,,the ,,sewerage ,,of ,,sea ,,coast ,,towns ,,by ,,henry ,c4 ,,adams ,,contents ,,chapter ,i4 ,,the ,,formation ,,of ,,tides ,,and ,,currents ,,ii4 ,,observations ,,of ,,the ,,rise ,,and ,,fall ,,of ,,tides ,,iii4 ,,current ,,observations ,,iv4 ,,selection ,,of ,,site ,,for ,,outfall ,,sewer4 ,v4 ,,volume ,,of ,,sewage ,,vi4 ,,gauging ,,flow ,,in ,,sewers ,,vii4 ,,rainfall ,,viii4 ,,storm ,,water ,,in ,,sewers ,,ix4 ,,wind ,,and ,,windmills ,x4 ,,the ,,design ,,of ,,sea ,,outfalls ,,xi ,,action ,,of ,,sea ,,water ,,on ,,cement ,,xii4 ,,diving ,,xiii4 ,,the ,,discharge ,,of ,,sea ,,outfall ,,sewers ,,xiv4 ,,trigonometrical ,,surveying ,,xv4 ,,hydrographical ,,surveying ,,preface4 ,these notes are internal primarily for those engineers who1 having a general knowledge of sewerage1 are called upon to prepare a scheme for a sea coast town1 or are desirous of being able to meet such a call when made4 ,although many details of the subject have been dealt with separately in other volumes1 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 scheme1 particularly with regard to taking and recording current and tidal observations1 and it is in the hope that it might be helpful to others in a similar difficulty to have all the information then obtained1 and that subsequently gained on other schemes1 brought together within a small compass that this book has written4 #fj1 ,queen ,victoria ,st1 ,london1 ,e4,c4 ,,chapter ,i4 ,,the ,,formation ,,of ,,tides ,,and ,,currents4 ,it has often been stated that no two well-designed sewerage schemes are alike1 and although this truism is usually applied to inland towns1 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 waters4 ,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 advantage1 and at the least possible expense1 so that the maximum efficiency is combined with the minimum cost4 ,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 outfalls4 ,starting with the postulate that it is essential for the sewage to be effectually and permanently disposed of when it is discharged into tidal waters1 we find that this result is largely dependent on the nature of the currents1 which in their turn depend upon the rise and fall of the tide1 caused chiefly by the attraction of the moon1 but also to a less extent by the attraction of the sun4 ,the subject of sewage disposal in tidal waters1 therefore1 divides itself naturally into two parts3 first1 the consideration of the tides and currents2 and1 secondly1 the design of the works4 ,the tidal attraction is primarily due to the natural effect of gravity1 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 apart2 but as the tide-producing effect of the sun and moon is a differential attraction1 and not a direct one1 their relative effect is inversely as the cube of their distances4 ,the mass of the sun is about #cbd1jjj times as great as that of the earth1 and it is about #ic millions of miles away1 while the mass of the moon is about #a-hjth of that of the earth1 but it averages only #bdj1jjj miles away1 varying between #bbj1jjj miles when it is said to be in perigee1 and #bfj1jjj when in apogee4 ,the resultant effect of each of these bodies is a strong pull of the earth towards them1 that of the moon being in excess of that of the sun as #a is to #j4dde1 because1 although its mass is much less than that of the sun1 it is considerably nearer to the earth4 ,about one-third of the surface of the globe is occupied by land1 and the remaining two-thirds by water4 ,the latter1 being a mobile substance1 is affected by this pull1 which results in a banking up of the water in the form of the crest of a tidal wave4 ,it has been asserted in recent years that this tidal action also takes place in a similar manner in the crust of the earth1 though in a lesser degree1 resulting in a heaving up and down amounting to one foot2 but we are only concerned with the action of the sea at present4 ,now1 although this pull is felt in all seas1 it is only in the ,southern ,ocean that a sufficient expanse of water exists for the tidal action to be fully developed4 ,this ocean has an average width of #a1ejj miles1 and completely encircles the earth on a circumferential line #ac1ejj miles long2 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 place4 ,at the same time1 the water is acted on by the centripetal effect of gravity1 which1 tending to draw it as near as possible to the centre of the earth1 acts in opposition to the attraction of the sun and moon1 so that at the sides of the earth #ij degrees away1 where the attraction of the sun and moon is less1 the centripetal force has more effect1 and the water is drawn so as to form the trough of the wave1 or low water1 at those points4 ,there is also the centrifugal force contained in the revolving globe1 which has an equatorial diameter of about #h1jjj miles and a circumference of #be1acb miles4 ,as it takes #bc hr4 #ef min #d sec1 or1 say1 twenty-four hours1 to make a complete revolution1 the surface at the equator travels at a speed of approximately #be1acb_/bd #a1jdg miles per hour4 ,this centrifugal force is always constant1 and tends to throw the water off from the surface of the globe in opposition to the centripetal force1 which tends to retain the water in an even layer around the earth4 ,it is asserted1 however1 as an explanation of the phenomenon which occurs1 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 moon1 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 moon1 to the extent due to the length of the diameter of the earth4 ,the result of this is that the centrifugal force overbalances the centripetal force1 and the water tends to fly off1 forming an anti-lunar wave crest at that point approximately equal1 and opposite1 to the wave crest at the point nearest to the moon4 ,as the earth revolves1 the crest of high water of the lunar tide remains opposite the centre of attraction of the sun and moon1 so that a point on the surface will be carried from high water towards and past the trough of the wave1 or low water1 then past the crest of the anti-lunar tide1 or high water again1 and back to its original position under the moon4 ,but while the earth is revolving the moon has traveled #ac degrees along the elliptical orbit in which she revolves around the earth1 from west to east1 once in #bg days #g hr4 #dc min1 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 #eb min1 so that1 although we are taught that the tide regularly ebbs and flows twice in twenty-four hours1 it will be seen that the tidal day averages #bd hr4 #eb min1 the high water of each tide in the ,southern ,ocean being at #ab hr4 #bf min intervals4 ,as a matter of fact1 the tidal day varies from #bd hr4 #ce min at new and full moon to #be hr4 #be min at the quarters4 ,although the moon revolves around the earth in approximately #bg-a_/c days1 the earth has moved #bg degrees on its elliptical orbit around the sun1 which it completes once in #cfe days1 so that the period which elapses before the moon again occupies the same relative position to the sun is #bi days #ab hr4 #dc min1 which is the time occupied by the moon in completing her phases1 and is known as a lunar month or a lunation4 ,considered from the point of view of a person on the earth1 this primary tidal wave constantly travels round the ,southern ,ocean at a speed of #ac1ejj miles in #bd hr4 #eb min1 thus having a velocity of #edc miles per hour1 and measuring a length of #ac1ejj_/b #f1gej miles from crest to crest4 ,if a map of the world be examined it will be noticed that there are three large oceans branching off the ,southern ,ocean1 namely1 the ,atlantic1 ,pacific1 and ,indian ,oceans2 and although there is the same tendency for the formation of tides in these oceans1 they are too restricted for any very material tidal action to take place4 ,as the crest of the primary tidal wave in its journey round the world passes these oceans1 the surface of the water is raised in them1 which results in secondary or derivative tidal waves being sent through each ocean to the furthermost parts of the globe2 and as the trough of the primary wave passes the same points the surface of the water is lowered1 and a reverse action takes place1 so that the derivative waves oscillate backwards and forwards in the branch oceans1 the complete cycle occupying on the average #ab hr4 #bf min ,every variation of the tides in the ,southern ,ocean is accurately reproduced in every sea connected with it4 ,wave motion consists only in a vertical movement of the particles of water by which a crest and trough is formed alternately1 the crest being as much above the normal horizontal line as the trough is below it2 and in the tidal waves this motion extends through the whole depth of the water from the surface to the bottom1 but there is no horizontal movement except of form4 ,the late ,mr4 ,j4 ,scott ,russell described it as the transference of motion without the transference of matter2 of form without the substance2 of force without the agent4 ,the action produced by the sun and moon jointly is practically the resultant of the effects which each would produce separately1 and as the net tide-producing effect of the moon is to raise a crest of water #a4d ft above the trough1 and that of the sun is #j4f ft 7being in the proportion of ,i to #j4dde71 when the two forces are acting in conjunction a wave #a4d #j4f #b ft high is produced in the ,southern ,ocean1 and when acting in opposition a wave #a4d - #j4f #j4h ft high is formed4 ,as the derivative wave1 consisting of the large mass of water set in motion by the comparatively small rise and fall of the primary wave1 is propagated through the branch oceans1 it is affected by many circumstances1 such as the continual variation in width between the opposite shores1 the alterations in the depth of the channels1 and the irregularity of the coast line4 ,when obstruction occurs1 as1 for example1 in the ,bristol ,channel1 where there is a gradually rising bed with a converging channel1 the velocity1 and_/or the amount of rise and fall of the derivative wave is increased to an enormous extent2 in other places where the oceans widen out1 the rise and_/or velocity is diminished1 and similarly where a narrow channel occurs between two pieces of land an increase in the velocity of the wave will take place1 forming a race in that locality4 ,although the laws governing the production of tides are well understood1 the irregularities in the depths of the oceans and the outlines of the coast1 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 alone4 ,the average rate of travel and the course of the flood tide of the derivative waves around the shores of ,great ,britain are as follows3--#aej miles per hour from ,land's ,end to ,lundy ,island2 #ij miles per hour from ,lundy to ,st4 ,david's ,head2 #bb miles per hour from ,st4 ,david's ,head to ,holy head2 #de-a_/b miles per hour from ,holyhead to ,solway ,firth2 #aid miles per hour from the ,north of ,ireland to the ,north of ,scotland2 #eb miles per hour from the ,north of ,scotland to the ,wash2 #bj miles per hour from the ,wash to ,yarmouth2 #aj miles per hour from ,yarmouth to ,harwich4 ,along the south coast from ,land's ,end to ,beachy ,head the average velocity is #dj miles per hour1 the rate reducing as the wave approaches ,dover1 in the vicinity of which the tidal waves from the two different directions meet1 one arriving approximately twelve hours later than the other1 thus forming tides which are a result of the amalgamation of the two waves4 ,on the ebb tide the direction of the waves is reversed4 ,the mobility of the water around the earth causes it to be very sensitive to the varying attraction of the sun and moon1 due to the alterations from time to time in the relative positions of the three bodies4 ,fig4 ,footnote3 ,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 moon4 ,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 force4 ,the tide at ,c is due to the excess of the centrifugal force over the centripetal force4 ,these tides are known as spring tides4 ,fig4 #b ,footnote3 ,plate ,i shows the positions occupied at the time of full moon4 ,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 force4 ,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 force4 ,these tides are also known as spring tides4 ,fig4 #c ,footnote3 ,plate ,i shows the positions occupied when the moon is in the first quarter2 the position at the third quarter being similar1 except that the moon would then be on the side of the earth nearest to ,b1 ,the tide at ,a is compounded of high water of the solar tide superimposed upon low water of the lunar tide1 so that the sea is at a higher level than in the case of the low water of spring tides4 ,the tide at ,d is due to the attraction of the moon less the excess of centripetal force over centrifugal force1 and the tide at ,b is due to the excess of centrifugal force over centripetal force4 ,these are known as neap tides1 and1 as the sun is acting in opposition to the moon1 the height of high water is considerably less than at the time of spring tides4 ,the tides are continually varying between these extremes according to the alterations in the attracting forces1 but the joint high tide lies nearer to the crest of the lunar than of the solar tide4 ,it is obvious that1 if the attracting force of the sun and moon were equal1 the height of spring tides would be double that due to each body separately1 and that there would be no variation in the height of the sea at the time of neap tides4 ,it will now be of interest to consider the minor movements of the sun and moon1 as they also affect the tides by reason of the alterations they cause in the attractive force4 ,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 equator4 ,at the vernal equinox 7,march #bj7 the equator is vertically under the sun1 which then declines to the south until the summer solstice 7,june #ba71 when it reaches its maximum south declination4 ,it then moves northwards1 passing vertically over the equator again at the autumnal equinox 7,september #ba71 and reaches its maximum northern declination on the winter solstice 7,december #ba74 ,the declination varies from about #bd degrees above to #bd degrees below the equator4 ,the sun is nearest to the ,southern ,ocean1 where the tides are generated1 when it is in its southern declination1 and furthest away when in the north1 but the sun is actually nearest to the earth on ,december #ca 7perihelion7 and furthest away on ,july ,i 7aphelion71 the difference between the maximum and minimum distance being one-thirtieth of the whole4 ,the moon travels in a similar diagonal direction around the earth1 varying between #ah-a_/b degrees and #bh-a_/b degreed above and below the equator4 ,the change from north to south declination takes place every fourteen days1 but these changes do not necessarily take place at the change in the phases of the moon4 ,when the moon is south of the equator1 she is nearer to the ,southern ,ocean1 where the tides are generated4 ,the new moon is nearest to the sun1 and crosses the meridian at midday1 while the full moon crosses it at midnight4 ,the height of the afternoon tide varies from that of the morning tide2 sometimes one is the higher and sometimes the other1 according to the declination of the sun and moon4 ,this is called the diurnal inequality4 ,the average difference between the night and morning tides is about #e in on the east coast and about #h;in on the west coast4 ,when there is a considerable difference in the height of high water of two consecutive tides1 the ebb which follows the higher tide is lower than that following the lower high water1 and as a general rule the higher the tide rises the lower it will fall4 ,the height of spring tides varies throughout the year1 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 equator4 ,in the ,southern ,ocean high water of spring tides occurs at mid-day on the meridian of ,greenwich and at midnight on the #ahj meridian1 and is later on the coasts of other seas in proportion to the time taken for the derivative waves to reach them1 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 ,thames4 ,the spring tides around the coast of ,england are four inches higher on the average at the time of new moon than at full moon1 the average rise being about #ae ft1 while the average rise at neaps is #aa ft #f in4 ,the height from high to low water of spring tides is approximately double that of neap tides1 while the maximum height to which spring tides rise is about #cc per cent4 more than neaps1 taking mean low water of spring tides as the datum4 ,extraordinarily high tides may be expected when the moon is new or full1 and in her position nearest to the earth at the same time as her declination is near the equator1 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 sea1 and then changes when the tide starts to rise1 so as to blow straight on to the shore4 ,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 place1 and a reduction of pressure will facilitate its rising elsewhere1 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 higher4 ,as exemplifying the effect of violent gales in the ,atlantic on the tides of the ,bristol ,channel1 the following extract from ,the ,surveyor1 ,engineer1 and ,architect of #ahdj1 dealing with observations taken on ,mr4 ,bunt's self-registering tide gauge at ,hotwell ,house1 ,clifton1 may be of interest4 ,date3 ,times of ,high ,water4 ,difference in ,jan #ahdj4 ,tide ,gauge4 ,tide ,table4 ,tide ,table4 ,h4,m4 ,h4,m4 #bgth1 p4m4444444 #j4 #h 4444444 #j4 #g 44444 #a min earlier4 #bhth1 a4m4444444 #j4dg 4444444 #j4cd 44444 #ac min earlier4 #bhth1 p4m4444444 #aa4da 4444444 #a4 #g 44444 #hf min later4 #bith1 a4m4444444 #a4bi 4444444 #a4dg 44444 #ah min later4 #bith1 p4m4444444 #b4cb 4444444 #b4cj 44444 #b min earlier4 ,although the times of the tides varied so considerably1 their heights were exactly as predicted in the tide-table4 ,the records during a storm on ,october #bi1 #ahch1 gave an entirely different result1 as the time was retarded only ten or twelve minutes1 but the height was increased by #h ft ,on another occasion the tide at ,liverpool was increased #g ft by a gale4 ,the ,bristol ,channel holds the record for the greatest tide experienced around the shores of ,great ,britain1 which occurred at ,chepstow in #ahhc1 and had a rise of #dh ft #f in ,the configuration of the ,bristol ,channel is1 of course1 conducive to large tides1 but abnormally high tides do not generally occur on our shores more frequently than perhaps once in ten years1 the last one occurring in the early part of #aijd1 although there may foe many extra high ones during this period of ten years from on-shore gales4 ,where tides approach a place from different directions there may be an interval between the times of arrival1 which results in there being two periods of high and low water1 as at ,southampton1 where the tides approach from each side of the ,isle of ,wight4 ,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 place1 and when this1 together with the height to which the tide rises above low water is ascertained by actual observation1 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 time4 ,by means of a tide-predicting machine1 invented by ,lord ,kelvin1 the tides for a whole year can be calculated in from three to four hours4 ,this machine is fully described in the ,minutes of ,proceedings1 ,inst4,c4,e41 ,vol4 ,,lxv4 ,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 place4 ,the range of a tide is the height between high and low water of that tide1 and the rise of a tide is the height between high water of that tide and the mean low water level of spring tides4 ,it follows1 therefore1 that for spring tides the range and rise are synonymous terms1 but at neap tides the range is the total height between high and low water1 while the rise is the difference between high water of the neap tide and the mean low water level of spring tides4 ,neither the total time occupied by the flood and ebb tides nor the rate of the rise and fall are equal1 except in the open sea1 where there are fewer disturbing conditions4 ,in restricted areas of water the ebb lasts longer than the flood4 ,although the published tide-tables give much detailed information1 it only applies to certain representative ports1 and even then it is only correct in calm weather and with a very steady wind1 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 works4 ,it is impracticable for these observations to be continued over the lengthy period necessary to obtain the fullest and most accurate results1 but1 premising a general knowledge of the natural phenomena which affect the tides1 as briefly described herein1 he will be able to gauge the effect of the various disturbing causes1 and interpret the records he obtains so as to arrive at a tolerably accurate estimate of what may be expected under any particular circumstances4 ,generally about #be per cent4 of the tides in a year are directly affected by the wind1 etc41 the majority varying from #f in to #ab in in height and from five to fifteen minutes in time4 ,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 conditions4 ,the ,liverpool tide-tables are based on observations spread over ten years1 and even longer periods have been adopted in other places4 ,much valuable information on this subject is contained in the following books1 among others--and the writer is indebted to the various authors for some of the data contained in this and subsequent chapters--,the ,tides1 by ,g4 ,h4 ,darwin1 #ahhf2 ,baird's ,manual of ,tidal ,observations1 #ahhf2 and ,tides and ,waves1 by ,w4 ,h4 ,wheeler1 #aijf1 together with the articles in the ,encyclopaedia ,britannica and ,chambers's ,encyclopaedia4 ,chapter ,,ii ,observations of the rise and fall of tides4 ,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 tides1 as well as the rate of rise and fall of the various tides4 ,this is done by means of a tide recording instrument similar to ,fig4 #d1 which represents one made by ,mr4 ,j4 ,h4 ,steward1 of #deg1 ,west ,strand1 ,london1 ,w4,c4 ,it consists of a drum about #e in diameter and #aj in high1 which revolves by clockwork once in twenty-four hours1 the same mechanism also driving a small clock4 ,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 drum4 ,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 float1 #h inches diameter1 which rises and falls with the tide1 so that every movement of the tide is reproduced moment by moment upon the chart as it revokes4 ,the instrument is enclosed in an ebonized cabinet1 having glazed doors in front and at both sides1 giving convenient access to all parts4 ,inasmuch as the height and the time of the tide vary every day1 it is practicable to read three days' tides on one chart1 instead changing it every day4 ,when the diagrams are taken of1 the lines representing the water levels should be traced on to a continuous strip of tracing linen1 so that the variations can be seen at a glance extra lines should be drawn1 on the tracing showing the time at which the changes of the moon occur4 ,fig4 #e is a reproduction to a small scale of actual records taken over a period of eighteen days1 which shows true appearance of the diagrams when traced on the continuous strip4 ,these observations show very little difference between the spring and neap tides1 and are interesting as indicating the unreliability of basing general deductions upon data obtained during a limited period only4 ,at the time of the spring tides at the beginning of ,june the conditions were not favourable to big tides1 as although the moon was approaching her perigee1 her declination had nearly reached its northern limit and the declination of the sun was #bb ,,in ,the first quarter of the moon coincided very closely with the moon's passage over the equator1 so that the neaps would be bigger than usual4 ,at the period of the spring3 tides1 about the middle of ,june1 although the time of full moon corresponded with her southernmost declination1 she was approaching her apogee1 and the declination of the sun was #bc #af' ,n41 so that the tides would be lower than usual4 ,in order to ensure accurate observations1 the position chosen for the tide gauge should be in deep water in the immediate vicinity of the locus in quo1 but so that it is not affected by the waves from passing vessels4 ,wave motion is most felt where the float is in shallow water4 ,a pier or quay wall will probably be most convenient1 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 water4 ,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 level1 and a small pipe is then laid under the beach from the well to1 and below1 low water1 so that the water stands continuously in the well at the same level as the sea4 ,the gauge should be fixed on bearers1 about #c ft #f in from the floor1 in a wooden shed1 similar to a watchman's box1 but provided with a door1 erected on the pier or other site fixed upon for the observations4 ,a hole must be formed in the floor and a galvanized iron or timber tube about #aj in square reaching to below low water level fixed underneath1 so that when the float is suspended from the recording instrument it shall hang vertically down the centre of the tube4 ,the shed and tube must of course be fixed securely to withstand wind and waves4 ,the inside of the tube must be free from all projections or floating matter which would interfere with the movements of the float1 the bottom should be closed1 and about four lin diameter holes should be cleanly formed in the sides near to the bottom for the ingress and egress of the water4 ,with a larger number of holes the wave action will cause the diagram to be very indistinct1 and probably lead to incorrectness in determining the actual levels of the tides2 and if the tube is considerably larger than the float1 the latter will swing laterally and give incorrect readings4 ,a bench mark at some known height above ordnance datum should be set up in the hut1 preferably on the top of the tube4 ,at each visit the observer should pull the float wire down a short distance1 and allow it to return slowly1 thus making a vertical mark on the diagram1 and should then measure the actual level of the surface of the water below the bench mark in the hut1 so that the water line on the chart can be referred to ordnance datum4 ,he should also note the correct time from his watch1 so as to subsequently rectify any inaccuracy in the rate of revolution of the drum4 ,the most suitable period for taking these observations is from about the middle of ,march to near the end of ,june1 as this will include records of the high spring equinoctial tides and the low bird tides of ,june4 ,a chart similar to ,fig4 #f should be prepared from the diagrams1 showing the rise and fall of the highest spring tides1 the average spring tides1 the average neap tides1 and the lowest neap tides1 which will be found extremely useful in considering the levels of1 and the discharge from1 the sea outfall pipe4 ,the levels adopted for tide work vary in different ports4 ,trinity high-water mark is the datum adopted for the ,port of ,london by the ,thames ,conservancy2 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 ,docks1 and is #ab #dh ft above ,ordnance datum4 ,the ,liverpool tide tables give the heights above the ,old ,dock ,sill1 which is now non-existent1 but the level of it has been carefully preserved near the same position1 on a stone built into the western wall of the ,canning ,half ,tide ,dock4 ,this level is #dj ft below ,ordnance datum4 ,at ,bristol the levels are referred to the ,old ,cumberland ,basin 7,o4,c4,b471 which is an imaginary line #eh ft below ,ordnance datum4 ,it is very desirable that for sewage work all tide levels should be reduced to ,ordnance datum4 ,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 datum4 ,ordnance datum is officially described as the assumed mean water level at ,liverpool1 which was ascertained from observations made by the ,ordnance ,survey ,department in ,march1 #ahdd1 but subsequent records taken in ,may and ,june1 #ahei1 by a self-recording gauge on ,st4 ,george's ,pier1 showed that the true mean level of the sea at ,liverpool is #j4jfh ft below the assumed level4 ,the general mean level of the sea around the coast of ,england1 as determined by elaborate records taken at #bi places during the years #ahei-fj1 was originally said to be1 and is still1 officially recognised by the ,ordnance ,survey ,department to be #j4fe ft1 or #g4h in1 above ,ordnance datum1 but included in these #bi stations were #h at which the records were admitted to be imperfectly taken4 ,if these #h stations are omitted from the calculations1 the true general mean level of the sea would be #j4fbc ft1 or #g4dgf in1 above ,ordnance datum1 or #j4fia ft above the true mean level of the sea at ,liverpool4 ,the local mean seal level at various stations around the coast varies from #j4ihb ft below the general mean sea level at ,plymouth1 to #a4bfj ft above it at ,harwich1 the places nearest to the mean being ,weymouth 74#jhi ft below7 and ,hull 74#jch ft above74 ,it may be of interest to mention that ,ordnance datum for ,ireland is the level of low water of spring tides in ,dublin ,bay1 which is #ba ft below a mark on the base of ,poolbeg ,lighthouse1 and #g4df ft below ,english ,ordnance datum4 ,the lines of high and low water mark of ordinary tides shown upon ,ordnance maps represent mean tides2 that is1 tides halfway between the spring and the neap tides1 and are generally surveyed at the fourth tide before new and full moon4 ,the foreshore of tidal water below mean high water belongs to the ,crown1 except in those cases where the rights have been waived by special grants4 ,mean high water is1 strictly speaking1 the average height of all high waters1 spring and neap1 as ascertained over a long period4 ,mean low water of ordinary spring tides is the datum generally adopted for the soundings on the ,admiralty ,charts1 although it is not universally adhered to2 as1 for instance1 the soundings in ,liverpool ,bay and the river ,mersey are reduced to a datum #bj ft below the old dock sill1 which is #abe ft below the level of low water of ordinary spring tides4 ,the datum of each chart varies as regards ,ordnance datum1 and in the case of charts embracing a large area the datum varies along the coast4 ,the following table gives the fall during each half-hour of the typical tides shown in ,fig1 #f 7see page #ae71 from which it will be seen that the maximum rate occurs at about half-tide1 while very little movement takes place during the half-hour before and the half-hour after the turn of the tide3-- ,table ,i4 ,rate of fall of tides4 ,state of ,eqionoctial ,ordinary ,ordinary ,lowest ,tide4 ,tides4 ,spring ,tides4 ,neap ,tides4 ,neap ,tides4 ,high water -- -- -- -- #a_/b hour after #j4dd #j4dj #j4bb #j4ai #a #j4if #j4hj #j4dj #j4ca #a-a_/b #a4ci #a4ad #j4fh #j4ec #b #a4he #a4ef #j4gb #j4ei #b-a_/b #a4ia #a4fd #j4hd #j4fh #c #a4id #a4ff #j4hf #j4gj #c-a_/b #a4id #a4ff #j4hf #j4gj #d #a4ia #a4fd #j4hd #j4fh #d-a_/b #a4ce #a4af #j4ei #j4dh #e #a4bg #a4ji #j4eg #j4df #e-a_/b #a4jf #j4ia #j4dg #j4ch #f #a4jd #j4hi #j4df #j4cg #f-a_/b #j4ec #j4de #j4bd #j4ah ,totals4444 #ag ft #f in #ae ft #j in #g ft #i in #f ft #c in ,the extent to which the level of high water varies from tide to tide is shown in ,fig4 #g ,footnote3 ,plate ,,iii41 which embraces a period of six months1 and is compiled from calculated heights without taking account of possible wind disturbances4 ,the varying differences between the night and morning tides are shown very clearly on this diagram2 in some cases the night tide is the higher one1 and in others the morning tide2 and while at one time each successive tide is higher than the preceding one1 at another time the steps showing3 the set-back of the tide are very marked4 ,during the earlier part of the year the spring-tides at new moon were higher than those at full moon1 but towards ,june the condition became reversed4 ,the influence of the position of the sun and moon on the height of the tide is apparent throughout1 but is particularly marked during the exceptionally low spring tides in the early part of ,june1 when the time of new moon practically coincides with the moon in apogee and in its most northerly position furthest removed from the equator4 ,inasmuch as the tidal waves themselves have no horizontal motion1 it is now necessary to consider by what means the movement of water along the shores is caused4 ,the sea is1 of course1 subject to the usual law governing the flow of water1 whereby it is constantly trying to find its own level4 ,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 flat1 and does not lead to any appreciable movement2 but as the tidal wave approaches within a few miles of the shore1 it runs into shallow water1 where its progress is checked1 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 gradient1 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 shore4 ,the rate of this current depends upon the steepness of the gradient1 and the momentum acquired will1 ,in some ,instances1 cause the current to continue to run in the same direction for some time after the tide has turned1 i4e41 after the direction of the gradient has been reversed2 so that the tide may be making--or falling--in one direction1 while the current is running the opposite way4 ,it will be readily seen1 then1 that the flow of the current will be slack about the time of high and low water1 so that its maximum rate will be at half-ebb and half-flood4 ,if the tide were flowing into an enclosed or semi- enclosed space1 the current could not run after the tide turned1 and the reversal of both would be simultaneous1 unless1 indeed1 the current turned before the tide4 ,wind waves are only movements of the surface of the water1 and do not generally extend for a greater depth below the trough of the wave than the crest is above it1 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 wind4 ,the strength of the wind is sometimes indicated wind at the time of making any tidal observations4 ,by reference to the ,beaufort ,scale1 which is a graduated classification adopted by ,admiral ,beaufort about the year #ahje4 ,the following table gives the general description1 velocity1 and pressure of the wind corresponding to the tabular numbers on the scale3-- ,illustration3 ,,plate ,,iii ,,period ,,of ,,six ,,months4 ,to face page #bj ,the figures indicating the pressure of the wind in the foregoing table are low compared with those given by other authorities4 ,from ,mutton's formula1 the pressure against a plane surface normal to the wind would be #j4ig lb per sq4 foot1 with an average velocity of #ae miles per hour 7#bb ft per sec471 compared with o4#fg lb given by ,admiral ,beaufort1 and for a velocity of #ej miles per hour 7#gc4c ft per sec47 #aj4ge lb1 compared with #g4glb ,semitone's formula1 which is frequently used1 gives the pressure as #j4jje,v#b 7miles per hour71 so that for #ae miles per hour velocity the pressure would be #a4abe lb1 and for #ej miles it would be l#b4e lb ,it must not be forgotten1 however1 that1 although over a period of one hour the wind may average this velocity or pressure1 it will vary considerably from moment to moment1 being far in excess at one time1 and practically calm at another4 ,the velocity of the wind is usually taken by a cup anemometer having four #i in cups on arms #b ft long4 ,the factor for reducing the records varies from #b to #c1 according to the friction and lubrication1 the average being #b4b4 ,the pressure is obtained by multiplying the ,beaufort number cubed by #j4jaje2 and the velocity is found by multiplying the square root of the ,beaufort number cubed by #a4hg4 ,a tidal wave will traverse the open sea in a straight line1 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 velocity1 so that on plan the wave assumes a convex shape and the branch waves reaching the shore form an acute angle with the coast line4 ,,chapter ,,iii4 ,,current ,,observations4 ,there is considerable diversity in the design of floats employed in current observations1 dependant to some extent upon whether it is desired to ascertain the direction of the surface drift or of a deep current1 it does not by any means follow that they run in simultaneous directions4 ,there is also sometimes considerable difference in the velocity of the current at different depths--the surface current being more susceptible to influence of wind4 ,a good form of deep float is seen in ,fig4 #h4 ,it consists of a rod #b in by #b in1 or #d sq in ,the lower end of which a hollow wooden box about #f in by #f in is fixed1 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 #i;in of the rod exposed above the surface4 ,a small hole is formed in the top of the box for the insertion the pebbles1 which is stopped up with a cork when the float is adjusted4 ,the length of the rod will vary according to the depth of water1 but it will generally be found convenient to employ a float about #aj ft and to have a spare one about #f ft deep1 but otherwise it is similar in all respects1 for use in shallow water4 ,a cheap float for gauging the surface drift can be made from an empty champagne bottle weighted with stones and partly filled with water4 ,the top #ab in of rods and the cord and neck of the bottle1 as the case may be1 should be painted red1 as this colour renders floats more conspicuous when in the water and gives considerable assistance in locating their position1 especially when they are at some distance from the observer4 ,a deep-sea float designed by ,mr4 ,g4 ,p4 ,bidden for ascertaining the set of the currents along the base of the ocean has recently been used by the ,north ,sea ,fisheries ,investigation ,committee4 ,it consists of a bottle shaped like a soda-water bottle1 made of strong glass to resist the pressure of the water1 and partly filled with water1 so that just sufficient air is left in it to cause it to float4 ,a length of copper wire heavy enough to cause it to sink is then attached to the bottle1 which is then dropped into the sea at a defined place4 ,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 sea4 ,about #bj per cent4 of the bottles were recovered1 either by being thrown up on the beach or by being fished up in trawl nets4 ,illustration3 ,,fig4 #h4--;,,detail ,,of ,,wood ,,tidal ,,float #aj ,,feet ,,deep4 ,a double float1 weighing about #aj lb complete1 was used for the tidal observations for the ,girdleness outfall sewer1 ,aberdeen4 ,the surface portion consisted of two sheet-iron cups soldered together1 making a float #i in in diameter and #f in deep4 ,the lower or submerged portion was made of zinc1 cylindrical in shape1 #af in diameter and #af in long1 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 float4 ,in gauging the currents the float is placed in the water at a defined point and allowed to drift1 its course being noted and afterwards transferred to a plan4 ,the time of starting should be recorded and observations of its exact position taken regularly at every quarter of an hour1 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 hour4 ,the method to be employed in ascertaining the exact position of the float from time to time is a matter which requires careful consideration1 and is dependent upon the degree of accuracy required according to the importance of the scheme and the situation of neighbouring towns1 frequented shores1 oyster beds1 and other circumstances likely to be injuriously affected by any possible or probable pollution by sewage4 ,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 position1 irrespective of the tipping and rolling of the boat1 and to observe simultaneously the bearing of two prominent landmarks1 the position of which on the plan is known1 at each of the quarter-hour periods at which the observations are to be taken4 ,this method only gives very approximate results1 and after checking the value of the observations made by its use1 with contemporary observations taken by means of theodolites on the shore1 the writer abandoned the system in favour of the theodolite method1 which1 however1 requires a larger staff1 and is therefore more expensive4 ,in every case it is necessary to employ a boat to follow the float1 not only so as to recover it at the end of each day's work1 but principally to assist in approximately locating the float1 which can then be found more readily when searching through the telescope of the theodolite4 ,the boat should be kept about #aj ft to #bj ft from the float on the side further removed from the observers1 except when surface floats are being used to ascertain the effect of the wind1 when the boat should be kept to leeward of the float4 ,although obviously with a large boat the observations can be pursued through rougher weather1 which is an important point1 still the difficulty of maintaining a large boat propelled by mechanical power1 or sail1 sufficiently near the float to assist the observers1 prevents its use1 and the best result will be obtained by employing a substantial1 seaworthy rowing boat with a broad beam4 ,the boatmen appreciate the inclusion of a mast1 sails1 and plenty of ballast in the equipment to facilitate their return home when the day's work is done1 which may happen eight or nine miles away1 with twilight fast passing into darkness4 ,there should be two boatmen1 or a man and a strong youth4 ,in working with theodolites1 it is as well before starting to select observation stations at intervals along the coast1 drive pegs in the ground so that they can easily be found afterwards1 and fix their position upon a #a_/bejj ordnance map in the usual manner4 ,it may1 however1 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 taken4 ,in this case the theodolite must be set up on magnetic north at an intermediate position1 and sights taken to at least two landmarks1 the positions of which are shown on the map1 and the point of observation subsequently plotted as near as possible by the use of these readings4 ,inasmuch as the sights will be taken from points on the edge of the shore1 which is1 of course1 shown on the map1 it is possible1 after setting up to magnetic north1 to fix the position with approximate accuracy by a sight to one landmark only1 but this should only be done in exceptional circumstances4 ,the method of taking the observations with two theodolites1 as adopted by the writer1 can best be explained by a reference to ,fig4 #i1 which represents an indented piece of the coast4 ,the end of the proposed sea outfall sewer1 from which point the observations would naturally start1 is marked #a1 the numerals #b1 #c1 #d1 etc41 indicating the positions of the float as observed from time to time4 ,many intermediate observations would be taken1 but in order to render the diagram more clear1 these have not been shown4 ,the lines of sight are marked #a;,a1 #a;,b1 etc4 ,the points marked ,a#a1 ,a#b1 etc41 indicate the first1 second1 etc41 and subsequent positions of observer ,a2 the points ,b#a1 ,b#b1 etc41 referring to observer ,b4 ,the dot-and-dash line shows the course taken by the float1 which is ascertained after plotting the various observations recorded4 ,it is very desirable to have a horse and trap in waiting to move the observers and their instruments from place to place as required1 and each observer should be provided with small flags about #b ft square1 one white and one blue1 for signalling purposes4 ,the instruments are first set up at ,a#a and ,b#a respectively1 and adjusted to read on to the predetermined point #a where the float is to be put in ,then as soon as the boatmen have reached the vicinity of this point1 the observers can1 by means of the flags1 direct them which way to row so as to bring the boat to the exact position required1 and when this is done the anchor is dropped until it is time to start1 which is signalled by the observers holding the flags straight above their heads4 ,this is also the signal used to indicate to the men that the day's work is finished1 and they can pick up the float and start for home4 ,illustration3 ,,fig4 #i4--,,plan ,,of ,,indented ,,coast-,,line ,,llustrating ,,method ,,of ,,taking ,,current ,,observations ,,with ,,two ,,theodolites4 ,directly the float is put in the water1 and at every even quarter of an hour afterwards1 each observer takes a reading of its exact position1 and notes the time4 ,as soon as the readings are taken to the float in position #b1 the observer ,a should take up his instrument and drive to ,a#b1 where he must set up ready to take reading #c a quarter of an hour after reading #b4 ,it will be noticed that he might possibly have been able to take the reading #c from the position ,a#a1 but the angle made by the lines of sight from the two instruments would have been too acute for accurate work1 and very probably the float would have been hidden by the headland1 so that he could not take the reading at all4 ,in order to be on the headland ,a#d at the proper time1 ,a must be working towards it by getting to position ,a#c by the time reading #d is due4 ,although the remainder of the course of the float can be followed from ,b#a and ,a#d1 the instruments would be reading too much in the same line1 so that ,b must move to ,b#b and then after reading #e and #f he should move to ,b#c4 ,as the float returns towards the starting point1 ,a can remain in the position ,a#d while ,b goes to ,b#d and then moves back along the shore as the float progresses4 ,the foregoing description is sufficient to indicate the general method of working1 but the details will of course vary according to the configuration of the shore and the course taken by the float4 ,good judgment is necessary in deciding when to move from one station to the next1 and celerity in setting up1 adjusting the instrument1 and taking readings is essential4 ,if the boatmen can be relied upon to keep their position near the float1 very long sights can be taken with sufficient accuracy by observing the position of the boat1 long after the float has ceased to be visible through the telescope4 ,the lines of sight from each station should be subsequently plotted on the #a_/bejj ordnance map2 the intersection of each two corresponding sight lines giving the position of the float at that time4 ,then if a continuous line is drawn passing through all the points of intersection it will indicate the course taken by the float4 ,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 code1 as follows4 ,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 shoulder4 ,,table #c4 ,,morse ,,alphabet4 ,e 4 ,a 4- ,r 4-4 ,l 4-44 ,w 4-- ,p 4--4 ,j 4--- ,i 44 ,u 44- ,f 44-4 ,s 444 ,v 444- ,h 4444 ,t - ,n -4 ,k -4- ,c -4-4 ,y -4-- ,d -44 ,x -44- ,b -444 ,m -- ,g --4 ,q --4- ,z --44 ,o --- ,the signal to attract attention at starting and to signify the end of the message is 44 44 44 continued until it is acknowledged with a similar sign by the other observer2 that for a repetition is 44 -- 44 which is signalled when any part of the message is not understood1 otherwise after each word is signalled the receiver waves - to indicate he understands it4 ,until proficiency is attained1 two copies of the alphabet should be kept by each observer for reference1 one for dispatching a message arranged in alphabetical order and the other far reading a message arranged as set out above4 ,the white flag should be used when standing against a dark background1 and the blue one when on the skyline or against a light background4 ,the conditions in tidal rivers vary somewhat from those occurring on the coast4 ,as the crest of the tidal wave passes the mouth of the river a branch wave is sent up the river4 ,this wave has first to overcome the water flowing down the river1 which is acting in opposition to it1 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 river4 ,the momentum acquired by the water passing up-stream carries it to a higher level towards the head of the river than at the mouth1 and1 similarly1 in returning1 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 adjoining4 ,owing to a flow of upland water down a river the ebb lasts longer than the flood tide by a period1 increasing in length as the distance from the mouth of the river increases2 and1 similarly to the sea1 the current may continue to run down a river after the tide has turned and the level of the water is rising4 ,the momentum of the tide running up the centre of the river is in excess of that along the banks1 so that the current changes near the shore before it does in the middle1 and1 as the sea water is of greater specific gravity than the fresh1 weighing #fd lb per cubic foot against #fb-a_/b lb1 it flows up the bed of the river at the commencement of the tide1 while the fresh water on the surface is running in the opposite direction4 ,after a time the salt water becomes diffused in the fresh1 so that the density of the water in a river decreases as the distance from the sea increases4 ,the disposal of sewage discharged into a river is due primarily to the mixing action which is taking place2 inasmuch as the tidal current which is the transporting agent rarely flows more rapidly than from two to four miles per hour1 or1 say1 twelve to fifteen miles per tide4 ,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 tide1 as this water occupies a certain amount of space1 according to the depth and width of the river1 and thus prevents the sea water flowing back to the position it occupied on the previous tide1 and carrying with it the matter in suspension4 ,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 day1 taking thirty days to travel the thirty-one miles to the sea1 while at the mouth of the river the rate does not exceed one- third of a mile per day4 ,,chapter ,,iv4 ,,selection ,,of ,,site ,,for ,,outfall ,,sewer4 ,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 point1 and the permanent success of any scheme of sewage disposal depends primarily upon the skill shown in this matter4 ,the first step is to obtain a general idea of the tidal conditions1 and to examine the ,admiralty charts of the locality1 which will show the general set of the main currents into which it is desirable the sewage should get as quickly as possible4 ,the main currents may be at some considerable distance from the shore1 especially if the town is situated in a bay1 when the main current will probably be found running across the mouth of it from headland to headland4 ,the sea outfall should not be in the vicinity of the bathing grounds1 the pier1 or parts of the shore where visitors mostly congregate2 it should not be near oyster beds or lobster grounds4 ,the prosperity--in fact1 the very existence--of most seaside towns depends upon their capability of attracting visitors1 whose susceptibilities must be studied before economic or engineering questions1 and there are always sentimental objections to sewage works1 however well designed and conducted they may be4 ,it is desirable that the sea outfall should be buried in the shore for the greater part of its length1 not only on account of these sentimental feelings1 but as a protection from the force of the waves1 and so that it should not interfere with boating2 and1 further1 where any part of the outfall between high and low water mark is above the shore1 scouring of the beach will inevitably take place on each side of it4 ,the extreme end of the outfall should be below low-water mark of equinoctial tides1 as it is very objectionable to have sewage running across the beach from the pipe to the water1 and if the foul matter is deposited at the edge of the water it will probably be brought inland by the rising tide4 ,several possible positions may present themselves for the sea outfall1 and a few trial current observations should be made in these localities at various states of the tides and plotted on to a #a3bejj ordnance map4 ,the results of these observations will probably reduce the choice of sites very considerably4 ,levels should be taken of the existing subsidiary sewers in the town1 or1 if there are none1 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 consideration4 ,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 water1 when1 obviously1 pumping or other methods of raising the sewage must be resorted to2 if they are above low water1 but below high water1 the sewage could be stored during high water and run off at or near low water2 or1 if they are above high water1 the sewage could run off continuously1 or at any particular time that might be decided4 ,observations of the currents should now be made from the selected points1 giving special attention to those periods during which it is possible to discharge the sewage having regard to the levels of the sewers4 ,these should be made with the greatest care and accuracy1 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 them1 by estimating1 and mentally eliminating1 any disturbing influences1 such as wind1 etc4 ,care must also be taken in noting the height of the tide and the relative positions of the sun1 moon1 and earth at the time of making the observations1 and in estimating from such information the extent to which the tides and currents may vary at other times when those bodies are differently situated4 ,it is obvious that if the levels of the sewers and other circumstances are such that the sewage can safely be discharged at low water1 and the works are to be constructed accordingly1 it is most important to have accurate information as to the level of the highest low water which may occur in any ordinary circumstances4 ,if the level of a single low water1 given by a casual observation1 is adopted without consideration of the governing conditions1 it may easily be that the tide in question is a low one1 that may not be repeated for several years1 and the result would be that1 instead of having a free outlet at low water1 the pipe would generally be submerged1 and its discharging capacity very greatly reduced4 ,the run of the currents will probably differ at each of the points under consideration1 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 water1 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 purified4 ,if these results are considered in conjunction with the levels of the sewers definite alternative schemes1 each of which would work satisfactory may be evolved1 and after settling them in rough outline1 comparative approximate estimates should be prepared1 when a final scheme may be decided upon which1 while giving the most efficient result at the minimum cost1 will not arouse sentimental objections to a greater extent than is inherent to all schemes of sewage disposal4 ,having thus selected the exact position of the outfall1 the current observations from that point should be completed1 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 tide4 ,this information is not particularly wanted by the engineer1 but the scheme will have to receive the sanction of the ,local ,government ,board or of ,parliament1 and probably considerable opposition will be raised by interested parties1 which must be met at all points and overcome4 ,in addition to this1 it may be possible1 and necessary1 when heavy rain occurs1 to allow the diluted sewage to escape into the sea at any stage of the tide2 and1 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 rainfall1 the aforesaid sentimentalists may conjure up many possibilities of serious results4 ,as far as possible the records should indicate the course taken by floats starting from the outfall1 at high water1 and at each regular hour afterwards on the ebb tide1 as well as at low water and every hour on the flood tide4 ,it is not1 however1 by any means necessary that they should be taken in this or any particular order1 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 day1 and while perhaps relatively the greatest amount of information can be gleaned from a series of observations taken at the same state of the tide1 but on tides of differing heights1 still1 every observation tells its own story and serves a useful purpose4 ,deep floats and surface floats should be used concurrently to show the effect of the wind1 the direction and force of which should be noted4 ,if it appears that with an on-shore wind floating particles would drift to the shore1 screening will be necessary before the sewage is discharged4 ,the floats should be followed as long as possible1 but at least until the turn of the current--that is to say1 a float put in at or near high water should be followed until the current has turned at or near low water1 and one put in at low water should be followed until after high water4 ,in all references to low water the height of the tide given is that of the preceding high water4 ,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 tide1 and all the information obtained on this point should be plotted on squared paper as shown on ,fig4 #aj1 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 sea4 ,the vertical lines represent the time before high or low water at which the current turned1 and the horizontal lines the height of the tide1 but the data will1 of course1 vary in different localities4 ,illustration3 ,hours before turn of tide4 ,,fig #aj ,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 taken4 ,for instance1 from the diagram given it can be seen that on a #bj ft tide the current will turn thirty minutes before the tide1 or on a #ae ft tide the current will turn one hour before the tide4 ,some of the points lie at a considerable distance from the regular curve1 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 notes1 and therefore those particular observations must be used with caution4 ,the rate of travel of the currents varies in accordance with the time they have been running4 ,directly after the turn there is scarcely any movement1 but the speed increases until it reaches a maximum about three hours later and then it decreases until the next turn1 when dead water occurs again4 ,those observations which were started at the turn of the current and continued through the whole tide should be plotted as shown in ,fig4 #aa1 which gives the curves relating to three different tides1 but1 provided a sufficiently large scale is adopted1 there is no reason why curves relating to the whole range of the tides should not be plotted on one diagram4 ,this chart shows the total distance that would be covered by a float according to the height of the tide2 it also indicates the velocity of the current from time to time4 ,it can be used in several ways1 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 outfall1 the diagram should be checked as far as possible by any observations that may be taken at other states of tides of the same heights4 ,suppose we require to know how far a float will travel if started at two hours after high water on a #ab ft tide4 ,from ,fig4 #aj we see that on a tide of this height the current turns two hours and a quarter before the tide2 therefore two hours after high water will be four hours and a quarter after the turn of the current4 ,if the float were started with the current1 we see from ,fig4 #aa that it would have travelled three miles in four hours and a quarter2 and subtracting this from four miles1 which is its full travel on a whole tide1 we see that it will only cover one mile in the two hours and a quarter remaining before the current turns to run back again4 ,although sewage discharged into the sea rapidly becomes so diffused as to lose its identity1 still occasionally the extraneous substances in it1 such as wooden matches1 banana skins1 etc41 may be traced for a considerable distance2 so that1 as the sewage continues to be discharged into the sea moving past the outfall1 there is formed what may be described as a body or column of water having possibilities of sewage contamination4 ,if the time during which sewage is discharged is limited to two hours1 and starts1 say1 at the turn of the current on a #ab ft tide1 we see from ,fig4 #aa that the front of this body of water will have reached a point five-eighths of a mile away when the discharge ceases2 so that there will be a virtual column of water of a total length of five-eighths of a mile1 in which is contained all that remains of the noxious matters1 travelling through the sea along the course of the current4 ,we see1 further1 that at a distance of three miles away this column would only take thirty minutes to pass a given point4 ,the extent of this column of water will vary considerably according to the tide and the time of discharge2 for instance1 on a #bb ft tide1 if the discharge starts one hour after the turn of the current and continues for two hours1 as in the previous example1 it will form a column four miles long1 whereas if it started two hours after the current1 and continued for the same length of time1 the column would be six miles and a half long1 but the percentage of sewage in the water would be infinitesimal4 ,illustration3 ,hours after turn of current ,,fig4 #aa ,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 point4 ,in other words1 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 connection4 ,assuming the period of discharge will be two hours1 and that the point which it is necessary to clear is situated three miles and a half from the outfall1 the permissible time to discharge the sewage according to the height of the tide can be obtained from ,fig4 #aa4 ,taking the #bb ft tide first1 it will be seen that if the float started with the current it would travel twelve miles in the tide2 three and a half from twelve leaves eight and a half miles4 ,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 end1 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 turns4 ,as on this tide high water is about fifteen minutes after the current1 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 water4 ,similarly with the #ab ft tide having a total travel of four miles3 three and a half from four leaves half a mile1 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 cease4 ,high water is two hours and a quarter after the current2 therefore the latest time for the period of discharge would be from two hours and a half to half an hour before high water1 but1 as during the first quarter of an hour the movement of the current1 though slight1 would be in the opposite direction1 it would be advisable to curtail the time of discharge1 and say that it should be limited to between two hours and a quarter and half an hour before high water4 ,it is obvious that if sewage is discharged about two hours after high water the current will be nearing its maximum speed1 but it will only have about three hours to run before it turns2 so that1 although the sewage may be removed with the maximum rapidity from the vicinity of the sea outfall1 it will not be carried to any very great distance1 and1 of course1 the greater the distance it is carried the more it will be diffused4 ,it must be remembered that the foregoing data are only applicable to the locality they relate to1 although after obtaining the necessary information similar diagrams can be made and used for other places2 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 water1 as the case may be1 according to the height of the tide4 ,,chapter ,v4 ,,volume ,,of ,,sewage4 ,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 constructed1 but where the scheme is an entirely new one the quantity must be estimated4 ,if there is a water supply system the amount of water consumed per day1 after making due allowance for the quantity used for trade purposes and street watering1 will be a useful guide4 ,the average amount of water used per head per day for domestic purposes only may be taken as follows3-- ,,daily ,,water ,,supply 7,gallons per head per day47 ,dietetic purposes 7cooking1 drinking1 c47 #a ,cleansing purposes 7washing house utensils1 clothes1 c47 #f ,if water-closets are in general use1 add #c ,if baths are in general use1 add #e ,total #ae ,it therefore follows that the quantity of domestic sewage to be expected will vary from #g to #ae gallons per head per day1 according to the extent of the sanitary conveniences installed in the town2 but with the advent of an up-to-date sewage scheme1 probably accompanied by a proper water supply1 a very large increase in the number of water-closets and baths may confidently be anticipated1 and it will rarely be advisable to provide for a less quantity of domestic sewage than #ae gallons per head per day for each of the resident inhabitants4 ,the problem is complicated in sea coast towns by the large influx of visitors during certain short periods of the year1 for whom the sewerage system must be sufficient1 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 absent4 ,the visitors are of two types--the daily trippers and those who spend several days or weeks in the town4 ,the daily tripper may not directly contribute much sewage to the sewers1 but he does indirectly through those who cater for his wants4 ,the resident visitor will spend most of the day out of doors1 and therefore cause less than the average quantity of water to be used for house-cleansing purposes1 in addition to which the bulk of the soiled linen will not be washed in the town4 ,an allowance of #aj gallons per head per day for the resident visitor and #e gallons per head per day for the trippers will usually be found a sufficient provision4 ,it is1 of course1 well known that the flow of sewage varies from day to day as well as from hour to hour1 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 scheme4 ,there are many important factors governing this variation1 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 wastes4 ,with a small population the hourly fluctuation in the quantity of sewage flowing into the sewers is very great1 but it reduces as the population increases1 owing to the diversity of the occupations and habits of the inhabitants4 ,in all cases where the residential portions of the district are straggling1 and the outfall works are situated at a long distance from the centre of the town1 the flow becomes steadier1 and the inequalities are not so prominently marked at the outlet end of the sewer4 ,the rate of flow increases more or less gradually to the maximum about midday1 and falls off in the afternoon in the same gradual manner4 ,the following table1 based on numerous gaugings1 represents approximately the hourly variations in the dry weather flow of the sewage proper from populations numbering from #a1jjj to #aj1jjj1 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 pipes1 and from defective water supply fittings as ascertained from the night gaugings4 ,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 to1 which must be the subject of special investigation in each case4 ,,table ,,no4 #d4 ,,approximate ,,hourly ,,variation ,,in ,,the ,,flow ,,of ,,sewage4 ,percentage of ,total ,flow ,passing ,off in each ,hour4 ---------------------------------------- ------------------- ,population4 ,hour4 ---------------------------------------- - #a1jjjb1jjjc1jjjd1jjje1jjjf1jjjh1jjjaj1j jj ---------------------------------------- ------------ ,midnight #a4j #a4j #a4b #a4c #a4e #a4e #a4h #b4j #a4j a4m4 #j4g #j4g #j4g #j4h #j4h #a4j #a4j #a4j #b4j nil nil nil nil #j4b #j4b #j4c #j4e #c4j nil nil nil nil nil nil nil #j4b #d4j nil nil nil nil nil nil nil nil #e4j nil nil nil nil nil nil nil #j4b #f4j #j4b #j4b #j4c #j4e #j4f #j4e #j4g #j4h #g4j #j4e #j4e #a4j #a4e #a4f #a4g #b4j #b4e #h4j #a4j #a4e #b4j #b4e #c4j #c4e #d4j #e4j #i4j #c4e #d4e #d4e #d4h #e4e #e4h #f4j #f4e #aj4j #f4e #f4e #f4h #g4j #g4e #g4g #h4j #h4j #aa4j #aj4e #aa4j #aj4e #aj4j #i4f #i4c #i4j #h4h ,noon #aa4j #aa4c #aj4h #aj4c #i4c #i4e #i4b #i4j #a4j p4m4 #f4j #e4e #f4j #f4g #g4j #g4b #g4c #g4e #b4j #g4j #g4c #g4j #g4j #f4e #f4e #f4b #f4j #c4j #f4h #f4e #f4e #f4e #f4e #f4c #f4c #f4j #d4j #g4e #g4e #g4c #g4j #f4g #f4e #f4b #f4g #e4j #f4e #f4e #f4e #f4c #f4j #f4j #f4j #e4h #f4j #d4e #d4e #d4g #d4h #e4j #e4j #e4j #e4b #g4j #f4e #f4b #f4j #e4h #e4e #e4e #e4e #d4g #h4j #f4b #f4j #e4h #e4e #e4e #e4c #e4j #d4h #i4j #e4j #d4h #d4g #d4e #d4e #d4e #d4e #d4j #aj4j #d4h #d4f #d4b #d4j #c4h #c4e #c4j #c4j #aa4j #d4c #c4e #c4e #c4b #c4b #c4j #c4j #b4h ---------------------------------------- ------------ ,total #ajj4jajj4jajj4jajj4jajj4jajj4jajj4jajj4 j ---------------------------------------- ------------ ,,analysis ,,of ,,flow ,percentage of total flow passing off during period named4 ---------------------------------------- ---------------------------------------- ----- ,population4 ---------------------------------------- ----------------- #a1jjj #b1jjj #c1jjj #d1jjj #e1jjj #f1jjj #h1jjj #aj1jjj ---------------------------------------- -------------------------------------- #g4j a4m4 to #g4j p4m #gg4c #gh4h #gh4f #gh4g #gh4e #gh4h #gh4g #ge4b #g4j p4m4 to #g4j a4m #bb4g #ba4b #ba4d #ba4c #ba4e #ba4b #ba4c #ba4h ,maximum #ab hrs4 #hd4j #hc4f #hb4f #ha4g #ha4j #hj4f #gi4g #gh4b #aj #gb4h #gb4h #gb4a #ga4d #gj4j #fi4h #fi4b #fh4e #i #ff4c #ff4f #ff4a #fe4f #fd4e #fd4h #fd4b #fc4c #h #fa4h #fb4a #fa4d #fj4h #ei4e #ei4j #eh4b #eg4e #f #dh4h #di4a #dc4a #dg4e #df4h #df4e #df4j #de4h #c #bc4j #bh4h #bg4aa #bg4c #bf4h #bf4e #bf4b #be4h #b #ba4e #bb4c #ba4c #bj4c #ai4c #ah4e #ah4b #ag4c #a #aa4j #aa4c #aj4h #aj4c #i4h #i4e #i4b #i4j ,minimum #i #c4d #c4i #e4b #f4f #g4e #f4i #h4h #aj4j #aj #f4i #g4d #h4g #i4h #aj4g #aj4d #aa4h #ac4j ---------------------------------------- -------------------------------------- ,the data in the foregoing table1 so far as they relate to populations of one1 five1 and ten thousand respectively1 are reproduced graphically in ,fig4 #ab4 ,this table and diagram relate only to the flow of sewage--that is1 water which is intentionally fouled2 but unfortunately it is almost invariably found that the flow in the sewers is greater than is thus indicated1 and due allowance must be made accordingly4 ,the greater the amount of extra liquid flowing in the sewers as a permanent constant stream1 the less marked will be the hourly variations2 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 that1 taken as a percentage of the total daily flow1 the hourly variation was almost imperceptible4 ,illustration3 ,fig #ab ,hourly ,variation in ,flow of ,sewage4 ,provision must be made in the scheme for the leakage from the water fittings1 and for the subsoil water1 which will inevitably find its way into the sewers4 ,the quantity will vary very considerably1 and is difficult of estimation4 ,if the water is cheap1 and the supply plentiful1 the water authority may not seriously attempt to curtail the leakage2 but in other cases it will be reduced to a minimum by frequent house to house inspection2 some authorities going so far as to gratuitously fix new washers to taps when they are required4 ,theoretically1 there should be no infiltration of subsoil water1 as in nearly all modern sewerage schemes the pipes are tested and proved to be watertight before the trenches are filled in2 but in practice this happy state is not obtainable4 ,the pipes may not all be bedded as solidly as they should be1 and when the pressure of the earth comes upon them settlement takes place and the joints are broken4 ,joints may also be broken by careless filling of trenches1 or by men walking upon the pipes before they are sufficiently covered4 ,some engineers specify that all sewers shall be tested and proved to be absolutely water-tight before they are passed and covered in1 but make a proviso that if1 after the completion of the works1 the leakage into any section exceeds #a_/b cubic foot per minute per mile of sewer1 that length shall be taken up and relaid4 ,even if the greatest vigilance is exercised to obtain water-tight sewers1 the numerous house connections are each potential sources of leakage1 and when the scheme is complete there may be a large quantity of infiltration water to be dealt with4 ,where there are existing systems of old sewers the quantity of infiltration water can be ascertained by gauging the night flow2 and if it is proved to be excessive1 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 occurs1 and then to take such steps as may be practicable to reduce the quantity4 ,,chapter ,,vi4 ,,gauging ,,flow ,,in ,,sewers4 ,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 manhole1 which will pond up the sewage2 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 side4 ,the extreme variation in the flow of the sewage is so great1 however1 that if the notch is of a convenient width to take the maximum flow1 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 flow1 and there will be great probability of incorrect results being obtained by reason of solid sewage matter lodging on the notch4 ,when the depth on a l#b in notch is about #f in1 a variation of only #a-afth inch in the vertical measurement will represent a difference in the rate of the flow of approximately #dje gallons per hour1 or about #i1gjj gallons per day4 ,when the flow is about lin deep the same variation of #a-afth in will represent about #afb gallons per hour1 or #c1ijj gallons per day4 ,greater accuracy will be obtained if a properly-formed gauging pond is constructed independently of the manhole and a double rectangular notch1 similar to ,fig4 #ac1 or a triangular or ,v- shaped notch1 as shown in ,fig4 #ad1 used in lieu of the simpler form4 ,in calculating the discharge of weirs there are several formul to choose from1 all of which will give different results1 though comparative accuracy has been claimed for each4 ,taking first a single rectangular notch and reducing the formulae to the common form3 ,discharge per foot in width of weir ,c _/ ,h#c where ,h depth from the surface of still water above the weir to the level of the bottom of the notch1 the value of ,c will be as set out in the following table3-- ,,table ,no4 #e4 ,,rectangular ,,notches4 ,discharge per foot in width of notch ,c _/ ,h#c ---------------------------------------- -------------------------- ,values of ,c4 ---------------------------------------- ------------------------- ,h ,measured in ,feet4 ,inches4 ---------------------------------------- ---------------------- ,gallons ,c4 ft ,gallons ,c4 ft ,discharge in per hour4 per min per hour4 per min ---------------------------------------- ---------------------- ,authority4 ,box #gi1hie #bac4f #a1ibb #e4ac ,cotterill #gd1bif #aih4f #a1ghg #d4gh ,francis #gd1hbj #bjj4j #a1hjj #d4ha ,mo'esworth #hj1jeg #bad4j #a1ibf #e4ae ,santo ,crimp #gb1idi #aie4j #a1gee #d4fi ---------------------------------------- ---------------------- ,in the foregoing table ,francis' short formula is used1 which does not take into account the end contractions and therefore gives a slightly higher result than would otherwise be the case1 and in ,cotterill's formula the notch is taken as being half the width of the weir1 or of the stream above the weir4 ,if a cubic foot is taken as being equal to #f-a_/d gallons instead of #f4bce gallons1 then1 cubic feet per minute multiplied by #i1jjj equals gallons per day4 ,this table can be applied to ascertain the flow through the notch shown in ,fig4 #ac in the following way4 ,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 #d in ,using ,santo ,crimp's formula the result will be ,c_/,h#c #d4fi _/#dc #d4fi x #h #cg4eb cubic feet per foot in width of weir1 but as the weir is only #f in wide1 we must divide this figure by #b1 then #cg4eb_/b #ah4gf cubic feet1 which is the discharge per minute4 ------ ------ ,,fig4 #ac ------ ------ ------ ---------------------------------- ,fig4 #ac4-;,,elevation ,,of ,,double ,,rectangular ,,notched ,,gauging ,,weir4 ------ ------ ,,fig4 #ac _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ ---------------------------------- ,,fig4 #ad4-;,,elevation ,,of ,,triangular ,,notched ,,gauging ,,weir4 ,,fig4 #ae4-,,longitudinal ,,section1 ,,showing ,,weir1 ,,gauge-,,peg1 ,,and ,,hook-,,gauge ,if it is required to find the discharge in similar terms with a depth of water of #bj in1 two sets of calculations are required4 ,first #bj in depth on the notch #f in wide1 and then #d in depth on the notch1 #bh in minus #f in1 or #a ft wide4 7#a7 ,c_/ ,h#c #d4fi_/b _/ #ajc #b4cde x #ca4fb #gd4ae 7#b7 ,c_/ ,h#c #a4j x #d4fi _/ #dc #a4j x #d4fi x #h #cg4eb ,total in c4 ft per min #aaa4fg ,the actual discharge would be slightly in excess of this4 ,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 time4 ,in order to make allowance for this1 the head calculated to produce the velocity must be added to the actual head4 ,this can be embodied in the formula1 as1 for example1 ,santo ,crimp's formula for discharge in cubic feet per minute1 with ,h measured in feet1 is written #aie_/7aac 4#jce,v - ,h#b instead of the usual form of #aie_/ ,h#c1 which is used when there is no velocity to take into account4 ,the ,v represents the velocity in feet per second4 ,triangular or ,v notches are usually formed so that the angle between the two sides is #ij1 when the breadth at any point will always be twice the vertical height measured at the centre4 ,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 notch4 ,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 it4 ,the area of the #ij notch is half that of a circumscribing rectangular notch1 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 level1 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 time1 both being measured in the same unit1 therefore ,c _/ ,h#c becomes ,c x ,h x _/ ,h#c which equals ,c _/ ,h#e4 ,the constant ,c will1 however1 vary from that for the rectangular notch to give an accurate result4 ,,table ,no4 #f4 ,,triangular ,,or ,v ,,notches4 ,discharge ,c x _/ ,h#e4 ,values of ,c4 ---------------------------------------- --------------------- ,h ,measured in ,feet4 ,inches4 ---------------------------------------- ------------------- ,discharge in ,gallons ,c4 ft per ,gallons ,c4 ft per per hour min per hour4 min ---------------------------------------- ------------------- ,alexander #ei1hef #afj #abj4j #j4cba ,cotterill #eg1jac #aeb4d #aad4c #j4cjf ,molesworth #ei1bja #aeh4b #aah4g #j4cag ,thomson #eg1aff #aeb4h #aad4f #j4cjf ---------------------------------------- ------------------- ,cotterill's formula for the discharge in cubic feet per minute is #af x ,c x ,b _/ #b;g ,h#c when ,b breadth of notch in feet and ,h height of water in feet and can be applied to any proportion of notch4 ,when ,b #b;,h1 that is1 a #ij notch1 ,c 4#eie and the formula becomes #aeb4d _/ ,h#e1 and when ,b #d;,h1 that is1 a notch containing an angle of #abf #ea' #cf1 ,c 4#fb and the formula is then written #cah _/ ,h#e4 ,the measurements of the depth of the water above the notch should be taken by a hook-gauge1 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 obtainable1 and1 further1 capillary attraction causes the water to rise up the rule above the actual surface1 and thus to show a still greater depth4 ,when using a hook-gauge the top of the weir1 as well as the notch1 should be fixed level and a peg or stake fixed as far back as possible on the upstream side of the weir1 so that the top of the peg is level with the top of the weir1 instead of with the notch1 as is the case when a rule or gauge-slate is used4 ,the hook-gauge consists of a square rod of1 say1 lin side1 with a metal hook at the bottom1 as shown in ,fig4 #ae1 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 notch4 ,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 submerged4 ,the gauge is then gently raised until the point of the hook breaks the surface of the water1 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 weir4 ,,chapter ,,vii4 ,,rainfall4 ,the next consideration is the amount of rain-water for which provision should be made4 ,this depends on two factors3 first1 the amount of rain which may be expected to fall2 and1 secondly1 the proportion of this rainfall which will reach the sewers4 ,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 plant1 if any1 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 periods1 irrespective of the rate of flow4 ,some very complete and valuable investigations of the flow of rain-water in the ,birmingham sewers were carried out between #aijj and #aijd by ,mr4 ,d4 ,e4 ,lloyd-,davies1 ,m4,inst4,c4 ,e41 the results of which are published in ,vol4 ,,clxiv41 ,min ,proc4 ,inst4,c4,e4 ,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 district4 ,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 observation1 assuming the sewers to be flowing half full2 and adding to the time so obtained the period required for the rain to get into the sewers1 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 gutters4 ,with an average velocity of #c ft per second the time of concentration will be thirty minutes for each mile of sewer4 ,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 concentration4 ,he stated further that while the flow in the sewers was proportional to the aggregate rainfall during the time of concentration1 it was also directly proportional to the impermeable area4 ,putting this into figures1 we see that in a district where the whole area is impermeable1 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 it1 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 minutes1 and further1 that the total quantity of rainfall reaching the sewers will approximately equal the total quantity falling4 ,if1 however1 the impermeable area is #be per cent4 of the whole1 then the maximum flow of storm water will be #be per cent4 of the rain falling during the time of concentration1 viz41 ten minutes1 and the total quantity of storm water will be #be per cent4 of the total rainfall4 ,if the quantity of storm water is gauged throughout the year it will probably be found that1 on the average1 only from #gj per cent4 to #hj per cent4 of the rain falling on the impermeable areas will reach the sewers instead of #ajj per cent41 as suggested by ,mr4 ,lloyd-,davies1 the difference being accounted for by the rain which is required to wet the surfaces before any flow off can take place1 in addition to the rain-water collected in tanks for domestic use1 rain required to fill up gullies the water level of which has been lowered by evaporation1 and rain-water absorbed in the joints of the paving4 ,the intensity of the rainfall decreases as the period over which the rainfall is taken is increased4 ,for instance1 a rainfall of lin may occur in a period of twenty minutes1 being at the rate of #c in per hour1 but if a period of one hour is taken the fall during such lengthened time will be considerably less than #c in ,in towns where automatic rain gauges are installed and records kept1 the required data can be abstracted1 but in other cases it is necessary to estimate the quantity of rain which may have to be dealt with4 ,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 rains1 and the amount of risk which it is desirable to run must be settled after consideration of the details of each particular case4 ,the following table1 based principally upon observations taken at the ,birmingham ,observatory1 shows the approximate rainfall which may be taken according to the time of concentration4 ,,table ,no4 #g4 ,,intensity ,,of ,,rainfall ,,during ,,limited ,,periods4 ,equivalent rate in inches per hour of aggregate rainfall during ,time of ,concentration1 period of concentration ,a ,b ,c ,d ,e #e minutes 444444444444444 #a4ge #b4jj #c4jj -- -- #aj 444444444444444 #a4be #a4ej #b4jj -- -- #ae 444444444444444 #a4je #a4be #a4ej -- -- #bj 444444444444444 #j4ie #a4je #a4cj #a4bj #c4jj #be 444444444444444 #j4he #j4ie #a4ae -- -- #cj 444444444444444 #j4hj #j4ij #a4je #a4jj #b4ej #ce 444444444444444 #j4ge #j4he #j4ie -- -- #dj 444444444444444 #j4gj #j4hj #j4ij -- -- #de 444444444444444 #j4fe #j4ge #j4he -- -- #a hour 444444444444444444 #j4ej #j4fj #j4gj #j4ge #a4hj #a-a_/b 444444444444444444 #j4dj #j4ej #j4fj -- #a4dj #b 444444444444444444 #j4cj #j4dj #j4ej #j4ej #a4aj ,the figures in column ,a will not probably be exceeded more than once in each year1 those in column ,b will not probably be exceeded more than once in three years1 while those in column ,c will rarely be exceeded at all4 ,columns ,d and ,e refer to the records tabulated by the ,meteorological ,office1 the rainfall given in column ,d being described in their publication as falls too numerous to require insertion1 and those in column ,e as extreme falls rarely exceeded4 ,it must1 however1 be borne in mind that the ,meteorological ,office figures relate to records derived from all parts of the country1 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 magnitude4 ,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 hour1 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 acre4 ,this information is given in the following ,table ,no4 #h1 which is prepared from the figures given in ,table ,no4 #g1 and is applicable in the same manner4 ,,table ,no4 #h4 ,,maximum ,,flows ,,of ,,storm ,,water4 ---------------------------------------- -------------------- ,maximum storm water flow in cubic feet per min per acre of impervious area4 ,time of ,concentration4 ------------------------------ ,a ,b ,c ,d ,e ---------------------------------------- ---------------- #e minutes #ajf #aba #aha -- -- #aj #ge #ia #aba -- -- #ae #fd #ge #ia -- -- #bj #eg #fd #gi #gc #aha #be #ea #eg #gj -- -- #cj #dh #ed #fd #fa #aea #ce #de #ea #eg -- -- #dj #db #dh #ed -- -- #de #ci #de #ea -- -- #a hour #cj #cf #db #de #aji #a-a_/b #bd #cj #cf -- #he #b #ah #bd #cj #cj #fg ---------------------------------------- ----------------- l inch of rain #c1fcj cub4 feet per acre4 ,the amount of rainfall for which storage has to be provided is a difficult matter to determine2 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 reasons4 ,it is found that on the average the whole of the rain on a rainy day falls within a period of #b-a_/b hours2 therefore1 ignoring the relief which may be afforded by overflows1 if the sewers are tide-locked for a period of #b-a_/b hours or over it would appear to be necessary to provide storage for the rainfall of a whole day2 but in this case again it is permissible to run a certain amount of risk1 varying with the length of time the sewers are tide-locked1 because1 first of all1 it only rains on the average on about #afj days in the year1 and1 secondly1 when it does rain1 it may not be at the time when the sewers are tide-locked1 although it is frequently found that the heaviest storms occur just at the most inconvenient time1 namely1 about high water4 ,table ,no4 #i shows the frequency of heavy rain recorded during a period of ten years at the ,birmingham ,observatory1 which1 being in the centre of ,england1 may be taken as an approximate average of the country4 ,,table ,no4 #i4 ,,frequency ,,of ,,heavy ,,rain ---------------------------------------- --------------- ,total ,daily ,rainfall4 ,average ,frequency of ,rainfall ---------------------------------------- --------------- #j4d inches and over #aee times each year #j4e #ic #j4f #fh #j4g #ej #j4h #cc #j4i #bb #a4j #ag #a4a ,once each year #a4b ,once in #ag months #a4be #b years #a4c #b-a_/b #a4d #c-a_/c #a4e #e years #a4f #e years #a4g #e years #a4h #aj years #a4i #aj years #b4j #aj years ---------------------------------------- ---------- ,it will be interesting and useful to consider the records for the year #aijc1 which was one of the wettest years on record1 and to compare those taken in ,birmingham with the mean of those given in ,symons' ,rainfall1 taken at thirty-seven different stations distributed over the rest of the country4 ,,table ,no4 #aj4 ,,rainfall ,,for #aijc4 ,mean of #cg stations in ,birmingham ,england and ,wales4 ,daily ,rainfall of #b in and over 444444 ,none #a day ,daily ,rainfall of #a in and over 444444 #c days #f days ,daily ,rainfall of #a_/b in and over 4444 #ag days #be days ,number of rainy days444444444444444444 #agg days #baa days ,total rainfall 4444444444444444444444 #cc4hf in #dd4hi in ,amount per rainy day 4444444444444444 #j4ai in #j4ba in ,the year #aijc was an exceptional one1 but the difference existing between the figures in the above table and the average figures in ,table #i are very marked1 and serve to emphasise the necessity for close investigation in each individual case4 ,it must be further remembered that the wettest year is not necessarily the year of the heaviest rainfalls1 and it is the heavy rainfalls only which affect the design of sewerage works4 ,,chapter ,,viii4 ,,storm ,,water ,,in ,,sewers4 ,if the whole area of the district is not impermeable the percentage which is so must be carefully estimated1 and will naturally vary in each case4 ,the means of arriving at an estimate will also probably vary considerably according to circumstances1 but the following figures1 which relate to investigations recently made by the writer1 may be of interest4 ,in the town1 which has a population of #aj1jjj and an area of #b1jcg acres1 the total length of roads constructed was #gd1eej lineal feet1 and their average width was #cf ft1 including two footpaths4 ,the average density of the population was #d4i people per acre4 ,houses were erected adjoining a length of #dc1ghd lineal feet of roads1 leaving #cj1gff lineal feet1 which for distinction may be called undeveloped--that is1 the land adjoining them was not built over4 ,dividing the length of road occupied by houses by the total number of the inhabitants of the town1 the average length of road per head was #d4cg ft1 and assuming five people per house and one house on each side of the road we get ten people per two houses opposite each other4 ,then #aj x #d4cg #dc4g lineal feet of road frontage to each pair of opposite houses4 ,after a very careful inspection of the whole town1 the average area of the impermeable surfaces appertaining to each house was estimated at #fge sq4 ft1 of which #cjj sq4 ft was apportioned to the front roof and garden paths and #cge sq4 ft to the back roof and paved yards4 ,dividing these figures by #dc4ga in ft of road frontage per house1 we find that the effective width of the impermeable roadway is increased by #f ft #aj in for the front portions of each house1 and by a width of #h ft #g in1 for the back portions1 making a total width of #cf ft #b7f ft #aj in7 #b7h ft #g in7 #ff ft #aj in1 say #fg ft ,on this basis the impermeable area in the town therefore equals3 #dc1ghda in ft x #fg ft #b1icc1ebh2 and #cj1gff lin ft x #cf ft #a1ajg1egf4 ,total1 #d1jda1ajd sq4 ft1 or #ib4gg acres4 ,as the population is #aj1jjj the impermeable area equals #djd1 say1 #djj sq4 ft per head1 or 7#ib4gg x #ajj7 _/ #bjcg #d4e per cent1 of the whole area of the town4 ,it must be remembered that when rain continues for long periods1 ground which in the ordinary way would generally be considered permeable becomes soaked and eventually becomes more or less impermeable4 ,mr4 ,d4 ,e4 ,lloyd-,davies1 ,m4,inst4,c4,e41 gives two very interesting diagrams in the paper previously referred to1 which show the average percentage of effective impermeable area according to the population per acre4 ,this information1 which is applicable more to large towns1 has been embodied in ,fig4 #af1 from which it will be seen that1 for storms of short duration1 the proportion of impervious areas equals #e per cent4 with a population of #d4i per acre1 which is a very close approximation to the #d4e per cent4 obtained in the example just described4 ,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 of1 or appertaining to1 each house1 and divide it by five1 so as to get the area per head4 ,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 road1 and that due to the population distributed along it4 ,illustration3 ,,fig4 #af4--,,variation ,,in ,,average ,,percentage ,,of ,,effective ,,impermeable ,,area ,,according ,,to ,,density ,,of ,,population4 ,in addition to being undesirable from a sanitary point of view1 it is rarely economical to construct special storm water drains1 but in all cases where they exist1 allowance must be made for any rain that may be intercepted by them4 ,short branch sewers constructed for the conveyance of foul water alone are usually #i;in or #ab in in diameter1 not because those sizes are necessary to convey the quantity of liquid which may be expected1 but because it is frequently undesirable to provide smaller public sewers1 and there is generally sufficient room for the storm water without increasing the size of the sewer4 ,if this storm water were conveyed in separate sewers the cost would be double1 as two sewers would be required in the place of one4 ,in the main sewers the difference is not so great1 but generally one large sewer will be more economical than two smaller ones4 ,where duplicate sewers are provided and arranged1 so that the storm water sewer takes the rain-water from the roads1 front roofs and gardens of the houses1 and the foul water sewer takes the rain-water from the back roofs and paved yards1 it was found in the case previously worked out in detail that in built-up roads a width of #cf ft #b 7#h ft #g in7 #ec ft #b in1 or1 say1 #afj sq4 ft per lineal yard of road would drain to the storm water sewer1 and a width of #b 7#f ft #aj in7 #ac ft #h in1 or1 say1 #da sq4 ft per lineal yard of road to the foul water sewer4 ,this shows that even if the whole of the rain which falls on the impervious areas flows off1 only just under #hj per cent4 of it would be intercepted by the special storm water sewers4 ,taking an average annual rainfall of #cj in1 of which #ge per cent4 flows off1 the quantity reaching the storm water sewer in the course of a year from each lineal #cj #ge yard of road would be --- x #afj x --- #cjj cubic #ab #ajj feet #a1hge gallons4 ,illustration3 ,,fig4 #ag4--,,section ,,of ,,leap ,,weir ,,overflow ,the cost of constructing a separate surface water system will vary1 but may be taken at an average of1 approximately1 l#es4 #j;d4 per lineal yard of road4 ,to repay this amount in thirty years at #d per cent1 would require a sum of #aj4db;d41 say #aj-a_/b;d4 per annum2 that is to say1 the cost of taking the surface water into special #aj-a_/b d4 x #ajjj sewers is ---------------- #e4f1 say #f;d4 per #a1jjj #ahge gallons4 ,if the sewage has to be pumped1 the extra cost of pumping by reason of the increased quantity of surface water can be looked at from two different points of view3-- #a4 ,the net cost of the gas or other fuel or electric current consumed in lifting the water4 #b4 ,the cost of the fuel consumed plus wages1 stores1 etc41 and a proportion of the sum required to repay the capital cost of the pumping station and machinery4 ,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 schemes4 ,the actual cost of the fuel may be taken at approximately #a_/d d4 per #a1jjj gallons4 ,the annual works and capital charges1 exclusive of fuel1 should be divided by the normal quantity of sewage pumped per annum1 rather than by the maximum quantity which the pumps would lift if they were able to run continuously during the whole time4 ,for a town of about #aj1jjj inhabitants these charges may be taken at #a-a_/d d4 per #a1jjj gallons1 which makes the total cost of pumping1 inclusive of capital charges1 #a-a_/b d4 per #a1jjj gallons4 ,even if the extra cost of enlarging the sewers is added to this sum it will still be considerably below the sum of #f d41 which represents the cost of providing a separate system for the surface water4 ,unless it is permissible for the sewage to have a free outlet to the sea at all states of the tide1 the provision of effective storm overflows is a matter of supreme importance4 ,not only is it necessary for them to be constructed in well- considered positions1 but they must be effective in action4 ,a weir constructed along one side of a manhole and parallel to the sewer is rarely efficient1 as in times of storm the liquid in the sewer travels at a considerable velocity1 and the greater portion of it1 which should be diverted1 rushes past the weir and continues to flow in the sewer2 and if1 as is frequently the case1 it is desirable that the overflowing liquid should be screened1 and vertical bars are fixed on the weir for the purpose1 they block the outlet and render the overflow practically useless4 ,leap weir overflows are theoretically most suitable for separating the excess flow during times of storm1 but in practice they rarely prove satisfactory4 ,this is not the fault of the system1 but is1 in the majority of the cases1 if not all1 due to defective designing4 ,the general arrangement of a leap weir overflow is shown in ,fig4 #ag4 ,in normal circumstances the sewage flowing along the pipe ,a falls down the ramp1 and thence along the sewer ,b2 when the flow is increased during storms the sewage from ,a shoots out from the end of the pipe into the trough ,c1 and thence along the storm-water sewer ,d4 ,in order that it should be effective the first step is to ascertain accurately the gradient of the sewer above the proposed overflow1 then1 the size being known1 it is easy to calculate the velocity of flow for the varying depths of sewage corresponding with minimum flow1 average dry weather flow1 maximum dry weather flow1 and six times the dry weather flow4 ,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 depths1 taking into account the fact that the velocity at the invert and sides of the sewer is less than the average velocity of flow4 ,the ramp should be built in accordance with the calculated curves so as to avoid splashing as far as possible1 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 place4 ,due regard must be had to the altered circumstances which will arise when the growth of population occurs1 for which provision is made in the scheme1 so that the overflow will remain efficient4 ,the trough ,c is movable1 so that the width of the leap weir may be adjusted from time to time as required4 ,the overflow should be frequently inspected1 and the accumulated rubbish removed from the trough1 because sticks and similar matters brought down by the sewer will probably leap the weir instead of flowing down the ramp with the sewage4 ,it is undesirable to fix a screen in conjunction with this overflow1 but if screening is essential the operation should be carried out in a special manhole built lower down the course of the storm-water sewer4 ,considerable wear takes place on the ramp1 which should1 therefore1 be constructed of blue ,staffordshire or other hard bricks4 ,the ramp should terminate in a stone block to resist the impact of the falling water1 and the stones which may be brought with it1 which would crack stoneware pipes if such were used4 ,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 overflow1 the excess flow of storm-water may be diverted by an arrangement similar to that shown in ,fig4 #ah4 ,footnote3 ,,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 extent2 this gives the level of the lip of the diverting plate4 ,the ordinary sewage flow will pass steadily along the invert of the sewer under the plate until it rises up to that height1 when the opening becomes a submerged orifice1 and its discharging capacity becomes less than when the sewage was flowing freely4 ,this restricts the flow of the sewage1 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 sewer1 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 desirable1 so as to govern the direction of flow at the time the overflow is in action4 ,the diverting trough is movable1 and its height above the invert can be increased easily1 as may be necessary from time to time4 ,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 ,fig4 #ah4 ,footnote3 ,,plate ,,iv ,it is loose1 as is the trough1 and both can be lifted out when it is desired to have access to the invert of the sewer4 ,the screen is self- cleansing1 as any floating matter which may be washed against it does not stop on it and reduce its discharging capacity1 but is gradually drawn down by the flow of the sewage towards the diverting plate under which it will be carried4 ,the heavier matter in the sewage which flows along the invert will pass under the plate and be carried through to the outfall works1 instead of escaping by the overflow1 and perhaps creating a nuisance at that point4 ,,chapter ,,ix4 ,,wind ,,and ,,windmills4 ,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 possible4 ,if oil or gas engines are employed the man cannot be absent for many minutes together while the machinery is running1 and when it is not running1 as for instance during the night1 he must be prepared to start the pumps at very short notice1 should a heavy rain storm increase the flow in the sewers to such an extent that the pump well or storage tank becomes filled up4 ,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 clutch1 so that when the level of the sewage in the pump well reaches the highest point desired the pump may be started1 and when it is lowered to a predetermined low water level the pump will stop2 but it is impracticable to control the engine in the same way1 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 attendance4 ,an electric motor may be controlled by a float1 but in many cases trouble is experienced with the switch gear1 probably caused by its exposure to the damp air4 ,in all cases an alarm float should be fixed1 which would rise as the depth of the sewage in the pump well increased1 until the top water level was reached1 when the float would make an electrical contact and start a continuous ringing warning bell1 which could be placed either at the pumping station or at the man's residence4 ,on hearing the bell the man would know the pump well was full1 and that he must immediately repair to the pumping-station and start the pumps1 otherwise the building would be flooded4 ,if compressed air is available a hooter could be fixed1 which would be heard for a considerable distance from the station4 ,illustration3 ,,plate ,,iv4 ,,diverting ,,plate ,,overflow4 ,to face page #ff4 ,it is apparent1 therefore1 that a pumping machine is wanted which will work continuously without attention1 and will not waste money when there is nothing to pump4 ,there are two sources of power in nature which might be harnessed to give this result--water and wind4 ,the use of water on such a small scale is rarely economically practicable1 as even if the water is available in the vicinity of the pumping-station1 considerable work has generally to be executed at the point of supply1 not only to store the water in sufficient bulk at such a level that it can be usefully employed1 but also to lead it to the power-house1 and then to provide for its escape after it has done its work4 ,the power-house1 with its turbines and other machinery1 involves a comparatively large outlay1 but if the pump can be directly driven from the turbines1 so that the cost of attendance is reduced to a minimum1 the system should certainly receive consideration4 ,although the wind is always available in every district1 it is more frequent and powerful on the coast than inland4 ,the velocity of the wind is ever varying within wide limits1 and although the records usually give the average hourly velocity1 it is not constant even for one minute4 ,windmills of the modern type1 consisting of a wheel composed of a number of short sails fixed to a steel framework upon a braced steel tower1 have been used for many years for driving machinery on farms1 and less frequently for pumping water for domestic use4 ,in a very few cases it has been utilised for pumping sewage1 but there is no reason why1 under proper conditions1 it should not be employed to a greater extent4 ,the reliability of the wind for pumping purposes may be gauged from the figures in the following table1 ,no4 #aa1 which were observed in ,birmingham1 and comprise a period of ten years2 they are arranged in order corresponding with the magnitude of the annual rainfall3-- ,,table ,no4 #aa4 ,,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 #f m4p4h4 #aj m4p4h4 #ae m4p4h4 #bj m4p4h4 ---------------------------------------- ----------------------- #a444 #cchf #af #hh #bbj #cad #b444 #biab #ae #abj #bfj #ccd #c444 #bhhf #ci #acc #bfc #ccf #d444 #bfef #cf #abf #bdg #cbc #e444 #bfea #cd #adi #beh #ccj #f444 #bfjb #cd #acb #bfb #ccc #g444 #beaf #cc #aea #bgf #ccb #h444 #bbfg #df #aee #bgb #cbi #i444 #bbcj #bf #acj #bec #ccg #aj444 #baid #cg #acc #bgf #ccj ---------------------------------------- ----------------------- ,average #cad #acag #bejg #ccjh ,it may be of interest to examine the monthly figures for the two years included in the foregoing table1 which had the least and the most wind respectively1 such figures being set out in the following table3 ,,table ,no4 #ab ,,monthly ,,analysis ,,of ,,wind ,number of days in each month during which the mean velocity of the wind was respectively below the value mentioned hereunder4 ,month ,year of least wind 7,no4 #h7 ,year of most wind 7,no4 99#h997 #e #aj #ae #bj #e #aj #ae #bj m4p4h4 m4p4h4 m4p4h4 m4p4h4 m4p4h4 m4p4h4 m4p4h4 m4p4h4 ---------------------------------------- ------------------ ,jan4 #e #aa #bc #bg #c #f #ae #bc ,feb4 #e #ai #bc #bh #j #b #h #af ,mar4 #e #aj #bj #bc #j #a #aa #ah ,april #f #af #bc #bh #a #g #af #bf ,may #a #ad #bd #cj #c #aa #bd #ca ,june #a #ab #bb #bf #a #aj #ba #bg ,july #h #ah #bi #ca #a #ab #be #bi ,aug4 #b #i #bc #cj #a #i #ah #cj ,sept4 #a #ac #be #cj #a #ab #bd #bh ,oct4 #e #ag #ba #bf #j #d #af #bi ,nov4 #f #aa #bj #bf #c #g #ai #bh ,dec4 #a #e #ai #bd #b #g #bc #bi ---------------------------------------- ------------------ ,total #df #aee #bgb #cbi #af #hh #bbj #cad ,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 days1 and on two occasions only was it less than six miles per hour on three consecutive days4 ,it must be remembered1 however1 that this does not by any means imply that during such days the wind did not rise above six miles per hour1 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 time4 ,it will further be observed that the greatest differences between these two years occur in the figures relating to the light winds4 ,the number of days upon which the mean hourly velocity of the wind exceeds twenty miles per hour remains fairly constant year after year4 ,as the greatest difficulty in connection with pumping sewage is the influx of storm water in times of rain1 it will be useful to notice the rainfall at those times when the wind is at a minimum4 ,from the following figures 7,table ,no4 #ac7 it will be seen that1 generally speaking1 when there is very little wind there is very little rain ,taking the ten years enumerated in ,table ,no4 #aa1 we find that out of the #cad days on which the wind averaged less than six miles per hour only forty-eight of them were wet1 and then the rainfall only averaged 4l#c in on those days4 ,,table ,no4 #ac4 ,,wind ,,less ,,than #f ,m4,p4,h4 ---------------------------------------- -------------------------------------- ,ref4 ,no4 ,total ,no4 ,days on ,rainfall on each from ,table of days in which no ,rainy rainy day in ,no4 #aa4 each year4 rain fell4 days4 inches4 ---------------------------------------- -------------------------------------- #a #af #ad #b 4#fc and 4#bde #b #ae #ac #b 4#jb and 4#jb #c #ci #cd #e 4#jbe1 4#ja1 4#bf1 4#jb and 4#jc #d #cf #bi #g _/ 4#jb1 4#jh1 4#ace1 4#aj1 4#cde1 4#ah and 4#jb #e #cd #bh #f 4#aj1 4#dc1 4#ja1 4#jg1 4#age and 4#jg #f #cb #bg #e 4#aj1 4#aa1 4#jhe1 4#jd and 4#ace #g #cc #ba #b 4#dae and 4#gj #h #df #dj #f 4#jg1 4#jce1 4#jb1 4#jf1 4#ac and 4#jb #i #bf #bj #f 4#ade1 4#bj1 4#cc1 4#abe1 4#jae 4#jge #aj #cg #cj #g _/ 4#jc1 4#bc1 4#afe1 4#jb1 4#jie 4#jde and 4#jb ---------------------------------------- -------------------------------------- ,total #cad #bff #dh ,average rainfall on each of the #dh days 4#ac 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 mill1 but at the same time there are practical considerations which limit the height4 ,in ,america many towers are as much as #ajj ft high1 but ordinary workmen do not voluntarily climb to such a height1 with the result that the mill is not properly oiled4 ,about #dj ft is the usual height in this country1 and #fj ft should be used as a maximum4 ,mr4 ,george ,phelps1 in a paper read by him in #aijf before the ,association of ,water ,engineers1 stated that it was safe to assume that on an average a fifteen miles per hour wind was available for eight hours per day1 and from this he gave the following figures as representing the approximate average duty with1 a lift of l#jj ft1 including friction3-- ,,table ,,no4 #ad ,,duty ,,of ,,wintdmilu ,diameter of ,wheel4 #aj #ab #ad #af #ah #bj #be #cj #ce #dj ,the following table gives the result of tests carried out by the ,united ,states ,department of ,agriculture at ,cheyenne1 ,wyo41 with a l#d ft diameter windmill under differing wind velocities3-- ,,table ,no4 #ae4 ,,power or l#d-rx ,,windmill ,,in ,,varying ,,winds4 ,velocity of ,wind 7miles per hour74 #j--e #f-aj #aa-ae #af-bj #ba-be #bf-cj #ca-ce ,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 windmill1 but it is undesirable to rely entirely upon such a system1 even if two mills are erected so that the plant will be in duplicate1 because there is always the possibility1 although it may be remote1 of a lengthened period of calm1 when the sewage would accumulate2 and1 further1 the ,local ,government ,board would not approve the scheme unless it included an engine1 driven by gas1 oil1 or other mechanical power1 for emergencies4 ,in the case of water supply the difficulty may be overcome by providing large storage capacity1 but this cannot be done for sewage without creating an intolerable nuisance4 ,in the latter case the storage should not be less than twelve hours dry weather flow1 nor more than twenty-four4 ,with a well-designed mill1 as has already been indicated1 the wind will1 for the greater part of the year1 be sufficient to lift the whole of the sewage and storm-water1 but1 if it is allowed to do so1 the standby engine will deteriorate for want of use to such an extent that when urgently needed it will not be effective4 ,it is1 therefore1 desirable that the attendant should run the engine at least once in every three days to keep it in working order4 ,if it can be conveniently arranged1 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 evening4 ,the bulk of the day's sewage will then have been delivered1 and can be disposed of when it is fresh1 while at the same time the whole storage capacity is available for the night flow1 and any rainfall which may occur1 thus reducing the chances of the man being called up during the night4 ,about #bb per cent1 of the total daily dry weather flow of sewage is delivered between #g p4m4 and #g a4m4 ,the first cost of installing a small windmill is practically the same as for an equivalent gas or oil engine plant1 so that the only advantage to be looked for will be in the maintenance1 which in the case of a windmill is a very small matter1 and the saving which may be obtained by the reduction of the amount of attendance necessary4 ,generally speaking1 a mill #bj ft in diameter is the largest which should be used1 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 mill1 as compared with that done by a modern internal combustion engine4 ,mills smaller than #h ft in diameter are rarely employed1 and then only for small work1 such as a #b #a_/b in pump and a #c-;ft lift ,the efficiency of a windmill1 measured by the number of square feet of annular sail area1 decreases with the size of the mill1 the #h ft1 #aj ft1 and l#b ft mills being the most efficient sizes4 ,when the diameter exceeds l#b ft1 the efficiency rapidly falls off1 because the peripheral velocity remains constant for any particular velocity or pressure of the wind1 and as every foot increase in the diameter of the wheel makes an increase of over #c ft in the length of the circumference1 the greater the diameter the less the number of revolutions in any given time2 and consequently the kinetic flywheel action which is so valuable in the smaller sizes is to a great extent lost in the larger mills4 ,any type of pump can be used1 but the greatest efficiency will be obtained by adopting a single acting pump with a short stroke1 thus avoiding the liability1 inherent in a long pump rod1 to buckle under compression1 and obviating the use of a large number of guides which absorb a large part of the power given out by the mill4 ,although some of the older mills in this country are of foreign origin1 there are several ,british manufacturers turning out well-designed and strongly-built machines in large numbers4 ,fig4 #ai represents the general appearance and ,fig4 #bj the details of the type of mill made by the well-known firm of ,duke and ,ockenden1 of ,ferry ,wharf1 ,littlehampton1 ,sussex4 ,this firm has erected over #djj windmills1 which1 after the test of time1 have proved thoroughly efficient4 ,from ,fig4 #bj it will be seen that the power applied by the wheel is transmitted through spur and pinion gearing of #b #a_/b ratio to a crank shaft1 the gear wheel having internal annular teeth of the involute type1 giving a greater number of teeth always in contact than is the case with external gears4 ,this minimises wear1 which is an important matter1 as it is difficult to properly lubricate these appliances1 and they are exposed to and have to work in all sorts of weather4 ,illustration3 ,fig4 l#i4--;,general ,view of ,modern ,windmill4 ,illustration3 ,fig4 #bj4--;,details of ,windmill ,manufactured by ,messrs4 ,duke and ,ockenden1 ,littlehampton4 ,it will be seen that the strain on the crank shaft is taken by a bent crank which disposes the load centrally on the casting1 and avoids an overhanging crank disc1 which has been an objectionable feature in some other types4 ,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 stroke1 the difference in speed being most marked in the longest stroke1 where it is most required4 ,in order to transmit the circular internal motion a vertical connecting rod in compression is used1 which permits of a simple method of changing the length of stroke by merely altering the pin in the rocking lever1 the result being that the pump rod travels in a vertical line4 ,the governing is entirely automatic4 ,if the pressure on the wind wheel1 which it will be seen is set off the centre line of the mill and tower1 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 face1 thus decreasing the area exposed to the wind gradually until the wheel reaches its final position1 or is hauled out of gear1 when the edges only are opposed to the full force of the wind4 ,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 direction4 ,the pump rod in the windmill tower is provided with a swivel coupling1 enabling the mill head to turn completely round without altering the position of the rod4 ,,chapter ,x4 ,,the ,,design ,,of ,,see ,,outfalls4 ,the detail design of a sea outfall will depend upon the level of the conduit with reference to present surface of the shore1 whether the beach is being eroded or made up1 and1 if any part of the structure is to be constructed above the level of the shore1 whether it is likely to be subject to serious attack by waves in times of heavy gales4 ,if there is probability of the direction of currents being affected by the construction of a solid structure or of any serious scour being caused1 the design must be prepared accordingly4 ,while there are examples of outfalls constructed of glazed stoneware socketed pipes surrounded with concrete1 as shown in ,fig4 #ba1 cast iron pipes are used in the majority of cases4 ,there is considerable variation in the design of the joints for the latter class of pipes1 some of which are shown in ,figs4 #bb1 #bc1 and #bd4 ,spigot and socket joints 7,fig4 #bb71 with lead run in1 or even with rod lead or any of the patent forms caulked in cold1 are unsuitable for use below high-water mark on account of the water which will most probably be found in the trench4 ,pipes having plain turned and bored joints are liable to be displaced if exposed to the action of the waves1 but if such joints are also flanged1 as ,fig4 #bd1 or provided with lugs1 as ,fig4 #bc1 great rigidity is obtained when they are bolted up2 in addition to which the joints are easily made watertight4 ,when a flange is formed all round the joint1 it is necessary1 in order that its thickness may be kept within reasonable limits1 to provide bolts at frequent intervals4 ,a gusset piece to stiffen the flange should be formed between each hole and the next1 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 pipe1 as when the pipes are laid in a trench below water level it is not only difficult to insert the bolt1 but almost impracticable to tighten up the nut afterwards4 ,the pipes should be laid so that the two lowest bolt holes are placed equidistant on each side of the centre line1 as shown in the end views of ,figs4 ,nos4 #bc and #bd4 ,illustration3 ,fig4 #bl4-,stoneware ,pipe and ,concrete ,sea ,outfall4 ,with lug pipes1 fewer bolts are used1 and the lugs are made specially strong to withstand the strain put upon them in bolting up the pipes4 ,these pipes are easier and quicker to joint under water than are the flanged pipes1 so that their use is a distinct advantage when the hours of working are limited4 ,in some cases gun-metal bolts are used1 as they resist the action of sea water better than steel1 but they add considerably to the cost of the outfall sewer1 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 broken4 ,on the other hand1 there is a liability of severe corrosion of the metal taking place by reason of galvanic action between the gun-metal and the iron1 set up by the sea water in which they are immersed4 ,if the pipes are not to be covered with concrete1 and are thus exposed to the action of the sea water1 particular care should be taken to see that the coating by ,dr4 ,angus ,smith's process is perfectly applied to them4 ,illustration3 ,fig4 #bb4--,spigot and ,socket ,joint for ,cast ,iron ,pipes4 ,illustration3 ,fig4 #bc4--,lug ,joint for ,cast ,iron ,pipes4 ,illustration3 ,fig4 #bd4--,turned1 ,board1 and ,flanged ,joint for ,cast ,iron ,pipes4 ,steel pipes are1 on the whole1 not so suitable as cast iron4 ,they are1 of course1 obtainable in long lengths and are easily jointed1 but their lightness compared with cast iron pipes1 which is their great advantage in transport1 is a disadvantage in a sea outfall1 where the weight of the structure adds to its stability4 ,the extra length of steel pipes necessitates a greater extent of trench being excavated at one time1 which must be well timbered to prevent the sides falling in ,on the other hand1 cast iron pipes are more liable to fracture by heavy stones being thrown upon them by the waves1 but this is a contingency which does not frequently occur in practice4 ,according to ,trautwine1 the cast iron for pipes to resist sea water should be close-grained1 hard1 white metal4 ,in such metal the small quantity of contained carbon is chemically combined with the iron1 but in the darker or mottled metals it is mechanically combined1 and such iron soon becomes soft1 like plumbago1 under the influence of sea water4 ,hard white iron has been proved to resist sea water for forty years without deterioration1 whether it is continually under water or alternately wet and dry4 ,several types of sea outfalls are shown in ,figs4 #be to #ca4a ,in the example shown in ,fig4 #be a solid rock bed occurred a short distance below the sand1 which was excavated so as to allow the outfall to be constructed on the rock4 ,anchor bolts with clevis heads were fixed into the rock1 and then1 after a portion of the concrete was laid1 iron bands1 passing around the cast iron pipes1 were fastened to the anchors4 ,this construction would not be suitable below low-water mark4 ,fig4 #bf represents the ,aberdeen sea outfall1 consisting of cast iron pipes #g ft in diameter1 which are embedded in a heavy concrete breakwater #bd ft in width1 except at the extreme end1 where it is #cj ft wide4 ,the #d in wrought iron rods are only used to the last few pipes1 which were in #f ft lengths instead of #i ft1 as were the remainder4 ,fig4 #bg shows an inexpensive method of carrying small pipes1 the slotted holes in the head of the pile allowing the pipes to be laid in a straight line1 even if the pile is not driven quite true1 and if the level of the latter is not correct it can be adjusted by inserting a packing piece between the cradle and the head4 ,great ,crosby outfall sewer into the ,mersey is illustrated in ,fig4 #bh4 ,the piles are of greenheart1 and were driven to a solid foundation4 ,the #a #c_/d in sheeting was driven to support the sides of the excavation1 and was left in when the concrete was laid4 ,light steel rails were laid under the sewer1 in continuous lengths1 on steel sleepers and to #b ft gauge4 ,the invert blocks were of concrete1 and the pipes were made of the same material1 but were reinforced with steel ribs4 ,the ,waterloo 7near ,liverpool7 sea outfall is shown in ,fig4 #ca4 ,footnote #a3 ,plate ,v4 ,piling may be necessary either to support the pipes or to keep them secure in their proper position1 but where there is a substratum of rock the pipes may be anchored1 as shown in ,figs4 #be and #bf4 ,the nature of the piling to be adopted will vary according to the character of the beach4 ,figs4 #bg1 #bi1 #cj1 and #ca show various types4 ,with steel piling and bearers1 as shown in ,fig4 #bi1 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 piles1 and1 if the holes are not drilled in the piles until after they are driven to their final position1 considerable time is occupied1 and perhaps a tide lost in the attempt to drill them below water4 ,there is also the difficulty of tightening up the bolts when the sewer is partly below the surface of the shore1 as shown4 ,in both the types shown in ,figs4 #bi and #cj it is essential that the piles and the bearers should abut closely against the pipes2 otherwise the shock of the waves will cause the pipes to move and hammer against the framing1 and thus lead to failure of the structure4 ,piles similar to ,fig4 #ca can only be fixed in sand1 as was the case at ,waterloo1 because they must be absolutely true to line and level1 otherwise the pipes cannot be laid in the cradles4 ,the method of fixing these piles is described by ,mr4 ,ben ,howarth 7,minutes of ,proceedings of ,inst4,c4,e41 ,vol4 ,,clxxv47 as follows3--,the pile was slung vertically into position from a four-legged derrick1 two legs of which were on each side of the trench2 a small winch attached to one pair of the legs lifted and lowered the pile1 through a block and tackle4 ,when the pile was ready to be sunk1 a #b in iron pipe was let down the centre1 and coupled to a force-pump by means of a hose2 a jet of water was then forced down this pipe1 driving the sand and silt away from below the pile4 ,the pile was then rotated backwards and forwards about a quarter of a turn1 by men pulling on the arms2 the pile1 of course1 sank by its own weight1 the water-jet driving the sand up through the hollow centre and into the trench1 and it was always kept vertical by the sling from the derrick4 ,as soon as the pile was down to its final level the ground was filled in round the arms1 and in this running sand the pile became perfectly fast and immovable a few minutes after the sinking was completed4 ,the whole process1 from the first slinging of the pile to the final setting1 did not take more than #bj or #be minutes4 ,illustration3 ,,plate ,v4 ,,rock ,,bed4 ,fig4 #bf--;,,aberdeen ,,sea ,,outfall4 ,fig4 #bg--,,small ,,great ,,crosby ,,sea ,,outfall4 ,fig4 #bi--;,,cast ,,iron ,,pipe ,,on ,,steel ,,cast ,,and ,,bearers4 ,fig4 #ca--,,waterloo 7,,liverpool7 ,,sea ,,outfall4 7,to face page #hj47 ,screw piles may be used if the ground is suitable1 but1 if it is boulder clay or similar material1 the best results will probably be obtained by employing rolled steel joists as piles4 ,,chapter ,,xi4 ,,the ,,action ,,of ,,sea ,,water ,,on ,,cement4 ,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 beach2 and1 further1 whether the concrete1 after it is mixed1 will withstand the action of the elements1 exposed1 as it will be1 to air and sea-water1 rain1 hot sun1 and frosts4 ,some concrete structures have failed by decay of the material1 principally between high and low water mark1 and in order to ascertain the probable causes and to learn the precautions which it is necessary to take1 some elaborate experiments have been carried out4 ,to appreciate the chemical actions which may occur1 it will be as well to examine analyses of sea-water and cement4 ,the water of the ,irish ,channel is composed of ,sodium chloride44444444444444444444 #b4fdci per cent4 ,magnesium chloride44444444444444444 #j4caej ,magnesium sulphate44444444444444444 #j4bjff ,calcium sulphate4444444444444444444 #j4acca ,potassium chloride44444444444444444 #j4jgdf ,magnesium bromide444444444444444444 #j4jjgj ,calcium carbonate444444444444444444 #j4jjdg ,iron carbonate444444444444444444444 #j4jjje ,magnesium nitrate444444444444444444 #j4jjjb ,lithium chloride4444444444444444444 ,traces4 ,ammonium chloride444444444444444444 ,traces4 ,silica chloride44444444444444444444 ,traces4 ,water444444444444444444444444444444 #if4fadd -------- #ajj4jjjj ,an average analysis of a ,thames cement may be taken to be as follows3-- ,silica44444444444444444444444444444444 #bc4ed per cent4 ,insoluble residue 7sand1 clay1 etc474444444444444444444444444444 #j4dj ,alumina and ferric oxide444444444444444 #i4hf ,lime4444444444444444444444444444444444 #fb4jh ,magnesia4444444444444444444444444444444 #a4bj ,sulphuric anhydride44444444444444444444 #a4jh ,carbonic anhydride and water44444444444 #a4cd ,alkalies and loss on analysis4444444444 #j4ej ----- #ajj4jj ,the following figures give the analysis of a sample of cement expressed in terms of the complex compounds that are found3-- ,sodium silicate 7,na#b,si,o#c744444444 #c4dc per cent4 ,calcium sulphate 7,ca,s,o#d7444444444 #b4de ,dicalcium silicate 7,ca#b,si,o#d74444 #fa4hi ,dicalcium aluminate 7,ca#b;,al#b,o#e744 #ab4ad ,dicalcium ferrate 7,ca#b;,fe#b,o#e744444 #d4ce ,magnesium oxide 7,mg,o7444444444444 #j4ig ,calcium oxide 7,ca,o74444444444444 #ad4bb ,loss on analysis1 c4444444444444 #j4ee ----- #ajj4jj ,dr4 ,w4 ,michaelis1 the ,german cement specialist1 gave much consideration to this matter in #aijf1 and formed the opinion that the free lime in the ,portland cement1 or the lime freed in hardening1 combines with the sulphuric acid of the sea-water1 which causes the mortar or cement to expand1 resulting in its destruction4 ,he proposed to neutralise this action by adding to the mortar materials rich in silica1 such as trass1 which would combine with the lime4 ,mr4 ,j4 ,m4 ,o',hara1 of the ,southern ,pacific ,laboratory1 ,san ,francisco1 ,cal41 made a series of tests with sets of pats #d in diameter and #a_/b in thick at the centre1 tapering to a thin edge on the circumference1 and also with briquettes for ascertaining the tensile strength1 all of which were placed in water twenty-four hours after mixing4 ,at first some of the pats were immersed in a five-strength solution of sea-water having a chemical analysis as follows3-- ,sodium chloride44444444444444444444 #aa4e per cent4 ,magnesium chloride44444444444444444 #a4d ,magnesium sulphate44444444444444444 #j4i ,calcium sulphate4444444444444444444 #j4f ,water444444444444444444444444444444 #he4f #ajj4j ,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-water1 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 months4 ,strong solutions were next made of the individual salts contained in sea-water1 and pats were immersed as before1 when it was found that the magnesium sulphate present in the water acted upon the calcium hydrate in the cement1 forming calcium sulphate1 and leaving the magnesium hydrate free4 ,the calcium sulphate combines with the alumina of the cement1 forming calcium sulpho-aluminate1 which causes swelling and cracking of the concrete1 and in cements containing a high proportion of alumina1 leads to total destruction of all cohesion4 ,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-water1 and disintegration may be retarded or checked4 ,a high proportion of magnesia has been found in samples of cement which have failed under the action of sea water1 but the disastrous result cannot be attributed to this substance having been in excess in the original cement1 as it was probably due to the deposition of the magnesia salts from the sea-water2 although1 if magnesia were present in the cement in large quantities1 it would cause it to expand and crack1 still with the small proportion in which it occurs in ordinary cements it is probably inert4 ,the setting of cement under the action of water always frees a portion of the lime which was combined1 but over twice as much is freed when the cement sets in sea-water as in fresh water4 ,the setting qualities of cement are due to the iron and alumina combined with calcium1 so that for sea-coast work it is desirable for the alumina to be replaced by iron as far as possible4 ,the final hardening and strength of cement is due in a great degree to the tri-calcium silicate 7#c;,ca,o1 ,si,o#b7 which is soluble by the sodium chloride found in sea-water1 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 concrete4 ,the concrete is softened1 when there is an abnormal amount of sulphuric acid present1 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 cement4 ,the ferric oxide of the cement is unaffected by sea- water4 ,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 water1 but the #a to #c cement and sand briquette tests gave an opposite result4 ,at the end of twelve months1 however1 practically all the cements set in fresh water showed greater strength than those set in sea- water4 ,when briquettes which have been immersed in fresh water and have thoroughly hardened are broken1 the cores are found to be quite dry1 and if briquettes immersed in sea-water show a similar dryness there need be no hesitation in using the cement2 but if1 on the other hand1 the briquette shows that the sea-water has permeated to the interior1 the cement will lose strength by rotting until it has no cohesion at all4 ,it must be remembered that it is only necessary for the water to penetrate to a depth of #a_/b in on each side of a briquette to render it damp all through1 whereas in practical work1 if the water only penetrated to the same depth1 very little ill-effect would be experienced1 although by successive removals of a skin #a_/b in deep the structure might in time be imperilled4 ,the average strength in pounds per square inch of six different well-known brands of cement tested by ,mr4 ,o',hara was as follows3-- ,,table ,no4 #af4 ,,effect ,,of ,,sea ,,water ,,on ,,strength ,,of ,,cement4 ,neat cement #a cement to #c sand set in set in ,sea ,water ,fresh ,water ,sea ,water ,fresh ,water #g days #fhb #edh #bad #bbd #bh days #hcf #fdc #bic #cai #b months #iac #ffh #cac #cei #c months #hfa #ffg #cja #chg #f months #fcd #fed #cji #dbh #i months #edb #fhg #cag #dag #ab months #cgb #gjf #cbe #dcb ,some tests were also made by ,messrs4 ,westinghouse1 ,church1 ,kerr1 and ,co41 of ,new ,york1 to ascertain the effect of sea- water on the tensile strength of cement mortar4 ,three sets of briquettes were made1 having a minimum section of one square inch4 ,the first were mixed with fresh water and kept in fresh water2 the second were mixed with fresh water1 but kept immersed in pans containing salt water2 while the third were mixed with sea-water and kept in sea-water4 ,in the experiments the proportion of cement and sand varied from #a to #a to #a to #f4 ,the results of the tests on the stronger mixtures are shown in ,fig4 #cb4 ,the ,scandinavian ,portland cement manufacturers have in hand tests on cubes of cement mortar and cement concrete1 which were started in #ahif1 and are to extend over a period of twenty years4 ,a report upon the tests of the first ten years was submitted at the end of #aiji to the ,international ,association of ,testing ,materials at ,copenhagen1 and particulars of them are published in ,cement and ,sea-,water1 by ,a4 ,poulsen 7chairman of the committee71 ,j4 ,jorsen and ,co41 ,copenhagen1 #aiji1 price #cs4 ,illustration3 ,,fig4 #cb4--,tests of the ,tensile ,strength of ,cement and ,sand ,briquettes1 ,showing the ,effect of ,sea ,water4 ,cements from representative firms in different countries were obtained for use in making the blocks1 which had coloured glass beads and coloured crushed glass incorporated to facilitate identification4 ,each block of concrete was provided with a number plate and a lifting bolt1 and was kept moist for one month before being placed in position4 ,the sand and gravel were obtained from the beach on the west coast of ,jutland4 ,the mortar blocks were mixed in the proportion of #a to #a1 #a to #b1 and #a to #c1 and were placed in various positions1 some between high and low water1 so as to be exposed twice in every twenty- four hours1 and others below low water1 so as to be always submerged4 ,the blocks were also deposited under these conditions in various localities1 the mortar ones being placed at ,esbjerb at the south of ,denmark1 at ,vardo in the ,arctic ,ocean1 and at ,degerhamm on the ,baltic1 where the water is only one-seventh as salt as the ,north ,sea1 while the concrete blocks were built up in the form of a breakwater or groyne at ,thyboron on the west coast of ,jutland4 ,at intervals of three1 six1 and twelve months1 and two1 four1 six1 ten1 and twenty years1 some of the blocks have1 or will be1 taken up and subjected to chemical tests1 the material being also examined to ascertain the effect of exposure upon them4 ,the blocks tested at intervals of less than one year after being placed in position gave very variable results1 and the tests were not of much value4 ,the mortar blocks between high and low water mark of the ,arctic ,ocean at ,vardo suffered the worst1 and only those made with the strongest mixture of cement1 #a to #a1 withstood the severe frost experienced4 ,the best results were obtained when the mortar was made compact1 as such a mixture only allowed diffusion to take place so slowly that its effect was negligible2 but when1 on the other hand1 the mortar was loose1 the salts rapidly penetrated to the interior of the mass1 where chemical changes took place1 and caused it to disintegrate4 ,the concrete blocks made with #a to #c mortar disintegrated in nearly every case1 while the stronger ones remained in fairly good condition4 ,the best results were given by concrete containing an excess of very fine sand4 ,mixing very finely-ground silica1 or trass1 with the cement proved an advantage where a weak mixture was employed1 but in the other cases no benefit was observed4 ,the ,association of ,german ,portland ,cement ,manufacturers carried out a series of tests1 extending over ten years1 at their testing station at ,gross ,lichterfeld1 near ,berlin1 the results of which were tabulated by ,mr4 ,c4 ,schneider and ,professor ,gary4 ,in these tests the mortar blocks were made #c in cube and the concrete blocks l#b in cube2 they were deposited in two tanks1 one containing fresh water and the other sea-water1 so that the effect under both conditions might be noted4 ,in addition1 concrete blocks were made1 allowed to remain in moist sand for three months1 and were then placed in the form of a groyne in the sea between high and low-water mark4 ,some of the blocks were allowed to harden for twelve months in sand before being placed1 and these gave better results than the others4 ,two brands of ,german ,portland cement were used in these tests1 one1 from which the best results were obtained1 containing #fe4i per cent4 of lime1 and the other #fb4j per cent4 of lime1 together with a high percentage of alumina4 ,in this case1 also1 the addition of finely-ground silica1 or trass1 improved the resisting power of blocks made with poor mortars1 but did not have any appreciable effect on the stronger mixtures4 ,professor ,m4 ,mller1 of ,brunswick1 ,germany1 reported to the ,international ,association for ,testing ,materials1 at the ,copenhagen ,congress previously referred to1 the result of his tests on a small hollow1 trapezium shape1 reinforced concrete structure1 which was erected in the ,north ,sea1 the interior being filled with sandy mud1 which would be easily removable by flowing water4 ,the sides were #g cm4 thick1 formed of cement concrete #a3b #a_/b3b1 moulded elsewhere1 and placed in the structure forty days after they were made1 while the top and bottom were #e cm4 thick1 and consisted of concrete #a3c3c1 moulded in situ and covered by the tide within twenty-four hours of being laid4 ,the concrete moulded in situ hardened a little at first1 and then became soft when damp1 and friable when dry1 and white efflorescence appeared on the surface4 ,in a short time the waves broke this concrete away1 and exposed the reinforcement1 which rusted and disappeared1 with the result that in less than four years holes were made right through the concrete4 ,the sides1 which were formed of slabs allowed to harden before being placed in the structure1 were unaffected except for a slight roughening of the surface after being exposed alternately to the sea and air for a period1 of thirteen years4 ,professor ,mller 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 made4 ,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 time1 after which the cement and the sea- water were analysed1 and it was found that the sea-water had taken up the lime from the cement1 and the cement had absorbed the magnesia salts from the sea-water4 ,some tests were carried out in #aijh-i at the ,navy ,yard1 ,charlestown1 ,mass41 by the ,aberthaw ,construction ,company of ,boston1 in conjunction with the ,navy ,department4 ,the cement concrete was placed so that the lower portions of the surfaces of the specimens were always below water1 the upper portions were always exposed to the air1 and the middle portions were alternately exposed to each4 ,although the specimens were exposed to several months of winter frost as well as to the heat of the summer1 no change was visible in any part of the concrete at the end of six months4 ,mons4 ,r4 ,feret1 ,chief of the ,laboratory of ,bridges and ,roads1 ,boulogne-sur-,mer1 ,france1 has given expression to the following opinions3-- #a4 ,no cement or other hydraulic product has yet been found which presents absolute security against the decomposing action of sea-water4 #b4 ,the most injurious compound of sea-water is the acid of the dissolved sulphates1 sulphuric acid being the principal agent in the decomposition of cement4 #c4 ,portland cement for sea-water should be low in aluminium and as low as possible in lime4 #d4 ,puzzolanic material is a valuable addition to cement for sea-water construction1 #e4 ,as little gypsum as possible should be added for regulating the time of setting to cements which are to be used in sea- water4 #f4 ,sand containing a large proportion of fine grains must never be used in concrete or mortar for sea-water construction4 #g4 ,the proportions of the cement and aggregate for sea-water construction must be such as will produce a dense and impervious concrete4 ,on the whole1 sea-water has very little chemical effect on good ,portland cements1 such as are now easily obtainable1 and1 provided the proportion of aluminates is not too high1 the varying composition of the several well-known commercial cements is of little moment4 ,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 means1 such as occurs in practical work4 ,the destruction of concrete works on the sea coast is due to the alternate exposure to air and water1 frost1 and heat1 and takes the form of cracking or scaling1 the latter being the most usual when severe frosts are experienced4 ,when concrete blocks are employed in the construction of works1 they should be made as long as possible before they are required to be built in the structure1 and allowed to harden in moist sand1 or1 if this is impracticable1 the blocks should be kept in the air and thoroughly wetted each day4 ,on placing cement or concrete blocks in sea water a white precipitate is formed on their surfaces1 which shows that there is some slight chemical action1 but if the mixture is dense this action is restricted to the outside1 and does not harm the block4 ,cement mixed with sea water takes longer to harden than if mixed with fresh water1 the time varying in proportion to the amount of salinity in the water4 ,sand and gravel from the beach1 even though dry1 have their surfaces covered with saline matters1 which retard the setting of the cement1 even when fresh water is used1 as they become mixed with such water1 and thus permeate the whole mass4 ,if sea water and aggregate from the shore are used1 care must be taken to see that no decaying seaweed or other organic matter is mixed with it1 as every such piece will cause a weak place in the concrete4 ,if loam1 clay1 or other earthy matters from the cliffs have fallen down on to the beach1 the shingle must be washed before it is used in concrete4 ,exposure to damp air1 such as is unavoidable on the coast1 considerably retards the setting of cement1 so that it is desirable that it should not be further retarded by the addition of gypsum1 or calcium sulphate1 especially if it is to be used with sea water or sea-washed sand and gravel4 ,the percentage of gypsum found in cement is1 however1 generally considerably below the maximum allowed by the ,british ,standard ,specification1 viz41 #b per cent41 and is so small that1 for practical purposes1 it makes very little difference in sea coast work1 although of course1 within reasonable limits1 the quicker the cement sets the better4 ,when cement is used to joint stoneware pipe sewers near the coast1 allowance must be made for this retardation of the setting1 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 necessary4 ,a high proportion of aluminates tends to cause disintegration when exposed to sea water4 ,the most appreciable change which takes place in a good sound cement after exposure to the sea is an increase in the chlorides1 while a slight increase in the magnesia and the sulphates also takes place1 so that the proportion of sulphates and magnesia in the cement should be kept fairly low4 ,hydraulic lime exposed to the sea rapidly loses the lime and takes up magnesia and sulphates4 ,to summarise the information upon this point1 it appears that it is better to use fresh water for all purposes1 but if1 for the sake of economy1 saline matters are introduced into the concrete1 either by using sea water for mixing or by using sand and shingle from the beach1 the principal effect will be to delay the time of setting to some extent1 but the ultimate strength of the concrete will probably not be seriously affected4 ,when the concrete is placed in position the portion most liable to be destroyed is that between high and low water mark1 which is alternately exposed to the action of the sea and the air1 but if the concrete has a well-graded aggregate1 is densely mixed1 and contains not more than two parts of sand to one part of cement1 no ill-effect need be anticipated4 ,,chapter ,,xii ,,diving4 ,the engineer is not directly concerned with the various methods employed in constructing a sea outfall1 such matters being left to the discretion of the contractor4 ,it may1 however1 be briefly stated that the work frequently involves the erection of temporary steel gantries1 which must be very carefully designed and solidly built if they are to escape destruction by the heavy seas4 ,it is amazing to observe the ease with which a rough sea will twist into most fantastic shapes steel joists #aj in by #h;in1 or even larger in size4 ,any extra cost incurred in strengthening the gantries is well repaid if it avoids damage1 because otherwise there is not only the expense of rebuilding the structure to be faced1 but the construction of the work will be delayed possibly into another season4 ,in order to ensure that the works below water are constructed in a substantial manner1 it is absolutely necessary that the resident engineer1 at least1 should be able to don a diving dress and inspect the work personally4 ,the particular points to which attention must be given include the proper laying of the pipes1 so that the spigot of one is forced home into the socket of the other1 the provision and tightening up of all the bolts required to be fixed1 the proper driving of the piles and fixing the bracing1 the dredging of a clear space in the bed of the sea in front of the outlet pipe1 and other matters dependent upon the special form of construction adopted4 ,if a plug is inserted in the open end of the pipes as laid1 the rising of the tide will press on the plugged end and be of considerable assistance in pushing the pipes home2 it will therefore be necessary to re-examine the joints to see if the bolts can be tightened up any more4 ,messrs4 ,siebe1 ,gorman1 and ,co41 the well-known makers of submarine appliances1 have fitted up at their works at ,westminster ,bridge-road1 ,london1 ,s4,e41 an experimental tank1 in which engineers may make a few preliminary descents and be instructed in the art of diving2 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 inspect4 ,only a nominal charge of one guinea for two descents is made1 which sum1 less out-of-pocket expenses1 is remitted to the ,benevolent ,fund of the ,institution of ,civil ,engineers4 ,it is generally desirable that a complete outfit1 including the air pump1 should be provided for the sole use of the resident engineer1 and special men should be told off to assist him in dressing and to attend to his wants while he is below water4 ,he is then able to inspect the work while it is actually in progress1 and he will not hinder or delay the divers4 ,it is a wise precaution to be medically examined before undertaking diving work1 although1 with the short time which will generally be spent below water1 and the shallow depths usual in this class of work1 there is practically no danger2 but1 generally speaking1 a diver should be of good physique1 not unduly stout1 free from heart or lung trouble and varicose veins1 and should not drink or smoke to excess4 ,it is necessary1 however1 to have acquaintance with the physical principles involved1 and to know what to do in emergencies4 ,a considerable amount of useful information is given by ,mr4 ,r4 ,h4 ,davis in his ,diving ,manual 7,siebe1 ,gorman1 and ,co41 #es471 from which many of the following notes are taken4 ,a diving dress and equipment weighs about l#ge lb1 including a #dj lb lead weight carried by the diver on his chest1 a similar weight on his back1 and l#flb of lead on each boot4 ,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 body1 and by the time the top of the diver's head reaches the surface his breathing becomes laboured1 because the pressure of air in his lungs equals the atmospheric pressure1 while the pressure upon his chest and abdomen is greater by the weight of the water thereon4 ,he is thus breathing against a pressure1 and if he has to breathe deeply1 as during exertion1 the effect becomes serious2 so that the first thing he has to learn is to adjust the pressure of the spring on the outlet valve1 so that the amount of air pumped in under pressure and retained in the diving dress counterbalances the pressure of the water outside1 which is equal to a little under #a_/blb per square inch for every foot in depth4 ,if the diver be #f ft tall1 and stands in an upright position1 the pressure on his helmet will be about #clb per square inch less than on his boots4 ,the breathing is easier if the dress is kept inflated down to the abdomen1 but in this case there is danger of the diver being capsized and floating feet upwards1 in which position he is helpless1 and the air cannot escape by the outlet valve4 ,air is supplied to the diver under pressure by an air pump through a flexible tube called the air pipe2 and a light rope called a life line1 which is used for signalling1 connects the man with the surface4 ,the descent is made by a #c in shot-rope1 which has a heavy sinker weighing about #ej lb attached1 and is previously lowered to the bottom4 ,a #a-a_/d in rope about #ae ft long1 called a distance- line1 is attached to the shot-rope about #c ft above the sinker1 and on reaching the bottom the diver takes this line with him to enable him to find his way back to the shot-rope1 and thus reach the surface comfortably1 instead of being hauled up by his life line4 ,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 immersed1 because at the normal higher level the air pressure in the dress will be properly balanced against the water pressure2 but if he falls1 say #cj ft1 the pressure of the water on his body will be increased by about #ae lb per square inch1 and as the air pump cannot immediately increase the pressure in the dress to a corresponding extent1 the man's body in the unresisting dress will be forced into the rigid helmet1 and he will certainly be severely injured1 and perhaps even killed4 ,when descending under water the air pressure in the dress is increased1 and acts upon the outside of the drum of the ear1 causing pain1 until the air passing through the nose and up the ,eustachian tube inside the head reaches the back of the drum and balances the pressure4 ,this may be delayed1 or prevented1 if the tube is partially stopped up by reason of a cold or other cause1 but the balance can generally be brought about if the diver pauses in his descent and swallows his saliva2 or blocks up his nose as much as possible by pressing it against the front of the helmet1 closing the mouth and then making a strong effort at expiration so as to produce temporarily an extra pressure inside the throat1 and so blow open the tubes2 or by yawning or going through the motions thereof4 ,if this does not act he must come up again ,provided his ears are open1 and the air pumps can keep the pressure of air equal to that of the depth of the water in which the diver may be1 there is nothing to limit the rate of his descent4 ,now in breathing1 carbonic acid gas is exhaled1 the quality varying in accordance with the amount of work done1 from 4#jad cubic feet per minute when at rest to a maximum of about 4#jde1 and this gas must be removed by dilution with fresh air so as not to inconvenience the diver4 ,this is not a matter of much difficulty as the proportion in fresh air is about 4#jc per cent41 and no effect is felt until the proportion is increased to about #j4c per cent41 which causes one to breathe twice as deeply as usual2 at #j4f per cent4 there is severe panting2 and at a little over #a4j per cent4 unconsciousness occurs4 ,the effect of the carbonic acid on the diver1 however1 increases the deeper he descends2 and at a depth of #cc ft #a per cent4 of carbonic acid will have the same effect as #b per cent4 at the surface4 ,if the diver feels bad while under water he should signal for more air1 stop moving about1 and rest quietly for a minute or two1 when the fresh air will revive him4 ,the volume of air required by the diver for respiration is about #a4e cubic feet per minute1 and there is a non-return valve on the air inlet1 so that in the event of the air pipe being broken1 or the pump failing1 the air would not escape backwards1 but by closing the outlet valve the diver could retain sufficient air to enable him to reach the surface4 ,during the time that a diver is under pressure nitrogen gas from the air is absorbed by his blood and the tissues of his body4 ,this does not inconvenience him at the time1 but when he rises the gas is given off1 so that if he has been at a great depth for some considerable time1 and comes up quickly1 bubbles form in the blood and fill the right side of the heart with air1 causing death in a few minutes4 ,in less sudden cases the bubbles form in the brain or spinal cord1 causing paralysis of the legs1 which is called divers' palsy1 or the only trouble which is experienced may be severe pains in the joints and muscles4 ,it is necessary1 therefore1 that he shall come up by stages so as to decompress himself gradually and avoid danger4 ,the blood can hold about twice as much gas in solution as an equal quantity of water1 and when the diver is working in shallow depths1 up to1 say1 #cj ft1 the amount of nitrogen absorbed is so small that he can stop down as long as is necessary for the purposes of the work1 and can come up to the surface as quickly as he likes without any danger4 ,at greater depths approximately the first half of the upward journey may be done in one stage1 and the remainder done by degrees1 the longest rest being made at a few feet below the surface4 ,the following table shows the time limits in accordance with the latest ,british ,admiralty practice2 the time under the water being that from leaving the surface to the beginning of the ascent3-- ,,table ,no4 l#g4--;,,diving ,,data4 ,stoppages in ,total time minutes at for ascent ,depth in feet4 ,time under water4 different depths in minutes4 at #bj ft #aj ft ,up to #cf ,no limit - - #j to #a #cf to #db ,up to #c hours - - #a to #a-a_/b ,over #c hours - #e #f #db to #dh ,up to #a hour - - #a-a_/b #a to #c hours - #e #f-a_/b ,over #c hours - #aj #aa-a_/b #dh to #ed ,up to #a_/b hour - - #b #a_/b to #a-a_/b hour - #e #g #a-a_/b to #c hours - #aj #ab ,over #c hours - #bj #bb #ed to #fj ,up to #bj minutes - - #b #bj to #de minutes - #e #g #c_/d to #a-a_/b hour - #aj #ab #a-a_/b to #c hours #e #ae #bb ,over #c hours #aj #bj #cb ,when preparing to ascend the diver must tighten the air valve in his helmet to increase his buoyancy2 if the valve is closed too much to allow the excess air to escape1 his ascent will at first be gradual1 but the pressure of the water reduces1 the air in the dress expands1 making it so stiff that he cannot move his arms to reach the valve1 and he is blown up1 with ever-increasing velocity1 to the surface4 ,while ascending he should exercise his muscles freely during the period of waiting at each stopping place1 so as to increase the circulation1 and consequently the rate of deceleration4 ,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 night2 but when completed its position must be marked in a permanent manner4 ,the extreme end of the outfall should be indicated by a can buoy similar to that shown in ,fig4 #cc1 made by ,messrs4 ,brown1 ,lenox1 and ,co4 7,limited71 ,milwall1 ,london1 ,e41 which costs about #ge1 including a #bj cwt4 sinker and #aj fathoms of chain1 and is approved for the purpose by the ,board of ,trade4 ,illustration3 ,,fig #cc ,,can ,,buoy ,,for ,,marking ,,outfall ,,sewer4 ,it is not desirable to fasten the chain to any part of the outfall instead of using a sinker1 because at low water the slack of the chain may become entangled1 which by preventing the buoy from rising with the tide1 will lead to damage2 but a special pile may be driven for the purpose of securing the buoy1 at such a distance from the outlet that the chain will not foul it4 ,the buoy should be painted with alternate vertical stripes of yellow and green1 and lettered ,sewer ,outfall in white letters #ab in deep4 ,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 approval1 and no subsequent alteration in the works may be made without their consent being first obtained4 ,,chapter ,,xiii4 ,,the ,,discharge ,,of ,,sea ,,outfall ,,sewers4 ,the head which governs the discharge of a sea outfall pipe is measured from the surface of the sewage in the tank1 sewer1 or reservoir at the head of the outfall to the level of the sea4 ,as the sewage is run off the level of its surface is lowered1 and at the same time the level of the sea is constantly varying as the tide rises and falls1 so that the head is a variable factor1 and consequently the rate of discharge varies4 ,a curve of discharge may be plotted from calculations according to these varying conditions1 but it is not necessary2 and all requirements will be met if the discharges under certain stated conditions are ascertained4 ,the most important condition1 because it is the worst1 is that when the level of the sea is at high water of equinoctial spring tides and the reservoir is practically empty4 ,sea water has a specific gravity of #a4jbg1 and is usually taken as weighing #fd4ad lb per cubic foot1 while sewage may be taken as weighing #fb4de lb per cubic foot1 which is the weight of fresh water at its maximum density4 ,now the ratio of weight between sewage and sea water is as #a to #a4jbg1 so that a column of sea water l#b inches in height requires a column of fresh water #ab4cbd1 or say #ab-a_/c in1 to balance it2 therefore1 in order to ascertain the effective head producing discharge it will be necessary to add on #a_/c in for every foot in depth of the sea water over the centre of the outlet4 ,the sea outfall should be of such diameter that the contents of the reservoir can be emptied in the specified time--say1 three hours--while the pumps are working to their greatest power in pouring sewage into the reservoir during the whole of the period2 so that when the valves are closed the reservoir will be empty1 and its entire capacity available for storage until the valves are again opened4 ,to take a concrete example1 assume that the reservoir and outfall are constructed as shown in ,fig4 #cd1 and that it is required to know the diameter of outfall pipe when the reservoir holds #a1jjj1jjj gallons and the whole of the pumps together1 including any that may be laid down to cope with any increase of the population in the future1 can deliver #fjj1jjj gallons per hour4 ,when the reservoir is full the top water level will be #dc4jj ,o4,d41 but in order to have a margin for contingencies and to allow for the loss in head due to entry of sewage into the pipe1 for friction in passing around bends1 and for a slight reduction in discharging capacity of the pipe by reason of incrustation1 it will be desirable to take the reservoir as full1 but assume that the sewage is at the level #ca4jj4 ,the head of water in the sea measured above the centre of the pipe will be #ba ft1 so that 99,math3 #ba times #a_/c1 or #g in--say1 #j4eh ft--must be added to the height of high water1 thus reducing the effective head from #ca4jj - #aj4jj #ba4jj to #bj4db ft ,the quantity to be discharged will be 99,math3 frac#a1jjj1jjj 7#c 99 #fjj1jjj7c #icc1ccc gallons per hour #ae1eee gallons per minute1 or1 taking #f4bc gallons equal to #a cubic foot1 the quantity equals #b1dig cubic feet per min ,assume the required diameter to be #cj in1 then1 by ,hawksley's formula1 the head necessary to produce velocity 99,math3 frac,gals4 per min#bbae times diameter in inches#d frac#ae1eeebbae 99 #cjd #a4chi ft1 and the head to overcome friction 99,math3 frac,gals4 per min#b times ,length in yards#bdj 99 diameter in inches#e frac#ae1eeeb 99 #bjdbbdj 99 #cje #hd4gai4 ,then #a4chi #hd4gai #hf4ajh--say1 #hf4aa ft2 but the acutal head is #bj4db ft1 and the flow varies approximately as the square root of the head1 so that the true flow will be about 99,math3 #ae1eee 99 sqrtfrac#bj4dbhf4aa #gegd4h ,illustration3 ,,fig #cd ,,diagram ,,illustrating ,,calculations ,,for ,,the ,,discharge ,,of ,,sea ,,outfalls --say #g1ege gallons4 ,but a flow of #ae1eee gallons per minute is required1 as it varies approximately as the fifth power of the diameter1 the requisite diameter will be about 99,math3 sqrt#e;frac#cje times #ae1eeegege #cd4fd inches4 ,now assume a diameter of #dj in1 and repeat the calculations4 ,then head necessary to produce velocity 99,math3 frac#ae1eeebbae times #djd #j4jdd ft1 and head to overcome friction 99,math3 frac#ae1eeeb times #bjdbbdj times #dje #bj4ajd ft ,then #j4jdd #bj4ajd #bj4adh1 say #bj4ae ft1 and the true flow will therefore be about 99,math3 #ae1eee 99 sqrtfrac#bj4dbbj4ae #ae1fei gallons1 and the requisite diameter about 99,math3 sqrt#e;frac#dje 99 #ae1eeeae1fei #ci4id inches4 ,when1 therefore1 a #cj in diameter pipe is assumed1 a diameter of #cd4fd in is shown to be required1 and when #dj in is assumed #ci4id in is indicated4 ,let a difference between the two assumed diameters4 b increase found over lower diameter4 c decrease found under greater diameter4 d lower assumed diameter4 ,then true diameter 99,math3 d fracabbc #cj frac#aj times #d4fdd4fdj4jf #cj frac#df4dd4g #ci4hgb1 or1 say1 #dj in1 which equals the required diameter4 ,a simpler way of arriving at the size would be to calculate it by ,santo ,crimp's formula for sewer discharge1 namely1 velocity in feet per second 99,math3 #abd sqrt#c,r#b sqrt,s1 where ,r equals hydraulic mean depth in feet1 and ,s the ratio of fall to length2 the fall being taken as the difference in level between the sewage and the sea after allowance has been made for the differing densities4 ,in this case the fall is #bj4db ft in a length of #f1abf ft1 which gives a gradient of #a in #cjj4 ,the hydraulic mean depth equals 99,math3 fracd#d2 the required discharge1 #b1dig cubic feet per min1 equals the area1 99,math3 7fracpi d#bd7 multiplied by the velocity1 therefore the velocity in feet per second #d_/7pi d#b7 x #bdig_/fj #bdig_/7ae pi d#b7 and the formula then becomes #bdig_/7ae pi d#b7 #abd x 99 #crdroot7d#b7_/crdroot7#dc997 x sqrt7#a7_/sqrt7#cjj7 or d#b x #crdroot7d#b7 #crdroot7d#f7 7#bdig x #crdroot7#af7 x sqrt7#cjj77 _/ 7#abd x #ae x #c4adaei997 or 7#h x log d7_/#c log #bdig 7#a_/c x log #af7 799 x log #cjj7 - log #abd - log #ae - log #c4adaei2 or log d #c_/h 7#c4cigdai #j4djacgc #a4bchefa - #b4jicdbb - #a4agfjia - #j4digaej7 #c_/h 7#a4bgjfij7 #j4dgfeji4 99 d #b4iieh99 feet #ce4idif1 say #cf inches4 ,as it happens1 this could have been obtained direct from the tables where the discharge of a #cf in pipe at a gradient of #a in #cjj #b1ejf cubic feet per minute1 as against #b1dig cubic feet required1 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 hand4 ,this result differs somewhat from the one previously obtained1 but there remains a third method1 which we can now make trial of--namely1 ,saph and ,schoder's formula for the discharge of water mains1 ,v #agd #crdroot7,r#b7 x ,s4#ea994 ,substituting values similar to those taken previously1 this formula can be written #bdig_/7ae pi d#b7 #agd x #crdroot7d#b7_/crdroot7#db7 x #a4ea_/cjj4ea or d#b x #crdroot7d#b7 #crdroot7d#f7 7#bdig x #crdroot7#af7 x #cjj4ea7 _/ 7#agd x #ae x #c4adaei7 or99 log d #c_/h 7#c4cigdai #j4djacgc 7#ed x #b4dggaba7 - #b4bdjedi - #a4agfjia - #j4digaej7 #c_/h 7#a4bbbfdg7 #j4dehdic 99 d #b4hgd99 feet #cd4chh say #cd #a_/b inches4 ,by ,neville's general formula the velocity in feet per second #adj ,,sqrt7,,rs7-#aa7,,rs77#a_/c7 or1 assuming a diameter of #cg inches1 ,v #adj ,x ,,sqrt7#cg_/7ab x #d7 x #a_/cjj7 - #aa 7#cg_/7abx#dx#cjj777a_/c7 #adj x ,,sqrt7#cg_/addjj7 - #aa 7#cg_/addj77a_/c7 #g4jiffj - #a4ejfef #e4ei feet per second4 ,discharge area x velocity2 therefore1 the discharge in cubic feet per minute #e4ei x #fj x 7#c4adaei x #cgb7_/7d99abb7 #bejd compared with #b1dig c4f4m1 required1 showing that if this formula is used the pipe should be #cg in diameter4 ,the four formul1 therefore1 give different results1 as follows3-- ,hawksley #dj in ,neville #cg in ,santo ,crimp #cf in ,saph and ,schoder #cd-a_/b in ,the circumstances of the case would probably be met by constructing the outfall #cf in in diameter4 ,it is very rarely desirable to fix a flap-valve at the end of a sea outfall pipe1 as it forms a serious obstruction to the flow of the sewage1 amounting1 in one case the writer investigated1 to a loss of eight-ninths of the available head2 the head was exceptionally small1 and the flap valve practically absorbed it all4 ,the only advantage in using a flap valve occurs when the pipe is directly connected with a tank sewer below the level of high water1 in which case1 if the sea water were allowed to enter1 it would not only occupy space required for storing sewage1 but it would act on the sewage and speedily start decomposition1 with the consequent emission of objectionable odours4 ,if there is any probability of sand drifting over the mouth of the outfall pipe1 the latter will keep free much better if there is no valve4 ,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 automatic4 ,that is to say1 the sewage was proposed to be collected in a reservoir at the head of1 and directly connected to1 the outfall pipe1 at the outlet end of which a flap valve was to be fixed4 ,during high water the mouth of the outfall would be closed1 so that sewage would collect in the pipes1 and in the reservoir beyond2 then when the tide had fallen such a distance that its level was below the level of the sewage1 the flap valve would open1 and the sewage flow out until the tide rose and closed the valve4 ,there are several objections to this arrangement4 ,first of all1 a flap valve under such conditions would not remain watertight1 unless it were attended to almost every day1 which is1 of course1 impracticable when the outlet is below water4 ,as the valve would open when the sea fell to a certain level and remain open during the time it was below that level1 the period of discharge would vary from1 say1 two hours at neap tides to about four hours at springs2 and if the two hours were sufficient1 the four hours would be unnecessary4 ,then the sewage would not only be running out and hanging about during dead water at low tide1 but before that time it would be carried in one direction1 and after that time in the other direction2 so that it would be spread out in all quarters around the outfall1 instead of being carried direct out to sea beyond chance of return1 as would be the case in a well- designed scheme4 ,when opening the valve in the reservoir1 or other chamber1 to allow the sewage to flow through the outfall pipe1 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 pipes4 ,when there is considerable difference of level between the reservoir and the sea1 and the valve is opened somewhat quickly1 the sewage as it enters the sea will create a water-spout1 which may reach to a considerable height1 and which draws undesirable attention to the fact that the sewage is then being turned into the sea4 ,chapter ,,xiv ,,trigonometrical ,,surveying4 ,in the surveying work necessary to fix the positions of the various stations1 and of the float1 a few elementary trigonometrical problems are involved which can be advantageously explained by taking practical examples4 ,having selected the main station ,a1 as shown in ,fig4 #ce1 and measured the length of any line ,a ,b on a convenient piece of level ground1 the next step will be to fix its position upon the plan4 ,two prominent landmarks1 ,c and ,d1 such as church steeples1 flag-staffs1 etc41 the positions of which are shown upon the ordnance map1 are selected and the angles read from each of the stations ,a and ,b4 ,assume the line ,a ,b measures ll#g ft1 and the angular measurements reading from zero on that line are1 from ,a to point ,c1 #bi #bc' and to point ,d #hh #dc'1 and from ,b to point ,c #bab #dc'1 and to point ,d #bgb #ah' #cj4 ,the actual readings can be noted1 and then the arrangement of the lines and angles sketched out as shown in ,fig4 #ce1 from which it will be necessary to find the lengths ,,ac and ,,ad4 ,as the three angles of a triangle equal #ahj1 the angle ,b ,c ,a #ahj- #adg #ag'-bi #bc' #c #bj'1 the angle ,b ,d ,a #ahj-hg #da' #cj- #hh #dc' #c #ce' #cj4 ,in any triangle the sides are proportionate to the sines of the opposite angles1 and vice versa2 therefore1 ,a ,b 3 ,a ,c 33 sin ,b ,c ,a 3 sin ,a ,b ,c1 or sin ,b ,c ,a 3 ,a ,b 33 sin ,,abc 3 ,a ,c1 nr ,a ,c 7,a ,b sin ,a ,b ,c7 _/ 7sin ,b ,c ,a7 7#aag x sin #adg #ag'7 _/ 7sin #c #bj'7 or log ,a ,c log #aag ,l sin #adg #ag' - ,l sin #c #bj'4 ,the sine of an angle is equal to the sine of its supplement1 so that sin #adg #ag' sin #cb #dc'1 whence log ,a ,c #b4jfhahei #i4gcbghcg-h4gfdeaaa #c4jcfdehe ,therefore ,a ,c #ajhg4f feet4 ,similarly sin ,b ,d ,a3 ,a ,b 33 sin ,a ,b ,d3 ,a ,d ,a ,b sin ,a ,b ,d #aag x sin #hg #da' #cj therefore ,a ,d --------------- ----------------------- sin ,b ,d ,a sin #c #ce' #cj whence log ,a ,d log ll#g ,l sin #hg #da' #cj - ,l sin #c #ce' #cj #b4jfhahei #i4iiifdgde - #h4gifhhgge #c4bgjidef ,therefore ,,ad #ahff4ae feet4 ,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 known1 so that the triangles can be drawn upon the base ,a ,b by setting off the sides at the known angles1 and the draughtsmanship can be checked by measuring the other known side of each triangle4 ,the points ,c and ,d will then represent the positions of the two landmarks to which the observations were taken1 and if the triangles are drawn upon a piece of tracing paper1 and then superimposed upon the ordnance map so that the points ,c and ,d correspond with the landmarks1 the points ,a and ,b can be pricked through on to the map1 and the base line ,a ,b drawn in its correct position4 ,if it is desired to draw the base line on the map direct from the two known points1 it will be necessary to ascertain the magnitude of the angle ,a ,d ,c4 ,now1 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 sum2 that is3-- ,tan #a_/b 7,,acd - ,,adc73 tan #a_/b 7,,acd ,,adc733 ,,ad - ,,ac 3 ,,ad ,,ac1 but ,,acd ,,adc l#hj - ,,cad #abj #dj'1 therefore1 tan #a_/b 7,,acd - ,,adc73 tan #a_/b 7#abj #dj'733 7#ahff4ae - #ajhg4f73 7#ahff4ae #ajhg4f71 #ggh4ee tan #fj #bj' therefore1 tan #a_/b 7,,acd - ,,adc7 -------------------- #biec4ge or ,l tan #a_/b 7,,acd - ,,adc7 log #ggh4ee ,l tan #fj #bj' - log #biec4ge 4 #b4hiabhfe #aj4bdddl#ed - #c4dgjcgch #i4ffecbha 44 #a_/b 7,,acd - ,,adc7 #bd #di' #ec 44 ,,acd - ,,adc #di #ci' #df4 ,then algebraically 7,,acd ,,adc7 - 7,,acd - ,,adc7 ,,adc --------------------------- #b #abj #dj' - #di #ci' #df #ga #j' #ad 44 ,,adc ------------------------- ------------ #ce #cj' #g1 #b #b ,,acd #ahj - #ce #cj' #g - #ei #bj' #he #i' #ec4 ,illustration3 ,fig4 #ce4--;,arrangement of lines and ,angles ,showing ,theodolite ,readings and ,dimensions4 ,now join up points ,c and ,d on the plan1 and from point ,d set off the line ,d ,a1 making an angle of #ce #cj' #g with ,c ,d1 and having a length of l#hff4ae ft1 and from point ,c set off the angle ,a ,c ,d equal to #he #i' #ec4 ,then the line ,a ,c should measure l#jhg4f ft long1 and meet the line ,a ,d at the point ,a1 making an angle of #ei #bj'4 ,from point ,a draw a line ,a ,b1 ll#g ft long1 making an angle of #bi #bc' with the line ,a ,c2 join ,b ,c1 then the angle ,,abc should measure #adg #ag'1 and the angle ,b ,c ,a #c #bj'4 ,if the lines and angles are accurately drawn1 which can be proved by checking as indicated1 the line ,a ,b will represent the base line in its correct position on the plan4 ,the positions of the other stations can be calculated from the readings of the angles taken from such stations4 ,take stations ,e1 ,f1 ,g1 and ,h as shown in ,fig4 #cf991 the angles which are observed being marked with an arc4 ,it will be observed that two of the angles of each triangle are recorded1 so that the third is always known4 ,the full lines represent those sides1 the lengths of which are calculated1 so that the dimensions of two sides and the three angles of each triangle are known4 ,starting with station ,e1 ,sin ,a ,e ,d3 ,a ,d33 sin ,d ,a ,e3 ,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 ,d4 ,from station ,f1 ,e and ,g are visible1 but the landmark ,d cannot be seen2 therefore1 as the latter can be seen from ,g1 it will be necessary to fix the position of ,g first4 ,then1 sin ,e ,g ,d3 ,d ,e 33 sin ,e ,d ,g 3 ,e ,g1 ,d ,e sin ,e ,d ,g or ,,eg --------------- sin ,e ,g ,d ,now1 sin ,e ,f ,g3 ,e ,g 33 sin ,f ,e ,g 3 ,f ,g ,e ,g sin ,f ,e ,g ,f ,g ------------- sin ,e ,f ,g thus allowing the position of ,f to be fixed1 and then sin ,f ,h ,g 3 ,f ,g 33 sin ,f ,g ,h 3 ,f ,h ,f ,g sin ,f ,g ,h ,f ,h ------------- sin ,f ,h ,g ,illustration3 ,,fig #cf4--;,,diagram ,,illustrating ,,trigonometrical ,,survey ,,of ,,observation ,,stations4 ,in triangles such as ,e ,f ,g and ,f ,g ,h all three angles can be directly read1 so that any inaccuracy in the readings is at once apparent4 ,the station ,h and further stations along the coast being3 out of sight of landmark ,d1 it will be as well to connect the survey up with another landmark ,k1 which can be utilised in the forward work2 the line ,k ,h being equal to ,f ,h sin ,k ,f ,h ------------- sin ,f ,k ,h ,the distance between ,c and ,d in ,fig4 #ce is calculated in a similar manner1 because sin ,a ,c ,d 3 ,a ,d33 sin ,,cad 3 ,,cd1 ,,ad sin ,,cad #ahff4ae sin #ei #bj' or ,,cd ---------- ------------------- sin ,,scd sin #he #i' #ec or log ,,cd log #ahff4ae ,l sin #ei #bj' - ,l sin #he #i' #ec #c4bgjidef #i4icdegch - #i4iihdeaf #c4bjgjfgh4 ' 4 ,,cd #afaj4ij 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 obtained1 but this is a lengthy process1 and is not necessary in practical work4 ,it is desirable1 of course1 that the positions of all the stations be fixed with the greatest accuracy and plotted on the map1 then the position of the float can be located with sufficient correctness1 if the lines of sight obtained from the angles read with the theodolites are plotted1 and their point of intersection marked on the plan4 ,the distance between any two positions of the float can be scaled from the plan4 ,the reason why close measurement is unnecessary in connection with the positions of the float is that it represents a single point1 whereas the sewage escaping with considerable velocity from the outfall sewer spreads itself over a wide expanse of sea in front of the outlet1 and thus has a tangible area4 ,the velocity of any current is greatest in the centre1 and reduces as the distance from the centre increases1 until the edges of the current are lost in comparative still water2 so that observations taken of the course of one particle1 such as the float represents1 only approximately indicate the travel of the sewage through the sea4 ,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 fcal1 or other matter1 that it can be traced for any considerable distance beyond the outfall4 ,it is unlikely that such matters would reach the outlet1 except in a very finely divided state1 when they would be rapidly acted upon by the sea water1 which is a strong oxidising agent4 ,,chapter ,,xv4 ,,hydrographical ,,surveying4 ,hydrographical surveying is that branch of surveying which deals with the complete preparation of charts1 the survey of coast lines1 currents1 soundings1 etc41 and it is applied in connection with the sewerage of sea coast towns when it is necessary to determine the course of the currents1 or a float1 by observations taken from a boat to fixed points on shore1 the boat closely following the float4 ,it has already been pointed out that it is preferable to take the observations from the shore rather than the boat1 but circumstances may arise which render it necessary to adopt the latter course4 ,in the simplest case the position of the boat may be found by taking the compass bearings of two known objects on shore4 ,for example1 ,a and ,b in ,fig4 #cg may represent the positions of two prominent objects whose position is marked upon an ordnance map of the neighbourhood1 or they may be flagstaffs specially set up and noted on the map2 and let ,c represent the boat from which the bearings of ,a and ,b are taken by a prismatic compass1 which is marked from #j to #cfj4 ,let the magnetic variation be ,n4 #ae ,w41 and the observed bearings ,a #bij1 ,b #cbj1 then the position stands as in ,fig4 #ch1 or1 correcting for magnetic variation1 as in ,fig4 #ci1 from which it will be seen that the true bearing of ,c from ,a will be #bge-ahjie ,east of ,north1 or #e below the horizontal1 and the true bearing of ,c from ,b will be #cje-ahjabj ,east of ,north1 or #ce below the horizontal4 ,these directions being plotted will give the position of ,c by their intersection4 ,fig4 #dj shows the prismatic compass in plan and section4 ,it consists practically of an ordinary compass box with a prism and sight-hole at one side1 and a corresponding sight-vane on the opposite side4 ,when being used it is held horizontally in the left hand with the prism turned up in the position shown1 and the sight-vane raised4 ,when looking through the sight-hole the face of the compass-card can be seen by reflection from the back of the prism1 and at the same time the direction of any required point may be sighted with the wire in the opposite sight vane1 so that the bearing of the line between the boat and the required point may be read4 ,if necessary1 the compass-card may be steadied by pressing the stop at the base of the sight vane4 ,in recording the bearings allowance must in all cases be made for the magnetic pole4 ,the magnetic variation for the year #aiaj was about l#e #a_/b ,west of ,north1 and it is moving nearer to true ,north at the rate of about seven minutes per annum4 ,illustration3 ,,fig4 #cg4--,,position ,,of ,,boat ,,found ,,by ,,compass ,,bearings4 ,illustration3 ,,fig4 #ch4--,,reduction ,,of ,,bearings ,,to ,,magnetic ,,north4 ,illustration3 ,,fig4 #ci4--,,reduction ,,of ,,bearings ,,to ,,true ,,north4 ,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 coast1 by observations taken from the object4 ,they are ,euclid ,i4 7#cb71 ,the three interior angles of every triangle are together equal to two right angles2 ,euclid ,,iii4 7#bj71 ,the angle at the centre of a circle is double that of the angle at the circumference upon the same base--that is1 upon the same part of the circumference1 or in other words1 on a given chord the angle subtended by it at the centre of the circle is double the angle subtended by it at the circumference2 and ,euclid ,,iii4 7#ba71 ,the angles in the same segment of a circle are equal to one another4 ,illustration3 ,fig4 #dj4--,section and ,plan of ,prismatic ,compass4 ,having regard to this last proposition 7,euclid ,,iii41 #ba71 it will be observed that in the case of ,fig4 #cg it would not have been possible to locate the point ,c by reading the angle ,a ,c ,b alone1 as such point might be amywhere on the circumference of a circle of which ,a ,b was the chord4 ,the usual and more accurate method of determining the position of a floating object from the object1 itself1 or from a boat alongside1 is by taking angles with a sextant1 or box-sextant1 between three fixed points on shore in two operations4 ,let ,a ,b ,c1 ,fig4 #da1 be the three fixed points on shore1 the positions of which are measured and recorded upon an ordnance map1 or checked if they are already there4 ,let ,d be the floating object1 the position of which is required to be located1 and let the observed angles from the object be ,a ,d ,b #cj and ,b ,d ,c #de4 ,then on the map join ,a ,b and ,b ,c1 from ,a and ,b set off angles #ij - #cj #fj1 and they will intersect at point ,e1 which will be the centre of a circle1 which must be drawn1 with radius ,e ,a4 ,the circle will pass through ,a ,b1 and the point ,d will be somewhere on its circumference4 ,then from ,b and ,c set off angles #ij-de #de1 which will intersect at point ,f1 which will be the centre of a circle of radius ,f ,b1 which will pass through points ,b ,c1 and point ,d will be somewhere on the circumference of this circle also2 therefore the intersection of the two circles at ,d fixes that point on the map4 ,it will be observed that the three interior angles in the triangle ,a ,b ,e are together equal to two right angles 7,euclid ,i4 #cb71 therefore the angle ,a ,e ,b #ahj - #b x 7#ij - #cj7 #fjj1 so that the angle ,a ,e ,b is double the angle ,a ,d ,b 7,euclid ,,iii41 #bj71 and that as the angles subtending a given chord from any point of the circumference are equal 7,euclid ,,iii1 #ba71 the point that is common to the two circumferences is the required point4 ,when point ,d is inked in1 the construction lines are rubbed out ready for plotting the observations from the next position4 ,when the floating point is out of range of ,a1 a new fixed point will be required on shore beyond ,c1 so that ,b1 ,c1 and the new point will be used together4 ,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 length1 which shall form the two observed angles4 ,if1 now1 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 shore1 then the point from which the lines radiate will represent the position of the boat4 ,illustration3 ,fig4 #da4 ,geometrical ,diagram for ,locating ,observation ,point ,afloat4 ,the general appearance of a box-sextant is as shown in ,fig4 #db1 and an enlarged diagrammatic plan of it is shown in ,fig4 #dc4 ,it is about #c in in diameter1 and is made with or without the telescope2 it is used for measuring approximately the angle between any two lines by observing poles at their extremities from the point of intersection4 ,in ,fig4 #dc1 ,a is the sight- hole1 ,b is a fixed mirror having one-half silvered and the other half plain2 ,c is a mirror attached to the same pivot as the vernier arm ,d4 ,the side of the case is open to admit rays of light from the observed objects4 ,in making an observation of the angle formed by lines to two poles1 one pole would be seen through the clear part of mirror ,b1 and at the same time rays of light from the other pole would fall on to mirror ,c1 which should be moved until the pole is reflected on the silvered part of mirror ,b1 exactly in line1 vertically1 with the pole seen by direct vision1 then the angle between the two poles would be indicated on the vernier4 ,take the case of a single pole1 then the angle indicated should be zero1 but whether it would actually be so depends upon circumstances which may be explained as follows3 ,suppose the pole to be fixed at ,e1 which is extremely close1 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 instrument4 ,if the pole is placed farther off1 as at ,f1 the rays of light from the pole will take the course of the stroke-and-dot line1 and the vernier arm will require to be shifted nearer the zero of the scale4 ,after a distance of two chains between the pole and sextant is reached1 the rays of light from the pole to ,b and ,c are so nearly parallel that the error is under one minute1 and the instrument can be used under such conditions without difficulty occurring by reason of error4 ,to adjust the box-sextant the smoked glass slide should be drawn over the eyepiece1 and then1 if the sun is sighted1 it should appear as a perfect sphere when the vernier is at zero1 in whatever position the sextant may be held4 ,when reading the angle formed by the lines from two stations1 the nearer station should be sighted through the plain glass1 which may necessitate holding the instrument upside down4 ,when the angle to be read between two stations exceeds #ij1 an intermediate station should be fixed1 and the angle taken in two parts1 as in viewing large angles the mirror ,c is turned round to such an extent that its own reflection1 and that of the image upon it1 is viewed almost edgeways in the mirror ,b4 ,illustration3 ,fig4 #db4--;,box-,sextant4 ,it should be noted that the box-sextant only reads angles in the plane of the instrument1 so that if one object sighted is lower than the other1 the angle read will be the direct angle between them1 and not the horizontal angle1 as given by a theodolite4 ,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 it4 ,to illustrate this1 use may be made of an examination question in hydrographical surveying given at the ,royal ,naval ,college1 ,incidentally1 it shows one method of recording the observations4 ,the question was as follows3-- ,illustration3 ,fig4 #dc4--;,diagram ,showing ,principle of ,box- ,sextant ,from ,coastguard1 ,mound bore ,n4 #gg ,w4 7true7 #j4de of a mile1 and ,mill bore1 ,n4 #hh ,e1 #j4ef of a mile1 the following stations were taken to fix a shoal on which the sea breaks too heavily to risk the boat near3-- ,mound #fj ,c4,g4 #dg ,mill4 ,greek3 phi ,centre of shoal ,mound #ee ,c4,g4 #eg #cj' ,mill4 ,greek3 phi ,centre of shoal4 ,project the positions on a scale of #e in a mile1 giving the centre of the shoal4 ,it should be noted that the sign ,greek3 phi signifies stations in one line or in transit1 and ,c ,g indicates coastguard station4 ,the order of lettering in ,fig4 #dd shows the order of working4 ,illustration3 ,fig4 #dd4--,method of ,locating ,point in ,water ,when ,observations ,have to ,be ,taken ,beyond ,it4 ,the base lines ,a ,b and ,a ,c are set out from the lengths and directions given2 then1 when the boat at ,d is in transit with the centre of the shoal and the coastguard station1 the angle formed at ,d by lines from that point to ,b and ,a is #fj1 and the angle formed by lines to ,a and ,c is #dg4 ,if angles of #ij - #fj are set up at ,a and ,b1 their intersection at ,e will1 as has already been explained1 give the centre of a circle which will pass through points ,a1 ,b1 and ,d4 ,similarly1 by setting up angles of #ij-dg at ,a and ,c1 a circle is found which will pass through ,a ,c and ,d4 ,the intersection of these circles gives the position of the boat ,d1 and it is known that the shoal is situated somewhere in the straight line from ,d to ,a4 ,the boat was then moved to ,g1 so as to be in transit with the centre of the shoal and the mound1 and the angle ,b ,g ,a was found to be #ee1 and the angle ,a ,g ,c #eg #cj'4 ,by a similar construction to that just described1 the intersection of the circles will give the position of ,g1 and as the shoal is situated somewhere in the line ,g ,b and also in the line ,a ,d1 the intersection of these two lines at ,k will give its exact position4 ,aberdeen ,sea ,outfall ,admiralty1 ,diving ,regulations of --,charts1 ,datums for ,soundings on --,main ,currents ,shown on ,age of ,tide ,air ,pressure on ,tides1 ,effect of ,almanac1 ,nautical ,analysis of ,cement --,sea ,water ,anchor ,bolts for ,sea ,outfalls ,anemometer for ,measuring ,wind ,aphelion ,apogee ,atlantic ,ocean1 ,tides in ,autumnal ,equinox ,barometric ,pressure1 ,effect on ,tides of ,beach ,material1 ,use in ,concrete of ,beaufort ,scale for ,wind ,bench ,mark for ,tide ,gauge ,bird ,tides ,board of ,trade1 ,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 ,iron1 ,resistance to ,sea ,water of ,cement1 ,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 ,force1 ,effect on ,tides of ,centripetal ,force1 ,effect on ,tides of --,variations in ,intensity of ,charts1 ,datum for ,soundings on --,main ,currents ,shown on ,chepstow1 ,greatest ,tide at ,clifton1 ,tides at ,compass1 ,magnetic ,variation --,marine --,prismatic ,concentration of ,storm ,water in ,sewers ,concrete1 ,action of ,sea ,water on --,composition to ,withstand ,sea ,water --,destruction in ,sea ,water of ,crown1 ,foreshore owned by ,currents and ,tides4 ,lack of co-ordination in change of --,formation of --in ,rivers1 #cj --,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 ,plans1 ,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 ,schemes1 ,conditions governing ,diffusion of ,sewage in ,sea ,discharge from ,sea ,outfalls1 ,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 ,equipment1 ,weight of ,dublin1 ,datum for ,tides at ,earth1 ,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 ,floats1 ,deep and ,surface --to govern ,pumping ,plant ,foreshore owned by ,crown ,gauges1 ,measuring flow over ,weirs by ,gauging flow of ,sewage --1 ,formula3 for ,gradient1 ,effect on ,currents of ,surface --,tides of ,barometric ,gravity1 ,specific1 of ,sea ,water --,tides caused by ,great ,crosby ,sea ,outfall ,harbour and ,fisheries ,dept41 ,approval of ,outfall by ,harwich1 ,mean ,level of ,sea at ,high ,water ,mark of ,ordinary ,tides ,hook-,gauge1 for ,measuring flow over ,weirs ,hull1 ,mean ,level of ,sea at ,hydrographical ,surveying ,problems in ,current ,observations ,impermeable ,areas1 ,flow of ,rain off --,percentage of --per ,head of ,population ,indian ,ocean1 ,tides in ,infiltration ,water ,irish ,channel1 ,analysis of ,water in ,iron1 ,effect of ,sea ,water on ,cast ,june1 ,low ,spring3 ,tides in ,kelvin's ,tide ,predicting ,machine ,land1 ,area of ,globe ,occupied by ,leap-weir ,storm ,overflow ,liverpool1 ,datum for ,tides at --,soundings on ,charts of --,tide ,tables ,lloyd-,davies1 ,investigations by ,local ,government ,board1 ,current ,observations ,required for ,london1 ,datum for ,port of ,low ,water ,mark of ,ordinary ,tides ,lunar ,month ,lunation ,magnetic ,variation of ,compass ,marine ,compass ,mean ,high ,water ,mersey1 ,soundings on ,charts of ,mixing ,action of ,sewage and ,water ,moon1 ,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 ,tides1 lines on ,ordnance ,maps of ,ordnance ,datum for ,england --,ireland1 #ag --,records made to fix --,maps1 lines of ,high and ,low ,water on ,outfall ,sewers1 ,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 ,ocean1 ,tides in ,parliament1 ,current ,observations ,required for ,perigee ,perihelion ,piling for ,sea ,outfalls ,pipes1 ,joints of ,cast ,iron --,steel ,plymouth1 ,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 ,sea1 ,mean ,level of ,sea ,outfalls1 ,calculations for ,discharge of --,construction of --,design of --,lights and ,buoy to mark position of --,selection of ,site for ,seashore ,material used in ,concrete ,sea1 ,variation around ,coast in level of --,water1 ,analysis of --,effect on ,cast-,iron of --,effect on ,cement --,galvanic action in --,weight of ,secondary ,waves ,separate ,system of ,sewerage ,sewage1 ,effect of ,sea ,water on --,gauging flow of --,calculations for --,hourly and daily variation in flow of1 #db --,quantity to provide for ,sewers1 ,economic considerations in provision of ,surface ,water --,effect on ,design of ,scheme of ,subsidiary --,storm ,water in ,sextant1 ,box ,signalling1 ,flags for --,morse ,code for ,solstice1 ,summer and ,winter ,soundings on ,charts1 ,datum for ,southampton1 ,tides at ,southern ,ocean1 ,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 ,tanks1 ,automatic ,high ,water ,alarms for --,determination of ,capacity of --,for ,windmill ,pumps ,storm ,water in ,sewers --,overflows ,subsidiary ,sewers1 ,effect on ,design of ,scheme of ,summer ,solstice ,sun1 ,aphelion and ,perihelion --,declination of --,distance from ,earth --,effect on ,tides of --,mass of --,minor ,movements of ,surface ,water ,sewers1 ,average ,cost of --,economic ,considerations in ,provision of ,surveying1 ,problems in ,hydrographical --,trigonometrical ,thames ,conservancy ,datum --,flow of ,sewage in ,tidal ,action in ,crust of ,earth --,attraction --,day1 ,length of --,flap ,valves on ,sea ,outfall ,pipes --,observations1 ,best ,time to ,make --,records1 ,diagram of --,rivers1 ,tides and ,currents in --,waves1 ,length of ,primary --,secondary or ,derivative --,speed of ,primary --,velocity of ,tide ,gauge1 ,method of ,erecting --,selecting ,position of ,tide1 ,observations of ,rise and ,fall of ,tide-,predicting ,machine --,recording ,instrument --,tables ,tides1 ,abnormally ,high --,age of ,tides and ,currents1 ,lack of ,co-ordination in ,change of --,diagrammatic ,representation of ,principal --,diurnal ,inequality --,double1 #i --,effect of ,barometric ,pressure on --,centripetal and ,centrifugal ,force --,storms on1 --,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 ,wastes1 ,effect on flow of ,sewage of ,trass in ,cement for ,marine ,vork ,trigonometrical ,surveying for ,cuirent ,observations ,trinity ,high ,water ,mark ,upland ,water1 ,effect on ,rivers of ,valves on ,sea ,outfall ,pipes ,velocity of ,currents ,vernal ,equinox ,visitors1 ,quantity of ,sewage from ,volume of ,sewage ,water1 ,area of ,globe occupied by --,fittings1 ,leakage from --,power for ,pumping --,supply1 ,quantity per ,head for --,weight of ,waterloo ,sea ,outfall ,waves1 ,horizontal ,movement of --,motion of --,primary and ,secondary --,tidal --,wind ,weight of ,fresh ,water --,sea ,water --,sewage ,weirs for ,gauging ,sewage1 ,design of --,storm ,overflow by ,parallel ,weymouth1 ,mean ,level of ,sea at ,wind --,beaufort ,scale for ,wind1 ,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