force directed towards a fixed point,
and having an intensity inversely as the square of the distance; but
that any deviation from that law will cause it to move in a curve of a
different nature. Kepler ascertained by direct observation that the
planets describe ellipses round the sun, and later observations show
that comets also move in conic sections: it consequently follows that
the sun attracts all the planets and comets inversely as the square of
their distances from his centre; the sun therefore is the centre of a
force extending indefinitely in space, and including all the bodies of
the system in its action.

Kepler also deduced from observation, that the squares of the periodic
times of the planets, or the times of their revolutions round the sun,
are proportional to the cubes of their mean distances from his centre:
whence it follows, that the intensity of gravitation of all the bodies
towards the sun is the same at equal distances; consequently gravitation
is proportional to the masses, for if the planets and comets be supposed
to be at equal distances from the sun and left to the effects of
gravity, they would arrive at his surface at the same time. The
satellites also gravitate to their primaries according to the same law
that their primaries do to the sun. Hence, by the law of action and
reaction, each body is itself the centre of an attractive force
extending indefinitely in space, whence proceed all the mutual
disturbances that render the celestial motions so complicated, and their
investigation so difficult.

The gravitation of matter directed to a centre, and attracting directly
as the mass, and inversely as the square of the distance, does not
belong to it when taken in mass; particle acts on particle according to
the same law when at sensible distances from each other. If the sun
acted on the centre of the earth without attracting each of its
particles, the tides would be very much greater than they now are, and
in other respects they also would be very different. The gravitation of
the earth to the sun results from the gravitation of all its particles,
which in their turn attract the sun in the ratio of their respective
masses. There is a reciprocal action likewise between the earth and
every particle at its surface; were this not the case, and were any
portion of the earth, however small, to attract another portion and not
be itself attracted, the centre of gravity of the earth would be moved
in space, which is impossible.

The form of the planets results from the reciprocal attraction of their
component particles. A detached fluid mass, if at rest, would assume the
form of a sphere, from the reciprocal attraction of its particles; but
if the mass revolves about an axis, it becomes flattened at the poles,
and bulges at the equator, in consequence of the centrifugal force
arising from the velocity of rotation. For, the centrifugal force
diminishes the gravity of the particles at the equator, and equilibrium
can only exist when these two forces are balanced by an increase of
gravity; therefore, as the attractive force is the same on all particles
at equal distances from the centre of a sphere, the equatorial particles
would recede from the centre till their increase in number balanced the
centrifugal force by their attraction, consequently the sphere would
become an oblate spheroid; and a fluid partially or entirely covering a
solid, as the ocean and atmosphere cover the earth, must assume that
form in order to remain in equilibrio. The surface of the sea is
therefore spheroidal, and the surface of the earth only deviates from
that figure where it rises above or sinks below the level of the sea;
but the deviation is so small that it is unimportant when compared with
the magnitude of the earth. Such is the form of the earth and planets,
but the compression or flattening at their poles is so small, that even
Jupiter, whose rotation is the most rapid, differs but little from a
sphere. Although the planets attract each other as if they were spheres
on account of their immense distances, yet the satellites are near
enough to be sensibly affected in their motions by the forms of their
primaries. The moon for example is so near the earth, that the
reciprocal attraction between each of her particles and each of the
particles in the prominent mass at the terrestrial equator, occasions
considerable disturbances in the motions of both bodies. For, the action
of the moon on the matter at the earth's equator produces a nutation in
the axis of rotation, and the reaction of that matter on the moon is the
cause of a corresponding nutation in the lunar orbit.

If a sphere at rest in space receives an impulse passing through its
centre of gravity, all its parts will move with an equal velocity in a
straight line; but if the impulse does not pass through the centre of
gravity, its particles having unequal velocities, will give it a
rotatory motion at the same time that it is translated in space. These
motions are independent of one another, so that a contrary impulse
passing through its centre of gravity will impede its progression,
without interfering with its rotation. As the sun rotates about an axis,
it seems probable if an impulse in a contrary direction has not been
given to his centre of gravity, that he moves in space accompanied by
all those bodies which compose the solar system, a circumstance that
would in no way interfere with their relative motions; for, in
consequence of our experience that force is proportional to velocity,
the reciprocal attractions of a system remain the same, whether its
centre of gravity be at rest, or moving uniformly in space. It is
computed that had the earth received its motion from a single impulse,
such impulse must have passed through a point about twenty-five miles
from its centre.

Since the motions of the rotation and translation of the planets are
independent of each other, though probably communicated by the same
impulse, they form separate subjects of investigation.

A planet moves in its elliptical orbit with a velocity varying every
instant, in consequence of two forces, one tending to the centre of the
sun, and the other in the direction of a tangent to its orbit, arising
from the primitive impulse given at the time when it was launched into
space: should the force in the tangent cease, the planet would fall to
the sun by its gravity; were the sun not to attract it, the planet would
fly off in the tangent. Thus, when a planet is in its aphelion or at the
point where the orbit is farthest from the sun, his action overcomes its
velocity, and brings it towards him with such an accelerated motion,
that it at last overcomes the sun's attraction, and shoots past him;
then, gradually decreasing in velocity, it arrives at the aphelion where
the sun's attraction again prevails. In this motion the radii vectores,
or imaginary lines joining the centres of the sun and planets, pass over
equal areas in equal times.

If the planets were attracted by the sun only, this would ever be their
course; and because his action is proportional to his mass, which is
immensely larger than that of all the planets put together, the
elliptical is the nearest approximation to their true motions, which are
extremely complicated, in consequence of their mutual attraction, so
that they do not move in any known or symmetrical curve, but in paths
now approaching to, and now receding from the elliptical form, and their
radii vectores do not describe areas exactly proportional to the time.
Thus the areas become a test of the existence of disturbing forces.

To determine the motion of each body when disturbed by all the rest is
beyond the power of analysis; it is therefore necessary to estimate the
disturbing action of one planet at a time, whence arises the celebrated
problem of the three bodies, which originally was that of the moon, the
earth, and the sun, namely,--the masses being given of three bodies
projected from three given points, with velocities given both in
quantity and direction; and supposing the bodies to gravitate to one
another with forces that are directly as their masses, and inversely as
the squares of the distances, to find the lines described by these
bodies, and their position at any given instant.

By this problem the motions of translation of all the celestial bodies
are determined. It is one of extreme difficulty, and would be of
infinitely greater difficulty, if the disturbing action were not very
small, when compared with the central force. As the disturbing influence
of each body may be found separately, it is assumed that the action of
the whole system in disturbing any one planet is equal to the sum of all
the particular disturbances it experiences, on the general mechanical
principle, that the sum of any number of small oscillations is nearly
equal to their simultaneous and joint effect.

On account of the reciprocal action of matter, the stability of the
system depends on the intensity of the primitive momentum of the
planets, and the ratio of their masses to that of the sun: for the
nature of the conic sections in which the celestial bodies move, depends
on the velocity with which they were first propelled in space; had that
velocity been such as to make the planets move in orbits of unstable
equilibrium, their mutual attractions might have changed them into
parabolas or even hyperbolas; so that the earth and planets might ages
ago have been sweeping through the abyss of space: but as the orbits
differ very little from circles, the momentum of the planets when
projected, must have been exactly sufficient to ensure the permanency
and stability of the system. Besides the mass of the sun is immensely
greater than those of the planets; and as their inequalities bear the
same ratio to their elliptical motions as their masses do to that of the
sun, their mutual disturbances only increase or diminish the
eccentricities of their orbits by very minute quantities; consequently
the magnitude of the sun's mass is the principal cause of the stability
of the system. There is not in the physical world a more splendid
example of the adaptation of means to the accomplishment of the end,
than is exhibited in the nice adjustment of these forces.

The orbits of the planets have a very small inclination to the plane of
the ecliptic in which the earth moves; and on that account, astronomers
refer their motions to it at a given epoch as a known and fixed
position. The paths of the planets, when their mutual disturbances are
omitted, are ellipses nearly approaching to circles, whose planes,
slightly inclined to the ecliptic: cut it in straight lines passing
through the centre of the sun; the points where the orbit intersects the
plane of the ecliptic are its nodes.

The orbits of the recently discovered planets deviate more from the
ecliptic: that of Pallas has an inclination of 35° to it: on that
account it will be more difficult to determine their motions. These
little planets have no sensible effect in disturbing the rest, though
their own motions are rendered very irregular by the proximity of
Jupiter and Saturn.

The planets are subject to disturbances of two distinct kinds, both
resulting from the constant operation of their reciprocal attraction,
one kind depending upon their positions with regard to each other,
begins from zero, increases to a maximum, decreases and becomes zero
again, when the planets return to the same relative positions. In
consequence of these, the troubled planet is sometimes drawn away from
the sun, sometimes brought nearer to him; at one time it is drawn above
the plane of its orbit, at another time below it, according to the
position of the disturbing body. All such changes, being accomplished in
short periods, some in a few months, others in years, or in hundreds of
years, are denominated Periodic Inequalities.

The inequalities of the other kind, though occasioned likewise by the
disturbing energy of the planets, are entirely independent of their
relative positions; they depend on the relative positions of the orbits
alone, whose forms and places in space are altered by very minute
quantities in immense periods of time, and are therefore called Secular
Inequalities.

In consequence of disturbances of this kind, the apsides, or extremities
of the major axes of all the orbits, have a direct, but variable motion
in space, excepting those of Venus, which are retrograde; and the lines
of the nodes move with a variable velocity in the contrary direction.
The motions of both are extremely slow; it requires more than 109770
years for the major axis of the earth's orbit to accomplish a sidereal
revolution, and 20935 years to complete its tropical motion. The major
axis of Jupiter's orbit requires no less than 197561 years to perform
its revolution from the disturbing action of Saturn alone. The periods
in which the nodes revolve are also very great. Beside these, the
inclination and eccentricity of every orbit are in a state of perpetual,
but slow change. At the present time, the inclinations of all the orbits
are decreasing; but so slowly, that the inclination of Jupiter's orbit
is only six minutes less now than it was in the age of Ptolemy. The
terrestrial eccentricity is decreasing at the rate of 3914 miles in a
century; and if it were to decrease equably, it would be 36300 years
before the earth's orbit became a circle. But in the midst of all these
vicissitudes, the major axes and mean motions of the planets remain
permanently independent of secular changes; they are so connected by
Kepler's law of the squares of the periodic times being proportional to
the cubes of the mean distances of the planets from the sun, that one
cannot vary without affecting the other.

With the exception of these two elements, it appears, that all the
bodies are in motion, and every orbit is in a state of perpetual change.
Minute as these changes are, they might be supposed liable to accumulate
in the course of ages sufficiently to derange the whole order of nature,
to alter the relative positions of the planets, to put an end to the
vicissitudes of the seasons, and to bring about collisions, which would
involve our whole system, now so harmonious, in chaotic confusion. The
consequences being so dreadful, it is natural to inquire, what proof
exists that creation will be preserved from such a catastrophe? For
nothing can be known from observation, since the existence of the human
race has occupied but a point in duration, while these vicissitudes
embrace myriads of ages. The proof is simple and convincing. All the
variations of the solar system, as well secular as periodic, are
expressed analytically by the sines and cosines of circular arcs, which
increase with the time; and as a sine or cosine never can exceed the
radius, but must oscillate between zero and unity, however much the time
may increase, it follows, that when the variations have by slow changes
accumulated in however long a time to a maximum, they decrease by the
same slow degrees, till they arrive at their smallest value, and then
begin a new course, thus for ever oscillating about a mean value. This,
however, would not be the case if the planets moved in a resisting
medium, for then both the eccentricity and the major axes of the orbits
would vary with the time, so that the stability of the system would be
ultimately destroyed. But if the planets do move in an ethereal medium,
it must be of extreme rarity, since its resistance has hitherto been
quite insensible.

Three circumstances have generally been supposed necessary to prove the
stability of the system: the small eccentricities of the planetary
orbits, their small inclinations, and the revolution of all the bodies,
as well planets as satellites, in the same direction. These, however,
are not necessary conditions: the periodicity of the terms in which the
inequalities are expressed is sufficient to assure us, that though we do
not know the extent of the limits, nor the period of that grand cycle
which probably embraces millions of years, yet they never will exceed
what is requisite for the stability and harmony of the whole, for the
preservation of which every circumstance is so beautifully and
wonderfully adapted.

The plane of the ecliptic itself, though assumed to be fixed at a given
epoch for the convenience of astronomical computation, is subject to a
minute secular variation of 52"·109, occasioned by the reciprocal action
of the planets; but as this is also periodical, the terrestrial equator,
which is inclined to it at an angle of about 23° 28', will never
coincide with the plane of the ecliptic; so there never can be perpetual
spring.

The rotation of the earth is uniform; therefore day and night, summer
and winter, will continue their vicissitudes while the system endures,
or is untroubled by foreign causes.


                   Yonder starry sphere
     Of planets, and of fix'd, in all her wheels
     Resembles nearest, mazes intricate,
     Eccentric, intervolv'd, yet regular
     Then most, when most irregular they seem.


The stability of our system was established by La Grange, 'a discovery,'
says Professor Playfair, 'that must render the name for ever memorable
in science, and revered by those who delight in the contemplation of
whatever is excellent and sublime. After Newton's discovery of the
elliptical orbits of the planets, La Grange's discovery of their
periodical inequalities is without doubt the noblest truth in physical
astronomy; and, in respect of the doctrine of final causes, it may be
regarded as the greatest of all.'

Notwithstanding the permanency of our system, the secular variations in
the planetary orbits would have been extremely embarrassing to
astronomers, when it became necessary to compare observations separated
by long periods. This difficulty is obviated by La Place, who has shown
that whatever changes time may induce either in the orbits themselves,
or in the plane of the ecliptic, there exists an invariable plane
passing through the centre of gravity of the sun, about which the whole
system oscillates within narrow limits, and which is determined by this
property; that if every body in the system be projected on it, and if
the mass of each be multiplied by the area described in a given time by
its projection on this plane, the sum of all these products will be a
maximum. This plane of greatest inertia, by no means peculiar to the
solar system, but existing in every system of bodies submitted to their
mutual attractions only, always remains parallel to itself, and
maintains a fixed position, whence the oscillations of the system may be
estimated through unlimited time. It is situate nearly half way between
the orbits of Jupiter and Saturn, and is inclined to the ecliptic at an
angle of about 1° 35' 31".

All the periodic and secular inequalities deduced from the law of
gravitation are so perfectly confirmed by observations, that analysis
has become one of the most certain means of discovering the planetary
irregularities, either when they are too small, or too long in their
periods, to be detected by other methods. Jupiter and Saturn, however,
exhibit inequalities which for a long time seemed discordant with that
law. All observations, from those of the Chinese and Arabs down to the
present day, prove that for ages the mean motions of Jupiter and Saturn
have been affected by great inequalities of very long periods, forming
what appeared an anomaly in the theory of the planets. It was long known
by observation, that five times the mean motion of Saturn is nearly
equal to twice that of Jupiter; a relation which the sagacity of La
Place perceived to be the cause of a periodic inequality in the mean
motion of each of these planets, which completes its period in nearly
929 Julian years, the one being retarded, while the other is
accelerated. These inequalities are strictly periodical, since they
depend on the configuration of the two planets; and the theory is
perfectly confirmed by observation, which shows that in the course of
twenty centuries, Jupiter's mean motion has been accelerated by 3° 23',
and Saturn's retarded by 5° 13'.

It might be imagined that the reciprocal action of such planets as have
satellites would be different from the influence of those that have
none; but the distances of the satellites from their primaries are
incomparably less than the distances of the planets from the sun, and
from one another, so that the system of a planet and its satellites
moves nearly as if all those bodies were united in their common centre
of gravity; the action of the sun however disturbs in some degree the
motion of the satellites about their primary.

The changes that take place in the planetary system are exhibited on a
small scale by Jupiter and his satellites; and as the period requisite
for the development of the inequalities of these little moons only
extends to a few centuries, it may be regarded as an epitome of that
grand cycle which will not be accomplished by the planets in myriads of
centuries. The revolutions of the satellites about Jupiter are precisely
similar to those of the planets about the sun; it is true they are
disturbed by the sun, but his distance is so great, that their motions
are nearly the same as if they were not under his influence. The
satellites like the planets, were probably projected in elliptical
orbits, but the compression of Jupiter's spheroid is very great in
consequence of his rapid rotation; and as the masses of the satellites
are nearly 100000 times less than that of Jupiter, the immense quantity
of prominent matter at his equator must soon have given the circular
form observed in the orbits of the first and second satellites, which
its superior attraction will always maintain. The third and fourth
satellites being further removed from its influence, move in orbits with
a very small eccentricity. The same cause occasions the orbits of the
satellites to remain nearly in the plane of Jupiter's equator, on
account of which they are always seen nearly in the same line; and the
powerful action of that quantity of prominent matter is the reason why
the motion of the nodes of these little bodies is so much more rapid
than those of the planet. The nodes of the fourth satellite accomplish a
revolution in 520 years, while those of Jupiter's orbit require no less
than 50673 years, a proof of the reciprocal attraction between each
particle of Jupiter's equator and of the satellites. Although the two
first satellites sensibly move in circles, they acquire a small
ellipticity from the disturbances they experience.

The orbits of the satellites do not retain a permanent inclination,
either to the plane of Jupiter's equator, or to that of his orbit, but
to certain planes passing between the two, and through their
intersection; these have a greater inclination to his equator the
further the satellite is removed, a circumstance entirely owing to the
influence of Jupiter's compression.

A singular law obtains among the mean motions and mean longitudes of the
three first satellites. It appears from observation, that the mean
motion of the first satellite, plus twice that of the third, is equal to
three times that of the second, and that the mean longitude of the first
satellite, minus three times that of the second, plus twice that of the
third, is always equal to two right angles. It is proved by theory, that
if these relations had only been approximate when the satellites were
first launched into space, their mutual attractions would have
established and maintained them. They extend to the synodic motions of
the satellites, consequently they affect their eclipses, and have a very
great influence on their whole theory. The satellites move so nearly in
the plane of Jupiter's equator, which has a very small inclination to
his orbit, that they are frequently eclipsed by the planet. The instant
of the beginning or end of an eclipse of a satellite marks the same
instant of absolute time to all the inhabitants of the earth; therefore
the time of these eclipses observed by a traveller, when compared with
the time of the eclipse computed for Greenwich or any other fixed
meridian, gives the difference of the meridians in time, and
consequently the longitude of the place of observation. It has required
all the refinements of modern instruments to render the eclipses of
these remote moons available to the mariner; now however, that system of
bodies invisible to the naked eye, known to man by the aid of science
alone, enables him to traverse the ocean, spreading the light of
knowledge and the blessings of civilization over the most remote
regions, and to return loaded with the productions of another
hemisphere. Nor is this all: the eclipses of Jupiter's satellites have
been the means or a discovery, which, though not so immediately
applicable to the wants of man, unfolds a property of light, that
medium, without whose cheering influence all the beauties of the
creation would have been to us a blank. It is observed, that those
eclipses of the first satellite which happen when Jupiter is near
conjunction, are later by 16' 26" than those which take place when the
planet is in opposition. But as Jupiter is nearer to us when in
opposition by the whole breadth of the earth's orbit than when in
conjunction, this circumstance was attributed to the time employed by
the rays of light in crossing the earth's orbit, a distance of 192
millions of miles; whence it is estimated, that light travels at the
rate of 192000 miles in one second. Such is its velocity, that the
earth, moving at the rate of nineteen miles in a second, would take two
months to pass through a distance which a ray of light would dart over
in eight minutes. The subsequent discovery of the aberration of light
confirmed this astonishing result.

Objects appear to be situate in the direction of the rays that proceed
from them. Were light propagated instantaneously, every object, whether
at rest or in motion, would appear in the direction of these rays; but
as light takes some time to travel, when Jupiter is in conjunction, we
see him by means of rays that left him 16' 26" before; but during that
time we have changed our position, in consequence of the motion of the
earth in its orbit; we therefore refer Jupiter to a place in which he is
not. His true position is in the diagonal of the parallelogram, whose
sides are in the ratio of the velocity of light to the velocity of the
earth in its orbit, which is as 192000 to 19. In consequence of
aberration, none of the heavenly bodies are in the place in which they
seem to be. In fact, if the earth were at rest, rays from a star would
pass along the axis of a telescope directed to it; but if the earth were
to begin to move in its orbit with its usual velocity, these rays would
strike against the side of the tube; it would therefore be necessary to
incline the telescope a little, in order to see the star. The angle
contained between the axis of the telescope and a line drawn to the true
place of the star, is its aberration, which varies in quantity and
direction in different parts of the earth's orbit; but as it never
exceeds twenty seconds, in ordinary cases.

The velocity of light deduced from the observed aberration of the fixed
stars, perfectly corresponds with that given by the eclipses of the
first satellite. The same result obtained from sources so different,
leaves not a doubt of its truth. Many such beautiful coincidences,
derived from apparently the most unpromising and dissimilar
circumstances, occur in physical astronomy, and prove dependences which
we might otherwise be unable to trace. The identity of the velocity of
light at the distance of Jupiter and on the earth's surface shows that
its velocity is uniform; and if light consists in the vibrations of an
elastic fluid or ether filling space, which hypothesis accords best with
observed phenomena, the uniformity of its velocity shows that the
density of the fluid throughout the whole extent of the solar system,
must be proportional to its elasticity. Among the fortunate conjectures
which have been confirmed by subsequent experience, that of Bacon is not
the least remarkable. "It produces in me," says the restorer of true
philosophy, "a doubt, whether the face of the serene and starry heavens
be seen at the instant it really exists, or not till some time later;
and whether there be not, with respect to the heavenly bodies, a true
time and an apparent time, no less than a true place and an apparent
place, as astronomers say, on account of parallax. For it seems
incredible that the species or rays of the celestial bodies can pass
through the immense interval between them and us in an instant; or that
they do not even require some considerable portion of time."

As great discoveries generally lead to a variety of conclusions, the
aberration of light affords a direct proof of the motion of the earth in
its orbit; and its rotation is proved by the theory of falling bodies,
since the centrifugal force it induces retards the oscillations of the
pendulum in going from the pole to the equator. Thus a high degree of
scientific knowledge has been requisite to dispel the errors of the
senses.

The little that is known of the theories of the satellites of Saturn and
Uranus is in all respects similar to that of Jupiter. The great
compression of Saturn occasions its satellites to move nearly in the
plane of its equator. Of the situation of the equator of Uranus we know
nothing, nor of its compression. The orbits of its satellites are nearly
perpendicular to the plane of the ecliptic.

Our constant companion the moon next claims attention. Several
circumstances concur to render her motions the most interesting, and at
the same time the most difficult to investigate of all the bodies of our
system. In the solar system planet troubles planet, but in the lunar
theory the sun is the great disturbing cause; his vast distance being
compensated by his enormous magnitude, so that the motions of the moon
are more irregular than those of the planets; and on account of the
great ellipticity of her orbit and the size of the sun, the
approximations to her motions are tedious and difficult, beyond what
those unaccustomed to such investigations could imagine. Neither the
eccentricity of the lunar orbit, nor its inclination to the plane of the
ecliptic, have experienced any changes from secular inequalities; but
the mean motion, the nodes, and the perigee, are subject to very
remarkable variations.

From an eclipse observed at Babylon by the Chaldeans, on the 19th of
March, seven hundred and twenty-one years before the Christian era, the
place of the moon is known from that of the sun at the instant of
opposition; whence her mean longitude may be found; but the comparison
of this mean longitude with another mean longitude, computed back for
the instant of the eclipse from modern observations, shows that the moon
performs her revolution round the earth more rapidly and in a shorter
time now, than she did formerly; and that the acceleration in her mean
motion has been increasing from age to age as the square of the time;
all the ancient and intermediate eclipses confirm this result. As the
mean motions of the planets have no secular inequalities, this seemed to
be an unaccountable anomaly, and it was at one time attributed to the
resistance of an ethereal medium pervading space; at another to the
successive transmission of the gravitating force: but as La Place proved
that neither of these causes, even if they exist, have any influence on
the motions of the lunar perigee or nodes, they could not affect the
mean motion, a variation in the latter from such a cause being
inseparably connected with variations in the two former of these
elements. That great mathematician, however, in studying the theory of
Jupiter's satellites, perceived that the secular variations in the
elements of Jupiter's orbit, from the action of the planets, occasion
corresponding changes in the motions of the satellites: this led him to
suspect that the acceleration in the mean motion of the moon might be
connected with the secular variation in the eccentricity of the
terrestrial orbit; and analysis has proved that he assigned the true
cause.

If the eccentricity of the earth's orbit were invariable, the moon would
be exposed to a variable disturbance from the action of the sun, in
consequence of the earth's annual revolution; but it would be periodic,
since it would be the same as often as the sun, the earth, and the moon
returned to the same relative positions: on account however of the slow
and incessant diminution in the eccentricity of the terrestrial orbit,
the revolution of our planet is performed at different distances from
the sun every year. The position of the moon with regard to the sun,
undergoes a corresponding change; so that the mean action of the sun on
the moon varies from one century to another, and occasions the secular
increase in the moon's velocity called the acceleration, a name which is
very appropriate in the present age, and which will continue to be so
for a vast number of ages to come; because, as long as the earth's
eccentricity diminishes, the moon's mean motion will be accelerated; but
when the eccentricity has passed its minimum and begins to increase, the
mean motion will be retarded from age to age. At present the secular
acceleration is about 10", but its effect on the moon's place increases
as the square of the time. It is remarkable that the action of the
planets thus reflected by the sun to the moon, is much more sensible
than their direct action, either on the earth or moon. The secular
diminution in the eccentricity, which has not altered the equation of
the centre of the sun by eight minutes since the earliest recorded
eclipses, has produced a variation of 1° 48' in the moon's longitude,
and of 7° 12' in her mean anomaly.

The action of the sun occasions a rapid but variable motion in the nodes
and perigee of the lunar orbit; the former, though they recede during
the greater part of the moon's revolution, and advance during the
smaller, perform their sidereal revolutions in 6793^days.4212, and the
latter, though its motion is sometimes retrograde and sometimes direct,
in 3232^days.5807, or a little more than nine years: but such is the
difference between the disturbing energy of the sun and that of all the
planets put together, that it requires no less than 109770 years for the
greater axis of the terrestrial orbit to do the same. It is evident that
the same secular variation which changes the sun's distance from the
earth, and occasions the acceleration in the moon's mean motion, must
affect the motion of the nodes and perigee; and it consequently appears,
from theory as well as observation, that both these elements are subject
to a secular inequality, arising from the variation in the eccentricity
of the earth's orbit, which connects them with the acceleration; so that
both are retarded when the mean motion is anticipated. The secular
variations in these three elements are in the ratio of the numbers 3,
0.735, and 1; whence the three motions of the moon, with regard to the
sun, to her perigee, and to her nodes, are continually accelerated, and
their secular equations are as the numbers 1, 4, and 0.265, or according
to the most recent investigations as 1, 4, 6776 and 0.391. A comparison
of ancient eclipses observed by the Arabs, Greeks, and Chaldeans,
imperfect as they are, with modern observations, perfectly confirms
these results of analysis.

Future ages will develop these great inequalities, which at some most
distant period will amount to many circumferences. They are indeed
periodic; but who shall tell their period? Millions of years must elapse
before that great cycle is accomplished; but 'such changes, though rare
in time, are frequent in eternity.'

The moon is so near, that the excess of matter at the earth's equator
occasions periodic variations in her longitude and latitude; and, as the
cause must be proportional to the effect, a comparison of these
inequalities, computed from theory, with the same given by observation,
shows that the compression of the terrestrial spheroid, or the ratio of
the difference between the polar and equatorial diameter to the diameter
of the equator is 1/305.05. It is proved analytically, that if a fluid
mass of homogeneous matter, whose particles attract each other inversely
as the square of the distance, were to revolve about an axis, as the
earth, it would assume the form of a spheroid, whose compression is
1/230. Whence it appears, that the earth is not homogeneous, but decreases
in density from its centre to its circumference. Thus the moon's eclipses
show the earth to be round, and her inequalities not only determine the
form, but the internal structure of our planet; results of analysis which
could not have been anticipated. Similar inequalities in Jupiter's
satellites prove that his mass is not homogeneous, and that his
compression is 1/13·8.

The motions of the moon have now become of more importance to the
navigator and geographer than those of any other body, from the
precision with which the longitude is determined by the occultations of
stars and lunar distances. The lunar theory is brought to such
perfection, that the times of these phenomena, observed under any
meridian, when compared with that computed for Greenwich in the Nautical
Almanack, gives the longitude of the observer within a few miles. The
accuracy of that work is obviously of extreme importance to a maritime
nation; we have reason to hope that the new Ephemeris, now in
preparation, will be by far the most perfect work of the kind that ever
has been published.

From the lunar theory, the mean distance of the sun from the earth, and
thence the whole dimensions of the solar system are known; for the
forces which retain the earth and moon in their orbits, are respectively
proportional to the radii vectores of the earth and moon, each being
divided by the square of its periodic time; and as the lunar theory
gives the ratio of the forces, the ratio of the distance of the sun and
moon from the earth is obtained: whence it appears that the sun's
distance from the earth is nearly 396 times greater than that of the
moon.

The method however of finding the absolute distances of the celestial
bodies in miles, is in fact the same with that employed in measuring
distances of terrestrial objects. From the extremities of a known base
the angles which the visual rays from the object form with it, are
measured; their sum subtracted from two right-angles gives the angle
opposite the base; therefore by trigonometry, all the angles and sides
of the triangle may be computed; consequently the distance of the object
is found. The angle under which the base of the triangle is seen from
the object, is the parallax of that object; it evidently increases and
decreases with the distance; therefore the base must be very great
indeed, to be visible at all from the celestial bodies. But the globe
itself whose dimensions are ascertained by actual admeasurement,
furnishes a standard of measures, with which we compare the distances,
masses, densities, and volumes of the sun and planets.

The courses of the great rivers, which are in general navigable to a
considerable extent, prove that the curvature of the land differs but
little from that of the ocean; and as the heights of the mountains and
continents are, at any rate, quite inconsiderable when compared with the
magnitude of the earth, its figure is understood to be determined by a
surface at every point perpendicular to the direction of gravity, or of
the plumb-line, and is the same which the sea would have if it were
continued all round the earth beneath the continents. Such is the figure
that has been measured in the following manner:--

A terrestrial meridian is a line passing through both poles, all the
points of which have contemporaneously the same noon. Were the lengths
and curvatures of different meridians known, the figure of the earth
might be determined; but the length of one degree is sufficient to give
the figure of the earth, if it be measured on different meridians, and
in a variety of latitudes; for if the earth were a sphere, all degrees
would be of the same length, but if not, the lengths of the degrees will
be greatest where the curvature is least; a comparison of the length of
the degrees in different parts of the earth's surface will therefore
determine its size and form.

An arc of the meridian may be measured by observing the latitude of its
extreme points, and then measuring the distance between them in feet or
fathoms; the distance thus determined on the surface of the earth,
divided by the degrees and parts of a degree contained in the difference
of the latitudes, will give the exact length of one degree, the
difference of the latitudes being the angle contained between the
verticals at the extremities of the arc. This would be easily
accomplished were the distance unobstructed, and on a level with the
sea; but on account of the innumerable obstacles on the surface of the
earth, it is necessary to connect the extreme points of the arc by a
series of triangles, the sides and angles of which are either measured
or computed, so that the length of the arc is ascertained with much
laborious computation. In consequence of the inequalities of the
surface, each triangle is in a different plane; they must therefore be
reduced by computation to what they would have been, had they been
measured on the surface of the sea; and as the earth is spherical, they
require a correction to reduce them from plane to spherical triangles.

Arcs of the meridian have been measured in a variety of latitudes, both
north and south, as well as arcs perpendicular to the meridian. From
these measurements it appears that the length of the degrees increase
from the equator to the poles, nearly as the square of the sine of the
latitude; consequently, the convexity of the earth diminishes from the
equator to the poles. Many discrepancies occur, but the figure that most
nearly follows this law is an ellipsoid of revolution, whose equatorial
radius is 3962.6 miles, and the polar radius 3949.7; the difference, or
12.9 miles, divided by the equatorial radius, is 1/308·7, or 1/309
nearly; this fraction is called the compression of the earth, because,
according as it is greater or less, the terrestrial ellipsoid is more
or less flattened at the poles; it does not differ much from that given
by the lunar inequalities. If we assume the earth to be a sphere, the
length of a degree of the meridian is 69 1/22 British miles; therefore
360 degrees, or the whole circumference of the globe is 24856, and the
diameter, which is something less than a third of the circumference, is
7916 or 8000 miles nearly. Eratosthenes, who died 194 years before the
Christian era, was the first to give an approximate value of the earth's
circumference, by the mensuration of an arc between Alexandria and Syene.

But there is another method of finding the figure of the earth, totally
independent of either of the preceding. If the earth were a homogeneous
sphere without rotation, its attraction on bodies at its surface would
be everywhere the same; if it be elliptical, the force of gravity
theoretically ought to increase, from the equator to the pole as the
square of the sine of the latitude; but for a spheroid in rotation, by
the laws of mechanics the centrifugal force varies as the square of the
sine of the latitude from the equator where it is greatest, to the pole
where it vanishes; and as it tends to make bodies fly off the surface,
it diminishes the effects of gravity by a small quantity. Hence by
gravitation, which is the difference of these two forces, the fall of
bodies ought to be accelerated in going from the equator to the poles,
proportionably to the square of the sine of the latitude; and the weight
of the same body ought to increase in that ratio. This is directly proved
by the oscillations of the pendulum; for if the fall of bodies be
accelerated, the oscillations will be more rapid; and that they may
always be performed in the same time, the length of the pendulum must
be altered. Now, by numerous and very careful experiments, it is proved
that a pendulum, which makes 86400 oscillations in a mean day at the
equator, will do the same at every point of the earth's surface, if
its length be increased in going to the pole, as the square of the
sine of the latitude. From the mean of these it appears that the
compression of the terrestrial spheroid is about 1/342, which does not
differ much from that given by the lunar inequalities, and from the arcs
of the meridian. The near coincidence of these three values, deduced
by methods so entirely independent of each other, shows that the mutual
tendencies of the centres of the celestial bodies to one another, and
the attraction of the earth for bodies at its surface, result from the
reciprocal attraction of all their particles. Another proof may be added;
the nutation of the earth's axis, and the precession of the equinoxes,
are occasioned by the action of the sun and moon on the protuberant
matter at the earth's equator; and although these inequalities do not
give the absolute value of the terrestrial compression, they show that
the fraction expressing it is comprised between the limits
1/279 and 1/578.

It might be expected that the same compression should result from each,
if the different methods of observation could be made without error.
This, however, is not the case; for such discrepancies are found both
in the degrees of the meridian and in the length of the pendulum, as
show that the figure of the earth is very complicated; but they are
so small when compared with the general results, that they may be
disregarded. The compression deduced from the mean of the whole,
appears to be about 1/320; that given by the lunar theory has the advantage
of being independent of the irregularities at the earth's surface,
and of local attractions. The form and size of the earth being determined,
it furnishes a standard of measure with which the dimensions of the
solar system may be compared.

The parallax of a celestial body is the angle under which the radius
of the earth would be seen if viewed from the centre of that body;
it affords the means of ascertaining the distances of the sun, moon,
and planets. Suppose that, when the moon is in the horizon at the
instant of rising or setting, lines were drawn from her centre to the
spectator and to the centre of the earth, these would form a right-angled
triangle with the terrestrial radius, which is of a known length;
and as the parallax or angle at the moon can be measured, all the angles
and one side are given; whence the distance of the moon from the centre
of the earth may be computed. The parallax of an object may be found,
if two observers under the same meridian, but at a very great distance
from one another, observe its zenith distances on the same day at the
time of its passage over the meridian. By such contemporaneous
observations at the Cape of Good Hope and at Berlin, the mean horizontal
parallax of the moon was found to be 3454"·2; whence the mean distance
of the moon is about sixty times the mean terrestrial radius, or 240000
miles nearly. Since the parallax is equal to the radius of the earth
divided by the distance of the moon; under the same parallel of latitude
it varies with the distance of the moon from the earth, and proves the
ellipticity of the lunar orbit; and when the moon is at her mean
distance, it varies with the terrestrial radii, thus showing that the
earth is not a sphere.

Although the method described is sufficiently accurate for finding the
parallax of an object so near as the moon, it will not answer for the
sun which is so remote, that the smallest error in observation would
lead to a false result; but by the transits of Venus that difficulty
is obviated. When that planet is in her nodes, or within 1 1/4° of them,
that is, in, or nearly in the plane of the ecliptic, she is occasionally
seen to pass over the sun like a block spot. If we could imagine that
the sun and Venus had no parallax, the line described by the planet on
his disc, and the duration of the transit, would be the same to all
the inhabitants of the earth; but as the sun is not so remote but that
the semidiameter of the earth has a sensible magnitude when viewed from
his centre, the line described by the planet in its passage over his
disc appears to be nearer to his centre or farther from it, according
to the position of the observer; So that the duration of the transit
varies with the different points of the earth's surface at which it is
observed. This difference of time, being entirely the effect of parallax,
furnishes the means of computing it from the known motions of the earth
and Venus, by the same method as for the eclipses of the sun. In fact
the ratio of the distances of Venus and the sun from the earth at the
time of the transit, are known from the theory of their elliptical
motion; consequently, the ratio of the parallaxes of these two bodies,
being inversely as their distances, is given; and as the transit gives
the difference of the parallaxes, that of the sun is obtained. In 1769,
the parallax of the sun was determined by observations of a transit of
Venus made at Wardhus in Lapland, and at Otaheite in the South Sea,
the latter observation being the object of Cook's first voyage. The
transit lasted about six hours at Otaheite, and the difference in the
duration at these two stations was eight minutes; whence the sun's
parallax was found to be 8"·72; but by other considerations it has
subsequently been reduced to 8"·575; from which the mean distance of
the sun appears to be about 95996000, or ninety-six millions of miles
nearly. This is confirmed by an inequality in the motion of the moon,
which depends on the parallax of the sun, and which when compared
with observation gives 8"·6 for the sun's parallax.

The parallax of Venus is determined by her transits, that of Mars
by direct observation. The distances of these two planets from the
earth are therefore known in terrestrial radii; consequently their
mean distances from the sun may be computed and as the ratios of the
distances of the planets from the sun are known by Kepler's law,
their absolute distances in miles are easily found.

Far as the earth seems to be from the sun, it is near to him when
compared with Uranus; that planet is no less than 1843 millions of
miles from the luminary that warms and enlivens the world; to it,
situate on the verge of the system, the sun must appear not much
larger than Venus does to us. The earth cannot even be visible as a
telescopic object to a body so remote; yet man, the inhabitant of the
earth, soars beyond the vast dimensions of the system to which his
planet belongs, and assumes the diameter of its orbit as the base
of a triangle, whose apex extends to the stars.

Sublime as the idea is, this assumption proves ineffectual, for
the apparent places of the fixed stars are not sensibly changed by
the earth's annual revolution; and with the aid derived from the
refinements of modern astronomy and the most perfect instruments,
it is still a matter of doubt whether a sensible parallax has been
detected, even in the nearest of these remote suns. If a fixed star
had the parallax of one second, its distance from the sun would be
20500000 millions of miles. At such a distance not only the terrestrial
orbit shrinks to a point, but, where the whole solar system, when
seen in the focus of the most powerful telescope, might be covered
by the thickness of a spider's thread. Light, flying at the rate
of 200000 miles in a second, would take three years and seven days
to travel over that space; one of the nearest stars may therefore
have been kindled or extinguished more than three years before we
could have been aware of so mighty an event. But this distance must
be small when compared with that of the most remote of the bodies
which are visible in the heavens. The fixed stars are undoubtedly
luminous like the sun; it is therefore probable that they are not
nearer to one another than the sun is to the nearest of them. In
the milky way and the other starry nebulæ, some of the stars that
seem to us to be close to others, may be far behind them in the
boundless depth of space; nay, may rationally be supposed to be
situated many thousand times further off: light would therefore
require thousands of years to come to the earth from those myriads
of suns, of which our own is but 'the dim and remote companion.'

The masses of such planets as have no satellites are known by comparing
the inequalities they produce in the motions of the earth and of each
other, determined theoretically, with the same inequalities given by
observation, for the disturbing cause must necessarily be proportional
to the effect it produces. But as the quantities of matter in any two
primary planets are directly as the cubes of the mean distances at which
their satellites revolve, and inversely as the squares of their periodic
times, the mass of the sun and of any planets which have satellites, may
be compared with the mass of the earth. In this manner it is computed
that the mass of the sun is 354936 times greater than that of the earth;
whence the great perturbations of the moon and the rapid motion of the
perigee and nodes of her orbit. Even Jupiter, the largest of the
planets, is 1070.5 times less than the sun. The mass of the moon is
determined from four different sources,--from her action on the
terrestrial equator, which occasions the rotation in the axis of
rotation; from her horizontal parallax, from an inequality she produces
in the sun's longitude, and from her action on the titles. The three
first quantities, computed from theory, and compared with their observed
values, give her mass respectively equal to the 1/71, 1/74·2, and 1/69·2
part of that of the earth, which do not differ very much from each
other; but, from her action in raising  the tides, which furnishes
the fourth method, her mass appears to be about the seventy-fifth part
of that of the earth, a value that cannot differ much from the truth.

The apparent diameters of the sun, moon, and planets are determined by
measurement; therefore their real diameters may be compared with that of
the earth; for the real diameter of a planet is to the real diameter of
the earth, or 8000 miles, as the apparent diameter of the planet to the
apparent diameter of the earth as seen from the planet, that is, to
twice the parallax of the planet The mean apparent diameter of the sun
is 1920", and with the solar parallax 8"·65, it will be found that
the diameter of the sun is about 888000 miles; therefore, the centre of
the sun were to coincide with the centre of the earth, his volume would
not only include the orbit of the moon, but would extend nearly as far
again, for the moon's mean distance from the earth is about sixty times
the earth's mean radius or 240000 miles; so that twice the distance of
the moon is 480000 miles, which differs but little from the solar
radius; his equatorial radius is probably not much less than the major
axis of the lunar orbit.

The diameter of the moon is only 2160 miles; and Jupiter's diameter of
88000 miles is incomparably less than that of the sun The diameter of
Pallas does not much exceed 71 miles, so that an inhabitant of that
planet, in one of our steam-carriages, might go round his world in five
or six hours.

The oblate form of the celestial bodies indicates rotatory motion, and
this has been confirmed, in most cases, by tracing spots on their
surfaces, whence their poles and times of rotation have been determined.
The rotation of Mercury is unknown, on account of his proximity to the
sun; and that of the new planets has not yet been ascertained. The sun
revolves in twenty-five days ten hours, about an axis that is directed
towards a point half way between the pole star and Lyra, the plane of
rotation being inclined a little more than 70° to that on which the
earth revolves. From the rotation of the sun, there is every reason to
believe that he has a progressive motion in space, although the
direction to which he tends is as yet unknown; but in consequence of the
reaction of the planets, he describes a small irregular orbit about the
centre of inertia of the system, never deviating from his position by
more than twice his own diameter, or about seven times the distance of
the moon from the earth.

The sun and all his attendants rotate from west to east on axes that
remain nearly parallel to themselves in every point of their orbit, and
with angular velocities that are sensibly uniform. Although the
uniformity in the direction of their rotation is a circumstance hitherto
unaccounted for in the economy of Nature, yet from the design and
adaptation of every other part to the perfection of the whole, a
coincidence so remarkable cannot be accidental; and as the revolutions
of the planets and satellites are also from west to east, it is evident
that both must have arisen from the primitive causes which have
determined the planetary motions.

The larger planets rotate in shorter periods than the smaller planets
and the earth; their compression is consequently greater, and the action
of the sun and of their satellites occasions a nutation in their axes,
and a precession of their equinoxes, similar to that which obtains in
the terrestrial spheroid from the attraction of the sun and moon on the
prominent matter at the equator. In comparing the periods of the
revolutions of Jupiter and Saturn with the times of their rotation, it
appears that a year of Jupiter contains nearly ten thousand of his days,
and that of Saturn about thirty thousand Saturnian days.

The appearance of Saturn is unparalleled in the system of the world; he
is surrounded by a ring even brighter than himself, which always remains
in the plane of his equator, and viewed with a very good telescope, it
is found to consist of two concentric rings, divided by a dark band. By
the laws of mechanics, it is impossible that this body can retain its
position by the adhesion of its particles alone; it must necessarily
revolve with a velocity that will generate a centrifugal force
sufficient to balance the attraction of Saturn. Observation confirms the
truth of these principles, showing that the rings rotate about the
planet in 10 1/2 hours, which is considerably less than the time a
satellite would take to revolve about Saturn at the same distance. Their
plane is inclined to the ecliptic at an angle of 31°; and in consequence
of this obliquity of position they always appear elliptical to us, but
with an eccentricity so variable as even to be occasionally like a
straight line drawn across the planet. At present the apparent axes of
the rings are as 1000 to 160; and on the 29th of September, 1832,
the plane of the rings will pass through the centre of the earth
when they will be visible only with superior instruments, and will
appear like a fine line across the disc of Saturn. On the 1st of
December in the same year, the plane of the rings will pass through
the centre of the sun.

It is a singular result of the theory, that the rings could not maintain
their stability of rotation if they were everywhere of uniform
thickness; for the smallest disturbance would destroy the equilibrium,
which would become more and more deranged, till at last they would be
precipitated on the surface of the planet. The rings of Saturn must
therefore be irregular solids of unequal breadth in the different parts
of the circumference, so that their centres of gravity do not coincide
with the centres of their figures.

Professor Struve has also discovered that the centre of the ring is not
concentric with the centre of Saturn; the interval between the outer
edge of the globe of the planet and the outer edge of the ring on one
side, is 11"·073, and on the other side the interval is 11"·288;
consequently there is an eccentricity of the globe in the ring of
0"·215.

If the rings obeyed different forces, they would not remain in the same
plane, but the powerful attraction of Saturn always maintains them and
his satellites in the plane of his equator. The rings, by their mutual
action, and that of the sun and satellites, must oscillate about the
centre of Saturn, and produce phenomena of light and shadow, whose
periods extend to many years.

The periods of the rotation of the moon and the other satellites are
equal to the times of their revolutions, consequently these bodies
always turn the same face to their primaries; however, as the mean
motion of the moon is subject to a secular inequality which will
ultimately amount to many circumferences, if the rotation of the moon
were perfectly uniform, and not affected by the same inequalities, it
would cease exactly to counterbalance the motion of revolution; and the
moon, in the course of ages, would successively and gradually discover
every point other surface to the earth. But theory proves that this
never can happen; for the rotation of the moon, though it does not
partake of the periodic inequalities of her revolution, is affected by
the same secular variations, so that her motions of rotation and
revolution round the earth will always balance each other, and remain
equal. This circumstance arises from the form of the lunar spheroid,
which has three principal axes of different lengths at right angles to
each other. The moon is flattened at the poles from her centrifugal
force, therefore her polar axis is least; the other two are in the plane
of her equator, but that directed towards the earth is the greatest. The
attraction of the earth, as if it had drawn out that part of the moon's
equator, constantly brings the greatest axis, and consequently the same
hemisphere towards us, which makes her rotation participate in the
secular variations in her mean motion of revolution. Even if the angular
velocities of rotation and revolution had not been nicely balanced in
the beginning of the moon's motion, the attraction of the earth would
have recalled the greatest axis to the direction of the line joining the
centres of the earth and moon; so that it would vibrate on each side of
that line in the same manner as a pendulum oscillates on each side of
the vertical from the influence of gravitation.

No such libration is perceptible; and as the smallest disturbance would
make it evident, it is clear that if the moon has ever been touched by a
comet, the mass of the latter must have been extremely small; for if it
had been only the hundred-thousandth part of that of the earthy it would
have rendered the libration sensible. A similar libration exists in the
motions of Jupiter's satellites; but although the comet of 1767 and 1779
passed through the midst of them, their libration still remains
insensible. It is true, the moon is liable to librations depending on
the position of the spectator; at her rising, part of the western edge
of her disc is visible, which is invisible at her setting, and the
contrary takes place with regard to her eastern edge. There are also
librations arising from the relative positions of the earth and moon in
their respective orbits, but as they are only optical appearances, one
hemisphere will be eternally concealed from the earth. For the same
reason, the earth, which must be so splendid an object to one lunar
hemisphere, will be for ever veiled from the other. On account of these
circumstances, the remoter hemisphere of the moon has its day a
fortnight long, and a night of the same duration not even enlightened by
a moon, while the favoured side is illuminated by the reflection of the
earth during its long night. A moon exhibiting a surface thirteen times
larger than ours, with all the varieties of clouds, land, and water
coming successively into view, would be a splendid object to a lunar
traveller in a journey to his antipodes.

The great height of the lunar mountains probably has a considerable
influence on the phenomena of her motion, the more so as her compression
is small, and her mass considerable.

In the curve passing through the poles, and that diameter of the moon
which always points to the earth, nature has furnished a permanent
meridian, to which the different spots on her surface have been
referred, and their positions determined with as much accuracy as those
of many of the most remarkable places on the surface of our globe.

The rotation of the earth which determines the length of the day may be
regarded as one of the most important elements in the system of the
world. It serves as a measure of time, and forms the standard of
comparison for the revolutions of the celestial bodies, which by their
proportional increase or decrease would soon disclose any changes it
might sustain. Theory and observation concur in proving, that among the
innumerable vicissitudes that prevail throughout creation, the period of
the earth's diurnal rotation is immutable. A fluid, as Mr. Babbage
observes, in falling from a higher to a lower level, carries with it the
velocity due to its revolution with the earth at a greater distance from
its centre. It will therefore accelerate, although to an almost
infinitesimal extent, the earth's daily rotation. The sum of all these
increments of velocity, arising from the descent of all the rivers on
the earth's surface, would in time become perceptible, did not nature,
by the process of evaporation, raise the waters back to their sources;
and thus again by removing matter to a greater distance from the centre,
destroy the velocity generated by its previous approach; so that the
descent of the rivers does not affect the earth's rotation. Enormous
masses projected by volcanoes from the equator to the poles, and the
contrary, would indeed affect it, but there is no evidence of such
convulsions. The disturbing action of the moon and planets, which has so
powerful an effect on the revolution of the earth, in no way influences
its rotation: the constant friction of the trade winds on the mountains
and continents between the tropics does not impede its velocity, which
theory even proves to be the same, as if the sea together with the earth
formed one solid mass. But although these circumstances be inefficient,
a variation in the mean temperature would certainly occasion a
corresponding change in the velocity of rotation: for in the science of
dynamics, it is a principle in a system of bodies, or of particles
revolving about a fixed centre, that the momentum, or sum of the
products of the mass of each into its angular velocity and distance from
the centre is a constant quantity, if the system be not deranged by an
external cause. Now since the number of particles in the system is the
same whatever its temperature may be, when their distances from the
centre are diminished, their angular velocity must be increased in order
that the preceding quantity may still remain constant. It follows then,
that as the primitive momentum of rotation with which the earth was
projected into space must necessarily remain the same, the smallest
decrease in heat, by contracting the terrestrial spheroid, would
accelerate its rotation, and consequently diminish the length of the
day. Notwithstanding the constant accession of heat from the sun's rays,
geologists have been induced to believe from the nature of fossil
remains, that the mean temperature of the globe is decreasing.

The high temperature of mines, hot springs, and above all, the internal
fires that have produced, and do still occasion such devastation on our
planet, indicate an augmentation of heat towards its centre the increase
of density in the strata corresponding to the depth and the form of the
spheroid, being what theory assigns to a fluid mass in rotation, concur
to induce the idea that the temperature of the earth was originally so
high as to reduce all the substances of which it is composed to a state
of fusion, and that in the course of ages it has cooled down to its
present state; that it is still becoming colder, and that it will
continue to do so, till the whole mass arrives at the temperature of the
medium in which it is placed, or rather at a state of equilibrium
between this temperature, the cooling power of its own radiation, and
the heating effect of the sun's rays. But even if this cause be
sufficient to produce the observed effects, it must be extremely slow in
its operation; for in consequence of the rotation of the earth being a
measure of the periods of the celestial motions, it has been proved,
that if the length of the day had decreased by the three hundredth part
of a second since the observations of Hipparchus two thousand years ago,
it would have diminished the secular equation of the moon by 4"·4. It
is therefore beyond a doubt, that the mean temperature of the earth
cannot have sensibly varied during that time; if then the appearances
exhibited by the strata really owing to a decrease of internal
temperature, it either shows the immense periods requisite to produce
geological changes to which two thousand years are as nothing, or that
the mean temperature of the earth had arrived at a state of equilibrium
before these observations. However strong the indication of the
primitive fluidity of the earth, as there is no direct proof, it can
only be regarded as a very probable hypothesis; but one of the most
profound philosophers and elegant writers of modern times has found, in
the secular variation of the eccentricity of the terrestrial orbit, an
evident cause of decreasing temperature. That accomplished author, in
pointing out the mutual dependences of phenomena, says--'It is evident
that the mean temperature of the whole surface of the globe, in so far
as it is maintained by the action of the sun at 8 higher degree than it
would have were the sun extinguished, must depend on the mean quantity
of the sun's rays which it receives, or, which comes to the same thing,
on the total quantity received in a given invariable time: and the
length of the year being unchangeable in all the fluctuations of the
planetary system, it follows, that the total amount of solar radiation
will determine, _cœteris paribus_, the general climate of the earth. Now
it is not difficult to show, that this amount is inversely proportional
to the minor axis of the ellipse described by the earth about the sun,
regarded as slowly variable; and that, therefore, the major axis
remaining, as we know it to be, constant, and the orbit being actually
in a state of approach to a circle, and consequently the minor axis
being on the increase, the mean annual amount of solar radiation
received by the whole earth must be actually on the decrease. We have,
therefore, an evident real cause to account for the phenomenon.' The
limits of the variation in the eccentricity of the earth's orbit are
unknown; but if its ellipticity has ever been as great as that of the
orbit of Mercury or Pallas, the mean temperature of the earth must have
been sensibly higher than it is at present; whether it was great enough
to render our northern climates fit for the production of tropical
plants, and for the residence of the elephant, and the other inhabitants
of the torrid zone, it is impossible to say.

The relative quantity of heat received by the earth at different moments
during a single revolution, varies with the position of the perigee of
its orbit, which accomplishes a tropical revolution in 20935 years. In
the year 1250 of our era, and 29653 years before it, the perigee
coincided with the summer solstice; at both these periods the earth was
nearer the sun during the summer, and farther from him in the winter
than in any other position of the apsides: the extremes of temperature
must therefore have been greater than at present; but as the terrestrial
orbit was probably more elliptical at the distant epoch, the heat of the
summers must have been very great though possibly compensated by the
rigour of the winters; at all events, none of these changes affect the
length of the day.

It appears from the marine shells found on the tops of the highest
mountains, and in almost every part of the globe, that immense
continents have been elevated above the ocean, which must have which
must have engulphed others. Such a catastrophe would be occasioned by a
variation in the position of the axis of rotation on the surface of the
earth; for the seas ending to the new equator would leave some portions
of the globe, and overwhelm others.

But theory proves that neither nutation, precession, nor any of the
disturbing forces that affect the system, have the smallest influence on
the axis of rotation, which maintains a permanent position on the
surface, if the earth be not disturbed in its rotation by some foreign
cause, as the collision of a comet which may have happened in the
immensity of time. Then indeed, the equilibrium could only have been
restored by the rushing of the seas to the new equator, which they would
continue to do, till the surface was every where perpendicular to the
direction of gravity. But it is probable that such an accumulation of
the waters would not be sufficient to restore equilibrium if the
derangement had been great; for the mean density of the sea is only
about a fifth part of the mean density of the earth, and the mean depth
even of the Pacific ocean is not more than four miles, whereas the
equatorial radius of the earth exceeds the polar radius by twenty-five
or thirty miles; consequently the influence of the sea on the direction
of gravity is very small; and as it appears that a great change in the
position of the axes is incompatible with the law of equilibrium, the
geological phenomena must be ascribed to an internal cause. Thus amidst
the mighty revolutions which have swept innumerable races of organized
beings from the earth, which have elevated plains, and buried mountains
in the ocean, the rotation of the earth, and the position of the axis on
its surface, have undergone but slight variations.

It is beyond a doubt that the strata increase in density from the
surface of the earth to its centre, which is even proved by the lunar
inequalities; and it is manifest from the mensuration of arcs of the
meridian and the lengths of the seconds pendulum that the strata are
elliptical and concentric. This certainly would have happened if the
earth had originally been fluid, for the denser parts must have subsided
towards the centre, as it approached a state of equilibrium; but the
enormous pressure of the superincumbent mass is a sufficient cause for
these phenomena. Professor Leslie observes, that air compressed into the
fiftieth part of its volume has its elasticity fifty times augmented; if
it continue to contract at that rate, it would, from its own incumbent
weight, acquire the density of water at the depth of thirty-four miles.
But water itself would have its density doubled at the depth of
ninety-three miles, and would even attain the density of quicksilver at
a depth of 362 miles. In descending therefore towards the centre through
4000 miles, the condensation of ordinary materials would surpass the
utmost powers of conception. But a density so extreme is not borne out
by astronomical observation. It might seem therefore to follow, that our
planet must have a widely cavernous structure, and that we tread on a
crust or shell, whose thickness bears a very small proportion to the
diameter of its sphere. Possibly too this great condensation at the
central regions may be counterbalanced by the increased elasticity due
to a very elevated temperature. Dr. Young says that steel would be
compressed into one-fourth, and stone into one-eighth of its bulk at the
earth's centre. However we are yet ignorant of the laws of compression
of solid bodies beyond a certain limit; but, from the experiments of Mr.
Perkins, they appear to be capable of a greater degree of compression
than has generally been imagined.

It appears then, that the axis of rotation is invariable on the surface
of the earth, and observation shows, that were it not for the action of
the sun and moon on the matter at the equator, it would remain parallel
to itself in every point of its orbit.

The attraction of an exterior body not only draws a spheroid towards it;
but, as the force varies inversely as the square of the distance, it
gives it a motion about its centre of gravity, unless when the
attracting body is situated in the prolongation of one of the axes of
the spheroid.

The plane of the equator is inclined to the plane of the ecliptic at an
angle of about 23° 28', and the inclination of the lunar orbit on the
same is nearly 5°; consequently, from the oblate figure of the earth,
the sun and moon acting obliquely and unequally on the different parts
of the terrestrial spheroid, urge the plane of the equator from its
direction, and force it to move from east to west, so that the
equinoctial points have a slow retrograde motion on the plane of the
ecliptic of about 50"·412 annually. The direct tendency of this action
would be to make the planes of the equator and ecliptic coincide; but in
consequence of the rotation of the earth, the inclination of the two
planes remains constant, as a top in spinning preserves the same
inclination to the plane of the horizon. Were the earth spherical this
effect would not be produced, and the equinoxes would always correspond
to the same points of the ecliptic, at least as far as this kind of
action is concerned. But another and totally different cause operates on
this motion, which has already been mentioned. The action of the planets
on one another and on the sun, occasions a very slow variation in the
position of the plane of the ecliptic, which affects its inclination on
the plane of the equator, and gives the equinoctial points a slow but
direct motion on the ecliptic of 0"·312 annually, which is entirely
independent of the figure of the earth, and would be the same if it were
a sphere. Thus the sun and moon, by moving the plane of the equator,
cause the equinoctial points to retrograde on the ecliptic; and the
planets, by moving the plane of the ecliptic, give them a direct motion,
but much less than the former; consequently the difference of the two is
the mean precession, which is proved, both by theory and observation, to
be about 50"·1 annually. As the longitudes of all the fixed stars are
increased by this quantity, the effects of precession are soon detected;
it was accordingly discovered by Hipparchus, in the year 128 before
Christ, from a comparison of his own observations with those of
Timocharis, 155 years before. In the time of Hipparchus the entrance of
the sun into the constellation Aries was the beginning of spring, but
since then the equinoctial points have receded 30°; so that the
constellations called the signs of the zodiac are now at a considerable
distance from those divisions of the ecliptic which bear their names.
Moving at the rate of 50"·1 annually, the equinoctial points will
accomplish a revolution in 25868 years; but as the precession varies in
different centuries, the extent of this period will be slightly
modified. Since the motion of the sun is direct, and that of the
equinoctial points retrograde, he takes a shorter time to return to the
equator than to arrive at the same stars; so that the tropical year of
365.242264 days must be increased by the time he takes to move through
an arc of 50"·1, in order to have the length of the sidereal year. By
simple proportion it is the 0.014119th part of a day, so that the
sidereal year is 365.256383.

The mean annual precession is subject to a secular variation; for
although the change in the plane of the ecliptic which is the orbit of
the sun, be independent of the form of the earth, yet by bringing the
sun, moon and earth into different relative positions from age to age,
it alters the direct action of the two first on the prominent matter at
the equator; on this account the motion of the equinox is greater by
0"·455 now than it was in the lime of Hipparchus; consequently the
actual length of the tropical year is about 4"·154 shorter than it was
at that time. The utmost change that it can experience from this cause
amounts to 43".

Such is the secular motion of the equinoxes, but it is sometimes
increased and sometimes diminished by periodic variations, whose periods
depend on the relative positions of the sun and moon with regard to the
earth, and occasioned by the direct action of these bodies on the
equator. Dr. Bradley discovered that by this action the moon causes the
pole of the equator to describe a small ellipse in the heavens, the
diameters of which are 16" and 20". The period of this inequality is
nineteen years, the time employed by the nodes of the lunar orbit to
accomplish a revolution. The sun causes a small variation in the
description of this ellipse; it runs through its period in half a year.
This nutation in the earth's axis affects both the precession and
obliquity with small periodic variations; but in consequence of the
secular variation in the position of the terrestrial orbit, which is
chiefly owing to the disturbing energy of Jupiter on the earth, the
oblique of the ecliptic is annually diminished by 0"·52109. With
regard to the fixed stars, this variation in the course of ages may
amount to tea or eleven degrees; but the obliquity of the ecliptic to
the equator can never vary more than two or three degrees, since the
equator will follow in some measure the motion of the ecliptic.

It is evident that the places of all the celestial bodies are affected
by precession and nutation, and therefore all observations of them must
be corrected for these inequalities.

The densities of bodies are proportional to their masses divided by
their volumes; hence if the sun and planets be assumed to be spheres,
their volumes will be as the cubes of their diameters. Now the apparent
diameters of the sun and earth at their mean distance, are 1922" and
17"·08, and the mass of the earth is the 1/354936th part of that of the
sun taken as the unit; it follows therefore, that the earth is nearly
four times as dense as the sun; but the sun is so large that his
attractive force would cause bodies to fall through about 450 feet
in a second; consequently if he were even habitable by human beings,
they would be unable to move, since their weight would be thirty
times as great as it is here. A moderate sized man would weigh about
two tons at the surface of the sun. On the contrary, at the surface
of the four new planets we should be so light, that it would be
impossible to stand from the excess of our muscular force, for a man
would only weigh a few pounds. All the planets and satellites appear
to be of less density than the earth. The motions of Jupiter's
satellites show that his density increases towards his centre; and
the singular irregularities in the form of Saturn, and the great
compression of Mars, prove the internal structure of these two planets
to be very far from uniform.

Astronomy has been of immediate and essential use in affording
invariable standards for measuring duration, distance, magnitude, and
velocity. The sidereal day, measured by the time elapsed between two
consecutive transits of any star at the same meridian, and the sidereal
year, are immutable units with which to compare all great periods of
time; the oscillations of the isochronous pendulum measure its smaller
portions. By these invariable standards alone we can judge of the slow
changes that other elements of the system may have undergone in the
lapse of ages.

The returns of the sun to the same meridian, and to the same equinox or
solstice, have been universally adopted as the measure of our civil days
and years. The solar or astronomical day is the time that elapses
between two consecutive noons or midnights; it is consequently longer
than the sidereal day, on account of the proper motion of the sun during
a revolution of the celestial sphere; but as the sun moves with greater
rapidity at the winter than at the summer solstice, the astronomical day
is more nearly equal to the sidereal day in summer than in winter. The
obliquity of the ecliptic also affects its duration, for in the
equinoxes the arc of the equator is less than the corresponding arc of
the ecliptic, and in the solstices it is greater. The astronomical day
is therefore diminished in the first case, and increased in the second.
If the sun moved uniformly in the equator at the rate of 59' 8"·3
every day, the solar days would be all equal; the time therefore, which
is reckoned by the arrival of an imaginary sun at the meridian, or of
one which is supposed to move in the equator, is denominated mean solar
time, such as is given by clocks and watches in common life: when it is
reckoned by the arrival of the real sun at the meridian, it is apparent
time, such as is given by dials. The difference between the time shown
by a clock and a dial is the equation of time given in the Nautical
Almanac, and sometimes amounts to as much as sixteen minutes. The
apparent and mean time coincide four times in the year.

Astronomers begin the day at noon, but in common reckoning the day
begins at midnight. In England it is divided into twenty-four hours,
which are counted by twelve and twelve; but in France, astronomers
adopting decimal division, divide the day into ten hours, the hour into
one hundred minutes, and the minute into a hundred seconds, because of
the facility in computation, and in conformity with their system of
weights and measures. This subdivision is not used in common life, nor
has it been adopted in any other country, though their scientific
writers still employ that division of time. The mean length of the day,
though accurately determined, is not sufficient for the purposes either
of astronomy or civil life. The length of the year is pointed out by
nature as a measure of long periods; but the incommensurability that
exists between the lengths of the day, and the revolutions of the sun,
renders it difficult to adjust the estimation of both in whole numbers.
If the revolution of the sun were accomplished in 365 days, all the
years would be of precisely the same number of days, and would begin and
end with the sun at the same point of the ecliptic; but as the sun's
revolution includes the fraction of a day, a civil year and a revolution
of the sun have not the same duration. Since the fraction is nearly the
fourth of a day, four years are nearly equal to four revolutions of the
sun, so that the addition of a supernumerary day every fourth year
nearly compensates the difference; but in process of time further
correction will be necessary, because the fraction is less than the
fourth of a day. The period of seven days, by far the most permanent
division of time, and the most ancient monument of astronomical
knowledge, was used by the Brahmins in India with the same denominations
employed by us, and was alike found in the Calendars of the Jews,
Egyptians, Arabs, and Assyrians; it has survived the fall of empires,
and has existed among all successive generations, a proof of their
common origin.

The new moon immediately following the winter solstice in the 707th year
of Rome was made the 1st of January of the first year of Cæsar; the
25th of December in his 45th year, is considered as the date of Christ's
nativity; and Cæsar's 46th year is assumed to be the first of our era.
The preceding year is called the first year before Christ by
chronologists, but by astronomers it is called the year 0. The
astronomical year begins on the 31st of December at noon; and the date
of an observation expresses the days and hours which actually elapsed
since that time.

Some remarkable astronomical eras are determined by the position of the
major axis of the solar ellipse. Moving at the rate of 61"·906
annually, it accomplishes a tropical revolution in 20935 years. It
coincided with the line of the equinoxes 4000 or 4089 years before the
Christian era, much about the time chronologists assign for the creation
of man. In 6485 the major axis will again coincide with the line of the
equinoxes, but then the solar perigee will coincide with the equinox of
spring; whereas at the creation of man it coincided with the autumnal
equinox. In the year 1250 the major axis was perpendicular to the line
of the equinoxes, and then the solar perigee coincided with the solstice
of winter, and the apogee with the solstice of summer. On that account
La Place proposed the year 1250 as a universal epoch, and that the
vernal equinox of that year should be the first day of the first year.

The variations in the positions of the solar ellipse occasion
corresponding changes in the length of the seasons. In its present
position spring is shorter than summer, and autumn longer than winter;
and while the solar perigee continues as it now is, between the solstice
of winter and the equinox of spring, the period including spring and
summer will be longer than that including autumn and winter: in this
century the difference is about seven days. These intervals will be
equal towards the year 6485, when the perigee comes to the equinox of
spring. Were the earth's orbit circular, the seasons would be equal;
their differences arise from the eccentricity of the earth's orbit,
small as it is; but the changes are so gradual as to be imperceptible in
the short space of human life.

No circumstance in the whole science of astronomy excites a deeper
interest than its application to chronology. 'Whole nations,' says La
Place, 'have been swept from the earth, with their language, arts and
sciences, leaving but confused masses of ruin to mark the place where
mighty cities stood; their history, with the exception of a few doubtful
traditions, has perished; but the perfection of their astronomical
observations marks their high antiquity, fixes the periods of their
existence, and proves that even at that early period they must have made
considerable progress in science.'

The ancient state of the heavens may now be computed with great
accuracy; and by comparing the results of computation with ancient
observations, the exact period at which they were made may be verified
if true, or if false, their error may be detected. If the date be
accurate, and the observation good, it will verify the accuracy of
modern tables, and show to how many centuries they may be extended,
without the fear of error. A few examples will show the importance of
this subject.

At the solstices the sun is at his greatest distance from the equator,
consequently his declination at these times is equal to the obliquity of
the ecliptic, which in former times was determined from the meridian
length of the shadow of the style of a dial on the day of the solstice.
The lengths of the meridian shadow at the summer and winter solstice are
recorded to have been observed at the city of Layang, in China, 1100
years before the Christian era. From these, the distances of the sun
from the zenith of the city of Layang are known. Half the sum of these
zenith distances determines the latitude, and half their difference
gives the obliquity of the ecliptic at the period of the observation;
and as the law of the variation in the obliquity is known, both the time
and place of the observations have been verified by computation from
modern tables. Thus the Chinese had made some advances in the science of
astronomy at that early period; the whole chronology of the Chinese is
founded on the observations of eclipses, which prove the existence of
that empire for more than 4700 years. The epoch of the lunar tables of
the Indians, supposed by Bailly to be 3000 before the Christian era, was
proved by La Place from the acceleration of the moon, not to be more
ancient than the time of Ptolemy. The great inequality of Jupiter and
Saturn whose cycle embraces 929 years, is peculiarly fitted for marking
the civilization of a people. The Indians had determined the mean
motions of these two planets in that part of their periods when the
apparent menu motion of Saturn was at the slowest, and that of Jupiter
the most rapid. The periods in which that happened were 3102 years
before the Christian era, and the year 1491 after it.

The returns of comets to their perihelia may possibly mark the present
state of astronomy to future ages.

The places of the fixed stars are affected by the precession of the
equinoxes; and as the law of that variation is known, their positions at
any time may be computed. Now Eudoxus, a contemporary of Plato, mentions
a star situate in the pole of the equator, and from computation it
appears that  _χ_ Draconis was not very far from that place about 3000
years ago; but as Eudoxus lived only about 2150 years ago, he must have
described an anterior state of the heavens, supposed to be the same that
was determined by Chiron, about the time of the siege of Troy. Every
circumstance concurs in showing that astronomy was cultivated in the
highest ages of antiquity.

A knowledge of astronomy leads to the interpretation of hieroglyphical
characters, since astronomical signs are often found on the ancient
Egyptian monuments, which were probably employed by the priests to
record dates. On the ceiling of the portico of a temple among the ruins
of Tentyris, there is a long row of figures of men and animals,
following each other in the some direction among these are the twelve
signs of the zodiac, placed according to the motion of the sun: it is
probable that the first figure in the procession represents the
beginning of the year. Now the first is the Lion as if coming out of the
temple; and as it is well known that the agricultural year of the
Egyptians commenced at the solstice of summer, the epoch of the
inundations of the Nile, if the preceding hypothesis be true, the
solstice at the time the temple was built must have happened in the
constellation of the lion; but as the solstice now happens 21° 6' north
of the constellation of the Twins, it is easy to compute that the zodiac
of Tentyris must have been made 4000 years ago.

The author had occasion to witness an instance of this most interesting
application of astronomy, in ascertaining the dale of a papyrus sent
from Egypt by Mr. Salt, in the hieroglyphical researches of the late Dr.
Thomas Young, whose profound and varied acquirements do honour not only
to his country, but to the age in which he lived. The manuscript was
found in a mummy case; it proved to be a horoscope of the age of
Ptolemy, and its antiquity was determined from the configuration of the
heavens at the time of its construction.

The form of the earth furnishes a standard of weights and measures for
the ordinary purposes of life, as well as for the determination of the
masses and distances of the heavenly bodies. The length of the pendulum
vibrating seconds in the latitude of London forms the standard of the
British measure of extension. Its length oscillating in vacuo at the
temperature of 62° of Fahrenheit, and reduced to the level of the sea,
was determined by Captain Kater, in parts of the imperial standard yard,
to be 39.1387 inches. The weight of a cubic inch of water at the
temperature of 62° Fahrenheit, barometer 30, was also determined in
parts of the imperial troy pound, whence a standard both of weight and
capacity is deduced. The French have adopted the metre for their unit of
linear measure, which is the ten millionth part of that quadrant of the
meridian passing through Formentera and Greenwich, the middle of which
is nearly in the forty-fifth degree of latitude. Should the national
standards of the two countries be lost in the vicissitudes of human
affairs, both may be recovered, since they are derived from natural
standards presumed to be invariable. The length of the pendulum would be
found again with more facility than the metre; but as no measure is
mathematically exact, an error in the original standard may at length
become sensible in measuring a great extent, whereas the error that must
necessarily arise in measuring the quadrant of the meridian is rendered
totally insensible by subdivision in taking its ten millionth part. The
French have adopted the decimal division not only in time, but in their
degrees, weights, and measures, which affords very great facility in
computation. It has not been adopted by any other people; though nothing
is more desirable than that all nations should concur in using the same
division and standards, not only on account of the convenience, but as
affording a more definite idea of quantity. It is singular that the
decimal division of the day, of degrees, weights and measures, was
employed in China 4000 years ago; and that, at the time Ibn Yunus made
his observations at Cairo, about the year 1000, the Arabians were in the
habit of employing the vibrations of the pendulum in their astronomical
observations.

One of the most immediate and striking effects of a gravitating force
external to the earth is the alternate rise and fall of the surface of
the sea twice in the course of a lunar day, or 24^h 50^m 48^s of mean solar
time. As it depends on the action of the sun and moon, it is classed
among astronomical problems, of which it is by far the most difficult
and the least satisfactory. The form of the surface of the ocean in
equilibrio, when revolving with the earth round its axis, is an
ellipsoid flattened at the poles; but the action of the sun and moon,
especially of the moon, disturbs the equilibrium of the ocean.

If the moon attracted the centre of gravity of the earth and all its
particles with equal and parallel forces, the whole system of the earth
and the waters that cover it, would yield to these forces with a common
motion, and the equilibrium of the seas would remain undisturbed. The
difference of the forces, and the inequality of their directions, alone
trouble the equilibrium.

It is proved by daily experience, as well as by strict mechanical
reasoning, that if a number of waves or oscillations be excited in a
fluid by different forces, each pursues its course, and has its effect
independently of the rest. Now in the tides there are three distinct
kinds of oscillations, depending on different causes, producing their
effects independently of each other, which may therefore be estimated
separately.

The oscillations of the first kind which are very small, are independent
of the rotation of the earth; and as they depend on the motion of the
disturbing body in its orbit, they are of long periods. The second kind
of oscillations depends on the rotation of the earth, therefore their
period is nearly a day: and the oscillations of the third kind depend on
an angle equal to twice the angular rotation of the earth; and
consequently happen twice in twenty-four hours. The first afford no
particular interest, and are extremely small; but the difference of two
consecutive tides depends on the second. At the time of the solstices,
this difference which, according to Newton's theory, ought to be very
great, is hardly sensible on our shores. La Place has shown that this
discrepancy arises from the depth of the sea, and that if the depth were
uniform, there would be no difference in the consecutive tides, were it
not for local circumstances: it follows therefore, that as this
difference is extremely small, the sea, considered in a large extent,
must be nearly of uniform depth, that is to say, there is a certain mean
depth from which the deviation is not great. The mean depth of the
Pacific Ocean is supposed to be about four miles, that of the Atlantic
only three. From the formulæ which determine the difference of the
consecutive tides it is also proved that the precession of the
equinoxes, and the nutation in the earth's axis, are the same as if the
sea formed one solid mass with the earth.

The third kind of oscillations are the semidiurnal tides, so remarkable
on our coasts; they are occasioned by the combined action of the sun and
moon, but as the effect of each is independent of the other, they may be
considered separately.

The particles of water under the moon are more attracted than the centre
of gravity of the earth, in the inverse ratio of the square of the
distances; hence they have a tendency to leave the earth, but are
retained by their gravitation, which this tendency diminishes. On the
contrary, the moon attracts the centre of the earth more powerfully than
she attracts the particles of water in the hemisphere opposite to her;
so that the earth has a tendency to leave the waters but is retained by
gravitation, which this tendency again diminishes. Thus the waters
immediately under the moon are drawn from the earth at the same time
that the earth is drawn from those which are diametrically opposite to
her; in both instances producing an elevation of the ocean above the
surface of equilibrium of nearly the same height; for the diminution of
the gravitation of the particles in each position is almost the same, on
account of the distance of the moon being great in comparison of the
radius of the earth. Were the earth entirely covered by the sea, the
water thus attracted by the moon would assume the form of an oblong
spheroid, whose greater axis would point towards the moon, since the
columns of water under the moon and in the direction diametrically
opposite to her are rendered lighter, in consequence of the diminution
of their gravitation in order to preserve the equilibrium, the axes 90°
distant would be shortened. The elevation, on account of the smaller
space to which it is confined, is twice as great as the depression,
because the contents of the spheroid always remain the same. The effects
of the sun's attraction are in all respects similar to those of the
moon's, though really less in degree, on account of his distance; he
therefore only modifies the form of this spheroid a little. If the
waters were capable of instantly assuming the form of equilibrium, that
is, the form of the spheroid, its summit would always point to the moon,
notwithstanding the earth's rotation; but on account of their
resistance, the rapid motion produced in them by rotation prevents them
from assuming at every instant the form which the equilibrium of the
forces acting on them requires. Hence, on account of the inertia of the
waters, if the tides be considered relatively to the whole earth and
open sea, there is a meridian about 30° eastward of the moon, where it
is always high water both in the hemisphere where the moon is, and in
that which is opposite. On the west side of this circle the tide is
flowing, on the east it is ebbing, and on the meridian at 90° distant,
it is everywhere low water. It is evident that these tides must happen
twice in a day, since in that time the rotation of the earth brings the
same point twice under the meridian of the moon, once under the superior
and once under the inferior meridian.

In the semidiurnal tides there are two phenomena particularly to be
distinguished, one that happens twice in a month, and the other twice in
a year.

The first phenomenon is, that the tides are much increased in the
syzigies, or at the time of new and full moon. In both cases the sun and
moon are in the same meridian, for when the moon is new they are in
conjunction, and when she is full they are in opposition. In each of
these positions their action is combined to produce the highest or
spring tides under that meridian, and the lowest in those points that
are 90° distant. It is observed that the higher the sea rises in the
full tide, the lower it is in the ebb. The neap tides lake place when
the moon is in quadrature, they neither rise so high nor sink so low as
the spring tides. The spring tides are much increased when the moon is
in perigee. It is evident that the spring tides must happen twice a
month, since in that time the moon is once new and once full.

The second phenomenon in the tides is the augmentation which occurs at
the time of the equinoxes when the sun's declination is zero, which
happens twice every year. The greatest tides take place when a new or
full moon happens, near the equinoxes while the moon is in perigee. The
inclination of the moon's orbit on the ecliptic is 5° 9'; hence in
the equinoxes the action of the moon would be increased if her node were
to coincide with her perigee. The equinoctial gales often raise these
tides to a great height. Beside these remarkable variations, there are
others arising from the declination of the moon, which has a great
influence on the ebb and flow of the waters.

Both the height and time of high water are thus perpetually changing;
therefore, in solving the problem, it is required to determine the
heights to which they rise, the times at which they happen, and the
daily variations.

The periodic motions of the waters of the ocean on the hypothesis of an
ellipsoid of revolution entirely covered by the sea, are very far from
according with observation; this arises from the very great
irregularities in the surface of the earth, which is but partially
covered by the sea, the variety in the depths of the ocean, the manner
in which it is spread out on the earth, the position and inclination of
the shores, the currents, the resistance the waters meet with, all of
them causes which it is impossible to estimate, but which modify the
oscillations of the great mass of the ocean. However, amidst all these
irregularities, the ebb and flow of the sea maintain a ratio to the
forces producing them sufficient to indicate their nature, and to verify
the law of the attraction of the sun and moon on the sea. La Place
observes, that the investigation of such relations between cause and
effect is no less useful in natural philosophy than the direct solution
of problems, either to prove the existence of the causes, or trace the
laws of their effects. Like the theory of probabilities, it is a happy
supplement to the ignorance and weakness of the human mind. Thus the
problem of the tides does not admit of a general solution; it is
certainly necessary to analyse the funeral phenomena which ought to
result from the attraction of the sun and moon, but these must be
corrected in each particular case by those local observations which are
modified by the extent and depth of the sea, and the peculiar
circumstances of the port.

Since the disturbing action of the sun and moon can only become sensible
in a very great extent of water, it is evident that the Pacific ocean is
one of the principal sources of our tides; but in consequence of the
rotation of the earth, and the inertia of the ocean, high water does not
happen till some time after the moon's southing. The tide raised in that
world of waters is transmitted to the Atlantic, and from that sea it
moves in a northerly direction along the coasts of Africa and Europe,
arriving later and later at each place. This great wave however is
modified by the tide raised in the Atlantic, which sometimes combines
with that from the Pacific in raising the sea, and sometimes is in
opposition to it, so that the tides only rise in proportion to their
difference. This great combined wave, reflected by the shores of the
Atlantic, extending nearly from pole to pole, still coming northward,
occurs through the Irish and British channels into the North sea, so
that the tides in our ports are modified by those of another hemisphere.
Thus the theory of the tides in each port, both as to their height and
the times at which they take place, is really a matter of experiment,
and can only be perfectly determined by the mean of a very great number
of observations including several revolutions of the moon's nodes.

The height to which the tides rise is much greater in narrow channels
than in the open sea, on account of the obstructions they meet with. In
high latitudes where the ocean is less directly under the influence of
the luminaries, the rise and fall of the sea is inconsiderable, so that,
in all probability, there is no tide at the poles, or only a small
annual and monthly one. The ebb and flow of the sea are perceptible in
rivers to a very great distance from their estuaries. In the straits of
Pauxis, in the river of the Amazons, more than five hundred miles from
the sea, the tides are evident. It requires so many days for the tide to
ascend this mighty stream, that the returning tides meet a succession of
those which are coming up; so that every possible variety occurs in some
part or other of its shores, both as to magnitude and time. It requires
a very wide expanse of water to accumulate the impulse of the sun and
moon, so as to render their influence sensible; on that account the
tides in the Mediterranean and Black Sea are scarcely perceptible.

These perpetual commotions in the waters of the ocean are occasioned by
forces that bear a very small proportion to terrestrial gravitation: the
sun's action in raising the ocean is only the 1/38448000 of gravitation
at the earth's surface, and the action of the moon is little more than
twice as much these forces being in the ratio of 1 to 2.35333. From this
ratio the mass of the moon is found to be only 1/15 part of that of the
earth. The initial state of the ocean has no influence on the tides;
for whatever its primitive conditions may have been, they must soon have
vanished by the friction and mobility of the fluid. One of the most
remarkable circumstances in the theory of the tides is the assurance
that in consequence of the density of the sea being only one-fifth of
the mean density of the earth, the stability of the equilibrium of the
ocean never can be subverted by any physical cause whatever. A general
inundation arising from the mere instability of the ocean is therefore
impossible.

The atmosphere when in equilibrio is an ellipsoid flattened at the poles
from its rotation with the earth: in that state its strata are of
uniform density at equal heights above the level of the sea, and it is
sensibly of finite extent, whether it consists of particles infinitely
divisible or not. On the latter hypothesis it must really be finite; and
even if the particles of matter be infinitely divisible, it is known by
experience to be of extreme tenuity at very small heights. The barometer
rises in proportion to the superincumbent pressure. Now at the
temperature of melting ice, the density of mercury is to that of air as
10320 to 1; and as the mean height of the barometer is 29.528 inches,
the height of the atmosphere by simple proportion is 30407 feet, at the
mean temperature of 62°, or 34153 feet, which is extremely small, when
compared with the radius of the earth. The action of the sun and moon
disturbs the equilibrium of the atmosphere, producing oscillations
similar to those in the ocean, which occasion periodic variations in the
heights of the barometer. These, however, are so extremely small, that
their existence in latitudes so far removed from the equator is
doubtful; a series of observations within the tropics can alone decide
this delicate point. La Place seems to think that the flux and reflux
distinguishable at Paris may be occasioned by the rise and fall of the
ocean, which forms a variable base to so great a portion of the
atmosphere.

The attraction of the sun and moon has no sensible effect on the trade
winds; the heat of the sun occasions these aerial currents, by rarefying
the air at the equator, which causes the cooler and more dense part of
the atmosphere to rush along the surface of the earth to the equator,
while that which is heated is carried along the higher strata to the
poles, forming two currents in the direction of the meridian. But the
rotatory velocity of the air corresponding to its geographical situation
decreases towards the poles; in approaching the equator it must
therefore revolve more slowly than the corresponding parts of the earth,
and the bodies on the surface of the earth must strike against it with
the excess of their velocity, and by its reaction they will meet with a
resistance contrary to their motion of rotation; so that the wind will
appear, to a person supposing himself to be at rest, to blow in a
contrary direction to the earth's rotation, or from east to west, which
is the direction of the trade winds. The atmosphere scatters the sun's
rays, and gives all the beautiful tints and cheerfulness of day. It
transmits the blue light in greatest abundance; the higher we ascend,
the sky assumes a deeper hue, but in the expanse of space the sun and
stars must appear like brilliant specks in profound blackness.

The sun and most of the planets appear to be surrounded with atmospheres
of considerable density. The attraction of the earth has probably
deprived the moon of hers, for the refraction of the air at the surface
of the earth is at least a thousand times as great as at the moon. The
lunar atmosphere, therefore, must be of a greater degree of rarity than
can be produced by our best air-pumps; consequently no terrestrial
animal could exist in it.

Many philosophers of the highest authority concur in the belief that
light consists in the undulations of a highly elastic ethereal medium
pervading space, which, communicated to the optic nerves produce the
phenomena of vision. The experiments of our illustrious countryman, Dr.
Thomas Young, and those of the celebrated Fresnel, show that this theory
accords better with all the observed phenomena than that of the emission
of particles from the luminous body. As sound is propagated by the
undulations of the air, its theory is in a great many respects similar
to that of light. The grave or low tones are produced by very slow
vibrations, which increase in frequency progressively as the note
becomes more acute. When the vibrations of a musical chord, for example,
are less than sixteen in a second, it will not communicate a continued
sound to the ear; the vibrations or pulses increase in number with the
acuteness of the note, till at last all sense of pitch is lost. The
whole extent of human hearing, from the lowest notes of the organ to the
highest known cry of insects, as of the cricket, includes about nine
octaves.

The undulations of light are much more rapid than those of sound, but
they are analogous in this respect, that as the frequency of the
pulsations in sound increases from the low tones to the higher, so those
of light augment in frequency, from the red rays of the solar spectrum
to the extreme violet. By the experiments of Sir William Herschel, it
appears that the heat communicated by the spectrum increases from the
violet to the red rays; but that the maximum of the hot invisible rays
is beyond the extreme red. Heat in all probability consists, like light
and sound, in the undulations of an elastic medium. All the principal
phenomena of heat may actually be illustrated by a comparison with those
of sound. The excitation of heat and sound are not only similar, but
often identical, as in friction and percussion; they are both
communicated by contact and by radiation; and Dr. Young observes, that
the effect of radiant heat in raising the temperature of a body upon
which it falls, resembles the sympathetic agitation of a string, when
the sound of another string, which is in unison with it, is transmitted
to it through the air. Light, heat, sound, and the waves of fluids are
all subject to the same laws of reflection, and, indeed, their
undulating theories are perfectly similar. If, therefore, we may judge
from analogy, the undulations of the heat producing rays must be less
frequent than those of the extreme red of the solar spectrum; but if the
analogy were perfect, the interference of two hot rays ought to produce
cold, since darkness results from the interference of two undulations of
light, silence ensues from the interference of two undulations of sound;
and still water, or no tide, is the consequence of the interference of
two tides.

The propagation of sound requires a much denser medium than that of
either light or heat; its intensity diminishes as the rarity of the air
increases; so that, at a very small height above the surface of the
earth, the noise of the tempest ceases, and the thunder is heard no more
in those boundless regions where the heavenly bodies accomplish their
periods in eternal and sublime silence.

What the body of the sun may be, it is impossible to conjecture; but he
seems to be surrounded by an ocean of flame through which his dark
nucleus appears like black spots, often of enormous size. The solar
rays, which probably arise from the chemical processes that continually
take place at his surface, are transmitted through space in all
directions; but, notwithstanding the sun's magnitude, and the
inconceivable heat that must exist where such combustion is going on, as
the intensity both of his light and heat diminishes with the square of
the distance, his kindly influence can hardly be felt at the boundaries
of our system. Much depends on the manner in which the rays fall, as we
readily perceive from the different climates on our globe. In winter the
earth is nearer the sun by 1/30th than in summer, but the rays strike
the northern hemisphere more obliquely in winter than in the other half
of the year. In Uranus the sun must be seen like a small but brilliant
star, not above the hundred and fiftieth part so bright as he appears
to us; that is however 2000 times brighter than our moon to us, so
that he really is a sun to Uranus, and probably imparts some degree
of warmth. But if we consider that water would not remain fluid in any
part of Mars, even at his equator, and that in the temperate zones of
the same planet even alcohol and quicksilver would freeze, we may form
some idea of the cold that must reign in Uranus, unless indeed the
ether has a temperature. The climate of Venus more nearly resembles
that of the earth, though, excepting perhaps at her poles, much too
hot for animal and vegetable life as they exist here; but in Mercury
the mean heat, arising only from the intensity of the sun's rays,
must be above that of boiling quick-silver, and water would boil even
at his poles. Thus the planets, though kindred with the earth in
motion and structure, are totally unfit for the habitation of such
a being as man.

The direct light of the sun has been estimated to be equal to that of
5563 wax candles of a moderate size, supposed to be placed at the
distance of one foot from the object: that of the moon is probably only
equal to the light of one candle at the distance of twelve feet;
consequently the light of the sun is more than three hundred thousand
times greater than that of the moon; for which reason the light of the
moon imparts no heat, even when brought to a focus by a mirror.

In adverting to the peculiarities in the form and nature of the earth
and planets, it is impossible to pass in silence the magnetism of the
earth, the director of the mariner's compass, and his guide through the
ocean. This property probably arises from metallic iron in the interior
of the earth, or from the circulation of currents of electricity round
it: its influence extends over every part of its surface, but its
accumulation and deficiency determine the two poles of this great
magnet, which are by no means the same as the poles of the earth's
rotation. In consequence of their attraction and repulsion, a needle
freely suspended, whether it be magnetic or not, only remains in
equilibrio when in the magnetic meridian, that is, in the plane which
passes through the north and south magnetic poles. There are places
where the magnetic meridian coincides with the terrestrial meridian; in
these a magnetic needle freely suspended, points to the true north, but
if it be carried successively to different places on the earth's
surface, its direction will deviate sometimes to the east and sometimes
to the west of north. Lines drawn on the globe through all the places
where the needle points due north and south, are called lines of no
variation, and are extremely complicated. The direction of the needle is
not even constant in the same place, but changes in a few years,
according to a law not yet determined. In 1657, the line of no variation
passed through London. In the year 1819, Captain Parry, in his voyage to
discover the north-west passage round America, sailed directly over the
magnetic pole; and in 1824, Captain Lyon, when on en expedition for the
same purpose, found that the variation of the compass was 37° 30'
west, and that the magnetic pole was then situate in 63° 26' 51"
north latitude, and in 80° 51' 25" west longitude. It appears
however from later researches that the law of terrestrial magnetism is
of considerable complication, and the existence of more than one
magnetic pole in either hemisphere has been rendered highly probable.
The needle is also subject to diurnal variations; in our latitudes it
moves slowly westward from about three in the morning till two, and
returns to its former position in the evening.

A needle suspended so as only to be moveable in the vertical plane, dips
or become more and more inclined to the horizon the nearer it is brought
to the magnetic pole. Captain Lyon found that the dip in the latitude
and longitude mentioned was 86° 32'. What properties the planets may
have in this respect, it is impossible to know, but it is probable that
the moon has become highly magnetic, in consequence of her proximity to
the earth, and because her greatest diameter always points towards it.

The passage of comets has never sensibly disturbed the stability of the
solar system; their nucleus is rare, and their transit so rapid, that
the time has not been long enough to admit of a sufficient accumulation
of impetus to produce a perceptible effect. The comet of 1770 passed
within 80000 miles of the earth without even affecting our tides, and
swept through the midst of Jupiter's satellites without deranging the
motions of those little moons. Had the mass of that comet been equal to
the mass of the earth, its disturbing action would have shortened the
year by the ninth of a day; but, as Delambre's computations from the
Greenwich observations of the sun, show that the length of the year has
not been sensibly affected by the approach of the comet. La Place proved
that its mass could not be so much as the 5000th part of that of the
earth. The paths of comets have every possible inclination to the plane
of the ecliptic, and unlike the planets, their motion is frequently
retrograde. Comets are only visible when near their perihelia. Then
their velocity is such that its square is twice as great as that of a
body moving in a circle at the same distance; they consequently remain a
very short time within the planetary orbits; and as all the conic
sections of the same focal distance sensibly coincide through a small
arc on each side of the extremity of their axis, it is difficult to
ascertain in which of these curves the comets move, from observations
made, as they necessarily must be, at their perihelia: but probably they
all move in extremely eccentric ellipses, although, in most cases, the
parabolic curve coincides most nearly with their observed motions. Even
if the orbit be determined with all the accuracy that the case admits
of, it may be difficult, or even impossible, to recognise a comet on its
return, because its orbit would be very much changed if it passed near
any of the large planets of this or of any other system, in consequence
of their disturbing energy, which would be very great on bodies of so
rare a nature. Halley and Clairaut predicted that, in consequence of the
attraction of Jupiter and Saturn, the return of the comet of 1759 would
be retarded 618 days, which was verified by the event as nearly as could
be expected.

The nebulous appearance of comets is perhaps occasioned by the vapours
which the solar heat raises at their surfaces in their passage at the
perihelia, and which are again condensed as they recede from the sun.
The comet of 1680 when in its perihelion was only at the distance of
one-sixth of the sun's diameter, or about 148000 miles from its surface;
it consequently would be exposed to a heat 27500 times greater than that
received by the earth. As the sun's heat is supposed to be in proportion
to the intensity of his height, it is probable that a degree of heat so
very intense would be sufficient to convert into vapour every
terrestrial substance with which we are acquainted.

In those positions of comets where only half of their enlightened
hemisphere ought to be seen, they exhibit no phases even when viewed
with high magnifying powers. Some slight indications however were once
observed by Hevelius and La Hire in 1682; and in 1811 Sir William
Herschel discovered a small luminous point, which he concluded to be the
disc of the comet. In general their masses are so minute, that they have
no sensible diameters, the nucleus being principally formed of denser
strata of the nebulous matter, but so rare that stars have been seen
through them. The transit of a comet over the sun's disc would afford
the best information on this point. It was computed that such an event
was to take place in the year 1627; unfortunately the sun was hid by
clouds in this country, but it was observed at Viviers and at Marseilles
at the time the comet must have been on it, but no spot was seen. The
tails are often of very great length, and are generally situate in the
planes of their orbits; they follow them in their descent towards the
sun, but precede them in their return, with a small degree of curvature;
but their extent and form must vary in appearance, according to the
position of their orbits with regard to the ecliptic. The tail of the
comet of 1680 appeared, at Paris, to extend over sixty-two degrees. The
matter of which the tail is composed must be extremely buoyant to
precede a body moving with such velocity; indeed the rapidity of its
ascent cannot be accounted for. The nebulous part of comets diminishes
every time they return to their perihelia; after frequent returns they
ought to lose it altogether, and present the appearance of a fixed
nucleus; this ought to happen sooner in comets of short periods. La
Place supposes that the comet of 1682 must be approaching rapidly to
that state. Should the substances be altogether or even to a great
degree evaporated, the comet wilt disappear for ever. Possibly comets
may have vanished from our view sooner than they otherwise would have
done from this cause. Of about six hundred comets that have been seen at
different times, three are now perfectly ascertained to form part of our
system; that is to say, they return to the sun at intervals of 76, 6 1/3,
and 3 1/4 years nearly.

A hundred and forty comets have appeared within the earth's orbit during
the last century that have not again been seen; if a thousand years be
allowed as the average period of each, it may be computed by the theory
of probabilities, that the whole number that range within the earth's
orbit must be 1400; but Uranus being twenty times more distant, there
may be no less than 11,200,000 comets that come within the known extent
of our system. In such a multitude of wandering bodies it is just
possible that one of them may come in collision with the earth; but even
if it should, the mischief would be local, and the equilibrium soon
restored. It is however more probable that the earth would only be
deflected a little from its course by the near approach of the comet,
without being touched. Great as the number of comets appears to be, it
is absolutely nothing when compared to the number of the fixed stars.
About two thousand only are visible to the naked eye, but when we view
the heavens with a telescope, their number seems to be limited only by
the imperfection of the instrument. In one quarter of an hour Sir
William Herschel estimated that 116000 stars passed through the field of
his telescope, which subtended an angle of 15'. This however was
stated as a specimen of extraordinary crowding; but at an average the
whole expanse of the heavens must exhibit about a hundred millions of
fixed stars that come within the reach of telescopic vision.

Many of the stars have a very small progressive motion, especially _μ_
Cassiopeia and 61 Cygni, both small stars; and, as the sun is decidedly
a star, it is an additional reason for supposing the solar system to be
in motion. The distance of the fixed stars is too great to admit of
their exhibiting a sensible disc; but in all probability they are
spherical, and must certainly be so, if gravitation pervades all space.
With a fine telescope they appear like a point of light; their twinkling
arises from sudden changes in the refractive power of the air, which
would not be sensible if they had discs like the planets. Thus we can
learn nothing of the relative distances of the stars from us and from
one another, by their apparent diameters; but their annual parallax
being insensible, shows that we must be one hundred millions of millions
of miles from the nearest; many of them however must be vastly more
remote, for of two stars that appear close together, one may be far
beyond the other in the depth of space. The light of Sirius, according
to the observations of Mr. Herschel, is 324 times greater than that of a
star of the sixth magnitude; if we suppose the two to be really of the
same size, their distances from us must be in the ratio of 57.3 to 1,
because light diminishes as the square of the distance of the luminous
body increases.

Of the absolute magnitude of the stars, nothing is known, only that many
of them must be much larger than the sun, from the quantity of light
emitted by them. Dr. Wollaston determined the approximate ratio that the
light of a wax candle bears to that of the sun, moon, and stars, by
comparing their respective images reflected from small glass globes
filled, with mercury, whence a comparison was established between the
quantities of light emitted by the celestial bodies themselves. By this
method he found that the light of the sun is about twenty millions of
millions of times greater than that of Sirius, the brightest, and
supposed to be the nearest of the fixed stars. If Sirius had a parallax
of half a second, its distance from the earth would be 525481 times the
distance of the sun from the earth; and therefore Sirius, placed where
the sun is, would appear to us to be 3.7 times as large as the sun, and
would give 13.8 times more light; but many of the fixed stars must be
immensely greater than Sirius. Sometimes stars have all at once
appeared, shone with a brilliant light, and then vanished. In 1572 a
star was discovered in Cassiopeia, which rapidly increased in brightness
till it even surpassed that of Jupiter; it then gradually diminished in
splendour, and after exhibiting all the variety of tints that indicates
the changes of combustion, vanished sixteen months after its discovery,
without altering its position. It is impossible to imagine any thing
more tremendous than a conflagration that could be visible at such a
distance. Some stars are periodic, possibly from the intervention of
opaque bodies revolving about them, or from extensive spots on their
surfaces. Many thousands of stars that seem to be only brilliant points,
when carefully examined are found to be in reality systems of two or
more suns revolving about a common centre. These double and multiple
stars are extremely remote, requiring the most powerful telescopes to
show them separately.

The first catalogue of double stars in which their places and relative
positions are determined, was accomplished by the talents and industry
of Sir William Herschel, to whom astronomy is indebted for so many
brilliant discoveries, and with whom originated the idea of their
combination in binary and multiple systems, an idea which his own
observations had completely established, but which has since received
additional confirmation from those of his son and Sir James South, the
former of whom, as well as Professor Struve of Dorpat, have added many
thousands to their numbers. The motions of revolution round a common
centre of many have been clearly established, and their periods
determined with considerable accuracy. Some have already since their
first discovery accomplished nearly a whole revolution, and one, if the
latest observations can be depended on, is actually considerably
advanced in its second period. These interesting systems thus present a
species of sidereal chronometer, by which the chronology of the heavens
will be marked out to future ages by epochs of their own, liable to no
fluctuations from planetary disturbances such as obtain in our system.

Possibly among the multitudes of small stars, whether double or
insulated, some may be found near enough to exhibit distinct parallactic
motions, or perhaps something approaching to planetary motion, which may
prove that solar attraction is not confined to our system, or may lead
to the discovery of the proper motion of the sun. The double stars are
of various hues, but most frequently exhibit the contrasted colours. The
large star is generally yellow, orange, or red; and the small star blue,
purple, or green. Sometimes a white star is combined with a blue or
purple, and more rarely a red and white are united. In many cases, these
appearances are due to the influences of contrast on our judgment of
colours. For example, in observing a double star where the large one is
of a full ruby red, or almost blood colour, and the small one a fine
green, the latter lost its colour when the former was hid by the cross
wires of the telescope. But there are a vast number of instances where
the colours are too strongly marked to be merely imaginary. Mr. Herschel
observes in one of his papers in the _Philosophical Transactions_, as a
very remarkable fact, that although red single stars are common enough,
no example of an insulated blue, green, or purple one has as yet been
produced.

In some parts of the heavens, the stars are so near together as to form
clusters, which to the unassisted eye appear like thin white clouds;
such is the milky way, which has its brightness from the diffused light
of myriads of stars. Many of these clouds, however, are never resolved
into separate stars, even by the highest magnifying powers. This
nebulous matter exists in vast abundance in space. No fewer than 2500
nebulæ were observed by Sir William Herschel, whose places have been
computed from his observations, reduced to a common epoch, and arranged
into a catalogue in order of right ascension by his sister Miss Caroline
Herschel, a lady so justly celebrated for astronomical knowledge and
discovery. The nature and use of this matter scattered over the heavens
in such a variety of forms is involved in the greatest obscurity. That
it is a self-luminous, phosphorescent material substance, in a highly
dilated or gaseous state, but gradually subsiding by the mutual
gravitation of its particles into stars and sidereal systems, is the
hypothesis which seems to be most generally received; but the only way
that any real knowledge on this mysterious subject can be obtained, is
by the determination of the form, place, and present state of each
individual nebula, and a comparison of these with future observations
will show generations to come the changes that may now be going on in
these rudiments of future systems. With this view, Mr. Herschel is now
engaged in the difficult and laborious investigation, which is
understood to be nearly approaching its completion, and the results of
which we may therefore hope ere long to see made public. The most
conspicuous of these appearances are found in Orion, and in the girdle
of Andromeda. It is probable that light must be millions of years
travelling to the earth from some of the nebulæ.

So numerous are the objects which meet our view in the heavens, that we
cannot imagine a part of space where some light would not strike the
eye: but as the fixed stars would not be visible at such distances, if
they did not shine by their own light, it is reasonable to infer that
they are suns; and if so, they are in all probability attended by
systems of opaque bodies, revolving about them as the planets do about
ours. But although there be no proof that planets not seen by us revolve
about these remote suns, certain it is, that there are many invisible
bodies wandering in space, which, occasionally coming within the sphere
of the earth's attraction, are ignited by the velocity with which they
pass through the atmosphere, and are precipitated with great violence on
the earth. The obliquity of the descent of meteorites, the peculiar
matter of which they are composed, and the explosion with which their
fall is invariably accompanied, show that they are foreign to our
planet. Luminous spots altogether independent of the phases have
occasionally appeared on the dark part of the moon, which have been
ascribed to the light arising from the eruption of volcanoes; whence it
has been supposed that meteorites have been projected from the moon by
the impetus of volcanic eruption; it has even been computed, that if a
stone were projected from the moon in a vertical line, and with an
initial velocity of 10992 feet in a second, which is more than four
times the velocity of a ball when first discharged from a cannon,
instead of falling back to the moon by the attraction of gravity, it
would come within the sphere of the earth's attraction, and revolve
about it like a satellite. These bodies, impelled either by the
direction of the primitive impulse, or by the disturbing action of the
sun, might ultimately penetrate the earth's atmosphere, and arrive at
its surface. But from whatever source meteoric stones may come, it seems
highly probable, that they have a common origin, from the uniformity, we
may almost say identity, of their chemical composition.

The known quantity of matter bears a very small proportion to the
immensity of space. Large as the bodies are, the distances that separate
them are immeasurably greater; but as design is manifest in every part
of creation, it is probable that if the various systems in the universe
had been nearer to one another, their mutual disturbances would have
been inconsistent with the harmony and stability of the whole. It is
clear that space is not pervaded by atmospheric air, since its
resistance would long ere this have destroyed the velocity of the
planets; neither can we affirm it to be void, when it is traversed in
all directions by light, heat, gravitation, and possibly by influences
of which we can form no idea; but whether it be replete with an ethereal
medium, time alone will show.

Though totally ignorant of the laws which obtain in the more distant
regions of creation, we are assured, that one alone regulates the
motions of our own system; and as general laws form the ultimate object
of philosophical research, we cannot conclude these remarks without
considering the nature of that extraordinary power, whose effects we
have been endeavouring to trace through some of their mazes. It was at
one time imagined, that the acceleration in the moon's mean motion was
occasioned by the successive transmission of the gravitating force; but
it has been proved, that, in order to produce this effect, its velocity
must be about fifty millions of times greater than that of light, which
flies at the rate of 200000 miles in a second; its action even at the
distance of the sun may therefore be regarded as instantaneous; yet so
remote are the nearest of the fixed stars, that it may be doubted
whether the sun has any sensible influence on them.

The analytical expression for the gravitating force is a straight line;
the curves in which the celestial bodies move by the force of
gravitation are only lines of the second order; the attraction of
spheroids according to any other law would be much more complicated; and
as it is easy to prove that matter might have been moved according to an
infinite variety of laws, it may be concluded, that gravitation must
have been selected by Divine wisdom out of an infinity of other laws,
its being the most simple, and that which gives the greatest stability
to the celestial motions.

It is a singular result of the simplicity of the laws of nature, which
admit only of the observation and comparison of ratios, that the
gravitation and theory of the motions of the celestial bodies are
independent of their absolute magnitudes and distances; consequently if
all the bodies in the solar system, their mutual distances, and their
velocities, were to diminish proportionally, they would describe curves
in all respect similar to those in which they now move; and the system
might be successively reduced to the smallest sensible dimensions, and
still exhibit the same appearances. Experience shows that a very
different law of attraction prevails when the particles of matter are
placed within inappreciable distances from each other, as in chemical
and capillary attractions, and the attraction of cohesion; whether it be
a modification of gravity, or that some new and unknown power comes into
action, does not appear; but as a change in the law of the force takes
place at one end of the scale, it is possible that gravitation may not
remain the same at the immense distance of the fixed stars. Perhaps the
day may come when even gravitation, no longer regarded as an ultimate
principle, may be resolved into a yet more general cause, embracing
every law that regulates the material world.

The action of the gravitating force is not impeded by the intervention
even of the densest substances. If the attraction of the sun for the
centre of the earthy and for the hemisphere diametrically opposite to
him, was diminished by a difficulty in penetrating the interposed
matter, the tides would be more obviously affected. Its attraction is
the same also, whatever the substances of the celestial bodies may be,
for if the action of the sun on the earth differed by a millionth part
from his action on the moon, the difference would occasion a variation
in the sun's parallax amounting to several seconds, which is proved to
be impossible by the agreement of theory with observation. Thus all
matter is pervious to gravitation, and is equally attracted by it.

As far as human knowledge goes, the intensity of gravitation, has never
varied within the limits of the solar system; nor does even analogy lead
us to expect that it should; on the contrary, there is every reason to
be assured, that the great laws of the universe are immutable like their
Author. Not only the sun and planets, but the minutest particles in all
the varieties of their attractions and repulsions, nay even the
imponderable matter of the electric, galvanic, and magnetic fluids are
obedient to permanent laws, though we may not be able in every case to
resolve their phenomena into general principles. Nor can we suppose the
structure of the globe alone to be exempt from the universal fiat,
though ages may pass before the changes it has undergone, or that are
now in progress, can be referred to existing causes with the same
certainty with which the motions of the planets and all their secular
variations are referable to the law of gravitation. The traces of
extreme antiquity perpetually occurring to the geologist, give that
information as to the origin of things which we in vain look for in the
other parts of the universe. They date the beginning of time; since
there is every reason to believe, that the formation of the earth was
contemporaneous with that of the rest of the planets; but they show that
creation is the work of Him with whom 'a thousand years are as one day,
and one day as a thousand years.'



*** END OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON THE MECHANISMS OF THE HEAVENS ***


    

Updated editions will replace the previous one—the old editions will
be renamed.

Creating the works from print editions not protected by U.S. copyright
law means that no one owns a United States copyright in these works,
so the Foundation (and you!) can copy and distribute it in the United
States without permission and without paying copyright
royalties. Special rules, set forth in the General Terms of Use part
of this license, apply to copying and distributing Project
Gutenberg™ electronic works to protect the PROJECT GUTENBERG™
concept and trademark. Project Gutenberg is a registered trademark,
and may not be used if you charge for an eBook, except by following
the terms of the trademark license, including paying royalties for use
of the Project Gutenberg trademark. If you do not charge anything for
copies of this eBook, complying with the trademark license is very
easy. You may use this eBook for nearly any purpose such as creation
of derivative works, reports, performances and research. Project
Gutenberg eBooks may be modified and printed and given away—you may
do practically ANYTHING in the United States with eBooks not protected
by U.S. copyright law. Redistribution is subject to the trademark
license, especially commercial redistribution.


START: FULL LICENSE

THE FULL PROJECT GUTENBERG LICENSE

PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK

To protect the Project Gutenberg™ mission of promoting the free
distribution of electronic works, by using or distributing this work
(or any other work associated in any way with the phrase “Project
Gutenberg”), you agree to comply with all the terms of the Full
Project Gutenberg™ License available with this file or online at
www.gutenberg.org/license.

Section 1. General Terms of Use and Redistributing Project Gutenberg™
electronic works

1.A. By reading or using any part of this Project Gutenberg™
electronic work, you indicate that you have read, understand, agree to
and accept all the terms of this license and intellectual property
(trademark/copyright) agreement. If you do not agree to abide by all
the terms of this agreement, you must cease using and return or
destroy all copies of Project Gutenberg™ electronic works in your
possession. If you paid a fee for obtaining a copy of or access to a
Project Gutenberg™ electronic work and you do not agree to be bound
by the terms of this agreement, you may obtain a refund from the person
or entity to whom you paid the fee as set forth in paragraph 1.E.8.

1.B. “Project Gutenberg” is a registered trademark. It may only be
used on or associated in any way with an electronic work by people who
agree to be bound by the terms of this agreement. There are a few
things that you can do with most Project Gutenberg™ electronic works
even without complying with the full terms of this agreement. See
paragraph 1.C below. There are a lot of things you can do with Project
Gutenberg™ electronic works if you follow the terms of this
agreement and help preserve free future access to Project Gutenberg™
electronic works. See paragraph 1.E below.

1.C. The Project Gutenberg Literary Archive Foundation (“the
Foundation” or PGLAF), owns a compilation copyright in the collection
of Project Gutenberg™ electronic works. Nearly all the individual
works in the collection are in the public domain in the United
States. If an individual work is unprotected by copyright law in the
United States and you are located in the United States, we do not
claim a right to prevent you from copying, distributing, performing,
displaying or creating derivative works based on the work as long as
all references to Project Gutenberg are removed. Of course, we hope
that you will support the Project Gutenberg™ mission of promoting
free access to electronic works by freely sharing Project Gutenberg™
works in compliance with the terms of this agreement for keeping the
Project Gutenberg™ name associated with the work. You can easily
comply with the terms of this agreement by keeping this work in the
same format with its attached full Project Gutenberg™ License when
you share it without charge with others.

1.D. The copyright laws of the place where you are located also govern
what you can do with this work. Copyright laws in most countries are
in a constant state of change. If you are outside the United States,
check the laws of your country in addition to the terms of this
agreement before downloading, copying, displaying, performing,
distributing or creating derivative works based on this work or any
other Project Gutenberg™ work. The Foundation makes no
representations concerning the copyright status of any work in any
country other than the United States.

1.E. Unless you have removed all references to Project Gutenberg:

1.E.1. The following sentence, with active links to, or other
immediate access to, the full Project Gutenberg™ License must appear
prominently whenever any copy of a Project Gutenberg™ work (any work
on which the phrase “Project Gutenberg” appears, or with which the
phrase “Project Gutenberg” is associated) is accessed, displayed,
performed, viewed, copied or distributed:

    This eBook is for the use of anyone anywhere in the United States and most
    other parts of the world at no cost and with almost no restrictions
    whatsoever. You may copy it, give it away or re-use it under the terms
    of the Project Gutenberg License included with this eBook or online
    at www.gutenberg.org. If you
    are not located in the United States, you will have to check the laws
    of the country where you are located before using this eBook.
  
1.E.2. If an individual Project Gutenberg™ electronic work is
derived from texts not protected by U.S. copyright law (does not
contain a notice indicating that it is posted with permission of the
copyright holder), the work can be copied and distributed to anyone in
the United States without paying any fees or charges. If you are
redistributing or providing access to a work with the phrase “Project
Gutenberg” associated with or appearing on the work, you must comply
either with the requirements of paragraphs 1.E.1 through 1.E.7 or
obtain permission for the use of the work and the Project Gutenberg™
trademark as set forth in paragraphs 1.E.8 or 1.E.9.

1.E.3. If an individual Project Gutenberg™ electronic work is posted
with the permission of the copyright holder, your use and distribution
must comply with both paragraphs 1.E.1 through 1.E.7 and any
additional terms imposed by the copyright holder. Additional terms
will be linked to the Project Gutenberg™ License for all works
posted with the permission of the copyright holder found at the
beginning of this work.

1.E.4. Do not unlink or detach or remove the full Project Gutenberg™
License terms from this work, or any files containing a part of this
work or any other work associated with Project Gutenberg™.

1.E.5. Do not copy, display, perform, distribute or redistribute this
electronic work, or any part of this electronic work, without
prominently displaying the sentence set forth in paragraph 1.E.1 with
active links or immediate access to the full terms of the Project
Gutenberg™ License.

1.E.6. You may convert to and distribute this work in any binary,
compressed, marked up, nonproprietary or proprietary form, including
any word processing or hypertext form. However, if you provide access
to or distribute copies of a Project Gutenberg™ work in a format
other than “Plain Vanilla ASCII” or other format used in the official
version posted on the official Project Gutenberg™ website
(www.gutenberg.org), you must, at no additional cost, fee or expense
to the user, provide a copy, a means of exporting a copy, or a means
of obtaining a copy upon request, of the work in its original “Plain
Vanilla ASCII” or other form. Any alternate format must include the
full Project Gutenberg™ License as specified in paragraph 1.E.1.

1.E.7. Do not charge a fee for access to, viewing, displaying,
performing, copying or distributing any Project Gutenberg™ works
unless you comply with paragraph 1.E.8 or 1.E.9.

1.E.8. You may charge a reasonable fee for copies of or providing
access to or distributing Project Gutenberg™ electronic works
provided that:

    • You pay a royalty fee of 20% of the gross profits you derive from
        the use of Project Gutenberg™ works calculated using the method
        you already use to calculate your applicable taxes. The fee is owed
        to the owner of the Project Gutenberg™ trademark, but he has
        agreed to donate royalties under this paragraph to the Project
        Gutenberg Literary Archive Foundation. Royalty payments must be paid
        within 60 days following each date on which you prepare (or are
        legally required to prepare) your periodic tax returns. Royalty
        payments should be clearly marked as such and sent to the Project
        Gutenberg Literary Archive Foundation at the address specified in
        Section 4, “Information about donations to the Project Gutenberg
        Literary Archive Foundation.”
    
    • You provide a full refund of any money paid by a user who notifies
        you in writing (or by e-mail) within 30 days of receipt that s/he
        does not agree to the terms of the full Project Gutenberg™
        License. You must require such a user to return or destroy all
        copies of the works possessed in a physical medium and discontinue
        all use of and all access to other copies of Project Gutenberg™
        works.
    
    • You provide, in accordance with paragraph 1.F.3, a full refund of
        any money paid for a work or a replacement copy, if a defect in the
        electronic work is discovered and reported to you within 90 days of
        receipt of the work.
    
    • You comply with all other terms of this agreement for free
        distribution of Project Gutenberg™ works.
    

1.E.9. If you wish to charge a fee or distribute a Project
Gutenberg™ electronic work or group of works on different terms than
are set forth in this agreement, you must obtain permission in writing
from the Project Gutenberg Literary Archive Foundation, the manager of
the Project Gutenberg™ trademark. Contact the Foundation as set
forth in Section 3 below.

1.F.

1.F.1. Project Gutenberg volunteers and employees expend considerable
effort to identify, do copyright research on, transcribe and proofread
works not protected by U.S. copyright law in creating the Project
Gutenberg™ collection. Despite these efforts, Project Gutenberg™
electronic works, and the medium on which they may be stored, may
contain “Defects,” such as, but not limited to, incomplete, inaccurate
or corrupt data, transcription errors, a copyright or other
intellectual property infringement, a defective or damaged disk or
other medium, a computer virus, or computer codes that damage or
cannot be read by your equipment.

1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right
of Replacement or Refund” described in paragraph 1.F.3, the Project
Gutenberg Literary Archive Foundation, the owner of the Project
Gutenberg™ trademark, and any other party distributing a Project
Gutenberg™ electronic work under this agreement, disclaim all
liability to you for damages, costs and expenses, including legal
fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE
TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
DAMAGE.

1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
defect in this electronic work within 90 days of receiving it, you can
receive a refund of the money (if any) you paid for it by sending a
written explanation to the person you received the work from. If you
received the work on a physical medium, you must return the medium
with your written explanation. The person or entity that provided you
with the defective work may elect to provide a replacement copy in
lieu of a refund. If you received the work electronically, the person
or entity providing it to you may choose to give you a second
opportunity to receive the work electronically in lieu of a refund. If
the second copy is also defective, you may demand a refund in writing
without further opportunities to fix the problem.

1.F.4. Except for the limited right of replacement or refund set forth
in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO
OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.

1.F.5. Some states do not allow disclaimers of certain implied
warranties or the exclusion or limitation of certain types of
damages. If any disclaimer or limitation set forth in this agreement
violates the law of the state applicable to this agreement, the
agreement shall be interpreted to make the maximum disclaimer or
limitation permitted by the applicable state law. The invalidity or
unenforceability of any provision of this agreement shall not void the
remaining provisions.

1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
trademark owner, any agent or employee of the Foundation, anyone
providing copies of Project Gutenberg™ electronic works in
accordance with this agreement, and any volunteers associated with the
production, promotion and distribution of Project Gutenberg™
electronic works, harmless from all liability, costs and expenses,
including legal fees, that arise directly or indirectly from any of
the following which you do or cause to occur: (a) distribution of this
or any Project Gutenberg™ work, (b) alteration, modification, or
additions or deletions to any Project Gutenberg™ work, and (c) any
Defect you cause.

Section 2. Information about the Mission of Project Gutenberg™

Project Gutenberg™ is synonymous with the free distribution of
electronic works in formats readable by the widest variety of
computers including obsolete, old, middle-aged and new computers. It
exists because of the efforts of hundreds of volunteers and donations
from people in all walks of life.

Volunteers and financial support to provide volunteers with the
assistance they need are critical to reaching Project Gutenberg™’s
goals and ensuring that the Project Gutenberg™ collection will
remain freely available for generations to come. In 2001, the Project
Gutenberg Literary Archive Foundation was created to provide a secure
and permanent future for Project Gutenberg™ and future
generations. To learn more about the Project Gutenberg Literary
Archive Foundation and how your efforts and donations can help, see
Sections 3 and 4 and the Foundation information page at www.gutenberg.org.

Section 3. Information about the Project Gutenberg Literary Archive Foundation

The Project Gutenberg Literary Archive Foundation is a non-profit
501(c)(3) educational corporation organized under the laws of the
state of Mississippi and granted tax exempt status by the Internal
Revenue Service. The Foundation’s EIN or federal tax identification
number is 64-6221541. Contributions to the Project Gutenberg Literary
Archive Foundation are tax deductible to the full extent permitted by
U.S. federal laws and your state’s laws.

The Foundation’s business office is located at 809 North 1500 West,
Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up
to date contact information can be found at the Foundation’s website
and official page at www.gutenberg.org/contact

Section 4. Information about Donations to the Project Gutenberg
Literary Archive Foundation

Project Gutenberg™ depends upon and cannot survive without widespread
public support and donations to carry out its mission of
increasing the number of public domain and licensed works that can be
freely distributed in machine-readable form accessible by the widest
array of equipment including outdated equipment. Many small donations
($1 to $5,000) are particularly important to maintaining tax exempt
status with the IRS.

The Foundation is committed to complying with the laws regulating
charities and charitable donations in all 50 states of the United
States. Compliance requirements are not uniform and it takes a
considerable effort, much paperwork and many fees to meet and keep up
with these requirements. We do not solicit donations in locations
where we have not received written confirmation of compliance. To SEND
DONATIONS or determine the status of compliance for any particular state
visit www.gutenberg.org/donate.

While we cannot and do not solicit contributions from states where we
have not met the solicitation requirements, we know of no prohibition
against accepting unsolicited donations from donors in such states who
approach us with offers to donate.

International donations are gratefully accepted, but we cannot make
any statements concerning tax treatment of donations received from
outside the United States. U.S. laws alone swamp our small staff.

Please check the Project Gutenberg web pages for current donation
methods and addresses. Donations are accepted in a number of other
ways including checks, online payments and credit card donations. To
donate, please visit: www.gutenberg.org/donate.

Section 5. General Information About Project Gutenberg™ electronic works

Professor Michael S. Hart was the originator of the Project
Gutenberg™ concept of a library of electronic works that could be
freely shared with anyone. For forty years, he produced and
distributed Project Gutenberg™ eBooks with only a loose network of
volunteer support.

Project Gutenberg™ eBooks are often created from several printed
editions, all of which are confirmed as not protected by copyright in
the U.S. unless a copyright notice is included. Thus, we do not
necessarily keep eBooks in compliance with any particular paper
edition.

Most people start at our website which has the main PG search
facility: www.gutenberg.org.

This website includes information about Project Gutenberg™,
including how to make donations to the Project Gutenberg Literary
Archive Foundation, how to help produce our new eBooks, and how to
subscribe to our email newsletter to hear about new eBooks.