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Title: The Sewerage of Sea Coast Towns

Author: Henry Charles Adams

Release date: April 1, 2005 [eBook #7980]
                Most recently updated: December 31, 2020

Language: English

Credits: Produced by Tiffany Vergon, Ted Garvin, Charles Franks and the Online Distributed Proofreading Team


*** START OF THE PROJECT GUTENBERG EBOOK THE SEWERAGE OF SEA COAST TOWNS ***




Produced by Tiffany Vergon, Ted Garvin, Charles Franks
and the Online Distributed Proofreading Team.




THE SEWERAGE OF SEA COAST TOWNS

BY

HENRY C. ADAMS




CONTENTS

CHAPTER

I. THE FORMATION OF TIDES AND CURRENTS

II. OBSERVATIONS OF THE RISE AND FALL OF TIDES

III. CURRENT OBSERVATIONS

IV. SELECTION OF SITE FOR OUTFALL SEWER.

V. VOLUME OF SEWAGE

VI. GAUGING FLOW IN SEWERS

VII. RAINFALL

VIII. STORM WATER IN SEWERS

IX. WIND AND WINDMILLS

X. THE DESIGN OF SEA OUTFALLS

XI ACTION OF SEA WATER ON CEMENT

XII. DIVING

XIII. THE DISCHARGE OF SEA OUTFALL SEWERS

XIV. TRIGONOMETRICAL SURVEYING

XV. HYDROGRAPHICAL SURVEYING

PREFACE.

These notes are internal primarily for those engineers who,
having a general knowledge of sewerage, are called upon to
prepare a scheme for a sea coast town, or are desirous of being
able to meet such a call when made. Although many details of
the subject have been dealt with separately in other volumes,
the writer has a very vivid recollection of the difficulties he
experienced in collecting the knowledge he required when he was
first called on to prepare such a scheme, particularly with
regard to taking and recording current and tidal observations,
and it is in the hope that it might be helpful to others in a
similar difficulty to have all the information then obtained,
and that subsequently gained on other schemes, brought together
within a small compass that this book has written.

60, Queen Victoria St,
London, E.C.




CHAPTER I.

THE FORMATION OF TIDES AND CURRENTS.


It has often been stated that no two well-designed sewerage
schemes are alike, and although this truism is usually applied
to inland towns, it applies with far greater force to schemes
for coastal towns and towns situated on the banks of our large
rivers where the sewage is discharged into tidal waters. The
essence of good designing is that every detail shall be
carefully thought out with a view to meeting the special
conditions of the case to the best advantage, and at the least
possible expense, so that the maximum efficiency is combined
with the minimum cost. It will therefore be desirable to
consider the main conditions governing the design of schemes
for sea-coast towns before describing a few typical cases of
sea outfalls. Starting with the postulate that it is essential
for the sewage to be effectually and permanently disposed of
when it is discharged into tidal waters, we find that this
result is largely dependent on the nature of the currents,
which in their turn depend upon the rise and fall of the tide,
caused chiefly by the attraction of the moon, but also to a
less extent by the attraction of the sun. The subject of sewage
disposal in tidal waters, therefore, divides itself naturally
into two parts: first, the consideration of the tides and
currents; and, secondly, the design of the works.

The tidal attraction is primarily due to the natural effect of
gravity, whereby the attraction between two bodies is in direct
proportion to the product of their respective masses and in
inverse proportion to the square of their distance apart; but
as the tide-producing effect of the sun and moon is a
differential attraction, and not a direct one, their relative
effect is inversely as the cube of their distances. The mass of
the sun is about 324,000 times as great as that of the earth,
and it is about 93 millions of miles away, while the mass of
the moon is about 1-80th of that of the earth, but it averages
only 240,000 miles away, varying between 220,000 miles when it
is said to be in perigee, and 260,000 when in apogee. The
resultant effect of each of these bodies is a strong "pull" of
the earth towards them, that of the moon being in excess of
that of the sun as 1 is to 0.445, because, although its mass is
much less than that of the sun, it is considerably nearer to
the earth.

About one-third of the surface of the globe is occupied by
land, and the remaining two-thirds by water. The latter, being
a mobile substance, is affected by this pull, which results in
a banking up of the water in the form of the crest of a tidal
wave. It has been asserted in recent years that this tidal
action also takes place in a similar manner in the crust of the
earth, though in a lesser degree, resulting in a heaving up and
down amounting to one foot; but we are only concerned with the
action of the sea at present. Now, although this pull is felt
in all seas, it is only in the Southern Ocean that a sufficient
expanse of water exists for the tidal action to be fully
developed. This ocean has an average width of 1,500 miles, and
completely encircles the earth on a circumferential line 13,500
miles long; in it the attraction of the sun and moon raises the
water nearest to the centre of attraction into a crest which
forms high water at that place. At the same time, the water is
acted on by the centripetal effect of gravity, which, tending
to draw it as near as possible to the centre of the earth, acts
in opposition to the attraction of the sun and moon, so that at
the sides of the earth 90 degrees away, where the attraction of
the sun and moon is less, the centripetal force has more
effect, and the water is drawn so as to form the trough of the
wave, or low water, at those points. There is also the
centrifugal force contained in the revolving globe, which has
an equatorial diameter of about 8,000 miles and a circumference
of 25,132 miles. As it takes 23 hr. 56 min 4 sec, or, say,
twenty-four hours, to make a complete revolution, the surface
at the equator travels at a speed of approximately 25,132/24 =
1,047 miles per hour. This centrifugal force is always
constant, and tends to throw the water off from the surface of
the globe in opposition to the centripetal force, which tends
to retain the water in an even layer around the earth. It is
asserted, however, as an explanation of the phenomenon which
occurs, that the centripetal force acting at any point on the
surface of the earth varies inversely as the square of the
distance from that point to the moon, so that the centripetal
force acting on the water at the side of the earth furthest
removed from the moon is less effective than that on the side
nearest to the moon, to the extent due to the length of the
diameter of the earth. The result of this is that the
centrifugal force overbalances the centripetal force, and the
water tends to fly off, forming an anti-lunar wave crest at
that point approximately equal, and opposite, to the wave crest
at the point nearest to the moon. As the earth revolves, the
crest of high water of the lunar tide remains opposite the
centre of attraction of the sun and moon, so that a point on
the surface will be carried from high water towards and past
the trough of the wave, or low water, then past the crest of
the anti-lunar tide, or high water again, and back to its
original position under the moon. But while the earth is
revolving the moon has traveled 13 degrees along the elliptical
orbit in which she revolves around the earth, from west to
east, once in 27 days 7 hr. 43 min, so that the earth has to
make a fraction over a complete revolution before the same
point is brought under the centre of attraction again This
occupies on an average 52 min, so that, although we are taught
that the tide regularly ebbs and flows twice in twenty-four
hours, it will be seen that the tidal day averages 24 hr. 52
min, the high water of each tide in the Southern Ocean being at
12 hr. 26 min intervals. As a matter of fact, the tidal day
varies from 24 hr. 35 min at new and full moon to 25 hr. 25 min
at the quarters. Although the moon revolves around the earth in
approximately 27-1/3 days, the earth has moved 27 degrees on
its elliptical orbit around the sun, which it completes once in
365± days, so that the period which elapses before the moon
again occupies the same relative position to the sun is 29 days
12 hr. 43 min, which is the time occupied by the moon in
completing her phases, and is known as a lunar month or a
lunation.

Considered from the point of view of a person on the earth,
this primary tidal wave constantly travels round the Southern
Ocean at a speed of 13,500 miles in 24 hr. 52 min, thus having
a velocity of 543 miles per hour, and measuring a length of
13,500/2 = 6,750 miles from crest to crest. If a map of the
world be examined it will be noticed that there are three large
oceans branching off the Southern Ocean, namely, the Atlantic,
Pacific, and Indian Oceans; and although there is the same
tendency for the formation of tides in these oceans, they are
too restricted for any very material tidal action to take
place. As the crest of the primary tidal wave in its journey
round the world passes these oceans, the surface of the water
is raised in them, which results in secondary or derivative
tidal waves being sent through each ocean to the furthermost
parts of the globe; and as the trough of the primary wave
passes the same points the surface of the water is lowered, and
a reverse action takes place, so that the derivative waves
oscillate backwards and forwards in the branch oceans, the
complete cycle occupying on the average 12 hr. 26 min Every
variation of the tides in the Southern Ocean is accurately
reproduced in every sea connected with it.

Wave motion consists only in a vertical movement of the
particles of water by which a crest and trough is formed
alternately, the crest being as much above the normal
horizontal line as the trough is below it; and in the tidal
waves this motion extends through the whole depth of the water
from the surface to the bottom, but there is no horizontal
movement except of form. The late Mr. J. Scott Russell
described it as the transference of motion without the
transference of matter; of form without the substance; of force
without the agent.

The action produced by the sun and moon jointly is practically
the resultant of the effects which each would produce
separately, and as the net tide-producing effect of the moon is
to raise a crest of water 1.4 ft above the trough, and that of
the sun is 0.6 ft (being in the proportion of I to 0.445), when
the two forces are acting in conjunction a wave 1.4 + 0.6 = 2
ft high is produced in the Southern Ocean, and when acting in
opposition a wave 1.4 - 0.6 = 0.8 ft high is formed. As the
derivative wave, consisting of the large mass of water set in
motion by the comparatively small rise and fall of the primary
wave, is propagated through the branch oceans, it is affected
by many circumstances, such as the continual variation in width
between the opposite shores, the alterations in the depth of
the channels, and the irregularity of the coast line. When
obstruction occurs, as, for example, in the Bristol Channel,
where there is a gradually rising bed with a converging
channel, the velocity, and/or the amount of rise and fall of
the derivative wave is increased to an enormous extent; in
other places where the oceans widen out, the rise and/or
velocity is diminished, and similarly where a narrow channel
occurs between two pieces of land an increase in the velocity
of the wave will take place, forming a race in that locality.

Although the laws governing the production of tides are well
understood, the irregularities in the depths of the oceans and
the outlines of the coast, the geographical distribution of the
water over the face of the globe and the position and declivity
of the shores greatly modify the movements of the tides and
give rise to so many complications that no general formulae can
be used to give the time or height of the tides at any place by
calculation alone. The average rate of travel and the course of
the flood tide of the derivative waves around the shores of
Great Britain are as follows:--150 miles per hour from Land's
End to Lundy Island; 90 miles per hour from Lundy to St.
David's Head; 22 miles per hour from St. David's Head to Holy
head; 45-1/2 miles per hour from Holyhead to Solway Firth; 194
miles per hour from the North of Ireland to the North of
Scotland; 52 miles per hour from the North of Scotland to the
Wash; 20 miles per hour from the Wash to Yarmouth; 10 miles per
hour from Yarmouth to Harwich. Along the south coast from
Land's End to Beachy Head the average velocity is 40 miles per
hour, the rate reducing as the wave approaches Dover, in the
vicinity of which the tidal waves from the two different
directions meet, one arriving approximately twelve hours later
than the other, thus forming tides which are a result of the
amalgamation of the two waves. On the ebb tide the direction of
the waves is reversed.

The mobility of the water around the earth causes it to be very
sensitive to the varying attraction of the sun and moon, due to
the alterations from time to time in the relative positions of
the three bodies. Fig. [Footnote: Plate I] shows
diagrammatically the condition of the water in the Southern
Ocean when the sun and moon are in the positions occupied at
the time of new moon. The tide at A is due to the sum of the
attractions of the sun and moon less the effect due to the
excess of the centripetal force over centrifugal force. The
tide at C is due to the excess of the centrifugal force over
the centripetal force. These tides are known as "spring" tides.
Fig. 2 [Footnote: Plate I] shows the positions occupied at the
time of full moon. The tide at A is due to the attraction of
the sun plus the effect due to the excess of the centrifugal
force over the centripetal force. The tide at C is due to the
attraction of the moon less the effect due to the excess of the
centripetal force over centrifugal force. These tides are also
known as "spring" tides. Fig. 3 [Footnote: Plate I] shows the
positions occupied when the moon is in the first quarter; the
position at the third quarter being similar, except that the
moon would then be on the side of the earth nearest to B, The
tide at A is compounded of high water of the solar tide
superimposed upon low water of the lunar tide, so that the sea
is at a higher level than in the case of the low water of
spring tides. The tide at D is due to the attraction of the
moon less the excess of centripetal force over centrifugal
force, and the tide at B is due to the excess of centrifugal
force over centripetal force. These are known as "neap" tides,
and, as the sun is acting in opposition to the moon, the height
of high water is considerably less than at the time of spring
tides. The tides are continually varying between these extremes
according to the alterations in the attracting forces, but the
joint high tide lies nearer to the crest of the lunar than of
the solar tide. It is obvious that, if the attracting force of
the sun and moon were equal, the height of spring tides would
be double that due to each body separately, and that there
would be no variation in the height of the sea at the time of
neap tides.

It will now be of interest to consider the minor movements of
the sun and moon, as they also affect the tides by reason of
the alterations they cause in the attractive force. During the
revolution of the earth round the sun the successive positions
of the point on the earth which is nearest to the sun will form
a diagonal line across the equator. At the vernal equinox
(March 20) the equator is vertically under the sun, which then
declines to the south until the summer solstice (June 21), when
it reaches its maximum south declination. It then moves
northwards, passing vertically over the equator again at the
autumnal equinox (September 21), and reaches its maximum
northern declination on the winter solstice (December 21). The
declination varies from about 24 degrees above to 24 degrees
below the equator. The sun is nearest to the Southern Ocean,
where the tides are generated, when it is in its southern
declination, and furthest away when in the north, but the sun
is actually nearest to the earth on December 31 (perihelion)
and furthest away on July I (aphelion), the difference between
the maximum and minimum distance being one-thirtieth of the
whole.

The moon travels in a similar diagonal direction around the
earth, varying between 18-1/2 degrees and 28-1/2 degreed above
and below the equator. The change from north to south
declination takes place every fourteen days, but these changes
do not necessarily take place at the change in the phases of
the moon. When the moon is south of the equator, she is nearer
to the Southern Ocean, where the tides are generated. The new
moon is nearest to the sun, and crosses the meridian at midday,
while the full moon crosses it at midnight.

The height of the afternoon tide varies from that of the
morning tide; sometimes one is the higher and sometimes the
other, according to the declination of the sun and moon. This
is called the "diurnal inequality." The average difference
between the night and morning tides is about 5 in on the east
coast and about 8in on the west coast. When there is a
considerable difference in the height of high water of two
consecutive tides, the ebb which follows the higher tide is
lower than that following the lower high water, and as a
general rule the higher the tide rises the lower it will fall.
The height of spring tides varies throughout the year, being at
a maximum when the sun is over the equator at the equinoxes and
at a minimum in June at the summer solstice when the sun is
furthest away from the equator. In the Southern Ocean high
water of spring tides occurs at mid-day on the meridian of
Greenwich and at midnight on the 180° meridian, and is later on
the coasts of other seas in proportion to the time taken for
the derivative waves to reach them, the tide being about three-
fourths of a day later at Land's End and one day and a half
later at the mouth of the Thames. The spring tides around the
coast of England are four inches higher on the average at the
time of new moon than at full moon, the average rise being
about 15 ft, while the average rise at neaps is 11 ft 6 in.

The height from high to low water of spring tides is
approximately double that of neap tides, while the maximum
height to which spring tides rise is about 33 per cent. more
than neaps, taking mean low water of spring tides as the datum.
Extraordinarily high tides may be expected when the moon is new
or full, and in her position nearest to the earth at the same
time as her declination is near the equator, and they will be
still further augmented if a strong gale has been blowing for
some time in the same direction as the flood tide in the open
sea, and then changes when the tide starts to rise, so as to
blow straight on to the shore. The pressure of the air also
affects the height of tides in so far as an increase will tend
to depress the water in one place, and a reduction of pressure
will facilitate its rising elsewhere, so that if there is a
steep gradient in the barometrical pressure falling in the same
direction as the flood tide the tides will be higher. As
exemplifying the effect of violent gales in the Atlantic on the
tides of the Bristol Channel, the following extract from "The
Surveyor, Engineer, and Architect" of 1840, dealing with
observations taken on Mr. Bunt's self-registering tide gauge at
Hotwell House, Clifton, may be of interest.

Date:           Times of High Water.      Difference in
Jan 1840.      Tide Gauge.  Tide Table.    Tide Table.
                  H.M.         H.M.
27th, p.m.......  0. 8 ....... 0. 7 .....  1 min earlier.
28th, a.m.......  0.47 ....... 0.34 ..... 13 min earlier.
28th, p.m....... 11.41 ....... 1. 7 ..... 86 min later.
29th, a.m.......  1.29 ....... 1.47 ..... 18 min later.
29th, p.m.......  2.32 ....... 2.30 .....  2 min earlier.


Although the times of the tides varied so considerably, their
heights were exactly as predicted in the tide-table.

The records during a storm on October 29, 1838, gave an
entirely different result, as the time was retarded only ten or
twelve minutes, but the height was increased by 8 ft On another
occasion the tide at Liverpool was increased 7 ft by a gale.
The Bristol Channel holds the record for the greatest tide
experienced around the shores of Great Britain, which occurred
at Chepstow in 1883, and had a rise of 48 ft 6 in The
configuration of the Bristol Channel is, of course, conducive
to large tides, but abnormally high tides do not generally
occur on our shores more frequently than perhaps once in ten
years, the last one occurring in the early part of 1904,
although there may foe many extra high ones during this period
of ten years from on-shore gales. Where tides approach a place
from different directions there may be an interval between the
times of arrival, which results in there being two periods of
high and low water, as at Southampton, where the tides approach
from each side of the Isle of Wight.

The hour at which high water occurs at any place on the coast
at the time of new or full moon is known as the establishment
of that place, and when this, together with the height to which
the tide rises above low water is ascertained by actual
observation, it is possible with the aid of the nautical
almanack to make calculations which will foretell the time and
height of the daily tides at that place for all future time. By
means of a tide-predicting machine, invented by Lord Kelvin,
the tides for a whole year can be calculated in from three to
four hours. This machine is fully described in the Minutes of
Proceedings, Inst.C.E., Vol. LXV. The age of the tide at any
place is the period of time between new or full moon and the
occurrence of spring tides at that place. The range of a tide
is the height between high and low water of that tide, and the
rise of a tide is the height between high water of that tide
and the mean low water level of spring tides. It follows,
therefore, that for spring tides the range and rise are
synonymous terms, but at neap tides the range is the total
height between high and low water, while the rise is the
difference between high water of the neap tide and the mean low
water level of spring tides. Neither the total time occupied by
the flood and ebb tides nor the rate of the rise and fall are
equal, except in the open sea, where there are fewer disturbing
conditions. In restricted areas of water the ebb lasts longer
than the flood.

Although the published tide-tables give much detailed
information, it only applies to certain representative ports,
and even then it is only correct in calm weather and with a
very steady wind, so that in the majority of cases the engineer
must take his own observations to obtain the necessary local
information to guide him in the design of the works. It is
impracticable for these observations to be continued over the
lengthy period necessary to obtain the fullest and most
accurate results, but, premising a general knowledge of the
natural phenomena which affect the tides, as briefly described
herein, he will be able to gauge the effect of the various
disturbing causes, and interpret the records he obtains so as
to arrive at a tolerably accurate estimate of what may be
expected under any particular circumstances. Generally about 25
per cent. of the tides in a year are directly affected by the
wind, etc., the majority varying from 6 in to 12 in in height
and from five to fifteen minutes in time. The effect of a
moderately stiff gale is approximately to raise a tide as many
inches as it might be expected to rise in feet under normal
conditions. The Liverpool tide-tables are based on observations
spread over ten years, and even longer periods have been
adopted in other places.

Much valuable information on this subject is contained in the
following books, among others--and the writer is indebted to
the various authors for some of the data contained in this and
subsequent chapters--"The Tides," by G. H. Darwin, 1886;
Baird's Manual of Tidal Observations, 1886; and "Tides and
Waves," by W. H. Wheeler, 1906, together with the articles in
the "Encyclopaedia Britannica" and "Chambers's Encyclopaedia."




Chapter II

Observations of the rise and fall of tides.


The first step in the practical design of the sewage works is
to ascertain the level of high and low water of ordinary spring
and neap tides and of equinoctial tides, as well as the rate of
rise and fall of the various tides. This is done by means of a
tide recording instrument similar to Fig. 4, which represents
one made by Mr. J. H. Steward, of 457, West Strand, London,
W.C. It consists of a drum about 5 in diameter and 10 in high,
which revolves by clockwork once in twenty-four hours, the same
mechanism also driving a small clock. A diagram paper divided
with vertical lines into twenty-four primary spaces for the
hours is fastened round the drum and a pen or pencil attached
to a slide actuated by a rack or toothed wheel is free to work
vertically up and down against the drum. A pinion working in
this rack or wheel is connected with a pulley over which a
flexible copper wire passes through the bottom of the case
containing the gauge to a spherical copper float, 8 inches
diameter, which rises and falls with the tide, so that every
movement of the tide is reproduced moment by moment upon the
chart as it revokes. The instrument is enclosed in an ebonized
cabinet, having glazed doors in front and at both sides, giving
convenient access to all parts. Inasmuch as the height and the
time of the tide vary every day, it is practicable to read
three days' tides on one chart, instead changing it every day.
When the diagrams are taken of, the lines representing the
water levels should be traced on to a continuous strip of
tracing linen, so that the variations can be seen at a glance
extra lines should be drawn, on the tracing showing the time at
which the changes of the moon occur.

Fig. 5 is a reproduction to a small scale of actual records
taken over a period of eighteen days, which shows true
appearance of the diagrams when traced on the continuous strip.


These observations show very little difference between the
spring and neap tides, and are interesting as indicating the
unreliability of basing general deductions upon data obtained
during a limited period only. At the time of the spring tides
at the beginning of June the conditions were not favourable to
big tides, as although the moon was approaching her perigee,
her declination had nearly reached its northern limit and the
declination of the sun was 22° IN The first quarter of the moon
coincided very closely with the moon's passage over the
equator, so that the neaps would be bigger than usual. At the
period of the spring: tides, about the middle of June, although
the time of full moon corresponded with her southernmost
declination, she was approaching her apogee, and the
declination of the sun was 23° 16' N., so that the tides would
be lower than usual.

In order to ensure accurate observations, the position chosen
for the tide gauge should be in deep water in the immediate
vicinity of the locus in quo, but so that it is not affected by
the waves from passing vessels. Wave motion is most felt where
the float is in shallow water. A pier or quay wall will
probably be most convenient, but in order to obtain records of
the whole range of the tides it is of course necessary that the
float should not be left dry at low water. In some instances
the float is fixed in a well sunk above high water mark to such
a depth that the bottom of it is below the lowest low water
level, and a small pipe is then laid under the beach from the
well to, and below, low water, so that the water stands
continuously in the well at the same level as the sea.

The gauge should be fixed on bearers, about 3 ft 6 in from the
floor, in a wooden shed, similar to a watchman's box, but
provided with a door, erected on the pier or other site fixed
upon for the observations. A hole must be formed in the floor
and a galvanized iron or timber tube about 10 in square
reaching to below low water level fixed underneath, so that
when the float is suspended from the recording instrument it
shall hang vertically down the centre of the tube. The shed
and tube must of course be fixed securely to withstand wind and
waves. The inside of the tube must be free from all projections
or floating matter which would interfere with the movements of
the float, the bottom should be closed, and about four lin
diameter holes should be cleanly formed in the sides near to
the bottom for the ingress and egress of the water. With a
larger number of holes the wave action will cause the diagram
to be very indistinct, and probably lead to incorrectness in
determining the actual levels of the tides; and if the tube is
considerably larger than the float, the latter will swing
laterally and give incorrect readings.


A bench mark at some known height above ordnance datum should
be set up in the hut, preferably on the top of the tube. At
each visit the observer should pull the float wire down a short
distance, and allow it to return slowly, thus making a vertical
mark on the diagram, and should then measure the actual level
of the surface of the water below the bench mark in the hut, so
that the water line on the chart can be referred to ordnance
datum. He should also note the correct time from his watch, so
as to subsequently rectify any inaccuracy in the rate of
revolution of the drum.

The most suitable period for taking these observations is from
about the middle of March to near the end of June, as this will
include records of the high spring equinoctial tides and the
low "bird" tides of June. A chart similar to Fig. 6 should be
prepared from the diagrams, showing the rise and fall of the
highest spring tides, the average spring tides, the average
neap tides, and the lowest neap tides, which will be found
extremely useful in considering the levels of, and the
discharge from, the sea outfall pipe.

The levels adopted for tide work vary in different ports.
Trinity high-water mark is the datum adopted for the Port of
London by the Thames Conservancy; it is the level of the lower
edge of a stone fixed in the face of the river wall upon the
east side of the Hermitage entrance of the London Docks, and is
12 48 ft above Ordnance datum. The Liverpool tide tables give
the heights above the Old Dock Sill, which is now non-existent,
but the level of it has been carefully preserved near the same
position, on a stone built into the western wall of the Canning
Half Tide Dock. This level is 40 ft below Ordnance datum. At
Bristol the levels are referred to the Old Cumberland Basin
(O.C.B.), which is an imaginary line 58 ft below Ordnance
datum. It is very desirable that for sewage work all tide
levels should be reduced to Ordnance datum.

A critical examination of the charts obtained from the tide-
recording instruments will show that the mean level of the sea
does not agree with the level of Ordnance datum. Ordnance datum
is officially described as the assumed mean water level at
Liverpool, which was ascertained from observations made by the
Ordnance Survey Department in March, 1844, but subsequent
records taken in May and June, 1859, by a self-recording gauge
on St. George's Pier, showed that the true mean level of the
sea at Liverpool is 0.068 ft below the assumed level. The
general mean level of the sea around the coast of England, as
determined by elaborate records taken at 29 places during the
years 1859-60, was originally said to be, and is still,
officially recognised by the Ordnance Survey Department to be
0.65 ft, or 7.8 in, above Ordnance datum, but included in these
29 stations were 8 at which the records were admitted to be
imperfectly taken. If these 8 stations are omitted from the
calculations, the true general mean level of the sea would be
0.623 ft, or 7.476 in, above Ordnance datum, or 0.691 ft above
the true mean level of the sea at Liverpool. The local mean
seal level at various stations around the coast varies from
0.982 ft below the general mean sea level at Plymouth, to 1.260
ft above it at Harwich, the places nearest to the mean being
Weymouth (.089 ft below) and Hull (.038 ft above).

It may be of interest to mention that Ordnance datum for
Ireland is the level of low water of spring tides in Dublin
Bay, which is 21 ft below a mark on the base of Poolbeg
Lighthouse, and 7.46 ft below English Ordnance datum.

The lines of "high and low water mark of ordinary tides" shown
upon Ordnance maps represent mean tides; that is, tides halfway
between the spring and the neap tides, and are generally
surveyed at the fourth tide before new and full moon. The
foreshore of tidal water below "mean high water" belongs to the
Crown, except in those cases where the rights have been waived
by special grants. Mean high water is, strictly speaking, the
average height of all high waters, spring and neap, as
ascertained over a long period. Mean low water of ordinary
spring tides is the datum generally adopted for the soundings
on the Admiralty Charts, although it is not universally adhered
to; as, for instance, the soundings in Liverpool Bay and the river
Mersey are reduced to a datum 20 ft below the old dock sill, which
is 125 ft below the level of low water of ordinary spring tides.
The datum of each chart varies as regards Ordnance datum, and in the
case of charts embracing a large area the datum varies along the coast.

The following table gives the fall during each half-hour of the
typical tides shown in Fig, 6 (see page 15), from which it will
be seen that the maximum rate occurs at about half-tide, while
very little movement takes place during the half-hour before
and the half-hour after the turn of the tide:--

Table I.

Rate of fall of tides.

State of       Eqionoctial    Ordinary      Ordinary      Lowest
Tide.             Tides.    Spring Tides.  Neap Tides.  Neap Tides.

High water          --           --           --           --
1/2   hour after   0.44         0.40         0.22         0.19
1      "    "      0.96         0.80         0.40         0.31
1-1/2  "    "      1.39         1.14         0.68         0.53
2      "    "      1.85         1.56         0.72         0.59
2-1/2  "    "      1.91         1.64         0.84         0.68
3      "    "      1.94         1.66         0.86         0.70
3-1/2  "    "      1.94         1.66         0.86         0.70
4      "    "      1.91         1.64         0.84         0.68
4-1/2  "    "      1.35         1.16         0.59         0.48
5      "    "      1.27         1.09         0.57         0.46
5-1/2  "    "      1.06         0.91         0.47         0.38
6      "    "      1.04         0.89         0.46         0.37
6-1/2  "    "      0.53         0.45         0.24         0.18
Totals....      17 ft 6 in   15 ft 0 in    7 ft 9 in    6 ft 3 in

The extent to which the level of high water varies from tide to
tide is shown in Fig. 7 [Footnote: Plate III.], which embraces
a period of six months, and is compiled from calculated heights
without taking account of possible wind disturbances.

The varying differences between the night and morning tides are
shown very clearly on this diagram; in some cases the night
tide is the higher one, and in others the morning tide; and while
at one time each successive tide is higher than the preceding one,
at another time the steps showing: the set-back of the tide are
very marked. During the earlier part of the year the spring-tides
at new moon were higher than those at full moon, but towards June
the condition became reversed. The influence of the position of the
sun and moon on the height of the tide is apparent throughout,
but is particularly marked during the exceptionally low spring
tides in the early part of June, when the time of new moon
practically coincides with the moon in apogee and in its most
northerly position furthest removed from the equator.

Inasmuch as the tidal waves themselves have no horizontal
motion, it is now necessary to consider by what means the
movement of water along the shores is caused. The sea is, of
course, subject to the usual law governing the flow of water,
whereby it is constantly trying to find its own level. In a
tidal wave the height of the crest is so small compared with
the length that the surface gradient from crest to trough is
practically flat, and does not lead to any appreciable
movement; but as the tidal wave approaches within a few miles
of the shore, it runs into shallow water, where its progress is
checked, but as it is being pushed on from behind it banks up
and forms a crest of sufficient height to form a more or less
steep gradient, and to induce a horizontal movement of the
particles of water throughout the whole depth in the form of a
tidal current running parallel with the shore.

The rate of this current depends upon the steepness of the
gradient, and the momentum acquired will, In some Instances,
cause the current to continue to run in the same direction for
some time after the tide has turned, i.e., after the direction
of the gradient has been reversed; so that the tide may be
making--or falling--in one direction, while the current is
running the opposite way. It will be readily seen, then, that
the flow of the current will be slack about the time of high
and low water, so that its maximum rate will be at half-ebb and
half-flood. If the tide were flowing into an enclosed or semi-
enclosed space, the current could not run after the tide
turned, and the reversal of both would be simultaneous, unless,
indeed, the current turned before the tide.

Wind waves are only movements of the surface of the water, and
do not generally extend for a greater depth below the trough of
the wave than the crest is above it, but as they may affect the
movement of the floating particles of sewage to a considerable
extent it is necessary to record the direction and strength of
the wind.

The strength of the wind is sometimes indicated wind at the
time of making any tidal observations. By reference to the
Beaufort Scale, which is a graduated classification adopted by
Admiral Beaufort about the year 1805. The following table gives
the general description, velocity, and pressure of the wind
corresponding to the tabular numbers on the scale:--

[Illustration: PLATE III

PERIOD OF SIX MONTHS.

To face page 20]

The figures indicating the pressure of the wind in the
foregoing table are low compared with those given by other
authorities. From Mutton's formula, the pressure against a
plane surface normal to the wind would be 0.97 lb per sq. foot,
with an average velocity of 15 miles per hour (22 ft per sec.),
compared with o.67 lb given by Admiral Beaufort, and for a
velocity of 50 miles per hour (73.3 ft per sec.) 10.75 lb,
compared with 7.7lb Semitone's formula, which is frequently
used, gives the pressure as 0.005V^2 (miles per hour), so that
for 15 miles per hour velocity the pressure would be 1.125 lb,
and for 50 miles it would be l2.5 lb It must not be forgotten,
however, that, although over a period of one hour the wind may
_average_ this velocity or pressure, it will vary considerably
from moment to moment, being far in excess at one time, and
practically calm at another. The velocity of the wind is
usually taken by a cup anemometer having four 9 in cups on arms
2 ft long. The factor for reducing the records varies from 2 to
3, according to the friction and lubrication, the average being
2.2.

The pressure is obtained by multiplying the Beaufort number
cubed by 0.0105; and the velocity is found by multiplying the
square root of the Beaufort number cubed by 1.87.

A tidal wave will traverse the open sea in a straight line, but
as it passes along the coast the progress of the line nearest
the shore is retarded while the centre part continues at the
same velocity, so that on plan the wave assumes a convex shape
and the branch waves reaching the shore form an acute angle
with the coast line.




CHAPTER III.

CURRENT OBSERVATIONS.


There is considerable diversity in the design of floats
employed in current observations, dependant to some extent upon
whether it is desired to ascertain the direction of the surface
drift or of a deep current, it does not by any means follow
that they run in simultaneous directions. There is also
sometimes considerable difference in the velocity of the
current at different depths--the surface current being more
susceptible to influence of wind. A good form of deep float is
seen in Fig. 8. It consists of a rod 2 in by 2 in, or 4 sq in
The lower end of which a hollow wooden box about 6 in by 6 in
is fixed, into which pebbles are placed to overcome the
buoyancy of the float and cause it to take and maintain an
upright position in the water with a length of 9in of the rod
exposed above the surface. A small hole is formed in the top of
the box for the insertion the pebbles, which is stopped up with
a cork when the float is adjusted. The length of the rod will
vary according to the depth of water, but it will generally be
found convenient to employ a float about 10 ft and to have a
spare one about 6 ft deep, but otherwise it is similar in all
respects, for use in shallow water. A cheap float for gauging
the surface drift can be made from an empty champagne bottle
weighted with stones and partly filled with water. The top 12
in of rods and the cord and neck of the bottle, as the case may
be, should be painted red, as this colour renders floats more
conspicuous when in the water and gives considerable assistance
in locating their position, especially when they are at some
distance from the observer.

A deep-sea float designed by Mr. G. P. Bidden for ascertaining
the set of the currents along the base of the ocean has
recently been used by the North Sea Fisheries Investigation
Committee. It consists of a bottle shaped like a soda-water bottle,
made of strong glass to resist the pressure of the water, and
partly filled with water, so that just sufficient air is left
in it to cause it to float. A length of copper wire heavy enough
to cause it to sink is then attached to the bottle, which is then
dropped into the sea at a defined place. When the end of the wire
touches the bottom the bottle is relieved of some of its weight
and travels along with the currents a short distance above the bed
of the sea. About 20 per cent. of the bottles were recovered, either
by being thrown up on the beach or by being fished up in trawl nets.

[Illustration: FIG. 8.--DETAIL OF WOOD TIDAL FLOAT 10 FEET
DEEP.]

A double float, weighing about 10 lb complete, was used for the
tidal observations for the Girdleness outfall sewer, Aberdeen.
The surface portion consisted of two sheet-iron cups soldered
together, making a float 9 in in diameter and 6 in deep. The
lower or submerged portion was made of zinc, cylindrical in
shape, 16 in diameter and 16 in long, perforated at intervals
with lin diameter holes and suspended by means of a brass chain
from a swivel formed on the underside of the surface float.

In gauging the currents the float is placed in the water at a
defined point and allowed to drift, its course being noted and
afterwards transferred to a plan. The time of starting should
be recorded and observations of its exact position taken
regularly at every quarter of an hour, so that the time taken
in covering any particular distance is known and the length of
travel during any quarter-hour period multiplied by four gives
the speed of the current at that time in miles per hour.

The method to be employed in ascertaining the exact position of
the float from time to time is a matter which requires careful
consideration, and is dependent upon the degree of accuracy
required according to the importance of the scheme and the
situation of neighbouring towns, frequented shores, oyster
beds, and other circumstances likely to be injuriously affected
by any possible or probable pollution by sewage.

One method is to follow the float in a small boat carrying a
marine compass which has the card balanced to remain in a
horizontal position, irrespective of the tipping and rolling of
the boat, and to observe simultaneously the bearing of two
prominent landmarks, the position of which on the plan is
known, at each of the quarter-hour periods at which the
observations are to be taken. This method only gives very
approximate results, and after checking the value of the
observations made by its use, with contemporary observations
taken by means of theodolites on the shore, the writer
abandoned the system in favour of the theodolite method, which,
however, requires a larger staff, and is therefore more
expensive. In every case it is necessary to employ a boat to
follow the float, not only so as to recover it at the end of
each day's work, but principally to assist in approximately
locating the float, which can then be found more readily when
searching through the telescope of the theodolite. The boat
should be kept about 10 ft to 20 ft from the float on the side
further removed from the observers, except when surface floats
are being used to ascertain the effect of the wind, when the
boat should be kept to leeward of the float. Although obviously
with a large boat the observations can be pursued through
rougher weather, which is an important point, still the
difficulty of maintaining a large boat propelled by mechanical
power, or sail, sufficiently near the float to assist the
observers, prevents its use, and the best result will be
obtained by employing a substantial, seaworthy rowing boat with
a broad beam. The boatmen appreciate the inclusion of a mast,
sails, and plenty of ballast in the equipment to facilitate
their return home when the day's work is done, which may happen
eight or nine miles away, with twilight fast passing into
darkness. There should be two boatmen, or a man and a strong
youth.

In working with theodolites, it is as well before starting to
select observation stations at intervals along the coast, drive
pegs in the ground so that they can easily be found afterwards,
and fix their position upon a 1/2500 ordnance map in the usual
manner. It may, however, be found in practice that after
leaving one station it is not possible to reach the next one
before the time arrives for another sight to be taken. In this
case the theodolite must be set up on magnetic north at an
intermediate position, and sights taken to at least two
landmarks, the positions of which are shown on the map, and the
point of observation subsequently plotted as near as possible
by the use of these readings. Inasmuch as the sights will be
taken from points on the edge of the shore, which is, of
course, shown on the map, it is possible, after setting up to
magnetic north, to fix the position with approximate accuracy
by a sight to one landmark only, but this should only be done
in exceptional circumstances.

The method of taking the observations with two theodolites, as
adopted by the writer, can best be explained by a reference to
Fig. 9, which represents an indented piece of the coast. The
end of the proposed sea outfall sewer, from which point the
observations would naturally start, is marked 1, the numerals
2, 3, 4, etc., indicating the positions of the float as
observed from time to time. Many intermediate observations
would be taken, but in order to render the diagram more clear,
these have not been shown. The lines of sight are marked 1A,
1B, etc. The points marked A1, A2, etc., indicate the first,
second, etc., and subsequent positions of observer A; the
points B1, B2, etc., referring to observer B. The dot-and-dash
line shows the course taken by the float, which is ascertained
after plotting the various observations recorded.

It is very desirable to have a horse and trap in waiting to
move the observers and their instruments from place to place as
required, and each observer should be provided with small flags
about 2 ft square, one white and one blue, for signalling
purposes.

The instruments are first set up at A1 and B1 respectively, and
adjusted to read on to the predetermined point 1 where the
float is to be put in Then as soon as the boatmen have reached
the vicinity of this point, the observers can, by means of the
flags, direct them which way to row so as to bring the boat to
the exact position required, and when this is done the anchor is
dropped until it is time to start, which is signalled by the observers
holding the flags straight above their heads. This is also the
signal used to indicate to the men that the day's work is
finished, and they can pick up the float and start for home.

[Illustration: FIG. 9.--PLAN OF INDENTED COAST-LINE LLUSTRATING
METHOD OF TAKING CURRENT OBSERVATIONS WITH TWO THEODOLITES.]

Directly the float is put in the water, and at every even
quarter of an hour afterwards, each observer takes a reading of
its exact position, and notes the time. As soon as the readings
are taken to the float in position 2, the observer A should
take up his instrument and drive to A2, where he must set up
ready to take reading 3 a quarter of an hour after reading 2.
It will be noticed that he might possibly have been able to
take the reading 3 from the position A1, but the angle made by
the lines of sight from the two instruments would have been too
acute for accurate work, and very probably the float would have
been hidden by the headland, so that he could not take the
reading at all. In order to be on the headland A4 at the proper
time, A must be working towards it by getting to position A3 by
the time reading 4 is due. Although the remainder of the course
of the float can be followed from B1 and A4, the instruments
would be reading too much in the same line, so that B must move
to B2 and then after reading 5 and 6 he should move to B3. As
the float returns towards the starting point, A can remain in
the position A4 while B goes to B4 and then moves back along
the shore as the float progresses.

The foregoing description is sufficient to indicate the general
method of working, but the details will of course vary
according to the configuration of the shore and the course
taken by the float. Good judgment is necessary in deciding when
to move from one station to the next, and celerity in setting
up, adjusting the instrument, and taking readings is essential.
If the boatmen can be relied upon to keep their position near
the float, very long sights can be taken with sufficient
accuracy by observing the position of the boat, long after the
float has ceased to be visible through the telescope.

The lines of sight from each station should be subsequently
plotted on the 1/2500 ordnance map; the intersection of each
two corresponding sight lines giving the position of the float
at that time. Then if a continuous line is drawn passing
through all the points of intersection it will indicate the
course taken by the float.

It is very desirable that the observers should be able to
convey information to each other by signalling with the flags
according to the Morse code, as follows. The dashes represent a
movement of the flag from a position in front of the left
shoulder to near the ground on the right side and the dots a
movement from the left shoulder to the right shoulder.

TABLE 3.

MORSE ALPHABET.

E  .
A  .-
R  .-.
L  .-..
W  .--
P  .--.
J  .---
I  ..
U  ..-
F  ..-.
S  ...
V  ...-
H  ....
T  -
N  -.
K  -.-
C  -.-.
Y  -.--
D -..
X  -..-
B  -...
M  --
G  --.
Q  --.-
Z  --..
O  ---

The signal to attract attention at starting and to signify the
end of the message is  .. .. .. continued until it is
acknowledged with a similar sign by the other observer; that
for a repetition is .. -- .. which is signalled when any part
of the message is not understood, otherwise after each word is
signalled the receiver waves - to indicate he understands it.
Until proficiency is attained, two copies of the alphabet
should be kept by each observer for reference, one for
dispatching a message arranged in alphabetical order and the
other far reading a message arranged as set out above. The
white flag should be used when standing against a dark
background, and the blue one when on the skyline or against a
light background.

The conditions in tidal rivers vary somewhat from those
occurring on the coast. As the crest of the tidal wave passes
the mouth of the river a branch wave is sent up the river. This
wave has first to overcome the water flowing down the river,
which is acting in opposition to it, and in so doing causes a
banking up of the water to such a height that the inclination
of the surface is reversed to an extent sufficient to cause a
tidal current to run up the river. The momentum acquired by the
water passing up-stream carries it to a higher level towards
the head of the river than at the mouth, and, similarly, in
returning, the water flowing down the river gains sufficient
impetus to scoop out the water at the mouth and form a low
water below that in the sea adjoining. Owing to a flow of
upland water down a river the ebb lasts longer than the flood
tide by a period, increasing in length as the distance from the
mouth of the river increases; and, similarly to the sea, the
current may continue to run down a river after the tide has
turned and the level of the water is rising. The momentum of
the tide running up the centre of the river is in excess of
that along the banks, so that the current changes near the
shore before it does in the middle, and, as the sea water is of
greater specific gravity than the fresh, weighing 64 lb per
cubic foot against 62-1/2 lb, it flows up the bed of the river
at the commencement of the tide, while the fresh water on the
surface is running in the opposite direction. After a time the
salt water becomes diffused in the fresh, so that the density
of the water in a river decreases as the distance from the sea
increases. The disposal of sewage discharged into a river is
due primarily to the mixing action which is taking place;
inasmuch as the tidal current which is the transporting agent
rarely flows more rapidly than from two to four miles per hour,
or, say, twelve to fifteen miles per tide. The extent to which
the suspended matter is carried back again up stream when the
current turns depends upon the quantity of upland water which
has flowed into the upper tidal part of the river during the
ebb tide, as this water occupies a certain amount of space,
according to the depth and width of the river, and thus
prevents the sea water flowing back to the position it occupied
on the previous tide, and carrying with it the matter in
suspension. The permanent seaward movement of sewage discharged
into the Thames at Barking when there is only a small quantity
of upland water is at the rate of about one mile per day,
taking thirty days to travel the thirty-one miles to the sea,
while at the mouth of the river the rate does not exceed one-
third of a mile per day.




CHAPTER IV.

SELECTION OF SITE FOR OUTFALL SEWER.


The selection of the site for the sea outfall sewer is a matter
requiring a most careful consideration of the many factors
bearing on the point, and the permanent success of any scheme
of sewage disposal depends primarily upon the skill shown in
this matter. The first step is to obtain a general idea of the
tidal conditions, and to examine the Admiralty charts of the
locality, which will show the general set of the main currents
into which it is desirable the sewage should get as quickly as
possible. The main currents may be at some considerable
distance from the shore, especially if the town is situated in
a bay, when the main current will probably be found running
across the mouth of it from headland to headland. The sea
outfall should not be in the vicinity of the bathing grounds,
the pier, or parts of the shore where visitors mostly
congregate; it should not be near oyster beds or lobster
grounds. The prosperity--in fact, the very existence--of most
seaside towns depends upon their capability of attracting
visitors, whose susceptibilities must be studied before
economic or engineering questions, and there are always
sentimental objections to sewage works, however well designed
and conducted they may be.

It is desirable that the sea outfall should be buried in the
shore for the greater part of its length, not only on account
of these sentimental feelings, but as a protection from the
force of the waves, and so that it should not interfere with
boating; and, further, where any part of the outfall between
high and low water mark is above the shore, scouring of the
beach will inevitably take place on each side of it. The
extreme end of the outfall should be below low-water mark of
equinoctial tides, as it is very objectionable to have sewage
running across the beach from the pipe to the water, and if the
foul matter is deposited at the edge of the water it will
probably be brought inland by the rising tide. Several possible
positions may present themselves for the sea outfall, and a few
trial current observations should be made in these localities
at various states of the tides and plotted on to a 1:2500
ordnance map. The results of these observations will probably
reduce the choice of sites very considerably.

Levels should be taken of the existing subsidiary sewers in the
town, or, if there are none, the proposed arrangement of
internal sewers should be sketched out with a view to their
discharging their contents at one or other of the points under
consideration. It may be that the levels of the sewers are such
that by the time they reach the shore they are below the level
of low water, when, obviously, pumping or other methods of
raising the sewage must be resorted to; if they are above low
water, but below high water, the sewage could be stored during
high water and run off at or near low water; or, if they are
above high water, the sewage could run off continuously, or at
any particular time that might be decided.

Observations of the currents should now be made from the
selected points, giving special attention to those periods
during which it is possible to discharge the sewage having
regard to the levels of the sewers. These should be made with
the greatest care and accuracy, as the final selection of the
type of scheme to be adopted will depend very largely on the
results obtained and the proper interpretation of them, by
estimating, and mentally eliminating, any disturbing
influences, such as wind, etc. Care must also be taken in
noting the height of the tide and the relative positions of the
sun, moon, and earth at the time of making the observations,
and in estimating from such information the extent to which the
tides and currents may vary at other times when those bodies
are differently situated.

It is obvious that if the levels of the sewers and other
circumstances are such that the sewage can safely be discharged
at low water, and the works are to be constructed accordingly,
it is most important to have accurate information as to the
level of the highest low water which may occur in any ordinary
circumstances. If the level of a single low water, given by a
casual observation, is adopted without consideration of the
governing conditions, it may easily be that the tide in
question is a low one, that may not be repeated for several
years, and the result would be that, instead of having a free
outlet at low water, the pipe would generally be submerged, and
its discharging capacity very greatly reduced.

The run of the currents will probably differ at each of the
points under consideration, so that if one point were selected
the best result would be obtained by discharging the sewage at
high water and at another point at low water, whereas at a
third point the results would show that to discharge there
would not be satisfactory at any stage of the tide unless the
sewage were first partially or even wholly purified. If these
results are considered in conjunction with the levels of the
sewers definite alternative schemes, each of which would work
satisfactory may be evolved, and after settling them in rough
outline, comparative approximate estimates should be prepared,
when a final scheme may be decided upon which, while giving the
most efficient result at the minimum cost, will not arouse
sentimental objections to a greater extent than is inherent to
all schemes of sewage disposal.

Having thus selected the exact position of the outfall, the
current observations from that point should be completed, so
that the engineer may be in a position to state definitely the
course which would be taken by sewage if discharged under any
conditions of time or tide. This information is not
particularly wanted by the engineer, but the scheme will have
to receive the sanction of the Local Government Board or of
Parliament, and probably considerable opposition will be raised
by interested parties, which must be met at all points and
overcome. In addition to this, it may be possible, and
necessary, when heavy rain occurs, to allow the diluted sewage
to escape into the sea at any stage of the tide; and, while it
is easy to contend that it will not then be more impure than
storm water which is permitted to be discharged into inland
streams during heavy rainfall, the aforesaid sentimentalists
may conjure up many possibilities of serious results. As far as
possible the records should indicate the course taken by floats
starting from the outfall, at high water, and at each regular
hour afterwards on the ebb tide, as well as at low water and
every hour on the flood tide. It is not, however, by any means
necessary that they should be taken in this or any particular
order, because as the height of the tide varies each day an
observation taken at high water one day is not directly
comparable with one taken an hour after high water the next
day, and while perhaps relatively the greatest amount of
information can be gleaned from a series of observations taken
at the same state of the tide, but on tides of differing
heights, still, every observation tells its own story and
serves a useful purpose.

Deep floats and surface floats should be used concurrently to
show the effect of the wind, the direction and force of which
should be noted. If it appears that with an on-shore wind
floating particles would drift to the shore, screening will be
necessary before the sewage is discharged. The floats should be
followed as long as possible, but at least until the turn of
the current--that is to say, a float put in at or near high
water should be followed until the current has turned at or
near low water, and one put in at low water should be followed
until after high water. In all references to low water the
height of the tide given is that of the preceding high water.

The time at which the current turns relative to high and low
water at any place will be found to vary with the height of the
tide, and all the information obtained on this point should be
plotted on squared paper as shown on Fig. 10, which represents
the result of observations taken near the estuary of a large
river where the conditions would be somewhat different from
those holding in the open sea. The vertical lines represent the
time before high or low water at which the current turned, and
the horizontal lines the height of the tide, but the data will,
of course, vary in different localities.

[Illustration: Hours before turn of tide. FIG 10]

It will be noticed that certain of the points thus obtained can
be joined up by a regular curve which can be utilised for
ascertaining the probable time at which the current will turn
on tides of height intermediate to those at which observations
were actually taken. For instance, from the diagram given it
can be seen that on a 20 ft tide the current will turn thirty
minutes before the tide, or on a 15 ft tide the current will
turn one hour before the tide. Some of the points lie at a
considerable distance from the regular curve, showing that the
currents on those occasions were affected by some disturbing
influence which the observer will probably be able to explain
by a reference to his notes, and therefore those particular
observations must be used with caution.

The rate of travel of the currents varies in accordance with
the time they have been running. Directly after the turn there
is scarcely any movement, but the speed increases until it
reaches a maximum about three hours later and then it decreases
until the next turn, when dead water occurs again.

Those observations which were started at the turn of the
current and continued through the whole tide should be plotted
as shown in Fig. 11, which gives the curves relating to three
different tides, but, provided a sufficiently large scale is
adopted, there is no reason why curves relating to the whole
range of the tides should not be plotted on one diagram. This
chart shows the total distance that would be covered by a float
according to the height of the tide; it also indicates the
velocity of the current from time to time. It can be used in
several ways, but as this necessitates the assumption that with
tides of the same height the flow of the currents is absolutely
identical along the coast in the vicinity of the outfall, the
diagram should be checked as far as possible by any
observations that may be taken at other states of tides of the
same heights. Suppose we require to know how far a float will
travel if started at two hours after high water on a 12 ft
tide. From Fig. 10 we see that on a tide of this height the
current turns two hours and a quarter before the tide;
therefore two hours after high water will be four hours and a
quarter after the turn of the current. If the float were
started with the current, we see from Fig. 11 that it would
have travelled three miles in four hours and a quarter; and
subtracting this from four miles, which is its full travel on a
whole tide, we see that it will only cover one mile in the two
hours and a quarter remaining before the current turns to run
back again.

Although sewage discharged into the sea rapidly becomes so
diffused as to lose its identity, still occasionally the
extraneous substances in it, such as wooden matches, banana
skins, etc., may be traced for a considerable distance; so
that, as the sewage continues to be discharged into the sea
moving past the outfall, there is formed what may be described
as a body or column of water having possibilities of sewage
contamination. If the time during which sewage is discharged is
limited to two hours, and starts, say, at the turn of the
current on a 12 ft tide, we see from Fig. 11 that the front of
this body of water will have reached a point five-eighths of a
mile away when the discharge ceases; so that there will be a
virtual column of water of a total length of five-eighths of a
mile, in which is contained all that remains of the noxious
matters, travelling through the sea along the course of the
current. We see, further, that at a distance of three miles
away this column would only take thirty minutes to pass a given
point. The extent of this column of water will vary
considerably according to the tide and the time of discharge;
for instance, on a 22 ft tide, if the discharge starts one hour
after the turn of the current and continues for two hours, as
in the previous example, it will form a column four miles long,
whereas if it started two hours after the current, and
continued for the same length of time, the column would be six
miles and a half long, but the percentage of sewage in the
water would be infinitesimal.

[Illustration: Hours after turn of current FIG. 11]

In some cases it may be essential that the sewage should be
borne past a certain point before the current turns in order to
ensure that it shall not be brought back on the return tide to
the shore near the starting point. In other words, the sewage
travelling along the line of a branch current must reach the
junction on the line of the main current by a certain time in
order to catch the connection. Assuming the period of discharge
will be two hours, and that the point which it is necessary to
clear is situated three miles and a half from the outfall, the
permissible time to discharge the sewage according to the
height of the tide can be obtained from Fig. 11. Taking the 22
ft tide first, it will be seen that if the float started with
the current it would travel twelve miles in the tide; three and
a half from twelve leaves eight and a half miles. A vertical line
dropped from the intersection of the eight miles and a half line
with the curve of the current gives the time two hours and a half
before the end, or four hours after the start of the current at which
the discharge of the sewage must cease at the outfall in order that
the rear part of the column can reach the required point before
the current turns. As on this tide high water is about fifteen
minutes after the current, the latest time for the two hours of
discharge must be from one hour and three-quarters to three
hours and three-quarters after high water. Similarly with the
12 ft tide having a total travel of four miles: three and a
half from four leaves half a mile, and a vertical line from the
half-mile intersection gives one hour and three-quarters after
the start of the current as the time for discharge to cease.
High water is two hours and a quarter after the current;
therefore the latest time for the period of discharge would be
from two hours and a half to half an hour before high water,
but, as during the first quarter of an hour the movement of the
current, though slight, would be in the opposite direction, it
would be advisable to curtail the time of discharge, and say
that it should be limited to between two hours and a quarter
and half an hour before high water. It is obvious that if
sewage is discharged about two hours after high water the
current will be nearing its maximum speed, but it will only
have about three hours to run before it turns; so that,
although the sewage may be removed with the maximum rapidity
from the vicinity of the sea outfall, it will not be carried to
any very great distance, and, of course, the greater the
distance it is carried the more it will be diffused. It must be
remembered that the foregoing data are only applicable to the
locality they relate to, although after obtaining the necessary
information similar diagrams can be made and used for other
places; but enough has been said to show that when it is
necessary to utilise the full effect of the currents the sewage
should be discharged at a varying time before high or low
water, as the case may be, according to the height of the tide.




CHAPTER V.

VOLUME OF SEWAGE.


The total quantity of sewage to be dealt with per day can be
ascertained by gauging the flow in those cases where the sewers
are already constructed, but where the scheme is an entirely
new one the quantity must be estimated. If there is a water
supply system the amount of water consumed per day, after
making due allowance for the quantity used for trade purposes
and street watering, will be a useful guide. The average amount
of water used per head per day for domestic purposes only may
be taken as follows:--


DAILY WATER SUPPLY
(Gallons per head per day.)

Dietetic purposes (cooking, drinking, &c.)    1
Cleansing purposes (washing house utensils,
clothes, &c.)                                 6

If water-closets are in general use, add      3

If baths are in general use, add              5

Total                                        15

It therefore follows that the quantity of domestic sewage to be
expected will vary from 7 to 15 gallons per head per day,
according to the extent of the sanitary conveniences installed
in the town; but with the advent of an up-to-date sewage
scheme, probably accompanied by a proper water supply, a very
large increase in the number of water-closets and baths may
confidently be anticipated, and it will rarely be advisable to
provide for a less quantity of domestic sewage than 15 gallons
per head per day for each of the resident inhabitants. The
problem is complicated in sea coast towns by the large influx
of visitors during certain short periods of the year, for whom
the sewerage system must be sufficient, and yet it must not be
so large compared with the requirements of the residential
population that it cannot be kept in an efficient state during
that part of the year when the visitors are absent. The
visitors are of two types--the daily trippers and those who
spend several days or weeks in the town. The daily tripper may
not directly contribute much sewage to the sewers, but he does
indirectly through those who cater for his wants. The resident
visitor will spend most of the day out of doors, and therefore
cause less than the average quantity of water to be used for
house-cleansing purposes, in addition to which the bulk of the
soiled linen will not be washed in the town. An allowance of 10
gallons per head per day for the resident visitor and 5 gallons
per head per day for the trippers will usually be found a
sufficient provision.

It is, of course, well known that the flow of sewage varies
from day to day as well as from hour to hour, and while there
is no necessity to consider the daily variation--calculations
being based on the flow of the maximum day--the hourly
variation plays a most important part where storage of the
sewage for any length of time is an integral part of the
scheme. There are many important factors governing this
variation, and even if the most elaborate calculations are made
they are liable to be upset at any time by the unexpected
discharge of large quantities of trade wastes. With a small
population the hourly fluctuation in the quantity of sewage
flowing into the sewers is very great, but it reduces as the
population increases, owing to the diversity of the occupations
and habits of the inhabitants. In all cases where the
residential portions of the district are straggling, and the
outfall works are situated at a long distance from the centre
of the town, the flow becomes steadier, and the inequalities
are not so prominently marked at the outlet end of the sewer.
The rate of flow increases more or less gradually to the
maximum about midday, and falls off in the afternoon in the
same gradual manner. The following table, based on numerous
gaugings, represents approximately the hourly variations in the
dry weather flow of the sewage proper from populations
numbering from 1,000 to 10,000, and is prepared after deducting
all water which may be present in the sewers resulting from the
infiltration of subsoil water through leaky joints in the
pipes, and from defective water supply fittings as ascertained
from the night gaugings. Larger towns have not been included in
the table because the hourly rates of flow are generally
complicated by the discharge of the trade wastes previously
referred to, which must be the subject of special investigation
in each case.


[TABLE NO. 4.

APPROXIMATE HOURLY VARIATION IN THE FLOW OF SEWAGE.
Percentage of Total Flow Passing Off in each Hour.

-----------+------------------------------------------------
           |                   Population.
    Hour.  +-----+-----+-----+-----+-----+-----+-----+------
           |1,000|2,000|3,000|4,000|5,000|6,000|8,000|10,000
-----------+-----+-----+-----+-----+-----+-----+-----+------
 Midnight  | 1.0 | 1.0 | 1.2 | 1.3 | 1.5 | 1.5 | 1.8 | 2.0
  1.0 a.m. | 0.7 | 0.7 | 0.7 | 0.8 | 0.8 | 1.0 | 1.0 | 1.0
  2.0  "   | nil | nil | nil | nil | 0.2 | 0.2 | 0.3 | 0.5
  3.0  "   | nil | nil | nil | nil | nil | nil | nil | 0.2
  4.0  "   | nil | nil | nil | nil | nil | nil | nil | nil
  5.0  "   | nil | nil | nil | nil | nil | nil | nil | 0.2
  6.0  "   | 0.2 | 0.2 | 0.3 | 0.5 | 0.6 | 0.5 | 0.7 | 0.8
  7.0  "   | 0.5 | 0.5 | 1.0 | 1.5 | 1.6 | 1.7 | 2.0 | 2.5
  8.0  "   | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 5.0
  9.0  "   | 3.5 | 4.5 | 4.5 | 4.8 | 5.5 | 5.8 | 6.0 | 6.5
 10.0  "   | 6.5 | 6.5 | 6.8 | 7.0 | 7.5 | 7.7 | 8.0 | 8.0
 11.0  "   |10.5 |11.0 |10.5 |10.0 | 9.6 | 9.3 | 9.0 | 8.8
 Noon      |11.0 |11.3 |10.8 |10.3 | 9.3 | 9.5 | 9.2 | 9.0
  1.0 p.m. | 6.0 | 5.5 | 6.0 | 6.7 | 7.0 | 7.2 | 7.3 | 7.5
  2.0  "   | 7.0 | 7.3 | 7.0 | 7.0 | 6.5 | 6.5 | 6.2 | 6.0
  3.0  "   | 6.8 | 6.5 | 6.5 | 6.5 | 6.5 | 6.3 | 6.3 | 6.0
  4.0  "   | 7.5 | 7.5 | 7.3 | 7.0 | 6.7 | 6.5 | 6.2 | 6.7
  5.0  "   | 6.5 | 6.5 | 6.5 | 6.3 | 6.0 | 6.0 | 6.0 | 5.8
  6.0  "   | 4.5 | 4.5 | 4.7 | 4.8 | 5.0 | 5.0 | 5.0 | 5.2
  7.0  "   | 6.5 | 6.2 | 6.0 | 5.8 | 5.5 | 5.5 | 5.5 | 4.7
  8.0  "   | 6.2 | 6.0 | 5.8 | 5.5 | 5.5 | 5.3 | 5.0 | 4.8
  9.0  "   | 5.0 | 4.8 | 4.7 | 4.5 | 4.5 | 4.5 | 4.5 | 4.0
 10.0  "   | 4.8 | 4.6 | 4.2 | 4.0 | 3.8 | 3.5 | 3.0 | 3.0
 11.0  "   | 4.3 | 3.5 | 3.5 | 3.2 | 3.2 | 3.0 | 3.0 | 2.8
-----------+-----+-----+-----+-----+-----+-----+-----+------
     Total |100.0|100.0|100.0|100.0|100.0|100.0|100.0|100.0
-----------+-----+-----+-----+-----+-----+-----+-----+------

ANALYSIS OF FLOW]

Percentage of total flow passing off during period named.

---------------------+----------------------------------------------------------------+
                     |                          Population.                           |
                     +-------+-------+-------+-------+-------+-------+-------+--------+
                     | 1,000 | 2,000 | 3,000 | 4,000 | 5,000 | 6,000 | 8,000 | 10,000 |
---------------------+-------+-------+-------+-------+-------+-------+-------+--------+
7.0 a.m. to 7.0 p.m  |  77.3 |  78.8 |  78.6 |  78.7 |  78.5 |  78.8 |  78.7 |  75.2  |
7.0 p.m. to 7.0 a.m  |  22.7 |  21.2 |  21.4 |  21.3 |  21.5 |  21.2 |  21.3 |  21.8  |
Maximum 12 hrs.      |  84.0 |  83.6 |  82.6 |  81.7 |  81.0 |  80.6 |  79.7 |  78.2  |
    "   10  "        |  72.8 |  72.8 |  72.1 |  71.4 |  70.0 |  69.8 |  69.2 |  68.5  |
    "    9  "        |  66.3 |  66.6 |  66.1 |  65.6 |  64.5 |  64.8 |  64.2 |  63.3  |
    "    8  "        |  61.8 |  62.1 |  61.4 |  60.8 |  59.5 |  59.0 |  58.2 |  57.5  |
    "    6  "        |  48.8 |  49.1 |  43.1 |  47.5 |  46.8 |  46.5 |  46.0 |  45.8  |
    "    3  "        |  23.0 |  28.8 |  27.11|  27.3 |  26.8 |  26.5 |  26.2 |  25.8  |
    "    2  "        |  21.5 |  22.3 |  21.3 |  20.3 |  19.3 |  18.5 |  18.2 |  17.3  |
    "    1  "        |  11.0 |  11.3 |  10.8 |  10.3 |   9.8 |   9.5 |   9.2 |  9.0   |
Minimum  9  "        |   3.4 |   3.9 |   5.2 |   6.6 |   7.5 |   6.9 |   8.8 |  10.0  |
    "   10  "        |   6.9 |   7.4 |   8.7 |   9.8 |  10.7 |  10.4 |  11.8 |  13.0  |
---------------------+-------+-------+-------+-------+-------+-------+-------+--------+

The data in the foregoing table, so far as they relate to
populations of one, five, and ten thousand respectively, are
reproduced graphically in Fig. 12.

This table and diagram relate only to the flow of sewage--that
is, water which is intentionally fouled; but unfortunately it
is almost invariably found that the flow in the sewers is
greater than is thus indicated, and due allowance must be made
accordingly. The greater the amount of extra liquid flowing in
the sewers as a permanent constant stream, the less marked will
be the hourly variations; and in one set of gaugings which came
under the writer's notice the quantity of extraneous liquid in
the sewers was so greatly in excess of the ordinary sewage flow
that, taken as a percentage of the total daily flow, the hourly
variation was almost imperceptible.

[Illustration: Fig 12 Hourly Variation in Flow of Sewage.]

Provision must be made in the scheme for the leakage from the
water fittings, and for the subsoil water, which will
inevitably find its way into the sewers. The quantity will vary
very considerably, and is difficult of estimation. If the water
is cheap, and the supply plentiful, the water authority may not
seriously attempt to curtail the leakage; but in other cases it
will be reduced to a minimum by frequent house to house
inspection; some authorities going so far as to gratuitously
fix new washers to taps when they are required. Theoretically,
there should be no infiltration of subsoil water, as in nearly
all modern sewerage schemes the pipes are tested and proved to be
watertight before the trenches are filled in; but in practice this
happy state is not obtainable. The pipes may not all be bedded as
solidly as they should be, and when the pressure of the earth comes
upon them settlement takes place and the joints are broken. Joints
may also be broken by careless filling of trenches, or by men
walking upon the pipes before they are sufficiently covered.
Some engineers specify that all sewers shall be tested and
proved to be absolutely water-tight before they are "passed"
and covered in, but make a proviso that if, after the
completion of the works, the leakage into any section exceeds
1/2 cubic foot per minute per mile of sewer, that length shall
be taken up and relaid. Even if the greatest vigilance is
exercised to obtain water-tight sewers, the numerous house
connections are each potential sources of leakage, and when the
scheme is complete there may be a large quantity of
infiltration water to be dealt with. Where there are existing
systems of old sewers the quantity of infiltration water can be
ascertained by gauging the night flow; and if it is proved to
be excessive, a careful examination of the course of the sewers
should be made with a view to locating the places where the
greater part of the leakage occurs, and then to take such steps
as may be practicable to reduce the quantity.




CHAPTER VI.

GAUGING FLOW IN SEWERS.


A method frequently adopted to gauge the flow of the sewage is
to fix a weir board with a single rectangular notch across the
sewer in a convenient manhole, which will pond up the sewage;
and then to ascertain the depth of water passing over the notch
by measurements from the surface of the water to a peg fixed
level with the bottom of the notch and at a distance of two or
three feet away on the upstream side. The extreme variation in
the flow of the sewage is so great, however, that if the notch
is of a convenient width to take the maximum flow, the hourly
variation at the time of minimum flow will affect the depth of
the sewage on the notch to such a small extent that difficulty
may be experienced in taking the readings with sufficient
accuracy to show such variations in the flow, and there will be
great probability of incorrect results being obtained by reason
of solid sewage matter lodging on the notch. When the depth on
a l2 in notch is about 6 in, a variation of only 1-16th inch in
the vertical measurement will represent a difference in the
rate of the flow of approximately 405 gallons per hour, or
about 9,700 gallons per day. When the flow is about lin deep
the same variation of 1-16th in will represent about 162
gallons per hour, or 3,900 gallons per day. Greater accuracy
will be obtained if a properly-formed gauging pond is
constructed independently of the manhole and a double
rectangular notch, similar to Fig. 13, or a triangular or V-
shaped notch, as shown in Fig. 14, used in lieu of the simpler
form.

In calculating the discharge of weirs there are several formulæ
to choose from, all of which will give different results,
though comparative accuracy has been claimed for each. Taking
first a single rectangular notch and reducing the formulae to
the common form:

                                          ____
Discharge per foot in width of weir = C \/ H^3

where H = depth from the surface of still water above the weir to the level of
the bottom of the notch, the value of C will be as set out in the following
table:--

  TABLE No. 5.

  RECTANGULAR NOTCHES.
                                                  _____
       Discharge per foot in width of notch = C \/ H^3
  ------------------------------------------------------------------
                                Values of C.
  --------------------------------------+---------------------------
   H Measured in |        Feet.         |        Inches.
  ---------------+-----------+----------+-----------+---------------
                 | Gallons   |  C. ft  | Gallons   |  C. ft
  Discharge in   | per hour. | per min | per hour. | per min
  ---------------+-----------+----------+-----------+---------------
     Authority.  |           |          |           |
  Box            |   79,895  |   213.6  |    1,922  |      5.13
  Cotterill      |   74,296  |   198.6  |    1,787  |      4.78
  Francis        |   74,820  |   200.0  |    1,800  |      4.81
  Mo'esworth     |   80,057  |   214.0  |    1,926  |      5.15
  Santo Crimp    |   72,949  |   195.0  |    1,755  |      4.69
  ---------------+-----------+----------+-----------+---------------

In the foregoing table Francis' short formula is used, which
does not take into account the end contractions and therefore
gives a slightly higher result than would otherwise be the
case, and in Cotterill's formula the notch is taken as being
half the width of the weir, or of the stream above the weir. If
a cubic foot is taken as being equal to 6-1/4 gallons instead
of 6.235 gallons, then, cubic feet per minute multiplied by
9,000 equals gallons per day. This table can be applied to
ascertain the flow through the notch shown in Fig. 13 in the
following way. Suppose it is required to find the discharge in
cubic feet per minute when the depth of water measured in the
middle of the notch is 4 in Using Santo Crimp's formula the
result will be

C\/H^3 = 4.69 \/4^3 = 4.69 x 8 = 37.52

cubic feet per foot in width of weir, but as the weir is only 6
in wide, we must divide this figure by 2, then

37.52/2 = 18.76 cubic feet, which is the discharge per minute.



  +------+                    +------+
  |      |       FIG. 13      |      |
  |      |                    |      |
  |      |                    |      |
  |      +------+      +------+      |
  |             |      |             |
  |             |      |             |
  |             |      |             |
  |             +------+             |
  |                                  |
  |                                  |
  |                                  |
  |                                  |
  +----------------------------------+

Fig. 13.-ELEVATION OF DOUBLE RECTANGULAR NOTCHED GAUGING WEIR.


  +------+                    +------+
  |       \      FIG. 13     /       |
  |        \                /        |
  |         \              /         |
  |          \            /          |
  |           \          /           |
  |            \        /            |
  |             \      /             |
  |              \    /              |
  |               \  /               |
  |                \/                |
  |                                  |
  |                                  |
  |                                  |
  |                                  |
  |                                  |
  +----------------------------------+

FIG. 14.-ELEVATION OF TRIANGULAR NOTCHED GAUGING WEIR.

FIG. 15.-LONGITUDINAL SECTION, SHOWING WEIR, GAUGE-PEG, AND HOOK-GAUGE


If it is required to find the discharge in similar terms with a
depth of water of 20 in, two sets of calculations are required.
First 20 in depth on the notch 6 in wide, and then 4 in depth
on the notch, 28 in minus 6 in, or 1 ft wide.

       ____            _____
(1) C\/ H^3 = 4.69/2 \/ 10^3 = 2.345 x 31.62     =  74.15
       ____                ____
(2) C\/ H^3 = 1.0 x 4.69 \/ 4^3 = 1.0 x 4.69 x 8 =  37.52

Total in c. ft per min                          = 111.67

The actual discharge would be slightly in excess of this.

In addition to the circumstances already enumerated which
affect the accuracy of gaugings taken by means of a weir fixed
in a sewer there is also the fact that the sewage approaches
the weir with a velocity which varies considerably from time to
time. In order to make allowance for this, the head calculated
to produce the velocity must be added to the actual head. This
can be embodied in the formula, as, for example, Santo Crimp's
formula for discharge in cubic feet per minute, with H measured
in feet, is written

       __________________
  195\/(11^3 + .035V - H^2

instead of the usual form of
       ____
  195\/ H^3, which is used

when there is no velocity to take into account. The V
represents the velocity in feet per second.

Triangular or V notches are usually formed so that the angle
between the two sides is 90°, when the breadth at any point
will always be twice the vertical height measured at the
centre. The discharge in this case varies as the square root of
the fifth power of the height instead of the third power as
with the rectangular notch. The reason for the alteration of
the power is that _approximately_ the discharge over a notch
with any given head varies as the cross-sectional area of the
body of water passing over it. The area of the 90° notch is
half that of a circumscribing rectangular notch, so that the
discharge of a V notch is approximately equal to that of a
rectangular notch having a width equal to half the width of the
V notch at water level, and as the total width is equal to
double the depth of water passing over the notch the half width
is equal to the full depth and the discharge is equal to that
of a rectangular notch having a width equal to the depth of
water flowing over the V notch from time to time, both being
measured in the same unit, therefore
      ____                   ____                  ____
  C \/ H^3 becomes C x H x \/ H^3 which equals C \/ H^5.

The constant C will, however, vary from that for the
rectangular notch to give an accurate result.


  TABLE No. 6.

  TRIANGULAR OR V NOTCHES.
                    ____
  Discharge = C x \/ H^5.

  Values of C.

  --------------+-----------------------+------------------------
  H Measured in |         Feet.         |        Inches.
  --------------+----------+------------+-----------+------------
  Discharge in  | Gallons  | C. ft per  | Gallons   | C. ft per
                | per hour |    min     | per hour. |    min
  --------------+----------+------------+-----------+------------
  Alexander     |  59,856  |    160     |   120.0   |    0.321
  Cotterill     |  57,013  |    152.4   |   114.3   |    0.306
  Molesworth    |  59,201  |    158.2   |   118.7   |    0.317
  Thomson       |  57,166  |    152.8   |   114.6   |    0.306
  --------------+----------+------------+-----------+------------


Cotterill's formula for the discharge in cubic feet per minute
is
               _______
  16 x C x B \/ 2g H^3

when B = breadth of notch in feet and H = height of water in
feet and can be applied to any proportion of notch. When B =
2H, that is, a 90° notch, C = .595 and the formula becomes
          ____
  152.4 \/ H^5,

and when B = 4H, that is, a notch containing an angle of 126°
51' 36", C = .62 and the formula is then written
        ____
  318 \/ H^5.


The measurements of the depth of the water above the notch
should be taken by a hook-gauge, as when a rule or gauge-slate
is used the velocity of the water causes the latter to rise as
it comes in contact with the edge of the measuring instrument
and an accurate reading is not easily obtainable, and, further,
capillary attraction causes the water to rise up the rule above
the actual surface, and thus to show a still greater depth.
When using a hook-gauge the top of the weir, as well as the
notch, should be fixed level and a peg or stake fixed as far
back as possible on the upstream side of the weir, so that the
top of the peg is level with the top of the weir, instead of
with the notch, as is the case when a rule or gauge-slate is
used. The hook-gauge consists of a square rod of, say, lin
side, with a metal hook at the bottom, as shown in Fig. 15, and
is so proportioned that the distance from the top of the hook
to the top of the rod is equal to the difference in level of
the top of the weir and the sill of the notch. In using it the
rod of the hook-gauge is held against the side of the gauge-peg
and lowered into the water until the point of the hook is
submerged. The gauge is then gently raised until the point of
the hook breaks the surface of the water, when the distance
from the top of the gauge-peg to the top of the rod of the
hook-gauge will correspond with the depth of the water flowing
over the weir.




CHAPTER VII.

RAINFALL.


The next consideration is the amount of rain-water for which
provision should be made. This depends on two factors: first,
the amount of rain which may be expected to fall; and,
secondly, the proportion of this rainfall which will reach the
sewers. The maximum rate at which the rain-water will reach the
outfall sewer will determine the size of the sewer and capacity
of the pumping plant, if any, while if the sewage is to be
stored during certain periods of the tide the capacity of the
reservoir will depend upon the total quantity of rain-water
entering it during such periods, irrespective of the rate of
flow.

Some very complete and valuable investigations of the flow of
rain-water in the Birmingham sewers were carried out between
1900 and 1904 by Mr. D. E. Lloyd-Davies, M.Inst.C. E., the
results of which are published in Vol. CLXIV., Min Proc.
Inst.C.E. He showed that the quantity reaching the sewer at any
point was proportional to the time of concentration at that
point and the percentage of impermeable area in the district.
The time of concentration was arrived at by calculating the
time which the rain-water would take to flow through the
longest line of sewers from the extreme boundaries of the
district to the point of observation, assuming the sewers to be
flowing half full; and adding to the time so obtained the
period required for the rain to get into the sewers, which
varied from one minute where the roofs were connected directly
with the sewers to three minutes where the rain had first to
flow along the road gutters. With an average velocity of 3 ft
per second the time of concentration will be thirty minutes for
each mile of sewer. The total volume of rain-water passing into
the sewers was found to bear the same relation to the total
volume of rain falling as the maximum flow in the sewers bore
to the maximum intensity of rainfall during a period equal to
the time of concentration. He stated further that while the
flow in the sewers was proportional to the aggregate rainfall
during the time of concentration, it was also directly
proportional to the impermeable area. Putting this into
figures, we see that in a district where the whole area is
impermeable, if a point is taken on the main sewers which is so
placed that rain falling at the head of the branch sewer
furthest removed takes ten minutes to reach it, then the
maximum flow of storm water past that point will be
approximately equal to the total quantity of rain falling over
the whole drainage area during a period of ten minutes, and
further, that the total quantity of rainfall reaching the
sewers will approximately equal the total quantity falling. If,
however, the impermeable area is 25 per cent. of the whole,
then the maximum flow of storm water will be 25 per cent. of
the rain falling during the time of concentration, viz., ten
minutes, and the total quantity of storm water will be 25 per
cent. of the total rainfall.

If the quantity of storm water is gauged throughout the year it
will probably be found that, on the average, only from 70 per
cent. to 80 per cent. of the rain falling on the impermeable
areas will reach the sewers instead of 100 per cent., as
suggested by Mr. Lloyd-Davies, the difference being accounted
for by the rain which is required to wet the surfaces before
any flow off can take place, in addition to the rain-water
collected in tanks for domestic use, rain required to fill up
gullies the water level of which has been lowered by
evaporation, and rain-water absorbed in the joints of the
paving.

The intensity of the rainfall decreases as the period over
which the rainfall is taken is increased. For instance, a
rainfall of lin may occur in a period of twenty minutes, being
at the rate of 3 in per hour, but if a period of one hour is
taken the fall during such lengthened time will be considerably
less than 3 in In towns where automatic rain gauges are
installed and records kept, the required data can be
abstracted, but in other cases it is necessary to estimate the
quantity of rain which may have to be dealt with.

It is impracticable to provide sewers to deal with the maximum
quantity of rain which may possibly fall either in the form of
waterspouts or abnormally heavy torrential rains, and the
amount of risk which it is desirable to run must be settled
after consideration of the details of each particular case. The
following table, based principally upon observations taken at
the Birmingham Observatory, shows the approximate rainfall
which may be taken according to the time of concentration.


TABLE No. 7.

INTENSITY OF RAINFALL DURING LIMITED PERIODS.
                             Equivalent rate in inches per hour
                             of aggregate rainfall during
Time of Concentration,       period of concentration
                             A     B     C     D     E
 5 minutes  ...............  1.75  2.00  3.00  --    --
10   "      ...............  1.25  1.50  2.00  --    --
15   "      ...............  1.05  1.25  1.50  --    --
20   "      ...............  0.95  1.05  1.30  1.20  3.00
25   "      ...............  0.85  0.95  1.15  --    --
30   "      ...............  0.80  0.90  1.05  1.00  2.50
35   "      ...............  0.75  0.85  0.95  --    --
40   "      ...............  0.70  0.80  0.90  --    --
45   "      ...............  0.65  0.75  0.85  --    --
 1 hour  ..................  0.50  0.60  0.70  0.75  1.80
 1-1/2 " ..................  0.40  0.50  0.60  --    1.40
 2   "   ..................  0.30  0.40  0.50  0.50  1.10


The figures in column A will not probably be exceeded more than
once in each year, those in column B will not probably be
exceeded more than once in three years, while those in column C
will rarely be exceeded at all. Columns D and E refer to the
records tabulated by the Meteorological Office, the rainfall
given in column D being described in their publication as
"falls too numerous to require insertion," and those in column
E as "extreme falls rarely exceeded." It must, however, be
borne in mind that the Meteorological Office figures relate to
records derived from all parts of the country, and although the
falls mentioned may occur at several towns in any one year it
may be many years before the same towns are again visited by
storms of equal magnitude.

While it is convenient to consider the quantity of rainfall for
which provision is to be made in terms of the rate of fall in
inches per hour, it will be useful for the practical
application of the figures to know the actual rate of flow of
the storm water in the sewers at the point of concentration in
cubic feet per minute per acre. This information is given in
the following Table No. 8, which is prepared from the figures
given in Table No. 7, and is applicable in the same manner.



TABLE No. 8.

MAXIMUM FLOWS OF STORM WATER.


--------------------------+----------------------------------
                          |  Maximum storm water flow in
                          |   cubic feet per min per acre
                          |      of impervious area.
  Time of Concentration.  +------+------+------+------+------
                          |  A   |  B   |  C   |  D   |  E
--------------------------+------+------+------+------+------
   5 minutes              |  106 |  121 |  181 |   -- |   --
  10   "                  |   75 |   91 |  121 |   -- |   --
  15   "                  |   64 |   75 |   91 |   -- |   --
  20   "                  |   57 |   64 |   79 |   73 |  181
  25   "                  |   51 |   57 |   70 |   -- |   --
  30   "                  |   48 |   54 |   64 |   61 |  151
  35   "                  |   45 |   51 |   57 |   -- |   --
  40   "                  |   42 |   48 |   54 |   -- |   --
  45   "                  |   39 |   45 |   51 |   -- |   --
  1    hour               |   30 |   36 |   42 |   45 |  109
  1-1/2  "                |   24 |   30 |   36 |   -- |   85
  2      "                |   18 |   24 |   30 |   30 |   67
--------------------------+------+------+------+------+-------
        l inch of rain = 3,630 cub. feet per acre.



The amount of rainfall for which storage has to be provided is
a difficult matter to determine; it depends on the frequency
and efficiency of the overflows and the length of time during
which the storm water has to be held up for tidal reasons. It
is found that on the average the whole of the rain on a rainy
day falls within a period of 2-1/2 hours; therefore, ignoring
the relief which may be afforded by overflows, if the sewers
are tide-locked for a period of 2-1/2 hours or over it would
appear to be necessary to provide storage for the rainfall of a
whole day; but in this case again it is permissible to run a
certain amount of risk, varying with the length of time the
sewers are tide-locked, because, first of all, it only rains on
the average on about 160 days in the year, and, secondly, when
it does rain, it may not be at the time when the sewers are
tide-locked, although it is frequently found that the heaviest
storms occur just at the most inconvenient time, namely, about
high water. Table No. 9 shows the frequency of heavy rain
recorded during a period of ten years at the Birmingham
Observatory, which, being in the centre of England, may be
taken as an approximate average of the country.

TABLE No. 9.

FREQUENCY OF HEAVY RAIN
-------------------------------------------------------

Total Daily Rainfall.    Average Frequency of Rainfall

-------------------------------------------------------

0.4 inches and over         155 times each year
0.5        "                 93       "
0.6        "                 68       "
0.7        "                 50       "
0.8        "                 33       "
0.9        "                 22       "
1.0        "                 17       "
1.1        "                 Once each year
1.2        "                 Once in 17 months
1.25       "                     "    2 years
1.3        "                     "    2-1/2
1.4        "                     "    3-1/3
1.5        "                     "    5 years
1.6        "                     "    5 years
1.7        "                     "    5 years
1.8        "                     "   10 years
1.9        "                     "   10 years
2.0        "                     "   10 years

--------------------------------------------------

It will be interesting and useful to consider the records for
the year 1903, which was one of the wettest years on record,
and to compare those taken in Birmingham with the mean of those
given in "Symons' Rainfall," taken at thirty-seven different
stations distributed over the rest of the country.


TABLE No. 10.
RAINFALL FOR 1903.

                                                    Mean of 37
                                                    stations in
                                       Birmingham   England and
                                                    Wales.
Daily Rainfall of 2 in and over ......   None        1 day
Daily Rainfall of 1 in and over ......   3 days      6 days
Daily Rainfall of 1/2 in and over ....  17 days     25 days
Number of rainy days.................. 177 days    211 days
Total rainfall  ......................  33.86 in   44.89 in
Amount per rainy day  ................   0.19 in    0.21 in


The year 1903 was an exceptional one, but the difference
existing between the figures in the above table and the average
figures in Table 9 are very marked, and serve to emphasise the
necessity for close investigation in each individual case. It
must be further remembered that the wettest year is not
necessarily the year of the heaviest rainfalls, and it is the
heavy rainfalls only which affect the design of sewerage works.




CHAPTER VIII.

STORM WATER IN SEWERS.


If the whole area of the district is not impermeable the
percentage which is so must be carefully estimated, and will
naturally vary in each case. The means of arriving at an
estimate will also probably vary considerably according to
circumstances, but the following figures, which relate to
investigations recently made by the writer, may be of interest.
In the town, which has a population of 10,000 and an area of
2,037 acres, the total length of roads constructed was 74,550
lineal feet, and their average width was 36 ft, including two
footpaths. The average density of the population was 4.9 people
per acre. Houses were erected adjoining a length of 43,784
lineal feet of roads, leaving 30,766 lineal feet, which for
distinction may be called "undeveloped"--that is, the land
adjoining them was not built over. Dividing the length of road
occupied by houses by the total number of the inhabitants of
the town, the average length of road per head was 4.37 ft, and
assuming five people per house and one house on each side of
the road we get ten people per two houses opposite each other.
Then 10 x 4.37 = 43.7 lineal feet of road frontage to each pair
of opposite houses. After a very careful inspection of the
whole town, the average area of the impermeable surfaces
appertaining to each house was estimated at 675 sq. ft, of
which 300 sq. ft was apportioned to the front roof and garden
paths and 375 sq. ft to the back roof and paved yards. Dividing
these figures by 43.71 in ft of road frontage per house, we
find that the effective width of the impermeable roadway is
increased by 6 ft 10 in for the front portions of each house,
and by a width of 8 ft 7 in, for the back portions, making a
total width of 36 ft + 2(6 ft 10 in) + 2(8 ft 7 in) = 66 ft 10
in, say 67 ft On this basis the impermeable area in the town
therefore equals: 43,7841 in ft x 67 ft =2,933,528; and 30,766
lin ft x 36 ft = 1,107,576.

Total, 4,041,104 sq. ft, or 92.77 acres. As the population is
10,000 the impermeable area equals 404, say, 400 sq. ft per
head, or ~ (92.77 x 100) / 2037 = 4.5 per cent, of the whole
area of the town.

It must be remembered that when rain continues for long
periods, ground which in the ordinary way would generally be
considered permeable becomes soaked and eventually becomes more
or less impermeable. Mr. D. E. Lloyd-Davies, M.Inst.C.E., gives
two very interesting diagrams in the paper previously referred
to, which show the average percentage of effective impermeable
area according to the population per acre. This information,
which is applicable more to large towns, has been embodied in
Fig. 16, from which it will be seen that, for storms of short
duration, the proportion of impervious areas equals 5 per cent.
with a population of 4.9 per acre, which is a very close
approximation to the 4.5 per cent. obtained in the example just
described.

Where the houses are scattered at long intervals along a road
the better way to arrive at an estimate of the quantity of
storm water which may be expected is to ascertain the average
impervious area of, or appertaining to, each house, and divide
it by five, so as to get the area per head. Then the flow off
from any section of road is directly obtained from the sum of
the impervious area due to the length of the road, and that due
to the population distributed along it.

[Illustration: FIG. 16.--VARIATION IN AVERAGE PERCENTAGE OF
EFFECTIVE IMPERMEABLE AREA ACCORDING TO DENSITY OF POPULATION.]

In addition to being undesirable from a sanitary point of view,
it is rarely economical to construct special storm water
drains, but in all cases where they exist, allowance must be
made for any rain that may be intercepted by them. Short branch
sewers constructed for the conveyance of foul water alone are
usually 9in or 12 in in diameter, not because those sizes are
necessary to convey the quantity of liquid which may be
expected, but because it is frequently undesirable to provide
smaller public sewers, and there is generally sufficient room
for the storm water without increasing the size of the sewer.
If this storm water were conveyed in separate sewers the cost
would be double, as two sewers would be required in the place
of one. In the main sewers the difference is not so great, but
generally one large sewer will be more economical than two
smaller ones. Where duplicate sewers are provided and arranged,
so that the storm water sewer takes the rain-water from the
roads, front roofs and gardens of the houses, and the foul
water sewer takes the rain-water from the back roofs and paved
yards,

it was found in the case previously worked out in detail that
in built-up roads a width of 36 ft + 2 (8 ft 7 in) = 53 ft 2
in, or, say, 160 sq. ft per lineal yard of road would drain to
the storm water sewer, and a width of 2 (6 ft 10 in) = 13 ft 8
in, or, say, 41 sq. ft per lineal yard of road to the foul
water sewer. This shows that even if the whole of the rain
which falls on the impervious areas flows off, only just under
80 per cent. of it would be intercepted by the special storm water
sewers. Taking an average annual rainfall of 30 in, of which 75 per
cent. flows off, the quantity reaching the storm water sewer in the
course of a year from each lineal

                       30          75
yard of road would be --- x 160 x --- = 300 cubic
                       12         100
feet = 1,875 gallons.

[Illustration: FIG. 17.--SECTION OF "LEAP WEIR" OVERFLOW]

The cost of constructing a separate surface water system will
vary, but may be taken at an average of, approximately, l5s.
0d. per lineal yard of road. To repay this amount in thirty years
at 4 per cent, would require a sum of 10.42d., say 10-1/2d. per annum;
that is to say, the cost of taking the surface water into special

           10-1/2 d. x 1000
sewers is  ---------------- = 5.6, say 6d. per 1,000
                 1875
gallons.

If the sewage has to be pumped, the extra cost of pumping by
reason of the increased quantity of surface water can be looked
at from two different points of view:--

1. The net cost of the gas or other fuel or electric current
consumed in lifting the water.

2. The cost of the fuel consumed plus wages, stores, etc., and
a proportion of the sum required to repay the capital cost of
the pumping station and machinery.

The extra cost of the sewers to carry the additional quantity
of storm water might also be taken into account by working out
and preparing estimates for the alternative schemes.

The actual cost of the fuel may be taken at approximately 1/4
d. per 1,000 gallons. The annual works and capital charges,
exclusive of fuel, should be divided by the normal quantity of
sewage pumped per annum, rather than by the maximum quantity
which the pumps would lift if they were able to run
continuously during the whole time. For a town of about 10,000
inhabitants these charges may be taken at 1-1/4 d. per 1,000
gallons, which makes the total cost of pumping, inclusive of
capital charges, 1-1/2 d. per 1,000 gallons. Even if the extra
cost of enlarging the sewers is added to this sum it will still
be considerably below the sum of 6 d., which represents the
cost of providing a separate system for the surface water.

Unless it is permissible for the sewage to have a free outlet
to the sea at all states of the tide, the provision of
effective storm overflows is a matter of supreme importance.
Not only is it necessary for them to be constructed in well-
considered positions, but they must be effective in action. A
weir constructed along one side of a manhole and parallel to
the sewer is rarely efficient, as in times of storm the liquid
in the sewer travels at a considerable velocity, and the
greater portion of it, which should be diverted, rushes past
the weir and continues to flow in the sewer; and if, as is
frequently the case, it is desirable that the overflowing
liquid should be screened, and vertical bars are fixed on the
weir for the purpose, they block the outlet and render the
overflow practically useless.

Leap weir overflows are theoretically most suitable for
separating the excess flow during times of storm, but in
practice they rarely prove satisfactory. This is not the fault
of the system, but is, in the majority of the cases, if not
all, due to defective designing. The general arrangement of a
leap weir overflow is shown in Fig. 17. In normal circumstances
the sewage flowing along the pipe A falls down the ramp, and
thence along the sewer B; when the flow is increased during
storms the sewage from A shoots out from the end of the pipe
into the trough C, and thence along the storm-water sewer D. In
order that it should be effective the first step is to
ascertain accurately the gradient of the sewer above the
proposed overflow, then, the size being known, it is easy to
calculate the velocity of flow for the varying depths of sewage
corresponding with minimum flow, average dry weather flow,
maximum dry weather flow, and six times the dry weather flow.
The natural curve which the sewage would follow in its downward
path as it flowed out from the end of the sewer can then be
drawn out for the various depths, taking into account the fact
that the velocity at the invert and sides of the sewer is less
than the average velocity of flow. The ramp should be built in
accordance with the calculated curves so as to avoid splashing
as far as possible, and the level of the trough C fixed so that
when it is placed sufficiently far from A to allow the dry
weather flow to pass down the ramp it will at the same time
catch the storm water when the required dilution has taken
place. Due regard must be had to the altered circumstances
which will arise when the growth of population occurs, for
which provision is made in the scheme, so that the overflow
will remain efficient. The trough C is movable, so that the
width of the leap weir may be adjusted from time to time as
required. The overflow should be frequently inspected, and the
accumulated rubbish removed from the trough, because sticks and
similar matters brought down by the sewer will probably leap
the weir instead of flowing down the ramp with the sewage. It
is undesirable to fix a screen in conjunction with this
overflow, but if screening is essential the operation should be
carried out in a special manhole built lower down the course of
the storm-water sewer. Considerable wear takes place on the
ramp, which should, therefore, be constructed of blue
Staffordshire or other hard bricks. The ramp should terminate
in a stone block to resist the impact of the falling water, and
the stones which may be brought with it, which would crack
stoneware pipes if such were used.

In cases where it is not convenient to arrange a sudden drop in
the invert of the sewer as is required for a leap weir
overflow, the excess flow of storm-water may be diverted by an
arrangement similar to that shown in Fig. 18. [Footnote: PLATE
IV] In this case calculations must be made to ascertain the
depth at which the sewage will flow in the pipes at the time it
is diluted to the required extent; this gives the level of the
lip of the diverting plate. The ordinary sewage flow will pass
steadily along the invert of the sewer under the plate until it
rises up to that height, when the opening becomes a submerged
orifice, and its discharging capacity becomes less than when
the sewage was flowing freely. This restricts the flow of the
sewage, and causes it to head up on the upper side of the
overflow in an endeavour to force through the orifice the same
quantity as is flowing in the sewer, but as it rises the
velocity carries the upper layer of the water forward up the
diverting plate and thence into the storm overflow drain A deep
channel is desirable, so as to govern the direction of flow at
the time the overflow is in action. The diverting trough is
movable, and its height above the invert can be increased
easily, as may be necessary from time to time. With this
arrangement the storm-water can easily be screened before it is
allowed to pass out by fixing an inclined screen in the
position shown in Fig. 18. [Footnote: PLATE IV] It is loose, as
is the trough, and both can be lifted out when it is desired to
have access to the invert of the sewer. The screen is self-
cleansing, as any floating matter which may be washed against
it does not stop on it and reduce its discharging capacity, but
is gradually drawn down by the flow of the sewage towards the
diverting plate under which it will be carried. The heavier
matter in the sewage which flows along the invert will pass
under the plate and be carried through to the outfall works,
instead of escaping by the overflow, and perhaps creating a
nuisance at that point.




CHAPTER IX.

WIND AND WINDMILLS.


In small sewerage schemes where pumping is necessary the amount
expended in the wages of an attendant who must give his whole
attention to the pumping station is so much in excess of the
cost of power and the sum required for the repayment of the
loan for the plant and buildings that it is desirable for the
economical working of the scheme to curtail the wages bill as
far as possible. If oil or gas engines are employed the man
cannot be absent for many minutes together while the machinery
is running, and when it is not running, as for instance during
the night, he must be prepared to start the pumps at very short
notice, should a heavy rain storm increase the flow in the
sewers to such an extent that the pump well or storage tank
becomes filled up. It is a simple matter to arrange floats
whereby the pump may be connected to or disconnected from a
running engine by means of a friction clutch, so that when the
level of the sewage in the pump well reaches the highest point
desired the pump may be started, and when it is lowered to a
predetermined low water level the pump will stop; but it is
impracticable to control the engine in the same way, so that
although the floats are a useful accessory to the plant during
the temporary absence of the man in charge they will not
obviate his more or less constant attendance. An electric motor
may be controlled by a float, but in many cases trouble is
experienced with the switch gear, probably caused by its
exposure to the damp air. In all cases an alarm float should be
fixed, which would rise as the depth of the sewage in the pump
well increased, until the top water level was reached, when the
float would make an electrical contact and start a continuous
ringing warning bell, which could be placed either at the pumping
station or at the man's residence. On hearing the bell the man would
know the pump well was full, and that he must immediately repair to
the pumping-station and start the pumps, otherwise the building
would be flooded. If compressed air is available a hooter could be
fixed, which would be heard for a considerable distance from the station.

[Illustration: PLATE IV.

"DIVERTING PLATE" OVERFLOW.

To face page 66.]

It is apparent, therefore, that a pumping machine is wanted
which will work continuously without attention, and will not
waste money when there is nothing to pump. There are two
sources of power in nature which might be harnessed to give
this result--water and wind. The use of water on such a small
scale is rarely economically practicable, as even if the water
is available in the vicinity of the pumping-station,
considerable work has generally to be executed at the point of
supply, not only to store the water in sufficient bulk at such
a level that it can be usefully employed, but also to lead it
to the power-house, and then to provide for its escape after it
has done its work. The power-house, with its turbines and other
machinery, involves a comparatively large outlay, but if the
pump can be directly driven from the turbines, so that the cost
of attendance is reduced to a minimum, the system should
certainly receive consideration.

Although the wind is always available in every district, it is
more frequent and powerful on the coast than inland. The
velocity of the wind is ever varying within wide limits, and
although the records usually give the average hourly velocity,
it is not constant even for one minute. Windmills of the modern
type, consisting of a wheel composed of a number of short sails
fixed to a steel framework upon a braced steel tower, have been
used for many years for driving machinery on farms, and less
frequently for pumping water for domestic use. In a very few
cases it has been utilised for pumping sewage, but there is no
reason why, under proper conditions, it should not be employed
to a greater extent. The reliability of the wind for pumping
purposes may be gauged from the figures in the following table,
No. 11, which were observed in Birmingham, and comprise a
period of ten years; they are arranged in order corresponding
with the magnitude of the annual rainfall:--

TABLE No. 11.

MEAN HOURLY VELOCITY OF WIND

Reference | Rainfall |Number of days in year during which the mean  |
Number    | for      |hourly velocity of the wind was below         |
          | year     | 6 m.p.h. | 10 m.p.h. | 15 m.p.h. | 20 m.p.h. |
----------+----------+----------+-----------+-----------+-----------+
 1...       33·86         16          88         220        314
 2...       29·12         15         120         260        334
 3...       28·86         39         133         263        336
 4...       26·56         36         126         247        323
 5...       26·51         34         149         258        330
 6...       26·02         34         132         262        333
 7...       25·16         33         151         276        332
 8...       22·67         46         155         272        329
 9...       22·30         26         130         253        337
10...       21·94         37         133         276        330
----------+----------+----------+-----------+-----------+-----------+
            Average       31·4       131·7       250·7      330·8

It may be of interest to examine the monthly figures for the
two years included in the foregoing table, which had the least
and the most wind respectively, such figures being set out in
the following table:

TABLE No. 12

MONTHLY ANALYSIS OF WIND

Number of days in each month during which the mean velocity of
the wind was respectively below the value mentioned hereunder.


Month |  Year of least wind (No. 8) | Year of most wind (No. *8*) |
      |   5      10     15     20   |   5      10     15     20   |
      | m.p.h. m.p.h. m.p.h. m.p.h. | m.p.h. m.p.h. m.p.h. m.p.h. |
------+-------+-----+-------+-------+-------+------+------+-------+
Jan.      5      11     23     27       3       6     15     23
Feb.      5      19     23     28       0       2      8     16
Mar.      5      10     20     23       0       1     11     18
April     6      16     23     28       1       7     16     26
May       1      14     24     30       3      11     24     31
June      1      12     22     26       1      10     21     27
July      8      18     29     31       1      12     25     29
Aug.      2       9     23     30       1       9     18     30
Sept.     1      13     25     30       1      12     24     28
Oct.      5      17     21     26       0       4     16     29
Nov.      6      11     20     26       3       7     19     28
Dec.      1       5     19     24       2       7     23     29
------+-------+-----+-------+-------+-------+------+------+-------+
Total    46     155    272    329      16      88    220    314


During the year of least wind there were only eight separate
occasions upon which the average hourly velocity of the wind
was less than six miles per hour for two consecutive days, and
on two occasions only was it less than six miles per hour on
three consecutive days. It must be remembered, however, that
this does not by any means imply that during such days the wind
did not rise above six miles per hour, and the probability is
that a mill which could be actuated by a six-mile wind would
have been at work during part of the time. It will further be
observed that the greatest differences between these two years
occur in the figures relating to the light winds. The number of
days upon which the mean hourly velocity of the wind exceeds
twenty miles per hour remains fairly constant year after year.

As the greatest difficulty in connection with pumping sewage is
the influx of storm water in times of rain, it will be useful
to notice the rainfall at those times when the wind is at a
minimum. From the following figures (Table No. 13) it will be
seen that, generally speaking, when there is very little wind
there is very little rain Taking the ten years enumerated in
Table No. 11, we find that out of the 314 days on which the
wind averaged less than six miles per hour only forty-eight of
them were wet, and then the rainfall only averaged .l3 in on
those days.


TABLE No. 13.

WIND LESS THAN 6 M.P.H.

-----------+-------------+------------+--------+----------------------------------
 Ref. No.  |  Total No.  |  Days on   |        |   Rainfall on each
from Table | of days in  | which no   | Rainy  |     rainy day in
 No. 11.   |  each year. | rain fell. | days.  |       inches.
-----------+-------------+------------+--------+----------------------------------
     1     |     16      |     14     |    2   | .63 and .245
     2     |     15      |     13     |    2   | .02 and .02
     3     |     39      |     34     |    5   | .025, .01, .26, .02 and .03
     4     |     36      |     29     |    7   | / .02, .08, .135, .10, .345, .18
           |             |            |        | \ and .02
     5     |     34      |     28     |    6   | .10, .43, .01, .07, .175 and .07
     6     |     32      |     27     |    5   | .10, .11, .085, .04 and .135
     7     |     33      |     21     |    2   | .415 and .70
     8     |     46      |     40     |    6   | .07, .035, .02, .06, .13 and .02
     9     |     26      |     20     |    6   | .145, .20, .33, .125, .015 & .075
    10     |     37      |     30     |    7   | / .03, .23, .165, .02, .095
           |             |            |        | \ .045 and .02
-----------+-------------+------------+--------+----------------------------------
Total      |    314      |    266     |   48   | Average rainfall on each of
           |             |            |        |      the 48 days = .13 in


The greater the height of the tower which carries the mill the
greater will be the amount of effective wind obtained to drive
the mill, but at the same time there are practical
considerations which limit the height. In America many towers
are as much as 100 ft high, but ordinary workmen do not
voluntarily climb to such a height, with the result that the
mill is not properly oiled. About 40 ft is the usual height in
this country, and 60 ft should be used as a maximum.

Mr. George Phelps, in a paper read by him in 1906 before the
Association of Water Engineers, stated that it was safe to
assume that on an average a fifteen miles per hour wind was
available for eight hours per day, and from this he gave the
following figures as representing the approximate average duty
with, a lift of l00 ft, including friction:--

TABLE NO. 14
DUTY OF WINTDMILU

Diameter of Wheel.

10

12

14

16

18

20

25

30

35

40

The following table gives the result of tests carried out by
the United States Department of Agriculture at Cheyenne, Wyo.,
with a l4 ft diameter windmill under differing wind
velocities:--

TABLE No. 15.

POWER or l4-rx WINDMILL IN VARYING WINDS.

Velocity of Wind (miles per hour).

0--5 6-10 11-15 16-20 21-25 26-30 31-35


It will be apparent from the foregoing figures that practically
the whole of the pumping for a small sewerage works may be done
by means of a windmill, but it is undesirable to rely entirely
upon such a system, even if two mills are erected so that the
plant will be in duplicate, because there is always the
possibility, although it may be remote, of a lengthened period
of calm, when the sewage would accumulate; and, further, the
Local Government Board would not approve the scheme unless it
included an engine, driven by gas, oil, or other mechanical
power, for emergencies. In the case of water supply the
difficulty may be overcome by providing large storage capacity,
but this cannot be done for sewage without creating an
intolerable nuisance. In the latter case the storage should not
be less than twelve hours dry weather flow, nor more than
twenty-four. With a well-designed mill, as has already been
indicated, the wind will, for the greater part of the year, be
sufficient to lift the whole of the sewage and storm-water,
but, if it is allowed to do so, the standby engine will
deteriorate for want of use to such an extent that when
urgently needed it will not be effective. It is, therefore,
desirable that the attendant should run the engine at least
once in every three days to keep it in working order. If it can
be conveniently arranged, it is a good plan for the attendant
to run the engine for a few minutes to entirely empty the pump
well about six o'clock each evening. The bulk of the day's
sewage will then have been delivered, and can be disposed of
when it is fresh, while at the same time the whole storage
capacity is available for the night flow, and any rainfall
which may occur, thus reducing the chances of the man being
called up during the night. About 22 per cent, of the total
daily dry weather flow of sewage is delivered between 7 p.m.
and 7 a.m.

The first cost of installing a small windmill is practically
the same as for an equivalent gas or oil engine plant, so that
the only advantage to be looked for will be in the maintenance,
which in the case of a windmill is a very small matter, and the
saving which may be obtained by the reduction of the amount of
attendance necessary. Generally speaking, a mill 20 ft in
diameter is the largest which should be used, as when this size
is exceeded it will be found that the capital cost involved is
incompatible with the value of the work done by the mill, as
compared with that done by a modern internal combustion engine.


Mills smaller than 8 ft in diameter are rarely employed, and
then only for small work, such as a 2 1/2 in pump and a 3-ft
lift The efficiency of a windmill, measured by the number of
square feet of annular sail area, decreases with the size of
the mill, the 8 ft, 10 ft, and l2 ft mills being the most
efficient sizes. When the diameter exceeds l2 ft, the
efficiency rapidly falls off, because the peripheral velocity
remains constant for any particular velocity or pressure of the
wind, and as every foot increase in the diameter of the wheel
makes an increase of over 3 ft in the length of the
circumference, the greater the diameter the less the number of
revolutions in any given time; and consequently the kinetic
flywheel action which is so valuable in the smaller sizes is to
a great extent lost in the larger mills.

Any type of pump can be used, but the greatest efficiency will
be obtained by adopting a single acting pump with a short
stroke, thus avoiding the liability, inherent in a long pump
rod, to buckle under compression, and obviating the use of a
large number of guides which absorb a large part of the power
given out by the mill. Although some of the older mills in this
country are of foreign origin, there are several British
manufacturers turning out well-designed and strongly-built
machines in large numbers. Fig. 19 represents the general
appearance and Fig. 20 the details of the type of mill made by
the well-known firm of Duke and Ockenden, of Ferry Wharf,
Littlehampton, Sussex. This firm has erected over 400
windmills, which, after the test of time, have proved
thoroughly efficient. From Fig. 20 it will be seen that the
power applied by the wheel is transmitted through spur and
pinion gearing of 2 1/2 ratio to a crank shaft, the gear wheel
having internal annular teeth of the involute type, giving a
greater number of teeth always in contact than is the case with
external gears. This minimises wear, which is an important matter,
as it is difficult to properly lubricate these appliances, and they
are exposed to and have to work in all sorts of weather.

[Illustration:  Fig. l9.--General View of Modern Windmill.]

[Illustration:  Fig. 20.--Details of Windmill Manufactured by Messrs. Duke and
Ockenden, Littlehampton.]

It will be seen that the strain on the crank shaft is taken by
a bent crank which disposes the load centrally on the casting,
and avoids an overhanging crank disc, which has been an
objectionable feature in some other types. The position of the
crank shaft relative to the rocker pin holes is studied to give
a slow upward motion to the rocker with a more rapid downward
stroke, the difference in speed being most marked in the
longest stroke, where it is most required.

In order to transmit the circular internal motion a vertical
connecting rod in compression is used, which permits of a
simple method of changing the length of stroke by merely
altering the pin in the rocking lever, the result being that
the pump rod travels in a vertical line.

The governing is entirely automatic. If the pressure on the
wind wheel, which it will be seen is set off the centre line of
the mill and tower, exceeds that found desirable--and this can
be regulated by means of a spring on the fantail--the windmill
automatically turns on the turn-table and presents an ellipse
to the wind instead of a circular face, thus decreasing the
area exposed to the wind gradually until the wheel reaches its
final position, or is hauled out of gear, when the edges only
are opposed to the full force of the wind. The whole weight of
the mill is taken upon a ball-bearing turn-table to facilitate
instant "hunting" of the mill to the wind to enable it to take
advantage of all changes of direction. The pump rod in the
windmill tower is provided with a swivel coupling, enabling the
mill head to turn completely round without altering the
position of the rod.




CHAPTER X.

THE DESIGN OF SEE OUTFALLS.


The detail design of a sea outfall will depend upon the level
of the conduit with reference to present surface of the shore,
whether the beach is being eroded or made up, and, if any part
of the structure is to be constructed above the level of the
shore, whether it is likely to be subject to serious attack by
waves in times of heavy gales. If there is probability of the
direction of currents being affected by the construction of a
solid structure or of any serious scour being caused, the
design must be prepared accordingly.

While there are examples of outfalls constructed of glazed
stoneware socketed pipes surrounded with concrete, as shown in
Fig. 21, cast iron pipes are used in the majority of cases.
There is considerable variation in the design of the joints for
the latter class of pipes, some of which are shown in Figs. 22,
23, and 24. Spigot and socket joints (Fig. 22), with lead run
in, or even with rod lead or any of the patent forms caulked in
cold, are unsuitable for use below high-water mark on account
of the water which will most probably be found in the trench.
Pipes having plain turned and bored joints are liable to be
displaced if exposed to the action of the waves, but if such
joints are also flanged, as Fig. 24, or provided with lugs, as
Fig. 23, great rigidity is obtained when they are bolted up; in
addition to which the joints are easily made watertight. When a
flange is formed all round the joint, it is necessary, in order
that its thickness may be kept within reasonable limits, to
provide bolts at frequent intervals. A gusset piece to stiffen
the flange should be formed between each hole and the next, and
the bolt holes should be arranged so that when the pipes are
laid there will not be a hole at the bottom on the vertical
axis of the pipe, as when the pipes are laid in a trench below
water level it is not only difficult to insert the bolt, but
almost impracticable to tighten up the nut afterwards. The
pipes should be laid so that the two lowest bolt holes are
placed equidistant on each side of the centre line, as shown in
the end views of Figs. Nos. 23 and 24.

[Illustration:  Fig. 2l.-Stoneware Pipe and Concrete Sea Outfall.]

With lug pipes, fewer bolts are used, and the lugs are made
specially strong to withstand the strain put upon them in
bolting up the pipes. These pipes are easier and quicker to
joint under water than are the flanged pipes, so that their use
is a distinct advantage when the hours of working are limited.
In some cases gun-metal bolts are used, as they resist the
action of sea water better than steel, but they add
considerably to the cost of the outfall sewer, and the
principal advantage appears to be that they are possibly easier
to remove than iron or steel ones would be if at any time it
was required to take out any pipe which may have been
accidentally broken. On the other hand, there is a liability of
severe corrosion of the metal taking place by reason of
galvanic action between the gun-metal and the iron, set up by
the sea water in which they are immersed. If the pipes are not
to be covered with concrete, and are thus exposed to the action
of the sea water, particular care should be taken to see that
the coating by Dr. Angus Smith's process is perfectly applied
to them.

[Illustration:  Fig. 22.--Spigot and Socket Joint for Cast Iron Pipes.]

[Illustration:  Fig. 23.--Lug Joint for Cast Iron Pipes.]

[Illustration:  Fig. 24.--Turned, Board, and Flanged Joint for Cast Iron Pipes.]

Steel pipes are, on the whole, not so suitable as cast iron.
They are, of course, obtainable in long lengths and are easily
jointed, but their lightness compared with cast iron pipes,
which is their great advantage in transport, is a disadvantage
in a sea outfall, where the weight of the structure adds to its
stability. The extra length of steel pipes necessitates a
greater extent of trench being excavated at one time, which
must be well timbered to prevent the sides falling in On the
other hand, cast iron pipes are more liable to fracture by
heavy stones being thrown upon them by the waves, but this is a
contingency which does not frequently occur in practice.
According to Trautwine, the cast iron for pipes to resist sea
water should be close-grained, hard, white metal. In such metal
the small quantity of contained carbon is chemically combined
with the iron, but in the darker or mottled metals it is
mechanically combined, and such iron soon becomes soft, like
plumbago, under the influence of sea water. Hard white iron has
been proved to resist sea water for forty years without
deterioration, whether it is continually under water or
alternately wet and dry.

Several types of sea outfalls are shown in Figs. 25 to 31.[1]
In the example shown in Fig. 25 a solid rock bed occurred a
short distance below the sand, which was excavated so as to
allow the outfall to be constructed on the rock. Anchor bolts
with clevis heads were fixed into the rock, and then, after a
portion of the concrete was laid, iron bands, passing around
the cast iron pipes, were fastened to the anchors. This
construction would not be suitable below low-water mark. Fig.
26 represents the Aberdeen sea outfall, consisting of cast iron
pipes 7 ft in diameter, which are embedded in a heavy concrete
breakwater 24 ft in width, except at the extreme end, where it
is 30 ft wide. The 4 in wrought iron rods are only used to the
last few pipes, which were in 6 ft lengths instead of 9 ft, as
were the remainder. Fig. 27 shows an inexpensive method of
carrying small pipes, the slotted holes in the head of the pile
allowing the pipes to be laid in a straight line, even if the
pile is not driven quite true, and if the level of the latter
is not correct it can be adjusted by inserting a packing piece
between the cradle and the head.

Great Crosby outfall sewer into the Mersey is illustrated in
Fig. 28. The piles are of greenheart, and were driven to a
solid foundation. The 1 3/4 in sheeting was driven to support
the sides of the excavation, and was left in when the concrete
was laid. Light steel rails were laid under the sewer, in
continuous lengths, on steel sleepers and to 2 ft gauge. The
invert blocks were of concrete, and the pipes were made of the
same material, but were reinforced with steel ribs. The Waterloo
(near Liverpool) sea outfall is shown in Fig. 31.

[Footnote 1: Plate V.]

Piling may be necessary either to support the pipes or to keep
them secure in their proper position, but where there is a
substratum of rock the pipes may be anchored, as shown in Figs.
25 and 26. The nature of the piling to be adopted will vary
according to the character of the beach. Figs. 27, 29, 30, and
31 show various types. With steel piling and bearers, as shown
in Fig. 29, it is generally difficult to drive the piles with
such accuracy that the bearers may be easily bolted up through
the holes provided in the piles, and, if the holes are not
drilled in the piles until after they are driven to their final
position, considerable time is occupied, and perhaps a tide
lost in the attempt to drill them below water. There is also
the difficulty of tightening up the bolts when the sewer is
partly below the surface of the shore, as shown. In both the
types shown in Figs. 29 and 30 it is essential that the piles
and the bearers should abut closely against the pipes;
otherwise the shock of the waves will cause the pipes to move
and hammer against the framing, and thus lead to failure of the
structure.

Piles similar to Fig. 31 can only be fixed in sand, as was the
case at Waterloo, because they must be absolutely true to line
and level, otherwise the pipes cannot be laid in the cradles.
The method of fixing these piles is described by Mr. Ben
Howarth (Minutes of Proceedings of Inst.C.E., Vol. CLXXV.) as
follows:--"The pile was slung vertically into position from a
four-legged derrick, two legs of which were on each side of the
trench; a small winch attached to one pair of the legs lifted
and lowered the pile, through a block and tackle. When the pile
was ready to be sunk, a 2 in iron pipe was let down the centre,
and coupled to a force-pump by means of a hose; a jet of water
was then forced down this pipe, driving the sand and silt away
from below the pile. The pile was then rotated backwards and
forwards about a quarter of a turn, by men pulling on the arms;
the pile, of course, sank by its own weight, the water-jet
driving the sand up through the hollow centre and into the
trench, and it was always kept vertical by the sling from the
derrick. As soon as the pile was down to its final level the ground
was filled in round the arms, and in this running sand the pile
became perfectly fast and immovable a few minutes after the
sinking was completed. The whole process, from the first
slinging of the pile to the final setting, did not take more
than 20 or 25 minutes."

[Illustration: PLATE V.

ROCK BED. Fig. 26--ABERDEEN SEA OUTFALL. Fig. 27--SMALL GREAT
CROSBY SEA OUTFALL. Fig. 29--CAST IRON PIPE ON STEEL CAST AND
BEARERS. Fig. 31--WATERLOO (LIVERPOOL) SEA OUTFALL.]

(_To face page 80_.)

Screw piles may be used if the ground is suitable, but, if it
is boulder clay or similar material, the best results will
probably be obtained by employing rolled steel joists as piles.




CHAPTER XI.

THE ACTION OF SEA WATER ON CEMENT.


Questions are frequently raised in connection with sea-coast
works as to whether any deleterious effect will result from
using sea-water for mixing the concrete or from using sand and
shingle off the beach; and, further, whether the concrete,
after it is mixed, will withstand the action of the elements,
exposed, as it will be, to air and sea-water, rain, hot sun,
and frosts.

Some concrete structures have failed by decay of the material,
principally between high and low water mark, and in order to
ascertain the probable causes and to learn the precautions
which it is necessary to take, some elaborate experiments have
been carried out.

To appreciate the chemical actions which may occur, it will be
as well to examine analyses of sea-water and cement. The water
of the Irish Channel is composed of


Sodium chloride.................... 2.6439 per cent.
Magnesium chloride................. 0.3150   "   "
Magnesium sulphate................. 0.2066   "   "
Calcium sulphate................... 0.1331   "   "
Potassium chloride................. 0.0746   "   "
Magnesium bromide.................. 0.0070   "   "
Calcium carbonate.................. 0.0047   "   "
Iron carbonate..................... 0.0005   "   "
Magnesium nitrate.................. 0.0002   "   "
Lithium chloride................... Traces.
Ammonium chloride.................. Traces.
Silica chloride.................... Traces.
Water.............................. 96.6144
                                   --------
                                   100.0000


An average analysis of a Thames cement may be taken to be as
follows:--


Silica................................ 23.54 per cent.
Insoluble residue (sand, clay,
      etc.)............................ 0.40    "
Alumina and ferric oxide............... 9.86    "
Lime.................................. 62.08    "
Magnesia............................... 1.20    "
Sulphuric anhydride.................... 1.08    "
Carbonic anhydride and water........... 1.34    "
Alkalies and loss on analysis.......... 0.50    "
                                       -----
                                      100.00


The following figures give the analysis of a sample of cement
expressed in terms of the complex compounds that are found:--


Sodium silicate (Na2SiO3)........ 3.43 per cent.
Calcium sulphate (CaSO4)......... 2.45    "
Dicalcium silicate (Ca2SiO4).... 61.89    "
Dicalcium aluminate (Ca2Al2O5).. 12.14    "
Dicalcium ferrate (Ca2Fe2O5)..... 4.35    "
Magnesium oxide (MgO)............ 0.97    "
Calcium oxide (CaO)............. 14.22    "
Loss on analysis, &c............. 0.55    "
                                 -----
                                100.00


Dr. W. Michaelis, the German cement specialist, gave much
consideration to this matter in 1906, and formed the opinion
that the free lime in the Portland cement, or the lime freed in
hardening, combines with the sulphuric acid of the sea-water,
which causes the mortar or cement to expand, resulting in its
destruction. He proposed to neutralise this action by adding to
the mortar materials rich in silica, such as trass, which would
combine with the lime.

Mr. J. M. O'Hara, of the Southern Pacific Laboratory, San
Francisco, Cal., made a series of tests with sets of pats 4 in
diameter and 1/2 in thick at the centre, tapering to a thin
edge on the circumference, and also with briquettes for
ascertaining the tensile strength, all of which were placed
in water twenty-four hours after mixing. At first some of the
pats were immersed in a "five-strength solution" of sea-water
having a chemical analysis as follows:--

Sodium chloride.................... 11.5 per cent.
Magnesium chloride.................  1.4   "   "
Magnesium sulphate.................  0.9   "   "
Calcium sulphate...................  0.6   "   "
Water.............................. 85.6   "   "
                                   100.0

This strong solution was employed in order that the probable
effect of immersing the cement in sea-water might be
ascertained very much quicker than could be done by observing
samples actually placed in ordinary sea-water, and it is worthy
of note that the various mixtures which failed in this
accelerated test also subsequently failed in ordinary sea-water
within a period of twelve months.

Strong solutions were next made of the individual salts
contained in sea-water, and pats were immersed as before, when
it was found that the magnesium sulphate present in the water
acted upon the calcium hydrate in the cement, forming calcium
sulphate, and leaving the magnesium hydrate free. The calcium
sulphate combines with the alumina of the cement, forming
calcium sulpho-aluminate, which causes swelling and cracking of
the concrete, and in cements containing a high proportion of
alumina, leads to total destruction of all cohesion. The
magnesium hydrate has a tendency to fill the pores of the
concrete so as to make it more impervious to the destructive
action of the sea-water, and disintegration may be retarded or
checked. A high proportion of magnesia has been found in
samples of cement which have failed under the action of sea
water, but the disastrous result cannot be attributed to this
substance having been in excess in the original cement, as it
was probably due to the deposition of the magnesia salts from
the sea-water; although, if magnesia were present in the cement
in large quantities, it would cause it to expand and crack,
still with the small proportion in which it occurs in ordinary
cements it is probably inert. The setting of cement under the
action of water always frees a portion of the lime which was
combined, but over twice as much is freed when the cement sets
in sea-water as in fresh water. The setting qualities of cement
are due to the iron and alumina combined with calcium, so that
for sea-coast work it is desirable for the alumina to be
replaced by iron as far as possible. The final hardening and
strength of cement is due in a great degree to the tri-calcium
silicate (3CaO, SiO2) which is soluble by the sodium chloride
found in sea-water, so that the resultant effect of the action
of these two compounds is to enable the sea-water to gradually
penetrate the mortar and rot the concrete. The concrete is
softened, when there is an abnormal amount of sulphuric acid
present, as a result of the reaction of the sulphuric acid of
the salt dissolved by the water upon a part of the lime in the
cement. The ferric oxide of the cement is unaffected by sea-
water.

The neat cement briquette tests showed that those immersed in
sea-water attained a high degree of strength at a much quicker
rate than those immersed in fresh water, but the 1 to 3 cement
and sand briquette tests gave an opposite result. At the end of
twelve months, however, practically all the cements set in
fresh water showed greater strength than those set in sea-
water. When briquettes which have been immersed in fresh water
and have thoroughly hardened are broken, the cores are found to
be quite dry, and if briquettes immersed in sea-water show a
similar dryness there need be no hesitation in using the
cement; but if, on the other hand, the briquette shows that the
sea-water has permeated to the interior, the cement will lose
strength by rotting until it has no cohesion at all. It must be
remembered that it is only necessary for the water to penetrate
to a depth of 1/2 in on each side of a briquette to render it
damp all through, whereas in practical work, if the water only
penetrated to the same depth, very little ill-effect would be
experienced, although by successive removals of a skin 1/2 in
deep the structure might in time be imperilled.

The average strength in pounds per square inch of six different
well-known brands of cement tested by Mr. O'Hara was as
follows:--


TABLE No. 16.

EFFECT OF SEA WATER ON STRENGTH OF CEMENT.


                     Neat cement         1 cement to 3 sand
                        set in                 set in
                 Sea Water  Fresh Water  Sea Water  Fresh Water

 7 days             682        548          214        224
28 days             836        643          293        319
 2 months           913        668          313        359
 3 months           861        667          301        387
 6 months           634        654          309        428
 9 months           542        687          317        417
12 months           372        706          325        432


Some tests were also made by Messrs. Westinghouse, Church,
Kerr, and Co., of New York, to ascertain the effect of sea-
water on the tensile strength of cement mortar. Three sets of
briquettes were made, having a minimum section of one square
inch. The first were mixed with fresh water and kept in fresh
water; the second were mixed with fresh water, but kept
immersed in pans containing salt water; while the third were
mixed with sea-water and kept in sea-water. In the experiments
the proportion of cement and sand varied from 1 to 1 to 1 to 6.
The results of the tests on the stronger mixtures are shown in
Fig. 32.

The Scandinavian Portland cement manufacturers have in hand
tests on cubes of cement mortar and cement concrete, which were
started in 1896, and are to extend over a period of twenty
years. A report upon the tests of the first ten years was
submitted at the end of 1909 to the International Association
of Testing Materials at Copenhagen, and particulars of them are
published in "Cement and Sea-Water," by A. Poulsen (chairman of
the committee), J. Jorsen and Co., Copenhagen, 1909, price 3s.

[Illustration: FIG. 32.--Tests of the Tensile Strength of
Cement and Sand Briquettes, Showing the Effect of Sea Water.]

Cements from representative firms in different countries were
obtained for use in making the blocks, which had coloured glass
beads and coloured crushed glass incorporated to facilitate
identification. Each block of concrete was provided with a
number plate and a lifting bolt, and was kept moist for one
month before being placed in position. The sand and gravel were
obtained from the beach on the west coast of Jutland. The
mortar blocks were mixed in the proportion of 1 to 1, 1 to 2,
and 1 to 3, and were placed in various positions, some between
high and low water, so as to be exposed twice in every twenty-
four hours, and others below low water, so as to be always
submerged. The blocks were also deposited under these
conditions in various localities, the mortar ones being placed
at Esbjerb at the south of Denmark, at Vardo in the Arctic
Ocean, and at Degerhamm on the Baltic, where the water is only
one-seventh as salt as the North Sea, while the concrete blocks
were built up in the form of a breakwater or groyne at Thyboron
on the west coast of Jutland. At intervals of three, six, and
twelve months, and two, four, six, ten, and twenty years, some
of the blocks have, or will be, taken up and subjected to
chemical tests, the material being also examined to ascertain
the effect of exposure upon them. The blocks tested at
intervals of less than one year after being placed in position
gave very variable results, and the tests were not of much
value.

The mortar blocks between high and low water mark of the Arctic
Ocean at Vardo suffered the worst, and only those made with the
strongest mixture of cement, 1 to 1, withstood the severe frost
experienced. The best results were obtained when the mortar was
made compact, as such a mixture only allowed diffusion to take
place so slowly that its effect was negligible; but when, on
the other hand, the mortar was loose, the salts rapidly
penetrated to the interior of the mass, where chemical changes
took place, and caused it to disintegrate. The concrete blocks
made with 1 to 3 mortar disintegrated in nearly every case,
while the stronger ones remained in fairly good condition. The
best results were given by concrete containing an excess of
very fine sand. Mixing very finely-ground silica, or trass,
with the cement proved an advantage where a weak mixture was
employed, but in the other cases no benefit was observed.

The Association of German Portland Cement Manufacturers carried
out a series of tests, extending over ten years, at their
testing station at Gross Lichterfeld, near Berlin, the results
of which were tabulated by Mr. C. Schneider and Professor Gary.
In these tests the mortar blocks were made 3 in cube and the
concrete blocks l2 in cube; they were deposited in two tanks,
one containing fresh water and the other sea-water, so that the
effect under both conditions might be noted. In addition,
concrete blocks were made, allowed to remain in moist sand for
three months, and were then placed in the form of a groyne in
the sea between high and low-water mark. Some of the blocks
were allowed to harden for twelve months in sand before being
placed, and these gave better results than the others. Two
brands of German Portland cement were used in these tests, one,
from which the best results were obtained, containing 65.9 per
cent. of lime, and the other 62.0 per cent. of lime, together
with a high percentage of alumina. In this case, also, the
addition of finely-ground silica, or trass, improved the
resisting power of blocks made with poor mortars, but did not
have any appreciable effect on the stronger mixtures.

Professor M. Möller, of Brunswick, Germany, reported to the
International Association for Testing Materials, at the
Copenhagen Congress previously referred to, the result of his
tests on a small hollow, trapezium shape, reinforced concrete
structure, which was erected in the North Sea, the interior
being filled with sandy mud, which would be easily removable by
flowing water. The sides were 7 cm. thick, formed of cement
concrete 1:2 1/2:2, moulded elsewhere, and placed in the
structure forty days after they were made, while the top and
bottom were 5 cm. thick, and consisted of concrete 1:3:3,
moulded _in situ_ and covered by the tide within twenty-four
hours of being laid. The concrete moulded _in situ_ hardened a
little at first, and then became soft when damp, and friable
when dry, and white efflorescence appeared on the surface. In a
short time the waves broke this concrete away, and exposed the
reinforcement, which rusted and disappeared, with the result
that in less than four years holes were made right through the
concrete. The sides, which were formed of slabs allowed to
harden before being placed in the structure, were unaffected
except for a slight roughening of the surface after being
exposed alternately to the sea and air for a period, of
thirteen years. Professor Möller referred also to several cases
which had come under his notice where cement mortar or concrete
became soft and showed white efflorescence when it had been
brought into contact with sea-water shortly after being made.

In experiments in Atlantic City samples of dry cement in powder
form were put with sea-water in a vessel which was rapidly
rotated for a short time, after which the cement and the sea-
water were analysed, and it was found that the sea-water had
taken up the lime from the cement, and the cement had absorbed
the magnesia salts from the sea-water.

Some tests were carried out in 1908-9 at the Navy Yard,
Charlestown, Mass., by the Aberthaw Construction Company of
Boston, in conjunction with the Navy Department. The cement
concrete was placed so that the lower portions of the surfaces
of the specimens were always below water, the upper portions
were always exposed to the air, and the middle portions were
alternately exposed to each. Although the specimens were
exposed to several months of winter frost as well as to the
heat of the summer, no change was visible in any part of the
concrete at the end of six months.

Mons. R. Feret, Chief of the Laboratory of Bridges and Roads,
Boulogne-sur-Mer, France, has given expression to the following
opinions:--

1. No cement or other hydraulic product has yet been found
which presents absolute security against the decomposing action
of sea-water.

2. The most injurious compound of sea-water is the acid of the
dissolved sulphates, sulphuric acid being the principal agent
in the decomposition of cement.

3. Portland cement for sea-water should be low in aluminium and
as low as possible in lime.

4. Puzzolanic material is a valuable addition to cement for
sea-water construction,

5. As little gypsum as possible should be added for regulating
the time of setting to cements which are to be used in sea-
water.

6. Sand containing a large proportion of fine grains must never
be used in concrete or mortar for sea-water construction.

7. The proportions of the cement and aggregate for sea-water
construction must be such as will produce a dense and
impervious concrete.

On the whole, sea-water has very little chemical effect on good
Portland cements, such as are now easily obtainable, and,
provided the proportion of aluminates is not too high, the
varying composition of the several well-known commercial
cements is of little moment. For this reason tests on blocks
immersed in still salt water are of very little use in
determining the probable behaviour of concrete when exposed to
damage by physical and mechanical means, such as occurs in
practical work.

The destruction of concrete works on the sea coast is due to
the alternate exposure to air and water, frost, and heat, and
takes the form of cracking or scaling, the latter being the
most usual when severe frosts are experienced. When concrete
blocks are employed in the construction of works, they should
be made as long as possible before they are required to be
built in the structure, and allowed to harden in moist sand,
or, if this is impracticable, the blocks should be kept in the
air and thoroughly wetted each day. On placing cement or
concrete blocks in sea water a white precipitate is formed on
their surfaces, which shows that there is some slight chemical
action, but if the mixture is dense this action is restricted
to the outside, and does not harm the block.

Cement mixed with sea water takes longer to harden than if
mixed with fresh water, the time varying in proportion to the
amount of salinity in the water. Sand and gravel from the
beach, even though dry, have their surfaces covered with saline
matters, which retard the setting of the cement, even when
fresh water is used, as they become mixed with such water, and
thus permeate the whole mass. If sea water and aggregate from
the shore are used, care must be taken to see that no decaying
seaweed or other organic matter is mixed with it, as every such
piece will cause a weak place in the concrete. If loam, clay,
or other earthy matters from the cliffs have fallen down on to
the beach, the shingle must be washed before it is used in
concrete.

Exposure to damp air, such as is unavoidable on the coast,
considerably retards the setting of cement, so that it is
desirable that it should not be further retarded by the
addition of gypsum, or calcium sulphate, especially if it is to
be used with sea water or sea-washed sand and gravel. The
percentage of gypsum found in cement is, however, generally
considerably below the maximum allowed by the British Standard
Specification, viz., 2 per cent., and is so small that, for
practical purposes, it makes very little difference in sea
coast work, although of course, within reasonable limits, the
quicker the cement sets the better. When cement is used to
joint stoneware pipe sewers near the coast, allowance must be
made for this retardation of the setting, and any internal
water tests which may be specified to be applied must not be
made until a longer period has elapsed after the laying of the
pipes than would otherwise be necessary. A high proportion of
aluminates tends to cause disintegration when exposed to sea
water. The most appreciable change which takes place in a good
sound cement after exposure to the sea is an increase in the
chlorides, while a slight increase in the magnesia and the
sulphates also takes place, so that the proportion of sulphates
and magnesia in the cement should be kept fairly low. Hydraulic
lime exposed to the sea rapidly loses the lime and takes up
magnesia and sulphates.

To summarise the information upon this point, it appears that
it is better to use fresh water for all purposes, but if, for
the sake of economy, saline matters are introduced into the
concrete, either by using sea water for mixing or by using sand
and shingle from the beach, the principal effect will be to
delay the time of setting to some extent, but the ultimate
strength of the concrete will probably not be seriously
affected. When the concrete is placed in position the portion
most liable to be destroyed is that between high and low water
mark, which is alternately exposed to the action of the sea and
the air, but if the concrete has a well-graded aggregate, is
densely mixed, and contains not more than two parts of sand to
one part of cement, no ill-effect need be anticipated.




CHAPTER XII

DIVING.


The engineer is not directly concerned with the various methods
employed in constructing a sea outfall, such matters being left
to the discretion of the contractor. It may, however, be
briefly stated that the work frequently involves the erection
of temporary steel gantries, which must be very carefully
designed and solidly built if they are to escape destruction by
the heavy seas. It is amazing to observe the ease with which a
rough sea will twist into most fantastic shapes steel joists 10
in by 8in, or even larger in size. Any extra cost incurred in
strengthening the gantries is well repaid if it avoids damage,
because otherwise there is not only the expense of rebuilding
the structure to be faced, but the construction of the work
will be delayed possibly into another season.

In order to ensure that the works below water are constructed
in a substantial manner, it is absolutely necessary that the
resident engineer, at least, should be able to don a diving
dress and inspect the work personally. The particular points to
which attention must be given include the proper laying of the
pipes, so that the spigot of one is forced home into the socket
of the other, the provision and tightening up of all the bolts
required to be fixed, the proper driving of the piles and
fixing the bracing, the dredging of a clear space in the bed of
the sea in front of the outlet pipe, and other matters
dependent upon the special form of construction adopted. If a
plug is inserted in the open end of the pipes as laid, the
rising of the tide will press on the plugged end and be of
considerable assistance in pushing the pipes home; it will
therefore be necessary to re-examine the joints to see if the
bolts can be tightened up any more.

Messrs. Siebe, Gorman, and Co., the well-known makers of
submarine appliances, have fitted up at their works at
Westminster Bridge-road, London, S.E., an experimental tank, in
which engineers may make a few preliminary descents and be
instructed in the art of diving; and it is distinctly more
advantageous to acquire the knowledge in this way from experts
than to depend solely upon the guidance of the divers engaged
upon the work which the engineer desires to inspect. Only a
nominal charge of one guinea for two descents is made, which
sum, less out-of-pocket expenses, is remitted to the Benevolent
Fund of the Institution of Civil Engineers. It is generally
desirable that a complete outfit, including the air pump,
should be provided for the sole use of the resident engineer,
and special men should be told off to assist him in dressing
and to attend to his wants while he is below water. He is then
able to inspect the work while it is actually in progress, and
he will not hinder or delay the divers.

It is a wise precaution to be medically examined before
undertaking diving work, although, with the short time which
will generally be spent below water, and the shallow depths
usual in this class of work, there is practically no danger;
but, generally speaking, a diver should be of good physique,
not unduly stout, free from heart or lung trouble and varicose
veins, and should not drink or smoke to excess. It is
necessary, however, to have acquaintance with the physical
principles involved, and to know what to do in emergencies. A
considerable amount of useful information is given by Mr. R. H.
Davis in his "Diving Manual" (Siebe, Gorman, and Co., 5s.),
from which many of the following notes are taken.

A diving dress and equipment weighs about l75 lb, including a
40 lb lead weight carried by the diver on his chest, a similar
weight on his back, and l6lb of lead on each boot. Upon
entering the water the superfluous air in the dress is driven
out through the outlet valve in the helmet by the pressure of
the water on the legs and body, and by the time the top of the
diver's head reaches the surface his breathing becomes
laboured, because the pressure of air in his lungs equals the
atmospheric pressure, while the pressure upon his chest and
abdomen is greater by the weight of the water thereon.

He is thus breathing against a pressure, and if he has to
breathe deeply, as during exertion, the effect becomes serious;
so that the first thing he has to learn is to adjust the
pressure of the spring on the outlet valve, so that the amount
of air pumped in under pressure and retained in the diving
dress counterbalances the pressure of the water outside, which
is equal to a little under 1/2lb per square inch for every foot
in depth. If the diver be 6 ft tall, and stands in an upright
position, the pressure on his helmet will be about 3lb per
square inch less than on his boots. The breathing is easier if
the dress is kept inflated down to the abdomen, but in this
case there is danger of the diver being capsized and floating
feet upwards, in which position he is helpless, and the air
cannot escape by the outlet valve. Air is supplied to the diver
under pressure by an air pump through a flexible tube called
the air pipe; and a light rope called a life line, which is
used for signalling, connects the man with the surface. The
descent is made by a 3 in "shot-rope," which has a heavy sinker
weighing about 50 lb attached, and is previously lowered to the
bottom. A 1-1/4 in rope about 15 ft long, called a "distance-
line," is attached to the shot-rope about 3 ft above the
sinker, and on reaching the bottom the diver takes this line
with him to enable him to find his way back to the shot-rope,
and thus reach the surface comfortably, instead of being hauled
up by his life line. The diver must be careful in his movements
that he does not fall so as suddenly to increase the depth of
water in which he is immersed, because at the normal higher
level the air pressure in the dress will be properly balanced
against the water pressure; but if he falls, say 30 ft, the
pressure of the water on his body will be increased by about 15
lb per square inch, and as the air pump cannot immediately
increase the pressure in the dress to a corresponding extent,
the man's body in the unresisting dress will be forced into the
rigid helmet, and he will certainly be severely injured, and
perhaps even killed.

When descending under water the air pressure in the dress is
increased, and acts upon the outside of the drum of the ear,
causing pain, until the air passing through the nose and up the
Eustachian tube inside the head reaches the back of the drum
and balances the pressure. This may be delayed, or prevented,
if the tube is partially stopped up by reason of a cold or
other cause, but the balance can generally be brought about if
the diver pauses in his descent and swallows his saliva; or
blocks up his nose as much as possible by pressing it against
the front of the helmet, closing the mouth and then making a
strong effort at expiration so as to produce temporarily an
extra pressure inside the throat, and so blow open the tubes;
or by yawning or going through the motions thereof. If this
does not act he must come up again Provided his ears are
"open," and the air pumps can keep the pressure of air equal to
that of the depth of the water in which the diver may be, there
is nothing to limit the rate of his descent.

Now in breathing, carbonic acid gas is exhaled, the quality
varying in accordance with the amount of work done, from .014
cubic feet per minute when at rest to a maximum of about .045,
and this gas must be removed by dilution with fresh air so as
not to inconvenience the diver. This is not a matter of much
difficulty as the proportion in fresh air is about .03 per
cent., and no effect is felt until the proportion is increased
to about 0.3 per cent., which causes one to breathe twice as
deeply as usual; at 0.6 per cent. there is severe panting; and
at a little over 1.0 per cent. unconsciousness occurs. The
effect of the carbonic acid on the diver, however, increases
the deeper he descends; and at a depth of 33 ft 1 per cent. of
carbonic acid will have the same effect as 2 per cent. at the
surface. If the diver feels bad while under water he should
signal for more air, stop moving about, and rest quietly for a
minute or two, when the fresh air will revive him. The volume
of air required by the diver for respiration is about 1.5 cubic
feet per minute, and there is a non-return valve on the air
inlet, so that in the event of the air pipe being broken, or
the pump failing, the air would not escape backwards, but by
closing the outlet valve the diver could retain sufficient air
to enable him to reach the surface.

During the time that a diver is under pressure nitrogen gas
from the air is absorbed by his blood and the tissues of his
body. This does not inconvenience him at the time, but when he
rises the gas is given off, so that if he has been at a great
depth for some considerable time, and comes up quickly, bubbles
form in the blood and fill the right side of the heart with
air, causing death in a few minutes. In less sudden cases the
bubbles form in the brain or spinal cord, causing paralysis of
the legs, which is called divers' palsy, or the only trouble
which is experienced may be severe pains in the joints and
muscles. It is necessary, therefore, that he shall come up by
stages so as to decompress himself gradually and avoid danger.
The blood can hold about twice as much gas in solution as an
equal quantity of water, and when the diver is working in
shallow depths, up to, say, 30 ft, the amount of nitrogen
absorbed is so small that he can stop down as long as is
necessary for the purposes of the work, and can come up to the
surface as quickly as he likes without any danger. At greater
depths approximately the first half of the upward journey may
be done in one stage, and the remainder done by degrees, the
longest rest being made at a few feet below the surface.

The following table shows the time limits in accordance with
the latest British Admiralty practice; the time under the water
being that from leaving the surface to the beginning of the
ascent:--


TABLE No. l7.--DIVING DATA.

                                    Stoppages in     Total time
                                     minutes at      for ascent
Depth in feet.  Time under water.  different depths  in minutes.

                                   at 20 ft  10 ft

Up to 36        No limit                -      -     0 to 1

36 to 42        Up to 3 hours           -      -     1 to 1-1/2
                Over 3 hours            -      5     6

42 to 48        Up to 1 hour            -      -     1-1/2
                1 to 3 hours            -      5     6-1/2
                Over 3 hours            -     10    11-1/2

48 to 54        Up to 1/2 hour          -      -     2
                1/2 to 1-1/2 hour       -      5     7
                1-1/2 to 3 hours        -     10    12
                Over 3 hours            -     20    22

54 to 60        Up to 20 minutes        -      -     2
                20 to 45 minutes        -      5     7
                3/4 to 1-1/2 hour       -     10    12
                1-1/2 to 3 hours        5     15    22
                Over 3 hours           10     20    32


When preparing to ascend the diver must tighten the air valve
in his helmet to increase his buoyancy; if the valve is closed
too much to allow the excess air to escape, his ascent will at
first be gradual, but the pressure of the water reduces, the
air in the dress expands, making it so stiff that he cannot
move his arms to reach the valve, and he is blown up, with
ever-increasing velocity, to the surface. While ascending he
should exercise his muscles freely during the period of waiting
at each stopping place, so as to increase the circulation, and
consequently the rate of deceleration.

During the progress of the works the location of the sea
outfall will be clearly indicated by temporary features visible
by day and lighted by night; but when completed its position
must be marked in a permanent manner. The extreme end of the
outfall should be indicated by a can buoy similar to that shown
in Fig. 33, made by Messrs. Brown, Lenox, and Co. (Limited),
Milwall, London, E., which costs about £75, including a 20 cwt.
sinker and 10 fathoms of chain, and is approved for the purpose
by the Board of Trade.

[Illustration: FIG 33 CAN BUOY FOR MARKING OUTFALL SEWER.]

It is not desirable to fasten the chain to any part of the
outfall instead of using a sinker, because at low water the
slack of the chain may become entangled, which by preventing
the buoy from rising with the tide, will lead to damage; but a
special pile may be driven for the purpose of securing the
buoy, at such a distance from the outlet that the chain will
not foul it. The buoy should be painted with alternate vertical
stripes of yellow and green, and lettered "Sewer Outfall" in
white letters 12 in deep.

It must be remembered that it is necessary for the plans and
sections of outfall sewers and other obstructions proposed to
be placed in tidal waters to be submitted to the Harbour and
Fisheries Department of the Board of Trade for their approval,
and no subsequent alteration in the works may be made without
their consent being first obtained.




CHAPTER XIII.

THE DISCHARGE OF SEA OUTFALL SEWERS.


The head which governs the discharge of a sea outfall pipe is
measured from the surface of the sewage in the tank, sewer, or
reservoir at the head of the outfall to the level of the sea.
As the sewage is run off the level of its surface is lowered,
and at the same time the level of the sea is constantly varying
as the tide rises and falls, so that the head is a variable
factor, and consequently the rate of discharge varies. A curve
of discharge may be plotted from calculations according to
these varying conditions, but it is not necessary; and all
requirements will be met if the discharges under certain stated
conditions are ascertained. The most important condition,
because it is the worst, is that when the level of the sea is
at high water of equinoctial spring tides and the reservoir is
practically empty.

Sea water has a specific gravity of 1.027, and is usually taken
as weighing 64.14 lb per cubic foot, while sewage may be taken
as weighing 62.45 lb per cubic foot, which is the weight of
fresh water at its maximum density. Now the ratio of weight
between sewage and sea water is as 1 to 1.027, so that a column
of sea water l2 inches in height requires a column of fresh
water 12.324, or say 12-1/3 in, to balance it; therefore, in
order to ascertain the effective head producing discharge it
will be necessary to add on 1/3 in for every foot in depth of
the sea water over the centre of the outlet.

The sea outfall should be of such diameter that the contents of
the reservoir can be emptied in the specified time--say, three
hours--while the pumps are working to their greatest power in
pouring sewage into the reservoir during the whole of the
period; so that when the valves are closed the reservoir will
be empty, and its entire capacity available for storage until
the valves are again opened.

To take a concrete example, assume that the reservoir and
outfall are constructed as shown in Fig. 34, and that it is
required to know the diameter of outfall pipe when the
reservoir holds 1,000,000 gallons and the whole of the pumps
together, including any that may be laid down to cope with any
increase of the population in the future, can deliver 600,000
gallons per hour. When the reservoir is full the top water
level will be 43.00 O.D., but in order to have a margin for
contingencies and to allow for the loss in head due to entry of
sewage into the pipe, for friction in passing around bends, and
for a slight reduction in discharging capacity of the pipe by
reason of incrustation, it will be desirable to take the
reservoir as full, but assume that the sewage is at the level
31.00. The head of water in the sea measured above the centre
of the pipe will be 21 ft, so that

[*Math: $21 \times 1/3$],

or 7 in--say, 0.58 ft--must be added to the height of high
water, thus reducing the effective head from 31.00 - 10.00 =
21.00 to 20.42 ft The quantity to be discharged will be

[*Math: $\frac{1,000,000 + (3 * 600,000)}{3}$]

= 933,333 gallons per hour = 15,555 gallons per minute, or,
taking 6.23 gallons equal to 1 cubic foot, the quantity equals
2,497 cubic feet per min Assume the required diameter to be 30
in, then, by Hawksley's formula, the head necessary to produce
velocity =

[*Math: $\frac{Gals. per min^2}{215 \times diameter in
inches^4} = \frac{15,555^2}{215 * 30^4}$]

 = 1.389 ft, and the head to overcome friction =

[*Math: $\frac{Gals. per min^2 \times Length in yards}{240 *
diameter in inches^5} = \frac{15,555^2 * 2042}{240 * 30^5}]

= 84.719. Then 1.389 + 84.719 = 86.108--say, 86.11 ft; but the
acutal head is 20.42 ft, and the flow varies approximately as
the square root of the head, so that the true flow will be
about

[*Math: $15,555 * \sqrt{\frac{20.42}{86.11} = 7574.8$]

[Illustration: FIG 34 DIAGRAM ILLUSTRATING CALCULATIONS FOR THE
DISCHARGE OF SEA OUTFALLS]

--say 7,575 gallons. But a flow of 15,555 gallons per minute is
required, as it varies approximately as the fifth power of the
diameter, the requisite diameter will be about

[*Math: \sqrt[5]{\frac{30^5 \times 15,555}{7575}] = 34.64
inches.

Now assume a diameter of 40 in, and repeat the calculations.
Then head necessary to produce velocity

[*Math: = \frac{15,555^2}{215 \times 40^4}] = 0.044 ft, and
head to overcome friction =

[*Math: \frac{15,555^2 \times 2042}{240 \times 40^5}]

= 20.104 ft Then 0.044 + 20.104 = 20.148, say 20.15 ft, and the
true flow will therefore be about

[*Math: 15,555 * \sqrt{\frac{20.42}{20.15}}]

= 15,659 gallons, and the requisite diameter about

[*Math: \sqrt[5]{\frac{40^5 * 15,555}{15,659}}]

= 39.94 inches.

When, therefore, a 30 in diameter pipe is assumed, a diameter
of 34.64 in is shown to be required, and when 40 in is assumed
39.94 in is indicated.


Let _a_ = difference between the two assumed diameters. _b_ =
increase found over lower diameter. _c_ = decrease found under
greater diameter. _d_ = lower assumed diameter.


Then true diameter =

[*Math: d + \frac{ab}{b+c} = 30 + \frac{10 \times
4.64}{4.64+0.06} = 30 + \frac{46.4}{4.7} = 39.872],

or, say, 40 in, which equals the required diameter.

A simpler way of arriving at the size would be to calculate it
by Santo Crimp's formula for sewer discharge, namely, velocity
in feet per second =

[*Math: 124 \sqrt[3]{R^2} \sqrt{S}],

where R equals hydraulic mean depth in feet, and S = the ratio
of fall to length; the fall being taken as the difference in
level between the sewage and the sea after allowance has been
made for the differing densities. In this case the fall is
20.42 ft in a length of 6,126 ft, which gives a gradient of 1
in 300. The hydraulic mean depth equals

[*Math: \frac{d}{4}];

the required discharge, 2,497 cubic feet per min, equals the
area,

[*Math: (\frac{\pi d^2}{4})]

multiplied by the velocity, therefore the velocity in feet per
second = 4/(pi d^2) x 2497/60 = 2497/(15 pi d^2) and the
formula then becomes

2497/(15 pi d^2) = 124 x * 3rd_root(d^2)/3rd_root(4^3*) x
sqrt(1)/sqrt(300)

or d^2 x 3rd_root(d^2) = 3rd_root(d^6) = (2497 x 3rd_root(16) x
sqrt(300)) / (124 x 15 x 3.14159*)

or (8 x log d)/3 = log 2497 + (1/3 x log 16) + (* x log 300) -
log 124 - log 15 - log 3.14159;

or log d = 3/8 (3.397419 + 0.401373 + 1.238561 - 2.093422 -
1.176091 - 0.497150) = 3/8 (1.270690) = 0.476509.

* d = 2.9958* feet = 35.9496, say 36 inches.

As it happens, this could have been obtained direct from the
tables where the discharge of a 36 in pipe at a gradient of 1
in 300 = 2,506 cubic feet per minute, as against 2,497 cubic
feet required, but the above shows the method of working when
the figures in the tables do not agree with those relating to
the particular case in hand.

This result differs somewhat from the one previously obtained,
but there remains a third method, which we can now make trial
of--namely, Saph and Schoder's formula for the discharge of
water mains, V = 174 3rd_root(R^2) x S^.51*. Substituting
values similar to those taken previously, this formula can be
written

2497/(15 pi d^2) = 174 x 3rd_root(d_2)/3rd_root(4^2) x
1^.51/300^.51

or d^2 x 3rd_root(d^2) = 3rd_root(d^6) = (2497 x 3rd_root(16) x
300^.51) / (174 x 15 x 3.14159)

or* log d = 3/8 (3.397419 + 0.401373 + (54 x 2.477121) -
2.240549 - 1.176091 - 0.497150) = 3/8 (1.222647) = 0.458493

* d = 2.874* feet = 34.388 say 34 1/2 inches.

By Neville's general formula the velocity in feet per second =
140 SQRT(RS)-11(RS)^(1/3) or, assuming a diameter of 37 inches,


V = 140 X SQRT(37/(12 x 4) x 1/300) - 11 (37/(12x4x300))^(1/3)


= 140 x SQRT(37/14400) - 11 (37/1440)^(1/3)

= 7.09660 - 1.50656 = 5.59 feet per second.

Discharge = area x velocity; therefore, the discharge in cubic
feet per minute

= 5.59 x 60 x (3.14159 x 37^2)/(4*12^2) = 2504 compared with

2,497 c.f.m, required, showing that if this formula is used the
pipe should be 37 in diameter.

The four formulæ, therefore, give different results, as
follows:--

Hawksley = 40 in
Neville = 37 in
Santo Crimp = 36 in
Saph and Schoder = 34-1/2 in

The circumstances of the case would probably be met by
constructing the outfall 36 in in diameter.

It is very rarely desirable to fix a flap-valve at the end of a
sea outfall pipe, as it forms a serious obstruction to the flow
of the sewage, amounting, in one case the writer investigated,
to a loss of eight-ninths of the available head; the head was
exceptionally small, and the flap valve practically absorbed it
all. The only advantage in using a flap valve occurs when the
pipe is directly connected with a tank sewer below the level of
high water, in which case, if the sea water were allowed to
enter, it would not only occupy space required for storing
sewage, but it would act on the sewage and speedily start
decomposition, with the consequent emission of objectionable
odours. If there is any probability of sand drifting over the
mouth of the outfall pipe, the latter will keep free much
better if there is no valve. Schemes have been suggested in
which it was proposed to utilise a flap valve on the outlet so
as to render the discharge of the sewage automatic. That is to
say, the sewage was proposed to be collected in a reservoir at
the head of, and directly connected to, the outfall pipe, at
the outlet end of which a flap valve was to be fixed. During
high water the mouth of the outfall would be closed, so that
sewage would collect in the pipes, and in the reservoir beyond;
then when the tide had fallen such a distance that its level
was below the level of the sewage, the flap valve would open,
and the sewage flow out until the tide rose and closed the
valve. There are several objections to this arrangement. First
of all, a flap valve under such conditions would not remain
watertight, unless it were attended to almost every day, which
is, of course, impracticable when the outlet is below water. As
the valve would open when the sea fell to a certain level and
remain open during the time it was below that level, the period
of discharge would vary from, say, two hours at neap tides to
about four hours at springs; and if the two hours were
sufficient, the four hours would be unnecessary. Then the
sewage would not only be running out and hanging about during
dead water at low tide, but before that time it would be
carried in one direction, and after that time in the other
direction; so that it would be spread out in all quarters
around the outfall, instead of being carried direct out to sea
beyond chance of return, as would be the case in a well-
designed scheme.

When opening the valve in the reservoir, or other chamber, to
allow the sewage to flow through the outfall pipe, care should
be taken to open it at a slow rate so as to prevent damage by
concussion when the escaping sewage meets the sea water
standing in the lower portion of the pipes. When there is
considerable difference of level between the reservoir and the
sea, and the valve is opened somewhat quickly, the sewage as it
enters the sea will create a "water-spout," which may reach to
a considerable height, and which draws undesirable attention to
the fact that the sewage is then being turned into the sea.




Chapter XIV

TRIGONOMETRICAL SURVEYING.


In the surveying work necessary to fix the positions of the
various stations, and of the float, a few elementary
trigonometrical problems are involved which can be
advantageously explained by taking practical examples.

Having selected the main station A, as shown in Fig. 35, and
measured the length of any line A B on a convenient piece of
level ground, the next step will be to fix its position upon
the plan. Two prominent landmarks, C and D, such as church
steeples, flag-staffs, etc., the positions of which are shown
upon the ordnance map, are selected and the angles read from
each of the stations A and B. Assume the line A B measures ll7
ft, and the angular measurements reading from zero on that line
are, from A to point C, 29° 23' and to point D 88° 43', and
from B to point C 212° 43', and to point D 272° 18' 30". The
actual readings can be noted, and then the arrangement of the
lines and angles sketched out as shown in Fig. 35, from which
it will be necessary to find the lengths AC and AD. As the
three angles of a triangle equal 180°, the angle B C A = 180°-
147° 17'-29° 23'= 3° 20', the angle B D A = 180°-87° 41' 30"-
88° 43'= 3° 35' 30". In any triangle the sides are
proportionate to the sines of the opposite angles, and vice
versa; therefore,

A B : A C :: sin B C A : sin A B C, or sin B C A : A B :: sin
ABC : A C, nr A C = (A B sin A B C) / (sin B C A) = (117 x sin
147° 17') / (sin 3° 20')

or log A C = log 117 + L sin 147° 17' - L sin 3° 20'.

The sine of an angle is equal to the sine of its supplement, so
that sin 147° 17' = sin 32° 43', whence log A C = 2.0681859 +
9.7327837-8.7645111 = 3.0364585

Therefore A C = 1087.6 feet.



Similarly sin B D A: A B :: sin A B D: A D

                 A B sin A B D     117 x sin 87° 41' 30"
therefore A D = --------------- = -----------------------
                   sin B D A          sin 3° 35' 30"

whence log A D = log ll7 +  L sin 87° 41' 30" - L sin 3° 35' 30"
               = 2.0681859 + 9.99964745 - 8.79688775
               = 3.2709456

Therefore AD = 1866.15 feet.



The length of two of the sides and all three angles of each of
the two triangles A C B and A D B are now known, so that the
triangles can be drawn upon the base A B by setting off the
sides at the known angles, and the draughtsmanship can be
checked by measuring the other known side of each triangle. The
points C and D will then represent the positions of the two
landmarks to which the observations were taken, and if the
triangles are drawn upon a piece of tracing paper, and then
superimposed upon the ordnance map so that the points C and D
correspond with the landmarks, the points A and B can be
pricked through on to the map, and the base line A B drawn in
its correct position.

If it is desired to draw the base line on the map direct from
the two known points, it will be necessary to ascertain the
magnitude of the angle A D C. Now, in any triangle the tangent
of half the difference of two angles is to the tangent of half
their sum as the difference of the two opposite sides is to
their sum; that is:--



    Tan 1/2 (ACD - ADC): tan 1/2 (ACD + ADC)::
      AD - AC : AD + AC,

  but ACD + ADC = l80° - CAD = 120° 40',
  therefore, tan 1/2 (ACD - ADC): tan 1/2 (120° 40')::
         (1866.15 - 1087.6): (1866.15 + 1087.6),

                                    778.55 tan 60° 20'
  therefore, tan 1/2 (ACD - ADC) = --------------------
                                         2953.75

  or L tan 1/2 (ACD - ADC) = log 778.55 + L tan 60° 20'
        - log 2953.75 .
    = 2.8912865 + 10.2444l54 - 3.4703738
    = 9.6653281 .•. 1/2 (ACD - ADC) = 24° 49' 53"
    .•. ACD - ADC = 49° 39' 46".  Then algebraically

               (ACD + ADC) - (ACD - ADC)
        ADC = ---------------------------
                          2

                120° 40' - 49° 39' 46"     71° 0' 14"
    .•. ADC = ------------------------- = ------------ = 35° 30' 7",
                           2                    2

         ACD = 180° - 35° 30' 7" - 59° 20' = 85° 9' 53".



[Illustration:  Fig. 35.--Arrangement of lines and Angles
Showing Theodolite Readings and Dimensions.]

Now join up points C and D on the plan, and from point D set
off the line D A, making an angle of 35° 30' 7" with C D, and
having a length of l866.15 ft, and from point C set off the
angle A C D equal to 85° 9' 53". Then the line A C should
measure l087.6 ft long, and meet the line A D at the point A,
making an angle of 59° 20'. From point A draw a line A B, ll7
ft long, making an angle of 29° 23' with the line A C; join B
C, then the angle ABC should measure 147° 17', and the angle B
C A 3° 20'. If the lines and angles are accurately drawn, which
can be proved by checking as indicated, the line A B will
represent the base line in its correct position on the plan.

The positions of the other stations can be calculated from the
readings of the angles taken from such stations. Take stations
E, F, G, and H as shown in Fig. 36*, the angles which are
observed being marked with an arc.

It will be observed that two of the angles of each triangle are
recorded, so that the third is always known. The full lines
represent those sides, the lengths of which are calculated, so
that the dimensions of two sides and the three angles of each
triangle are known. Starting with station E,

Sin A E D: A D:: sin D A E: D E

       A D sin D A E
 D E = --------------
        sin A E D

or log D E = log A D + L sin D A E-L sin A E D.

From station F, E and G are visible, but the landmark D cannot
be seen; therefore, as the latter can be seen from G, it will
be necessary to fix the position of G first. Then,

sin E G D: D E :: sin E D G : E G,

        D E sin E D G
or EG= ---------------
          sin E G D

Now, sin E F G: E G :: sin F E G : F G

        E G sin F E G
  F G = -------------
          sin E F G

thus allowing the position of F to be fixed, and then

sin F H G : F G :: sin F G H : F H

       F G sin F G H
  F H= -------------
         sin F H G


[Illustration: FIG 36.--DIAGRAM ILLUSTRATING TRIGONOMETRICAL
SURVEY OF OBSERVATION STATIONS.]

In triangles such as E F G and F G H all three angles can be
directly read, so that any inaccuracy in the readings is at once
apparent. The station H and further stations along the coast being:
out of sight of landmark D, it will be as well to connect the survey
up with another landmark K, which can be utilised in the forward work;
the line K H being equal to


F H sin K F H
-------------
sin F K H


The distance between C and D in Fig. 35 is calculated in a
similar manner, because sin A C D : A D:: sin CAD : CD,


          AD sin CAD     1866.15 sin 59° 20'
or CD =   ----------  =  -------------------
            sin SCD         sin 85° 9' 53"

or log CD = log 1866.15 + L sin 59° 20'  - L sin 85° 9' 53"

          = 3.2709456 + 9.9345738 - 9.9984516

          = 3.2070678. ' . CD = 1610.90 ft


The distance between any two positions of the float can be
obtained by calculation in a similar way to that in which the
length C D was obtained, but this is a lengthy process, and is
not necessary in practical work. It is desirable, of course,
that the positions of all the stations be fixed with the
greatest accuracy and plotted on the map, then the position of
the float can be located with sufficient correctness, if the
lines of sight obtained from the angles read with the
theodolites are plotted, and their point of intersection marked
on the plan. The distance between any two positions of the
float can be scaled from the plan.

The reason why close measurement is unnecessary in connection
with the positions of the float is that it represents a single
point, whereas the sewage escaping with considerable velocity
from the outfall sewer spreads itself over a wide expanse of
sea in front of the outlet, and thus has a tangible area. The
velocity of any current is greatest in the centre, and reduces
as the distance from the centre increases, until the edges of
the current are lost in comparative still water; so that
observations taken of the course of one particle, such as the
float represents, only approximately indicate the travel of the
sewage through the sea. Another point to bear in mind is that
the dilution of the sewage in the sea is so great that it is
generally only by reason of the unbroken fæcal, or other
matter, that it can be traced for any considerable distance
beyond the outfall. It is unlikely that such matters would
reach the outlet, except in a very finely divided state, when
they would be rapidly acted upon by the sea water, which is a
strong oxidising agent.




CHAPTER XV.

HYDROGRAPHICAL SURVEYING.


Hydrographical surveying is that branch of surveying which
deals with the complete preparation of charts, the survey of
coast lines, currents, soundings, etc., and it is applied in
connection with the sewerage of sea coast towns when it is
necessary to determine the course of the currents, or a float,
by observations taken from a boat to fixed points on shore, the
boat closely following the float. It has already been pointed
out that it is preferable to take the observations from the
shore rather than the boat, but circumstances may arise which
render it necessary to adopt the latter course.

In the simplest case the position of the boat may be found by
taking the compass bearings of two known objects on shore. For
example, A and B in Fig. 37 may represent the positions of two
prominent objects whose position is marked upon an ordnance map
of the neighbourhood, or they may be flagstaffs specially set
up and noted on the map; and let C represent the boat from
which the bearings of A and B are taken by a prismatic compass,
which is marked from 0 to 360°. Let the magnetic variation be
N. 15° W., and the observed bearings A 290, B 320, then the
position stands as in Fig. 38, or, correcting for magnetic
variation, as in Fig. 39, from which it will be seen that the
true bearing of C from A will be 275-180=95° East of North, or
5° below the horizontal, and the true bearing of C from B will
be 305-180=120° East of North, or 35° below the horizontal.
These directions being plotted will give the position of C
by their intersection. Fig. 40 shows the prismatic compass in
plan and section. It consists practically of an ordinary compass
box with a prism and sight-hole at one side, and a corresponding
sight-vane on the opposite side. When being used it is held
horizontally in the left hand with the prism turned up in the
position shown, and the sight-vane raised. When looking through
the sight-hole the face of the compass-card can be seen by
reflection from the back of the prism, and at the same time the
direction of any required point may be sighted with the wire in the
opposite sight vane, so that the bearing of the line between the
boat and the required point may be read. If necessary, the
compass-card may be steadied by pressing the stop at the base of
the sight vane. In recording the bearings allowance must in all
cases be made for the magnetic pole. The magnetic variation for
the year 1910 was about l5 1/2° West of North, and it is moving
nearer to true North at the rate of about seven minutes per annum.

[Illustration: FIG. 37.--POSITION OF BOAT FOUND BY COMPASS
BEARINGS.]

[Illustration: FIG. 38.--REDUCTION OF BEARINGS TO MAGNETIC NORTH.]

[Illustration: FIG. 39.--REDUCTION OF BEARINGS TO TRUE NORTH.]

There are three of Euclid's propositions that bear very closely
upon the problems involved in locating the position of a
floating object with regard to the coast, by observations taken
from the object. They are Euclid I. (32), "The three interior
angles of every triangle are together equal to two right
angles"; Euclid III. (20),

"The angle at the centre of a circle is double that of the
angle at the circumference upon the same base--that is, upon
the same part of the circumference,"

or in other words, on a given chord the angle subtended by it
at the centre of the circle is double the angle subtended by it
at the circumference; and Euclid III. (21),

"The angles in the same segment of a circle are equal to one
another."

[Illustration:  Fig. 40.--Section and Plan of Prismatic
Compass.]

Having regard to this last proposition (Euclid III., 21), it
will be observed that in the case of Fig. 37 it would not have
been possible to locate the point C by reading the angle A C B
alone, as such point might be amywhere on the circumference of
a circle of which A B was the chord. The usual and more
accurate method of determining the position of a floating
object from the object, itself, or from a boat alongside, is by
taking angles with a sextant, or box-sextant, between three
fixed points on shore in two operations. Let A B C, Fig. 41, be
the three fixed points on shore, the positions of which are
measured and recorded upon an ordnance map, or checked if they
are already there. Let D be the floating object, the position
of which is required to be located, and let the observed angles
from the object be A D B 30° and B D C 45°. Then on the map
join A B and B C, from A and B set off angles = 90 - 30 = 60°,
and they will intersect at point E, which will be the centre of
a circle, which must be drawn, with radius E A. The circle will
pass through A B, and the point D will be somewhere on its
circumference. Then from B and C set off angles = 90-45 = 45°,
which will intersect at point F, which will be the centre of a
circle of radius F B, which will pass through points
B C, and point D will be somewhere on the circumference of this
circle also; therefore the intersection of the two circles at D
fixes that point on the map. It will be observed that the three
interior angles in the triangle A B E are together equal to two
right angles (Euclid I. 32), therefore the angle A E B = 180 -
2 x (90 - 30) = 600, so that the angle A E B is double the
angle A D B (Euclid III., 20), and that as the angles
subtending a given chord from any point of the circumference
are equal (Euclid III, 21), the point that is common to the two
circumferences is the required point. When point D is inked in,
the construction lines are rubbed out ready for plotting the
observations from the next position. When the floating point is
out of range of A, a new fixed point will be required on shore
beyond C, so that B, C, and the new point will be used
together. Another approximate method which may sometimes be
employed is to take a point on a piece of tracing paper and
draw from it three lines of unlimited length, which shall form
the two observed angles. If, now, this piece of paper is moved
about on top of the ordnance map until each of the three lines
passes through the corresponding fixed points on shore, then the
point from which the lines radiate will represent the position of
the boat.

[Illustration:  Fig. 41. Geometrical Diagram for Locating
Observation Point Afloat.]

The general appearance of a box-sextant is as shown in Fig. 42,
and an enlarged diagrammatic plan of it is shown in Fig. 43. It
is about 3 in in diameter, and is made with or without the
telescope; it is used for measuring approximately the angle
between any two lines by observing poles at their extremities
from the point of intersection. In Fig. 43, A is the sight-
hole, B is a fixed mirror having one-half silvered and the
other half plain; C is a mirror attached to the same pivot as
the vernier arm D. The side of the case is open to admit rays
of light from the observed objects. In making an observation of
the angle formed by lines to two poles, one pole would be seen
through the clear part of mirror B, and at the same time rays
of light from the other pole would fall on to mirror C, which
should be moved until the pole is reflected on the silvered
part of mirror B, exactly in line, vertically, with the pole
seen by direct vision, then the angle between the two poles
would be indicated on the vernier. Take the case of a single
pole, then the angle indicated should be zero, but whether it
would actually be so depends upon circumstances which may be
explained as follows: Suppose the pole to be fixed at E, which
is extremely close, it will be found that the arrow on the vernier
arm falls short of the zero of the scale owing to what may be
called the width of the base line of the instrument. If the pole
is placed farther off, as at F, the rays of light from the pole will
take the course of the stroke-and-dot line, and the vernier arm will
require to be shifted nearer the zero of the scale. After a distance
of two chains between the pole and sextant is reached, the rays of
light from the pole to B and C are so nearly parallel that the
error is under one minute, and the instrument can be used under
such conditions without difficulty occurring by reason of
error. To adjust the box-sextant the smoked glass slide should
be drawn over the eyepiece, and then, if the sun is sighted, it
should appear as a perfect sphere when the vernier is at zero,
in whatever position the sextant may be held. When reading the
angle formed by the lines from two stations, the nearer station
should be sighted through the plain glass, which may
necessitate holding the instrument upside down. When the angle
to be read between two stations exceeds 90°, an intermediate
station should be fixed, and the angle taken in two parts, as
in viewing large angles the mirror C is turned round to such an
extent that its own reflection, and that of the image upon it,
is viewed almost edgeways in the mirror B.

[Illustration:  Fig. 42.--Box-Sextant.]

It should be noted that the box-sextant only reads angles in
the plane of the instrument, so that if one object sighted is
lower than the other, the angle read will be the direct angle
between them, and not the horizontal angle, as given by a
theodolite.

The same principles may be adopted for locating the position of
an object in the water when the observations have to be taken
at some distance from it. To illustrate this, use may be made
of an examination question in hydrographical surveying given at
the Royal Naval College, Incidentally, it shows one method of
recording the observations. The question was as follows:--

[Illustration:  Fig. 43.--Diagram Showing Principle of Box-
Sextant]

"From Coastguard, Mound bore N. 77° W. (true) 0.45 of a mile,
and Mill bore, N. 88° E, 0.56 of a mile, the following stations
were taken to fix a shoal on which the sea breaks too heavily to
risk the boat near:--

Mound 60° C.G. 47° Mill.
[Greek:  phi]
Centre of shoal
Mound 55° C.G. 57° 30' Mill.
[Greek:  phi]
Centre of shoal.

Project the positions on a scale of 5 in = a mile, giving the
centre of the shoal." It should be noted that the sign [Greek:
phi] signifies stations in one line or "in transit," and C G
indicates coastguard station. The order of lettering in Fig. 44
shows the order of working.

[Illustration:  Fig. 44.--Method of Locating Point in Water
When Observations Have to Be Taken Beyond It.]

The base lines A B and A C are set out from the lengths and
directions given; then, when the boat at D is "in transit" with
the centre of the shoal and the coastguard station, the angle
formed at D by lines from that point to B and A is 60°, and the
angle formed by lines to A and C is 47°. If angles of 90° - 60°
are set up at A and B, their intersection at E will, as has
already been explained, give the centre of a circle which will
pass through points A, B, and D. Similarly, by setting up
angles of 90°-47° at A and C, a circle is found which will pass
through A C and D. The intersection of these circles gives the
position of the boat D, and it is known that the shoal is
situated somewhere in the straight line from D to A. The boat
was then moved to G, so as to be "in transit" with the centre
of the shoal and the mound, and the angle B G A was found to be
55°, and the angle A G C 57° 30'. By a similar construction to
that just described, the intersection of the circles will give
the position of G, and as the shoal is situated somewhere in
the line G B and also in the line A D, the intersection of
these two lines at K will give its exact position.


Aberdeen Sea Outfall
Admiralty, Diving Regulations of
  --Charts, Datums for Soundings on
  --Main Currents Shown on
Age of Tide
Air Pressure on Tides, Effect of
Almanac, Nautical
Analysis of Cement
  --Sea Water
Anchor Bolts for Sea Outfalls
Anemometer for Measuring Wind
Aphelion
Apogee
Atlantic Ocean, Tides in
Autumnal Equinox
Barometric Pressure, Effect on Tides of
Beach Material, Use in Concrete of
Beaufort Scale for Wind
Bench Mark for Tide Gauge
"Bird" Tides
Board of Trade, Approval of Outfall by
Bolts for Sea Outfall Pipes
Box Sextant
Bristol Channel
  --Datum for Tides at
Buoy for Marking Position of Outfall
Can Buoy to Mark Position of Outfall
Cast Iron, Resistance to Sea Water of
Cement, Action of Sea Water on
  --Analysis of
  --Characteristics Causing Hardening of
    --Setting of
  --Effect of Saline Matters on Strength of
    --Sea Water on Setting Time of
  --Physical Changes Due to Action of Sea Water on
  --Precautions in Marine Use of
  --Retardation of Setting Time of
  --Tests for Marine Use of
Centrifugal Force, Effect on Tides of
Centripetal Force, Effect on Tides of
  --Variations in Intensity of
Charts, Datum for Soundings on
  --Main Currents Shown on
Chepstow, Greatest Tide at
Clifton, Tides at
Compass, Magnetic Variation
  --Marine
  --Prismatic
Concentration of Storm Water in Sewers
Concrete, Action of Sea Water on
  --Composition to Withstand Sea Water
  --Destruction in Sea Water of
Crown, Foreshore owned by
Currents and Tides. Lack of co-ordination in change of
  --Formation of
  --in Rivers, 30
  --Observations of
  --Variation of Surface and Deep
  --Variations in Velocity of
Current Observations by Marine Compass
  --Theodolites
  --Floats for
  --Hydrographical Surveying for
  --Method of making
  --Plotting on Plans, The
  --Selecting Stations for
  --Special points for consideration in making
  --Suitable Boat for
  --Trigonometrical Surveying for
Datum Levels for Tides
Declination of Sun and Moon
Decompression after Diving
Density of Sea Water
Derivative Waves
Design of Schemes, Conditions governing
Diffusion of Sewage in Sea
Discharge from Sea Outfalls, Calculations for
  --Precautions necessary for
  --Time of
Disposal of Sewage by Diffusion
  --dependent on time of Discharge
Diurnal Inequality of Tides
Diverting-plate Storm Overflow
Diving
  --Illnesses caused by
  --Instruction in
  --Medical Examination previous to
  --Physical Principles involved in
  --Equipment
Diving Equipment, Weight of
Dublin, Datum for Tides at
Earth, Distance from Moon
    --Sun
  --Orbit around Sun of
  --Size of
  --Time and Speed of Revolution of
Equinox
Erosion of Shore caused by Sea Outfalls
Establishment
Flap Valves on Sea Outfall Pipes
Floats, Deep and Surface
  --to govern Pumping Plant
Foreshore owned by Crown
Gauges, Measuring flow over Weirs by
Gauging flow of Sewage
  --, Formula: for
Gradient, Effect on Currents of Surface
  --Tides of Barometric
Gravity, Specific, of Sea Water
  --Tides caused by
Great Crosby Sea Outfall
Harbour and Fisheries Dept., Approval of Outfall by
Harwich, Mean Level of Sea at
High Water Mark of Ordinary Tides
Hook-Gauge, for Measuring flow over Weirs
Hull, Mean Level of Sea at
Hydrographical Surveying Problems in Current Observations
Impermeable Areas, Flow of Rain off
  --Percentage of
  --per Head of Population
Indian Ocean, Tides in
Infiltration Water
Irish Channel, Analysis of Water in
Iron, Effect of Sea Water on Cast
June, Low Spring: Tides in
Kelvin's Tide Predicting Machine
Land, Area of Globe Occupied by
Leap-weir Storm Overflow
Liverpool, Datum for Tides at
  --Soundings on Charts of
  --Tide Tables
Lloyd-Davies, Investigations by
Local Government Board, Current Observations Required for
London, Datum for Port of
Low Water Mark of Ordinary Tides
Lunar Month
Lunation
Magnetic Variation of Compass
Marine Compass
Mean High Water
Mersey, Soundings on Charts of
Mixing Action of Sewage and Water
Moon, Declination of
  --Distance from Earth of
  --Effect on Tides of
  --Mass of
  --Minor Movements of
  --Orbit around Earth of
  --Perigee and Apogee
Morse Code for Signalling
Nautical Almanac
Neap Tides
  --Average Rise of
Orbit of Earth around Sun
  --Moon around Earth
Ordinary Tides, lines on Ordnance Maps of
Ordnance Datum for England
  --Ireland, 17
  --Records made to fix
  --Maps, lines of High and Low Water on
Outfall Sewers, Approval by Board of Trade of
  --Calculations for Discharge of
  --Construction of
  --Detail Designs for
  --Details of cast-iron Pipe Joints for
  --Flap Valves on end of
  --Inspection during Construction of
  --Marking position by Buoy of
  --Selection of Site for
Overflows for Storm Water
Pacific Ocean, Tides in
Parliament, Current Observations Required for
Perigee
Perihelion
Piling for Sea Outfalls
Pipes, Joints of Cast Iron
  --Steel
Plymouth, Mean Sea Level at
Predicting Tides
Primary Waves
Prismatic Compass
Pumping
  --Cost of
  --Plant
  --Management of
  --Utilisation of Windmills for
Pumps for Use with Windmills
Quantity of Rainfall to Provide for
  --Sewage to Provide for
Rainfall
  --at Times of Light Winds
  --Frequency of Heavy
  --in Sewers
  --Intensity of
  --Storage Capacity to be Provided for
  --To Provide for
Range of Tides
Rise of Tides
Screening Sewage before Discharge
  --Storm Water before Overflow
Sea, Mean Level of
Sea Outfalls, Calculations for Discharge of
  --Construction of
  --Design of
  --Lights and Buoy to mark position of
  --Selection of Site for
Seashore Material used in Concrete
Sea, Variation around Coast in level of
  --Water, Analysis of
  --Effect on Cast-Iron of
  --Effect on Cement
  --Galvanic action in
  --Weight of
Secondary Waves
Separate System of Sewerage
Sewage, Effect of Sea Water on
  --Gauging flow of
    --Calculations for
  --Hourly and daily variation in flow of, 42
  --Quantity to provide for
Sewers, Economic considerations in provision of Surface Water
  --Effect on Design of Scheme of Subsidiary
  --Storm Water in
Sextant, Box
Signalling, Flags for
  --Morse Code for
Solstice, Summer and Winter
Soundings on Charts, Datum for
Southampton, Tides at
Southern Ocean, High Water in
  --Origin of Tides in
  --Width and Length of
Specific Gravity of Sea Water
Spring Tides
  --Average Rise of
  --Variation in Height of
Storage Tanks, Automatic High Water Alarms for
  --Determination of Capacity of
  --For Windmill Pumps
Storm Water in Sewers
  --Overflows
Subsidiary Sewers, Effect on Design of Scheme of
Summer Solstice
Sun, Aphelion and Perihelion
  --Declination of
  --Distance from Earth
  --Effect on Tides of
  --Mass of
  --Minor Movements of
Surface Water Sewers, Average Cost of
  --Economic Considerations in Provision of
Surveying, Problems in Hydrographical
  --Trigonometrical
Thames Conservancy Datum
  --Flow of Sewage in
Tidal Action in Crust of Earth
  --Attraction
  --Day, Length of
  --Flap Valves on Sea Outfall Pipes
  --Observations, Best Time to Make
  --Records, Diagram of
  --Rivers, Tides and Currents in
  --Waves, Length of Primary
    --Secondary or Derivative
    --Speed of Primary
    --Velocity of
Tide Gauge, Method of Erecting
  --Selecting Position of
Tide, Observations of Rise and Fall of
Tide-Predicting Machine
  --Recording Instrument
  --Tables
Tides, Abnormally High
  --Age of
Tides and Currents, Lack of Co-ordination in Change of
  --Diagrammatic Representation of Principal
  --Diurnal Inequality
  --Double, 9
  --Effect of Barometric Pressure on
    --Centripetal and Centrifugal Force
    --Storms on,
  --Extraordinary High
  --Formation of
  --in Rivers
  --lines on Ordnance Maps of High and Low Water of
  --Propagation to Branch Oceans of
  --Proportionate Effect of Sun and Moon on
  --Range of
  --Rate of Rise and Fall of
  --Rise of
  --Spring and Neap
  --Variations in Height of
Towers for Windmills
Trade Wastes, Effect on flow of Sewage of
Trass in Cement for Marine Vork
Trigonometrical Surveying for Cuirent Observations
Trinity High Water Mark
Upland Water, Effect on Rivers of
Valves on Sea Outfall Pipes
Velocity of Currents
Vernal Equinox
Visitors, Quantity of Sewage from
Volume of Sewage
Water, Area of Globe occupied by
  --Fittings, Leakage from
  --Power for Pumping
  --Supply, Quantity per Head for
  --Weight of
Waterloo Sea Outfall
Waves, Horizontal Movement of
  --Motion of
  --Primary and Secondary
  --Tidal
  --Wind
Weight of Fresh Water
  --Sea Water
  --Sewage
Weirs for Gauging Sewage, Design of
  --Storm Overflow by Parallel
Weymouth, Mean Level of Sea at
Wind
  --Beaufort Scale for
Wind, Mean Hourly Velocity of
  --Measuring Velocity of
  --Monthly Analysis of
  --Power of Windmills According to Velocity of
  --Rainfall at Time of Light
  --Velocity and Pressure of
  --Waves
Windmills
  --Comparative Cost of
  --Details of Construction of
  --Effective Duty of
  --Efficient Sizes of
  --For Pumping Sewage
  --Height of Towers for
  --Power in Varying Winds of
Winter Solstice





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