The detail design of a sea outfall will depend upon the level of the conduit with reference to present surface of the shore, whether the beach is being eroded or made up, and, if any part of the structure is to be constructed above the level of the shore, whether it is likely to be subject to serious attack by waves in times of heavy gales. If there is probability of the direction of currents being affected by the construction of a solid structure or of any serious scour being caused, the design must be prepared accordingly.
While there are examples of outfalls constructed of glazed stoneware socketed pipes surrounded with concrete, as shown in Fig. 21, cast iron pipes are used in the majority of cases. There is considerable variation in the design of the joints for the latter class of pipes, some of which are shown in Figs. 22, 23, and 24. Spigot and socket joints (Fig. 22), with lead run in, or even with rod lead or any of the patent forms caulked in cold, are unsuitable for use below high-water mark on account of the water which will most probably be found in the trench. Pipes having plain turned and bored joints are liable to be displaced if exposed to the action of the waves, but if such joints are also flanged, as Fig. 24, or provided with lugs, as Fig. 23, great rigidity is obtained when they are bolted up; in addition to which the joints are easily made watertight. When a flange is formed all round the joint, it is necessary, in order that its thickness may be kept within reasonable limits, to provide bolts at frequent intervals. A gusset piece to stiffen the flange should be formed between each hole and the next, and the bolt holes should be arranged so that when the pipes are laid there will not be a hole at the bottom on the vertical axis of the pipe, as when the pipes are laid in a trench below water level it is not only difficult to insert the bolt, but almost impracticable to tighten up the nut afterwards. The pipes should be laid so that the two lowest bolt holes are placed equidistant on each side of the centre line, as shown in the end views of Figs. Nos. 23 and 24.
[Illustration: Fig. 2l.-Stoneware Pipe and Concrete Sea Outfall.]
With lug pipes, fewer bolts are used, and the lugs are made specially strong to withstand the strain put upon them in bolting up the pipes. These pipes are easier and quicker to joint under water than are the flanged pipes, so that their use is a distinct advantage when the hours of working are limited. In some cases gun-metal bolts are used, as they resist the action of sea water better than steel, but they add considerably to the cost of the outfall sewer, and the principal advantage appears to be that they are possibly easier to remove than iron or steel ones would be if at any time it was required to take out any pipe which may have been accidentally broken. On the other hand, there is a liability of severe corrosion of the metal taking place by reason of galvanic action between the gun-metal and the iron, set up by the sea water in which they are immersed. If the pipes are not to be covered with concrete, and are thus exposed to the action of the sea water, particular care should be taken to see that the coating by Dr. Angus Smith's process is perfectly applied to them.
[Illustration: Fig. 22.—Spigot and Socket Joint for Cast Iron Pipes.]
[Illustration: Fig. 23.—Lug Joint for Cast Iron Pipes.]
[Illustration: Fig. 24.—Turned, Board, and Flanged Joint for Cast Iron Pipes.]
Steel pipes are, on the whole, not so suitable as cast iron. They are, of course, obtainable in long lengths and are easily jointed, but their lightness compared with cast iron pipes, which is their great advantage in transport, is a disadvantage in a sea outfall, where the weight of the structure adds to its stability. The extra length of steel pipes necessitates a greater extent of trench being excavated at one time, which must be well timbered to prevent the sides falling in On the other hand, cast iron pipes are more liable to fracture by heavy stones being thrown upon them by the waves, but this is a contingency which does not frequently occur in practice. According to Trautwine, the cast iron for pipes to resist sea water should be close-grained, hard, white metal. In such metal the small quantity of contained carbon is chemically combined with the iron, but in the darker or mottled metals it is mechanically combined, and such iron soon becomes soft, like plumbago, under the influence of sea water. Hard white iron has been proved to resist sea water for forty years without deterioration, whether it is continually under water or alternately wet and dry.
Several types of sea outfalls are shown in Figs. 25 to 31.[1] In the example shown in Fig. 25 a solid rock bed occurred a short distance below the sand, which was excavated so as to allow the outfall to be constructed on the rock. Anchor bolts with clevis heads were fixed into the rock, and then, after a portion of the concrete was laid, iron bands, passing around the cast iron pipes, were fastened to the anchors. This construction would not be suitable below low-water mark. Fig. 26 represents the Aberdeen sea outfall, consisting of cast iron pipes 7 ft in diameter, which are embedded in a heavy concrete breakwater 24 ft in width, except at the extreme end, where it is 30 ft wide. The 4 in wrought iron rods are only used to the last few pipes, which were in 6 ft lengths instead of 9 ft, as were the remainder. Fig. 27 shows an inexpensive method of carrying small pipes, the slotted holes in the head of the pile allowing the pipes to be laid in a straight line, even if the pile is not driven quite true, and if the level of the latter is not correct it can be adjusted by inserting a packing piece between the cradle and the head.
Great Crosby outfall sewer into the Mersey is illustrated in Fig. 28. The piles are of greenheart, and were driven to a solid foundation. The 1 3/4 in sheeting was driven to support the sides of the excavation, and was left in when the concrete was laid. Light steel rails were laid under the sewer, in continuous lengths, on steel sleepers and to 2 ft gauge. The invert blocks were of concrete, and the pipes were made of the same material, but were reinforced with steel ribs. The Waterloo (near Liverpool) sea outfall is shown in Fig. 31.
[Footnote 1: Plate V.]
Piling may be necessary either to support the pipes or to keep them secure in their proper position, but where there is a substratum of rock the pipes may be anchored, as shown in Figs. 25 and 26. The nature of the piling to be adopted will vary according to the character of the beach. Figs. 27, 29, 30, and 31 show various types. With steel piling and bearers, as shown in Fig. 29, it is generally difficult to drive the piles with such accuracy that the bearers may be easily bolted up through the holes provided in the piles, and, if the holes are not drilled in the piles until after they are driven to their final position, considerable time is occupied, and perhaps a tide lost in the attempt to drill them below water. There is also the difficulty of tightening up the bolts when the sewer is partly below the surface of the shore, as shown. In both the types shown in Figs. 29 and 30 it is essential that the piles and the bearers should abut closely against the pipes; otherwise the shock of the waves will cause the pipes to move and hammer against the framing, and thus lead to failure of the structure.
Piles similar to Fig. 31 can only be fixed in sand, as was the case at Waterloo, because they must be absolutely true to line and level, otherwise the pipes cannot be laid in the cradles. The method of fixing these piles is described by Mr. Ben Howarth (Minutes of Proceedings of Inst.C.E., Vol. CLXXV.) as follows:—"The pile was slung vertically into position from a four-legged derrick, two legs of which were on each side of the trench; a small winch attached to one pair of the legs lifted and lowered the pile, through a block and tackle. When the pile was ready to be sunk, a 2 in iron pipe was let down the centre, and coupled to a force-pump by means of a hose; a jet of water was then forced down this pipe, driving the sand and silt away from below the pile. The pile was then rotated backwards and forwards about a quarter of a turn, by men pulling on the arms; the pile, of course, sank by its own weight, the water-jet driving the sand up through the hollow centre and into the trench, and it was always kept vertical by the sling from the derrick. As soon as the pile was down to its final level the ground was filled in round the arms, and in this running sand the pile became perfectly fast and immovable a few minutes after the sinking was completed. The whole process, from the first slinging of the pile to the final setting, did not take more than 20 or 25 minutes."
[Illustration: PLATE V.
ROCK BED. Fig. 26—ABERDEEN SEA OUTFALL. Fig. 27—SMALL GREATCROSBY SEA OUTFALL. Fig. 29—CAST IRON PIPE ON STEEL CAST ANDBEARERS. Fig. 31—WATERLOO (LIVERPOOL) SEA OUTFALL.]
(To face page 80.)
Screw piles may be used if the ground is suitable, but, if it is boulder clay or similar material, the best results will probably be obtained by employing rolled steel joists as piles.
Questions are frequently raised in connection with sea-coast works as to whether any deleterious effect will result from using sea-water for mixing the concrete or from using sand and shingle off the beach; and, further, whether the concrete, after it is mixed, will withstand the action of the elements, exposed, as it will be, to air and sea-water, rain, hot sun, and frosts.
Some concrete structures have failed by decay of the material, principally between high and low water mark, and in order to ascertain the probable causes and to learn the precautions which it is necessary to take, some elaborate experiments have been carried out.
To appreciate the chemical actions which may occur, it will be as well to examine analyses of sea-water and cement. The water of the Irish Channel is composed of
Sodium chloride……………….. 2.6439 per cent.Magnesium chloride…………….. 0.3150 " "Magnesium sulphate…………….. 0.2066 " "Calcium sulphate………………. 0.1331 " "Potassium chloride…………….. 0.0746 " "Magnesium bromide……………… 0.0070 " "Calcium carbonate……………… 0.0047 " "Iron carbonate………………… 0.0005 " "Magnesium nitrate……………… 0.0002 " "Lithium chloride………………. Traces.Ammonium chloride……………… Traces.Silica chloride……………….. Traces.Water………………………… 96.6144————100.0000
An average analysis of a Thames cement may be taken to be as follows:—
Silica………………………….. 23.54 per cent. Insoluble residue (sand, clay, etc.)………………………. 0.40 " Alumina and ferric oxide…………… 9.86 " Lime……………………………. 62.08 " Magnesia…………………………. 1.20 " Sulphuric anhydride……………….. 1.08 " Carbonic anhydride and water……….. 1.34 " Alkalies and loss on analysis………. 0.50 " ——- 100.00
The following figures give the analysis of a sample of cement expressed in terms of the complex compounds that are found:—
Sodium silicate (Na2SiO3)…….. 3.43 per cent.Calcium sulphate (CaSO4)……… 2.45 "Dicalcium silicate (Ca2SiO4)…. 61.89 "Dicalcium aluminate (Ca2Al2O5).. 12.14 "Dicalcium ferrate (Ca2Fe2O5)….. 4.35 "Magnesium oxide (MgO)………… 0.97 "Calcium oxide (CaO)…………. 14.22 "Loss on analysis, &c…………. 0.55 "——-100.00
Dr. W. Michaelis, the German cement specialist, gave much consideration to this matter in 1906, and formed the opinion that the free lime in the Portland cement, or the lime freed in hardening, combines with the sulphuric acid of the sea-water, which causes the mortar or cement to expand, resulting in its destruction. He proposed to neutralise this action by adding to the mortar materials rich in silica, such as trass, which would combine with the lime.
Mr. J. M. O'Hara, of the Southern Pacific Laboratory, San Francisco, Cal., made a series of tests with sets of pats 4 in diameter and 1/2 in thick at the centre, tapering to a thin edge on the circumference, and also with briquettes for ascertaining the tensile strength, all of which were placed in water twenty-four hours after mixing. At first some of the pats were immersed in a "five-strength solution" of sea-water having a chemical analysis as follows:—
Sodium chloride……………….. 11.5 per cent.Magnesium chloride…………….. 1.4 " "Magnesium sulphate…………….. 0.9 " "Calcium sulphate………………. 0.6 " "Water………………………… 85.6 " "100.0
This strong solution was employed in order that the probable effect of immersing the cement in sea-water might be ascertained very much quicker than could be done by observing samples actually placed in ordinary sea-water, and it is worthy of note that the various mixtures which failed in this accelerated test also subsequently failed in ordinary sea-water within a period of twelve months.
Strong solutions were next made of the individual salts contained in sea-water, and pats were immersed as before, when it was found that the magnesium sulphate present in the water acted upon the calcium hydrate in the cement, forming calcium sulphate, and leaving the magnesium hydrate free. The calcium sulphate combines with the alumina of the cement, forming calcium sulpho-aluminate, which causes swelling and cracking of the concrete, and in cements containing a high proportion of alumina, leads to total destruction of all cohesion. The magnesium hydrate has a tendency to fill the pores of the concrete so as to make it more impervious to the destructive action of the sea-water, and disintegration may be retarded or checked. A high proportion of magnesia has been found in samples of cement which have failed under the action of sea water, but the disastrous result cannot be attributed to this substance having been in excess in the original cement, as it was probably due to the deposition of the magnesia salts from the sea-water; although, if magnesia were present in the cement in large quantities, it would cause it to expand and crack, still with the small proportion in which it occurs in ordinary cements it is probably inert. The setting of cement under the action of water always frees a portion of the lime which was combined, but over twice as much is freed when the cement sets in sea-water as in fresh water. The setting qualities of cement are due to the iron and alumina combined with calcium, so that for sea-coast work it is desirable for the alumina to be replaced by iron as far as possible. The final hardening and strength of cement is due in a great degree to the tri-calcium silicate (3CaO, SiO2) which is soluble by the sodium chloride found in sea-water, so that the resultant effect of the action of these two compounds is to enable the sea-water to gradually penetrate the mortar and rot the concrete. The concrete is softened, when there is an abnormal amount of sulphuric acid present, as a result of the reaction of the sulphuric acid of the salt dissolved by the water upon a part of the lime in the cement. The ferric oxide of the cement is unaffected by sea- water.
The neat cement briquette tests showed that those immersed in sea-water attained a high degree of strength at a much quicker rate than those immersed in fresh water, but the 1 to 3 cement and sand briquette tests gave an opposite result. At the end of twelve months, however, practically all the cements set in fresh water showed greater strength than those set in sea- water. When briquettes which have been immersed in fresh water and have thoroughly hardened are broken, the cores are found to be quite dry, and if briquettes immersed in sea-water show a similar dryness there need be no hesitation in using the cement; but if, on the other hand, the briquette shows that the sea-water has permeated to the interior, the cement will lose strength by rotting until it has no cohesion at all. It must be remembered that it is only necessary for the water to penetrate to a depth of 1/2 in on each side of a briquette to render it damp all through, whereas in practical work, if the water only penetrated to the same depth, very little ill-effect would be experienced, although by successive removals of a skin 1/2 in deep the structure might in time be imperilled.
The average strength in pounds per square inch of six different well-known brands of cement tested by Mr. O'Hara was as follows:—
TABLE No. 16.
Neat cement 1 cement to 3 sandset in set inSea Water Fresh Water Sea Water Fresh Water
7 days 682 548 214 22428 days 836 643 293 3192 months 913 668 313 3593 months 861 667 301 3876 months 634 654 309 4289 months 542 687 317 41712 months 372 706 325 432
Some tests were also made by Messrs. Westinghouse, Church, Kerr, and Co., of New York, to ascertain the effect of sea- water on the tensile strength of cement mortar. Three sets of briquettes were made, having a minimum section of one square inch. The first were mixed with fresh water and kept in fresh water; the second were mixed with fresh water, but kept immersed in pans containing salt water; while the third were mixed with sea-water and kept in sea-water. In the experiments the proportion of cement and sand varied from 1 to 1 to 1 to 6. The results of the tests on the stronger mixtures are shown in Fig. 32.
The Scandinavian Portland cement manufacturers have in hand tests on cubes of cement mortar and cement concrete, which were started in 1896, and are to extend over a period of twenty years. A report upon the tests of the first ten years was submitted at the end of 1909 to the International Association of Testing Materials at Copenhagen, and particulars of them are published in "Cement and Sea-Water," by A. Poulsen (chairman of the committee), J. Jorsen and Co., Copenhagen, 1909, price 3s.
[Illustration: FIG. 32.—Tests of the Tensile Strength ofCement and Sand Briquettes, Showing the Effect of Sea Water.]
Cements from representative firms in different countries were obtained for use in making the blocks, which had coloured glass beads and coloured crushed glass incorporated to facilitate identification. Each block of concrete was provided with a number plate and a lifting bolt, and was kept moist for one month before being placed in position. The sand and gravel were obtained from the beach on the west coast of Jutland. The mortar blocks were mixed in the proportion of 1 to 1, 1 to 2, and 1 to 3, and were placed in various positions, some between high and low water, so as to be exposed twice in every twenty- four hours, and others below low water, so as to be always submerged. The blocks were also deposited under these conditions in various localities, the mortar ones being placed at Esbjerb at the south of Denmark, at Vardo in the Arctic Ocean, and at Degerhamm on the Baltic, where the water is only one-seventh as salt as the North Sea, while the concrete blocks were built up in the form of a breakwater or groyne at Thyboron on the west coast of Jutland. At intervals of three, six, and twelve months, and two, four, six, ten, and twenty years, some of the blocks have, or will be, taken up and subjected to chemical tests, the material being also examined to ascertain the effect of exposure upon them. The blocks tested at intervals of less than one year after being placed in position gave very variable results, and the tests were not of much value.
The mortar blocks between high and low water mark of the Arctic Ocean at Vardo suffered the worst, and only those made with the strongest mixture of cement, 1 to 1, withstood the severe frost experienced. The best results were obtained when the mortar was made compact, as such a mixture only allowed diffusion to take place so slowly that its effect was negligible; but when, on the other hand, the mortar was loose, the salts rapidly penetrated to the interior of the mass, where chemical changes took place, and caused it to disintegrate. The concrete blocks made with 1 to 3 mortar disintegrated in nearly every case, while the stronger ones remained in fairly good condition. The best results were given by concrete containing an excess of very fine sand. Mixing very finely-ground silica, or trass, with the cement proved an advantage where a weak mixture was employed, but in the other cases no benefit was observed.
The Association of German Portland Cement Manufacturers carried out a series of tests, extending over ten years, at their testing station at Gross Lichterfeld, near Berlin, the results of which were tabulated by Mr. C. Schneider and Professor Gary. In these tests the mortar blocks were made 3 in cube and the concrete blocks l2 in cube; they were deposited in two tanks, one containing fresh water and the other sea-water, so that the effect under both conditions might be noted. In addition, concrete blocks were made, allowed to remain in moist sand for three months, and were then placed in the form of a groyne in the sea between high and low-water mark. Some of the blocks were allowed to harden for twelve months in sand before being placed, and these gave better results than the others. Two brands of German Portland cement were used in these tests, one, from which the best results were obtained, containing 65.9 per cent. of lime, and the other 62.0 per cent. of lime, together with a high percentage of alumina. In this case, also, the addition of finely-ground silica, or trass, improved the resisting power of blocks made with poor mortars, but did not have any appreciable effect on the stronger mixtures.
Professor M. Möller, of Brunswick, Germany, reported to the International Association for Testing Materials, at the Copenhagen Congress previously referred to, the result of his tests on a small hollow, trapezium shape, reinforced concrete structure, which was erected in the North Sea, the interior being filled with sandy mud, which would be easily removable by flowing water. The sides were 7 cm. thick, formed of cement concrete 1:2 1/2:2, moulded elsewhere, and placed in the structure forty days after they were made, while the top and bottom were 5 cm. thick, and consisted of concrete 1:3:3, mouldedin situand covered by the tide within twenty-four hours of being laid. The concrete mouldedin situhardened a little at first, and then became soft when damp, and friable when dry, and white efflorescence appeared on the surface. In a short time the waves broke this concrete away, and exposed the reinforcement, which rusted and disappeared, with the result that in less than four years holes were made right through the concrete. The sides, which were formed of slabs allowed to harden before being placed in the structure, were unaffected except for a slight roughening of the surface after being exposed alternately to the sea and air for a period, of thirteen years. Professor Möller referred also to several cases which had come under his notice where cement mortar or concrete became soft and showed white efflorescence when it had been brought into contact with sea-water shortly after being made.
In experiments in Atlantic City samples of dry cement in powder form were put with sea-water in a vessel which was rapidly rotated for a short time, after which the cement and the sea- water were analysed, and it was found that the sea-water had taken up the lime from the cement, and the cement had absorbed the magnesia salts from the sea-water.
Some tests were carried out in 1908-9 at the Navy Yard, Charlestown, Mass., by the Aberthaw Construction Company of Boston, in conjunction with the Navy Department. The cement concrete was placed so that the lower portions of the surfaces of the specimens were always below water, the upper portions were always exposed to the air, and the middle portions were alternately exposed to each. Although the specimens were exposed to several months of winter frost as well as to the heat of the summer, no change was visible in any part of the concrete at the end of six months.
Mons. R. Feret, Chief of the Laboratory of Bridges and Roads, Boulogne-sur-Mer, France, has given expression to the following opinions:—
1. No cement or other hydraulic product has yet been found which presents absolute security against the decomposing action of sea-water.
2. The most injurious compound of sea-water is the acid of the dissolved sulphates, sulphuric acid being the principal agent in the decomposition of cement.
3. Portland cement for sea-water should be low in aluminium and as low as possible in lime.
4. Puzzolanic material is a valuable addition to cement for sea-water construction,
5. As little gypsum as possible should be added for regulating the time of setting to cements which are to be used in sea- water.
6. Sand containing a large proportion of fine grains must never be used in concrete or mortar for sea-water construction.
7. The proportions of the cement and aggregate for sea-water construction must be such as will produce a dense and impervious concrete.
On the whole, sea-water has very little chemical effect on good Portland cements, such as are now easily obtainable, and, provided the proportion of aluminates is not too high, the varying composition of the several well-known commercial cements is of little moment. For this reason tests on blocks immersed in still salt water are of very little use in determining the probable behaviour of concrete when exposed to damage by physical and mechanical means, such as occurs in practical work.
The destruction of concrete works on the sea coast is due to the alternate exposure to air and water, frost, and heat, and takes the form of cracking or scaling, the latter being the most usual when severe frosts are experienced. When concrete blocks are employed in the construction of works, they should be made as long as possible before they are required to be built in the structure, and allowed to harden in moist sand, or, if this is impracticable, the blocks should be kept in the air and thoroughly wetted each day. On placing cement or concrete blocks in sea water a white precipitate is formed on their surfaces, which shows that there is some slight chemical action, but if the mixture is dense this action is restricted to the outside, and does not harm the block.
Cement mixed with sea water takes longer to harden than if mixed with fresh water, the time varying in proportion to the amount of salinity in the water. Sand and gravel from the beach, even though dry, have their surfaces covered with saline matters, which retard the setting of the cement, even when fresh water is used, as they become mixed with such water, and thus permeate the whole mass. If sea water and aggregate from the shore are used, care must be taken to see that no decaying seaweed or other organic matter is mixed with it, as every such piece will cause a weak place in the concrete. If loam, clay, or other earthy matters from the cliffs have fallen down on to the beach, the shingle must be washed before it is used in concrete.
Exposure to damp air, such as is unavoidable on the coast, considerably retards the setting of cement, so that it is desirable that it should not be further retarded by the addition of gypsum, or calcium sulphate, especially if it is to be used with sea water or sea-washed sand and gravel. The percentage of gypsum found in cement is, however, generally considerably below the maximum allowed by the British Standard Specification, viz., 2 per cent., and is so small that, for practical purposes, it makes very little difference in sea coast work, although of course, within reasonable limits, the quicker the cement sets the better. When cement is used to joint stoneware pipe sewers near the coast, allowance must be made for this retardation of the setting, and any internal water tests which may be specified to be applied must not be made until a longer period has elapsed after the laying of the pipes than would otherwise be necessary. A high proportion of aluminates tends to cause disintegration when exposed to sea water. The most appreciable change which takes place in a good sound cement after exposure to the sea is an increase in the chlorides, while a slight increase in the magnesia and the sulphates also takes place, so that the proportion of sulphates and magnesia in the cement should be kept fairly low. Hydraulic lime exposed to the sea rapidly loses the lime and takes up magnesia and sulphates.
To summarise the information upon this point, it appears that it is better to use fresh water for all purposes, but if, for the sake of economy, saline matters are introduced into the concrete, either by using sea water for mixing or by using sand and shingle from the beach, the principal effect will be to delay the time of setting to some extent, but the ultimate strength of the concrete will probably not be seriously affected. When the concrete is placed in position the portion most liable to be destroyed is that between high and low water mark, which is alternately exposed to the action of the sea and the air, but if the concrete has a well-graded aggregate, is densely mixed, and contains not more than two parts of sand to one part of cement, no ill-effect need be anticipated.
The engineer is not directly concerned with the various methods employed in constructing a sea outfall, such matters being left to the discretion of the contractor. It may, however, be briefly stated that the work frequently involves the erection of temporary steel gantries, which must be very carefully designed and solidly built if they are to escape destruction by the heavy seas. It is amazing to observe the ease with which a rough sea will twist into most fantastic shapes steel joists 10 in by 8in, or even larger in size. Any extra cost incurred in strengthening the gantries is well repaid if it avoids damage, because otherwise there is not only the expense of rebuilding the structure to be faced, but the construction of the work will be delayed possibly into another season.
In order to ensure that the works below water are constructed in a substantial manner, it is absolutely necessary that the resident engineer, at least, should be able to don a diving dress and inspect the work personally. The particular points to which attention must be given include the proper laying of the pipes, so that the spigot of one is forced home into the socket of the other, the provision and tightening up of all the bolts required to be fixed, the proper driving of the piles and fixing the bracing, the dredging of a clear space in the bed of the sea in front of the outlet pipe, and other matters dependent upon the special form of construction adopted. If a plug is inserted in the open end of the pipes as laid, the rising of the tide will press on the plugged end and be of considerable assistance in pushing the pipes home; it will therefore be necessary to re-examine the joints to see if the bolts can be tightened up any more.
Messrs. Siebe, Gorman, and Co., the well-known makers of submarine appliances, have fitted up at their works at Westminster Bridge-road, London, S.E., an experimental tank, in which engineers may make a few preliminary descents and be instructed in the art of diving; and it is distinctly more advantageous to acquire the knowledge in this way from experts than to depend solely upon the guidance of the divers engaged upon the work which the engineer desires to inspect. Only a nominal charge of one guinea for two descents is made, which sum, less out-of-pocket expenses, is remitted to the Benevolent Fund of the Institution of Civil Engineers. It is generally desirable that a complete outfit, including the air pump, should be provided for the sole use of the resident engineer, and special men should be told off to assist him in dressing and to attend to his wants while he is below water. He is then able to inspect the work while it is actually in progress, and he will not hinder or delay the divers.
It is a wise precaution to be medically examined before undertaking diving work, although, with the short time which will generally be spent below water, and the shallow depths usual in this class of work, there is practically no danger; but, generally speaking, a diver should be of good physique, not unduly stout, free from heart or lung trouble and varicose veins, and should not drink or smoke to excess. It is necessary, however, to have acquaintance with the physical principles involved, and to know what to do in emergencies. A considerable amount of useful information is given by Mr. R. H. Davis in his "Diving Manual" (Siebe, Gorman, and Co., 5s.), from which many of the following notes are taken.
A diving dress and equipment weighs about l75 lb, including a 40 lb lead weight carried by the diver on his chest, a similar weight on his back, and l6lb of lead on each boot. Upon entering the water the superfluous air in the dress is driven out through the outlet valve in the helmet by the pressure of the water on the legs and body, and by the time the top of the diver's head reaches the surface his breathing becomes laboured, because the pressure of air in his lungs equals the atmospheric pressure, while the pressure upon his chest and abdomen is greater by the weight of the water thereon.
He is thus breathing against a pressure, and if he has to breathe deeply, as during exertion, the effect becomes serious; so that the first thing he has to learn is to adjust the pressure of the spring on the outlet valve, so that the amount of air pumped in under pressure and retained in the diving dress counterbalances the pressure of the water outside, which is equal to a little under 1/2lb per square inch for every foot in depth. If the diver be 6 ft tall, and stands in an upright position, the pressure on his helmet will be about 3lb per square inch less than on his boots. The breathing is easier if the dress is kept inflated down to the abdomen, but in this case there is danger of the diver being capsized and floating feet upwards, in which position he is helpless, and the air cannot escape by the outlet valve. Air is supplied to the diver under pressure by an air pump through a flexible tube called the air pipe; and a light rope called a life line, which is used for signalling, connects the man with the surface. The descent is made by a 3 in "shot-rope," which has a heavy sinker weighing about 50 lb attached, and is previously lowered to the bottom. A 1-1/4 in rope about 15 ft long, called a "distance- line," is attached to the shot-rope about 3 ft above the sinker, and on reaching the bottom the diver takes this line with him to enable him to find his way back to the shot-rope, and thus reach the surface comfortably, instead of being hauled up by his life line. The diver must be careful in his movements that he does not fall so as suddenly to increase the depth of water in which he is immersed, because at the normal higher level the air pressure in the dress will be properly balanced against the water pressure; but if he falls, say 30 ft, the pressure of the water on his body will be increased by about 15 lb per square inch, and as the air pump cannot immediately increase the pressure in the dress to a corresponding extent, the man's body in the unresisting dress will be forced into the rigid helmet, and he will certainly be severely injured, and perhaps even killed.
When descending under water the air pressure in the dress is increased, and acts upon the outside of the drum of the ear, causing pain, until the air passing through the nose and up the Eustachian tube inside the head reaches the back of the drum and balances the pressure. This may be delayed, or prevented, if the tube is partially stopped up by reason of a cold or other cause, but the balance can generally be brought about if the diver pauses in his descent and swallows his saliva; or blocks up his nose as much as possible by pressing it against the front of the helmet, closing the mouth and then making a strong effort at expiration so as to produce temporarily an extra pressure inside the throat, and so blow open the tubes; or by yawning or going through the motions thereof. If this does not act he must come up again Provided his ears are "open," and the air pumps can keep the pressure of air equal to that of the depth of the water in which the diver may be, there is nothing to limit the rate of his descent.
Now in breathing, carbonic acid gas is exhaled, the quality varying in accordance with the amount of work done, from .014 cubic feet per minute when at rest to a maximum of about .045, and this gas must be removed by dilution with fresh air so as not to inconvenience the diver. This is not a matter of much difficulty as the proportion in fresh air is about .03 per cent., and no effect is felt until the proportion is increased to about 0.3 per cent., which causes one to breathe twice as deeply as usual; at 0.6 per cent. there is severe panting; and at a little over 1.0 per cent. unconsciousness occurs. The effect of the carbonic acid on the diver, however, increases the deeper he descends; and at a depth of 33 ft 1 per cent. of carbonic acid will have the same effect as 2 per cent. at the surface. If the diver feels bad while under water he should signal for more air, stop moving about, and rest quietly for a minute or two, when the fresh air will revive him. The volume of air required by the diver for respiration is about 1.5 cubic feet per minute, and there is a non-return valve on the air inlet, so that in the event of the air pipe being broken, or the pump failing, the air would not escape backwards, but by closing the outlet valve the diver could retain sufficient air to enable him to reach the surface.
During the time that a diver is under pressure nitrogen gas from the air is absorbed by his blood and the tissues of his body. This does not inconvenience him at the time, but when he rises the gas is given off, so that if he has been at a great depth for some considerable time, and comes up quickly, bubbles form in the blood and fill the right side of the heart with air, causing death in a few minutes. In less sudden cases the bubbles form in the brain or spinal cord, causing paralysis of the legs, which is called divers' palsy, or the only trouble which is experienced may be severe pains in the joints and muscles. It is necessary, therefore, that he shall come up by stages so as to decompress himself gradually and avoid danger. The blood can hold about twice as much gas in solution as an equal quantity of water, and when the diver is working in shallow depths, up to, say, 30 ft, the amount of nitrogen absorbed is so small that he can stop down as long as is necessary for the purposes of the work, and can come up to the surface as quickly as he likes without any danger. At greater depths approximately the first half of the upward journey may be done in one stage, and the remainder done by degrees, the longest rest being made at a few feet below the surface.
The following table shows the time limits in accordance with the latest British Admiralty practice; the time under the water being that from leaving the surface to the beginning of the ascent:—
TABLE No. l7.—DIVING DATA.
Stoppages in Total timeminutes at for ascentDepth in feet. Time under water. different depths in minutes.
at 20 ft 10 ft
Up to 36 No limit - - 0 to 1
36 to 42 Up to 3 hours - - 1 to 1-1/2 Over 3 hours - 5 6
42 to 48 Up to 1 hour - - 1-1/2 1 to 3 hours - 5 6-1/2 Over 3 hours - 10 11-1/2
48 to 54 Up to 1/2 hour - - 2 1/2 to 1-1/2 hour - 5 7 1-1/2 to 3 hours - 10 12 Over 3 hours - 20 22
54 to 60 Up to 20 minutes - - 2 20 to 45 minutes - 5 7 3/4 to 1-1/2 hour - 10 12 1-1/2 to 3 hours 5 15 22 Over 3 hours 10 20 32
When preparing to ascend the diver must tighten the air valve in his helmet to increase his buoyancy; if the valve is closed too much to allow the excess air to escape, his ascent will at first be gradual, but the pressure of the water reduces, the air in the dress expands, making it so stiff that he cannot move his arms to reach the valve, and he is blown up, with ever-increasing velocity, to the surface. While ascending he should exercise his muscles freely during the period of waiting at each stopping place, so as to increase the circulation, and consequently the rate of deceleration.
During the progress of the works the location of the sea outfall will be clearly indicated by temporary features visible by day and lighted by night; but when completed its position must be marked in a permanent manner. The extreme end of the outfall should be indicated by a can buoy similar to that shown in Fig. 33, made by Messrs. Brown, Lenox, and Co. (Limited), Milwall, London, E., which costs about £75, including a 20 cwt. sinker and 10 fathoms of chain, and is approved for the purpose by the Board of Trade.
[Illustration: FIG 33 CAN BUOY FOR MARKING OUTFALL SEWER.]
It is not desirable to fasten the chain to any part of the outfall instead of using a sinker, because at low water the slack of the chain may become entangled, which by preventing the buoy from rising with the tide, will lead to damage; but a special pile may be driven for the purpose of securing the buoy, at such a distance from the outlet that the chain will not foul it. The buoy should be painted with alternate vertical stripes of yellow and green, and lettered "Sewer Outfall" in white letters 12 in deep.
It must be remembered that it is necessary for the plans and sections of outfall sewers and other obstructions proposed to be placed in tidal waters to be submitted to the Harbour and Fisheries Department of the Board of Trade for their approval, and no subsequent alteration in the works may be made without their consent being first obtained.
The head which governs the discharge of a sea outfall pipe is measured from the surface of the sewage in the tank, sewer, or reservoir at the head of the outfall to the level of the sea. As the sewage is run off the level of its surface is lowered, and at the same time the level of the sea is constantly varying as the tide rises and falls, so that the head is a variable factor, and consequently the rate of discharge varies. A curve of discharge may be plotted from calculations according to these varying conditions, but it is not necessary; and all requirements will be met if the discharges under certain stated conditions are ascertained. The most important condition, because it is the worst, is that when the level of the sea is at high water of equinoctial spring tides and the reservoir is practically empty.
Sea water has a specific gravity of 1.027, and is usually taken as weighing 64.14 lb per cubic foot, while sewage may be taken as weighing 62.45 lb per cubic foot, which is the weight of fresh water at its maximum density. Now the ratio of weight between sewage and sea water is as 1 to 1.027, so that a column of sea water l2 inches in height requires a column of fresh water 12.324, or say 12-1/3 in, to balance it; therefore, in order to ascertain the effective head producing discharge it will be necessary to add on 1/3 in for every foot in depth of the sea water over the centre of the outlet.
The sea outfall should be of such diameter that the contents of the reservoir can be emptied in the specified time—say, three hours—while the pumps are working to their greatest power in pouring sewage into the reservoir during the whole of the period; so that when the valves are closed the reservoir will be empty, and its entire capacity available for storage until the valves are again opened.
To take a concrete example, assume that the reservoir and outfall are constructed as shown in Fig. 34, and that it is required to know the diameter of outfall pipe when the reservoir holds 1,000,000 gallons and the whole of the pumps together, including any that may be laid down to cope with any increase of the population in the future, can deliver 600,000 gallons per hour. When the reservoir is full the top water level will be 43.00 O.D., but in order to have a margin for contingencies and to allow for the loss in head due to entry of sewage into the pipe, for friction in passing around bends, and for a slight reduction in discharging capacity of the pipe by reason of incrustation, it will be desirable to take the reservoir as full, but assume that the sewage is at the level 31.00. The head of water in the sea measured above the centre of the pipe will be 21 ft, so that
[*Math: $21 \times 1/3$],
or 7 in—say, 0.58 ft—must be added to the height of high water, thus reducing the effective head from 31.00 - 10.00 = 21.00 to 20.42 ft The quantity to be discharged will be
[*Math: $\frac{1,000,000 + (3 * 600,000)}{3}$]
= 933,333 gallons per hour = 15,555 gallons per minute, or, taking 6.23 gallons equal to 1 cubic foot, the quantity equals 2,497 cubic feet per min Assume the required diameter to be 30 in, then, by Hawksley's formula, the head necessary to produce velocity =
[*Math: $\frac{Gals. per min^2}{215 \times diameter in inches^4} = \frac{15,555^2}{215 * 30^4}$]
= 1.389 ft, and the head to overcome friction =
[*Math: $\frac{Gals. per min^2 \times Length in yards}{240 * diameter in inches^5} = \frac{15,555^2 * 2042}{240 * 30^5}]
= 84.719. Then 1.389 + 84.719 = 86.108—say, 86.11 ft; but the acutal head is 20.42 ft, and the flow varies approximately as the square root of the head, so that the true flow will be about
[*Math: $15,555 * \sqrt{\frac{20.42}{86.11} = 7574.8$]
[Illustration: FIG 34 DIAGRAM ILLUSTRATING CALCULATIONS FOR THEDISCHARGE OF SEA OUTFALLS]
—say 7,575 gallons. But a flow of 15,555 gallons per minute is required, as it varies approximately as the fifth power of the diameter, the requisite diameter will be about
[*Math: \sqrt[5]{\frac{30^5 \times 15,555}{7575}] = 34.64 inches.
Now assume a diameter of 40 in, and repeat the calculations.Then head necessary to produce velocity
[*Math: = \frac{15,555^2}{215 \times 40^4}] = 0.044 ft, and head to overcome friction =
[*Math: \frac{15,555^2 \times 2042}{240 \times 40^5}]
= 20.104 ft Then 0.044 + 20.104 = 20.148, say 20.15 ft, and the true flow will therefore be about
[*Math: 15,555 * \sqrt{\frac{20.42}{20.15}}]
= 15,659 gallons, and the requisite diameter about
[*Math: \sqrt[5]{\frac{40^5 * 15,555}{15,659}}]
= 39.94 inches.
When, therefore, a 30 in diameter pipe is assumed, a diameter of 34.64 in is shown to be required, and when 40 in is assumed 39.94 in is indicated.
Leta= difference between the two assumed diameters.b= increase found over lower diameter.c= decrease found under greater diameter.d= lower assumed diameter.
Then true diameter =
[*Math: d + \frac{ab}{b+c} = 30 + \frac{10 \times 4.64}{4.64+0.06} = 30 + \frac{46.4}{4.7} = 39.872],
or, say, 40 in, which equals the required diameter.
A simpler way of arriving at the size would be to calculate it by Santo Crimp's formula for sewer discharge, namely, velocity in feet per second =
[*Math: 124 \sqrt[3]{R^2} \sqrt{S}],
where R equals hydraulic mean depth in feet, and S = the ratio of fall to length; the fall being taken as the difference in level between the sewage and the sea after allowance has been made for the differing densities. In this case the fall is 20.42 ft in a length of 6,126 ft, which gives a gradient of 1 in 300. The hydraulic mean depth equals
[*Math: \frac{d}{4}];
the required discharge, 2,497 cubic feet per min, equals the area,
[*Math: (\frac{\pi d^2}{4})]
multiplied by the velocity, therefore the velocity in feet per second = 4/(pi d^2) x 2497/60 = 2497/(15 pi d^2) and the formula then becomes
2497/(15 pi d^2) = 124 x * 3rd_root(d^2)/3rd_root(4^3*) x sqrt(1)/sqrt(300)
or d^2 x 3rd_root(d^2) = 3rd_root(d^6) = (2497 x 3rd_root(16) x sqrt(300)) / (124 x 15 x 3.14159*)
or (8 x log d)/3 = log 2497 + (1/3 x log 16) + (* x log 300) - log 124 - log 15 - log 3.14159;
or log d = 3/8 (3.397419 + 0.401373 + 1.238561 - 2.093422 - 1.176091 - 0.497150) = 3/8 (1.270690) = 0.476509.
* d = 2.9958* feet = 35.9496, say 36 inches.
As it happens, this could have been obtained direct from the tables where the discharge of a 36 in pipe at a gradient of 1 in 300 = 2,506 cubic feet per minute, as against 2,497 cubic feet required, but the above shows the method of working when the figures in the tables do not agree with those relating to the particular case in hand.
This result differs somewhat from the one previously obtained, but there remains a third method, which we can now make trial of—namely, Saph and Schoder's formula for the discharge of water mains, V = 174 3rd_root(R^2) x S^.51*. Substituting values similar to those taken previously, this formula can be written
2497/(15 pi d^2) = 174 x 3rd_root(d_2)/3rd_root(4^2) x 1^.51/300^.51
or d^2 x 3rd_root(d^2) = 3rd_root(d^6) = (2497 x 3rd_root(16) x 300^.51) / (174 x 15 x 3.14159)
or* log d = 3/8 (3.397419 + 0.401373 + (54 x 2.477121) - 2.240549 - 1.176091 - 0.497150) = 3/8 (1.222647) = 0.458493
* d = 2.874* feet = 34.388 say 34 1/2 inches.
By Neville's general formula the velocity in feet per second = 140 SQRT(RS)-11(RS)^(1/3) or, assuming a diameter of 37 inches,
V = 140 X SQRT(37/(12 x 4) x 1/300) - 11 (37/(12x4x300))^(1/3)
= 140 x SQRT(37/14400) - 11 (37/1440)^(1/3)
= 7.09660 - 1.50656 = 5.59 feet per second.
Discharge = area x velocity; therefore, the discharge in cubic feet per minute
= 5.59 x 60 x (3.14159 x 37^2)/(4*12^2) = 2504 compared with
2,497 c.f.m, required, showing that if this formula is used the pipe should be 37 in diameter.
The four formulæ, therefore, give different results, as follows:—
Hawksley = 40 inNeville = 37 inSanto Crimp = 36 inSaph and Schoder = 34-1/2 in
The circumstances of the case would probably be met by constructing the outfall 36 in in diameter.
It is very rarely desirable to fix a flap-valve at the end of a sea outfall pipe, as it forms a serious obstruction to the flow of the sewage, amounting, in one case the writer investigated, to a loss of eight-ninths of the available head; the head was exceptionally small, and the flap valve practically absorbed it all. The only advantage in using a flap valve occurs when the pipe is directly connected with a tank sewer below the level of high water, in which case, if the sea water were allowed to enter, it would not only occupy space required for storing sewage, but it would act on the sewage and speedily start decomposition, with the consequent emission of objectionable odours. If there is any probability of sand drifting over the mouth of the outfall pipe, the latter will keep free much better if there is no valve. Schemes have been suggested in which it was proposed to utilise a flap valve on the outlet so as to render the discharge of the sewage automatic. That is to say, the sewage was proposed to be collected in a reservoir at the head of, and directly connected to, the outfall pipe, at the outlet end of which a flap valve was to be fixed. During high water the mouth of the outfall would be closed, so that sewage would collect in the pipes, and in the reservoir beyond; then when the tide had fallen such a distance that its level was below the level of the sewage, the flap valve would open, and the sewage flow out until the tide rose and closed the valve. There are several objections to this arrangement. First of all, a flap valve under such conditions would not remain watertight, unless it were attended to almost every day, which is, of course, impracticable when the outlet is below water. As the valve would open when the sea fell to a certain level and remain open during the time it was below that level, the period of discharge would vary from, say, two hours at neap tides to about four hours at springs; and if the two hours were sufficient, the four hours would be unnecessary. Then the sewage would not only be running out and hanging about during dead water at low tide, but before that time it would be carried in one direction, and after that time in the other direction; so that it would be spread out in all quarters around the outfall, instead of being carried direct out to sea beyond chance of return, as would be the case in a well- designed scheme.
When opening the valve in the reservoir, or other chamber, to allow the sewage to flow through the outfall pipe, care should be taken to open it at a slow rate so as to prevent damage by concussion when the escaping sewage meets the sea water standing in the lower portion of the pipes. When there is considerable difference of level between the reservoir and the sea, and the valve is opened somewhat quickly, the sewage as it enters the sea will create a "water-spout," which may reach to a considerable height, and which draws undesirable attention to the fact that the sewage is then being turned into the sea.
In the surveying work necessary to fix the positions of the various stations, and of the float, a few elementary trigonometrical problems are involved which can be advantageously explained by taking practical examples.
Having selected the main station A, as shown in Fig. 35, and measured the length of any line A B on a convenient piece of level ground, the next step will be to fix its position upon the plan. Two prominent landmarks, C and D, such as church steeples, flag-staffs, etc., the positions of which are shown upon the ordnance map, are selected and the angles read from each of the stations A and B. Assume the line A B measures ll7 ft, and the angular measurements reading from zero on that line are, from A to point C, 29° 23' and to point D 88° 43', and from B to point C 212° 43', and to point D 272° 18' 30". The actual readings can be noted, and then the arrangement of the lines and angles sketched out as shown in Fig. 35, from which it will be necessary to find the lengths AC and AD. As the three angles of a triangle equal 180°, the angle B C A = 180°- 147° 17'-29° 23'= 3° 20', the angle B D A = 180°-87° 41' 30"- 88° 43'= 3° 35' 30". In any triangle the sides are proportionate to the sines of the opposite angles, and vice versa; therefore,
A B : A C :: sin B C A : sin A B C, or sin B C A : A B :: sin ABC : A C, nr A C = (A B sin A B C) / (sin B C A) = (117 x sin 147° 17') / (sin 3° 20')
or log A C = log 117 + L sin 147° 17' - L sin 3° 20'.
The sine of an angle is equal to the sine of its supplement, so that sin 147° 17' = sin 32° 43', whence log A C = 2.0681859 + 9.7327837-8.7645111 = 3.0364585
Therefore A C = 1087.6 feet.
Similarly sin B D A: A B :: sin A B D: A D
A B sin A B D 117 x sin 87° 41' 30"therefore A D = ———————- = ———————————-sin B D A sin 3° 35' 30"
whence log A D = log ll7 + L sin 87° 41' 30" - L sin 3° 35' 30"= 2.0681859 + 9.99964745 - 8.79688775= 3.2709456
Therefore AD = 1866.15 feet.
The length of two of the sides and all three angles of each of the two triangles A C B and A D B are now known, so that the triangles can be drawn upon the base A B by setting off the sides at the known angles, and the draughtsmanship can be checked by measuring the other known side of each triangle. The points C and D will then represent the positions of the two landmarks to which the observations were taken, and if the triangles are drawn upon a piece of tracing paper, and then superimposed upon the ordnance map so that the points C and D correspond with the landmarks, the points A and B can be pricked through on to the map, and the base line A B drawn in its correct position.
If it is desired to draw the base line on the map direct from the two known points, it will be necessary to ascertain the magnitude of the angle A D C. Now, in any triangle the tangent of half the difference of two angles is to the tangent of half their sum as the difference of the two opposite sides is to their sum; that is:—
Tan 1/2 (ACD - ADC): tan 1/2 (ACD + ADC)::AD - AC : AD + AC,
but ACD + ADC = l80° - CAD = 120° 40',therefore, tan 1/2 (ACD - ADC): tan 1/2 (120° 40')::(1866.15 - 1087.6): (1866.15 + 1087.6),
778.55 tan 60° 20'therefore, tan 1/2 (ACD - ADC) = ——————————2953.75
or L tan 1/2 (ACD - ADC) = log 778.55 + L tan 60° 20'- log 2953.75 .= 2.8912865 + 10.2444l54 - 3.4703738= 9.6653281 .. 1/2 (ACD - ADC) = 24° 49' 53".. ACD - ADC = 49° 39' 46". Then algebraically
(ACD + ADC) - (ACD - ADC)ADC = —————————————-2
120° 40' - 49° 39' 46" 71° 0' 14".. ADC = ————————————- = —————— = 35° 30' 7",2 2
[Illustration: Fig. 35.—Arrangement of lines and AnglesShowing Theodolite Readings and Dimensions.]
Now join up points C and D on the plan, and from point D set off the line D A, making an angle of 35° 30' 7" with C D, and having a length of l866.15 ft, and from point C set off the angle A C D equal to 85° 9' 53". Then the line A C should measure l087.6 ft long, and meet the line A D at the point A, making an angle of 59° 20'. From point A draw a line A B, ll7 ft long, making an angle of 29° 23' with the line A C; join B C, then the angle ABC should measure 147° 17', and the angle B C A 3° 20'. If the lines and angles are accurately drawn, which can be proved by checking as indicated, the line A B will represent the base line in its correct position on the plan.
The positions of the other stations can be calculated from the readings of the angles taken from such stations. Take stations E, F, G, and H as shown in Fig. 36*, the angles which are observed being marked with an arc.
It will be observed that two of the angles of each triangle are recorded, so that the third is always known. The full lines represent those sides, the lengths of which are calculated, so that the dimensions of two sides and the three angles of each triangle are known. Starting with station E,
Sin A E D: A D:: sin D A E: D E
A D sin D A ED E = ———————sin A E D
or log D E = log A D + L sin D A E-L sin A E D.
From station F, E and G are visible, but the landmark D cannot be seen; therefore, as the latter can be seen from G, it will be necessary to fix the position of G first. Then,
sin E G D: D E :: sin E D G : E G,
D E sin E D Gor EG= ———————-sin E G D
Now, sin E F G: E G :: sin F E G : F G
E G sin F E GF G = ——————-sin E F G
thus allowing the position of F to be fixed, and then
sin F H G : F G :: sin F G H : F H
F G sin F G HF H= ——————-sin F H G
[Illustration: FIG 36.—DIAGRAM ILLUSTRATING TRIGONOMETRICALSURVEY OF OBSERVATION STATIONS.]
In triangles such as E F G and F G H all three angles can be directly read, so that any inaccuracy in the readings is at once apparent. The station H and further stations along the coast being: out of sight of landmark D, it will be as well to connect the survey up with another landmark K, which can be utilised in the forward work; the line K H being equal to
F H sin K F H ——————- sin F K H
The distance between C and D in Fig. 35 is calculated in a similar manner, because sin A C D : A D:: sin CAD : CD,
AD sin CAD 1866.15 sin 59° 20'or CD = ————— = —————————-sin SCD sin 85° 9' 53"
or log CD = log 1866.15 + L sin 59° 20' - L sin 85° 9' 53"
= 3.2709456 + 9.9345738 - 9.9984516
= 3.2070678. ' . CD = 1610.90 ft
The distance between any two positions of the float can be obtained by calculation in a similar way to that in which the length C D was obtained, but this is a lengthy process, and is not necessary in practical work. It is desirable, of course, that the positions of all the stations be fixed with the greatest accuracy and plotted on the map, then the position of the float can be located with sufficient correctness, if the lines of sight obtained from the angles read with the theodolites are plotted, and their point of intersection marked on the plan. The distance between any two positions of the float can be scaled from the plan.
The reason why close measurement is unnecessary in connection with the positions of the float is that it represents a single point, whereas the sewage escaping with considerable velocity from the outfall sewer spreads itself over a wide expanse of sea in front of the outlet, and thus has a tangible area. The velocity of any current is greatest in the centre, and reduces as the distance from the centre increases, until the edges of the current are lost in comparative still water; so that observations taken of the course of one particle, such as the float represents, only approximately indicate the travel of the sewage through the sea. Another point to bear in mind is that the dilution of the sewage in the sea is so great that it is generally only by reason of the unbroken fæcal, or other matter, that it can be traced for any considerable distance beyond the outfall. It is unlikely that such matters would reach the outlet, except in a very finely divided state, when they would be rapidly acted upon by the sea water, which is a strong oxidising agent.