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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/7980-8.txt b/7980-8.txt new file mode 100644 index 0000000..592e193 --- /dev/null +++ b/7980-8.txt @@ -0,0 +1,4991 @@ +Project Gutenberg's The Sewerage of Sea Coast Towns, by Henry C. Adams + +Copyright laws are changing all over the world. Be sure to check the +copyright laws for your country before downloading or redistributing +this or any other Project Gutenberg eBook. + +This header should be the first thing seen when viewing this Project +Gutenberg file. Please do not remove it. Do not change or edit the +header without written permission. + +Please read the "legal small print," and other information about the +eBook and Project Gutenberg at the bottom of this file. Included is +important information about your specific rights and restrictions in +how the file may be used. You can also find out about how to make a +donation to Project Gutenberg, and how to get involved. + + +**Welcome To The World of Free Plain Vanilla Electronic Texts** + +**eBooks Readable By Both Humans and By Computers, Since 1971** + +*****These eBooks Were Prepared By Thousands of Volunteers!***** + + +Title: The Sewerage of Sea Coast Towns + +Author: Henry C. Adams + +Release Date: April, 2005 [EBook #7980] +[Yes, we are more than one year ahead of schedule] +[This file was first posted on June 8, 2003] + +Edition: 10 + +Language: English + +Character set encoding: ISO-Latin-1 + +*** 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 + + + + + +End of Project Gutenberg's The Sewerage of Sea Coast Towns, by Henry C. Adams + +*** END OF THE PROJECT GUTENBERG EBOOK THE SEWERAGE OF SEA COAST TOWNS *** + +This file should be named 7980-8.txt or 7980-8.zip + +Produced by Tiffany Vergon, Ted Garvin, Charles Franks +and the Online Distributed Proofreading Team. + +Project Gutenberg eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the US +unless a copyright notice is included. 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