34499061911 Encyclopædia Britannica, Volume 28 — Water SupplyGeorge Frederick Deacon

WATER SUPPLY. This article is confined to the collection and storage of water for domestic and industrial uses and irrigation, and its purification on a large scale The conveyance of water is dealt with in the article Aqueduct.

Collecting Areas

Surface Waters.—Any area, large or small, of the earth’s surface from any part of which, if the ground were impermeable, water would flow by gravitation past any point in a natural watercourse is commonly known in Europe as the “hydrographic basin” above that point. In English it has been called indifferently the “catchment basin,” the “gathering ground,” the “drainage area” and the “watershed.” The latter term, though originally equivalent to the German Wasserscheide—“water-parting”—is perhaps least open to objection. The water-parting is the line bounding such an area and separating it from other watersheds. The banks of a watercourse or sides of a valley are distinguished as the right and left bank respectively, the spectator being understood to be looking down the valley.

The surface of the earth is rarely impermeable, and the structure of the rocks largely determines the direction of flow of so much of the rainfall as sinks into the ground and is not evaporated. Thus the figure and area of a surface watershed may not be coincident with that of the corresponding underground watershed; and the flow in any watercourse, especially from a small watershed, may, by reason of underground flow from or into other watersheds, be disproportionate to the area apparently drained by that watercourse.

When no reservoir exists, the volume of continuous supply from any watershed area is evidently limited to the minimum, or, so-called, extreme dry weather flow of the stream draining it. This cannot be determined from the rainfall; it entirely depends upon the power of the Dry weather flow
of stream.
soil and rock to store water in the particular area under consideration, and to yield it continuously to the stream by means of concentrated springs or diffused seepage. Mountain areas of 10,000 acres and upwards, largely covered with moorland, upon nearly impermeable rocks with few water-bearing fissures, yield in temperate climates, towards the end of the driest seasons, and therefore solely from underground, between a fifth and a quarter of a cubic foot per second per 1000 acres. Throughout the course of the river Severn, the head-waters of which are chiefly supplied from such formations, this rate does not materially change, even down to the city of Worcester, past which the discharge flows from 1,256,000 acres. But in smaller areas, which on the average arc necessarily nearer to the water-parting, the limits are much wider, and the rate of minimum discharge is generally smaller.

Thus, for example, on 1000 acres or less, it commonly falls to one-tenth of a cubic foot, and upon an upland Silurian area of 940 acres, giving no visible sign of any peculiarity, the discharge fell, on the 21st of September 1893, to one-thirty-fifth of a cubic foot per second per 1000 acres. In this case, however, some of the water probably passed through the beds and joints of rocks to an adjoining valley lying at a lower level, and had both streams been gauged the average would probably have been considerably greater. The Thames at Teddington, fed largely from cretaceous areas, fell during ten days in September 1898 (the artificial abstractions for the supply of London being added) to about one-sixth of a cubic foot, and since 1880 the discharge has occasionally fallen, in each of six other cases, to about one-fifth of a cubic foot per second per 1000 acres. Owing, however, to the very variable permeability of the strata, the tributaries of the Thames, when separately gauged in dry seasons, yield the most divergent results. It may be taken as an axiom that the variation of minimum discharges from their mean values increases as the separate areas diminish. In the eastern and south-eastern counties of England even greater variety of dry weather flow prevails than in the west, and upon the chalk formations there are generally no surface streams, except such as burst out after wet weather and form the so-called “bournes.” On the other hand, some rocks in mountain districts, notably the granites, owing to the great quantity of water stored in their numerous fissures or joints, commonly yield a much higher proportion of so-called dry weather flow.

When, however, a reservoir is employed to equalize the flow during and before the period of dry weather, the minimum flow continuously available may be increased to a much higher figure, depending upon the capacity of that reservoir in relation to the mean flow of the stream supplying Rainfall. it. In such a case the first essential in determining the yield is to ascertain the rainfall. For this purpose, if there are no rain-gauges on the drainage area in question, an estimate may be formed from numerous gaugings throughout the country, most of which are published in British Rainfall, initiated by the late Mr G. J. Symons, F.R.S., and now carried on by Dr H. R. Mill.[1] But except in the hands of those who have spent years in such investigations, this method may lead to most incorrect conclusions. If any observations exist upon the drainage area itself they are commonly only from a single gauge, and this gauge, unless the area is very level, may give results widely different from the mean fall on the whole area. Unqualified reliance upon single gauges in the past has been the cause of serious errors in the estimated relation between rainfall and flow off the ground.

The uncertainties are illustrated by the following actual example: A battery of fourteen rain-gauges, in the same vertical plane, on ground having the natural profile shown by the section (fig. 1), gave during three consecutive years the respective falls shown by the height of the dotted lines above the datum line.

Fig. 1.

Thus on the average, gauge C recorded 20% more than gauge D only 70 ft. distant; while at C, in 1897, the rainfall was actually 30% greater than at J only 560 ft. away. The greatly varying distribution of rainfall over that length of 1600 ft. is shown by the dotted lines measured upwards from the datum to have been remarkably consistent in the three years; and its cause—the path necessarily taken in a vertical plane by the prevailing winds blowing from A towards N—after passing the steep bank at C D—may be readily understood. Such examples show the importance of placing any rain-gauge, so far as possible, upon a plane surface of the earth—horizontal, or so inclined that, if produced, especially in the direction of prevailing winds, it will cut the mean levels of the area whose mean rainfall is intended to be represented by that gauge. It has been commonly stated that rainfall increases with the altitude. This is broadly true. A rain-cloud raised vertically upwards expands, cools and tends to precipitate; but in the actual passage of rain-clouds over the surface of the earth other influences are at work.

Fig. 2.

In fig. 2 the thick line represents the profile of a vertical section crossing two ranges of hills and one valley. The arrows indicate the directions of the prevailing winds. At the extreme left the rain-clouds are thrown up, and if this were all, they would precipitate a larger proportion of the moisture they contained as the altitude increased. But until the clouds rise above the hill there is an obvious countervailing tendency to compression, and in steep slopes this may reduce or entirely prevent precipitation until the summit is reached, when a fall of pressure with commotion must occur. Very high mountain ranges usually consist of many ridges, among which rain-clouds are entangled in their ascent, and in such cases precipitation towards the windward side of the main range, though on the leeward sides of the minor ridges of which it is formed, may occur to so large an extent that before the summit is reached the clouds are exhausted or nearly so, and in this case the total precipitation is less on the leeward than on the windward side of the main range; but in the moderate heights of the United Kingdom it more commonly happens from the causes explained that precipitation is prevented or greatly retarded until the summit of the ridge is reached. The following cause also contributes to the latter effect. Imagine eleven raindrops A to K to fall simultaneously and equi-distantly from the horizontal plane A M. A strong wind is urging the drops from left to right. The drops A and K may be readily conceived to be equally diverted by the wind, and to fall near the tops of the two hills respectively. Not so drop C, for directly the summit is passed the wind necessarily widens out vertically and, having a greater space to fill, loses forward velocity. It may even eddy backwards, as indicated by the curved arrows, and it is no uncommon thing, in walking up a steep hill in the contrary direction to the flight of the clouds, to find that the rain is coming from behind. Much the same tendency exists with respect to all drops between B and E, but at F the wind has begun to accommodate itself to the new regime and to assume more regular forward motion, and as J is approached, where vertical contraction of the passage through which the wind must pass takes place, there is an increasing tendency to lift the raindrops beyond their proper limits. The general effect is that the rain falling from between G and K is spread over a greater area of the earth G′K′ than that falling from the equal space between B and F, which reaches the ground within the smaller area B′F′. From this cause also, therefore, the leeward side of the valley receives more rain than the windward side. In the United Kingdom the prevailing winds are from the south-west, and some misapprehension has been caused by the bare, but perfectly correct, statement that the general slope towards the western coast is wetter than that towards the eastern. Over the whole width of the country from coast to coast, or of the Welsh mountain ranges only, this is so; but it is nevertheless true that the leeward side of an individual valley or range of hills generally receives more rain than the windward side. Successive abstraction of raindrops as the rain-clouds pass over ridge after ridge causes a gradually diminishing precipitation, but this is generally insufficient to reverse the local conditions, which tend to the contrary effect in individual ranges. The neglect of these facts has led to many errors in estimating the mean rainfall on watershed areas from the fall observed at gauges in particular parts of those areas.

In the simplest case of a single mountain valley to be used for the supply of an impounding reservoir, the rainfall should be known at five points, three being in the axis of the valley, of which one is near the point of intersection of that axis with the boundary of the watershed. Then, in order to connect with these the effect of the right- and left-hand slopes, there should be at least one gauge on each side about the middle height, and approximately in a line perpendicular to the axis of the valley passing through the central gauge. The relative depths recorded in the several gauges depend mainly upon the direction of the valley and steepness of the bounding hills. The gauge in the bottom of the valley farthest from the source will in a wide valley generally record the least rainfall, and one of those on the south-west side, the highest. Much will depend upon the judicious placing of the gauges. Each gauge should have for 10 or 15 yds. around it an uninterrupted plane fairly representing the general level or inclination, as the case may be, of the ground for a much larger distance around it. The earliest records of such gauges should be carefully examined, and if any apparently anomalous result is obtained, the cause should be traced, and when not found in the gauge itself, or in its treatment, other gauges should be used to check it. The central gauge is useful for correcting and checking the others, but in such a perfectly simple case as the straight valley above assumed it may be omitted in calculating the results, and if the other four gauges are properly placed, the arithmetical mean of their results will probably not differ widely from the true mean for the valley. But such records carried on for a year or many years would afford no knowledge of the worst conditions that could arise in longer periods, were it not for the existence of much older gauges not far distant and subject to somewhat similar conditions. The nearer such long-period gauges are to the local gauges the more likely are their records to rise and fall in the same proportion. The work of the late Mr James Glaisher, F.R.S., of the late Mr G. J. Symons, F.R.S., of the Meteorological Office and of the Royal Meteorological Society, has resulted in the establishment of a vast number of rain-gauges in different parts of the United Kingdom, and it is generally, though not always, found that the mean rainfall over a long period can be determined, for an area upon which the actual fall is known only for a short period, by assigning to the missing years of the short-period gauges, rainfalls bearing the same proportion to those of corresponding years in the long-period gauges, that the rainfalls of the known years in the short-period gauges bear to those of corresponding years in the long-period gauges. In making such comparisons, it is always desirable, if possible, to select as standards long-period gauges which are so situated that the short-period district lies between them. Where suitably placed long-period gauges exist, and where care has been exercised in ascertaining the authenticity of their records and in making the comparisons, the short records of the local gauges may be thus carried back into the long periods with nearly correct results.

Rainfall is proverbially uncertain; but it would appear from the most trustworthy records that at any given place the total rainfall during any period of 50 years will be within 1 or 2% of the total rainfall at the same place during any other period of 50 years, while the records of any period of 25 years will generally be found to fall within 3 1/2% of the mean of 50 years. It is equally satisfactory to know that there is a nearly constant ratio on any given area (exceeding perhaps 1000 acres) between the true mean annual rainfall, the rainfall of the driest year, the two driest consecutive years and any other groups of driest consecutive years. Thus in any period of 50 years the driest year (not at an individual gauge but upon such an area) will be about 63% of the mean for the 50 years.

That in the two driest consecutive years will be about 75% of the mean for the 50 years.

That in the three driest consecutive years will be about 80% of the mean for the 50 years.

That in the four driest consecutive years will be about 83% of the mean for the 50 years.

That in the five driest consecutive years will be about 85% of the mean for the 50 years.

That in the six driest consecutive years will be about 86 1/2% of the mean for the 50 years.

Apart altogether from the variations of actual rainfall produced by irregular surface levels, the very small area of a single rain-gauge is subject to much greater variations in short periods than can possibly occur over larger areas. If, therefore, instead of regarding only the mean rainfall of several gauges over a series of years, we compare the relative falls in short intervals of time among gauges yielding the same general averages, the discrepancies prove to be very great, and it follows that the maximum possible intensity of discharge from different areas rapidly increases as the size of the watershed decreases. Extreme cases of local discharge are due to the phenomena known in America as “cloud-bursts,” which occasionally occur in Great Britain and result in discharges, the intensities of which have rarely been recorded by rain-gauges. The periods of such discharges are so short, their positions so isolated and the areas affected so small, that we have little or no exact knowledge concerning them, though their disastrous results are well known. They do not directly affect the question of supply, but may very seriously affect the works from which that supply is given.

Where in this article the term “evaporation” is used alone, it is to be understood to include absorption by vegetation. Of the total quantity of rainfall a very variable proportion is rapidly absorbed or re-evaporated. Thus in the western mountain districts of Great Britain, Evaporation and absorption. largely composed of nearly impermeable rocks more or less covered with pasture and moorland, the water evaporated and absorbed by vegetation is from 13 to 15 in. out of a rainfall of 80 in., or from 16 to 19%, and is nearly constant down to about 60 in., where the proportion of loss is therefore from 22 to 25%. The Severn down to Worcester, draining 1,256,000 acres of generally flatter land largely of the same lithological character, gave in the dry season from the 1st of July 1887 to the 30th of June 1888 a loss of 17·93 in. upon a rainfall of 27·34 in. or about 66%; while in the wet season, 1st of July 1882 to the 30th of June 1883, the loss was 21·09 in. upon a rainfall of 43·26 in., or only 49%. Upon the Thames basin down to Teddington, having an area of 2,353,000 acres, the loss in the dry season from the 1st of July 1890 to the 30th of June 1891 was 17·22 in. out of a rainfall of 21·62 in., or 79%; while in the wet season, 1st of July 1888 to the 30th of June 1889, it was 18·96 out of 29·22 in., or only 65%. In the eastern counties the rainfall is lower and the evaporation approximately the same as upon the Thames area, so that the percentage of loss is greater. But these are merely broad examples and averages of many still greater variations over smaller areas. They show generally that, as the rainfall increases on any given area evaporation increases, but not in the same proportion. Again, the loss from a given rainfall depends greatly upon the previous season. An inch falling in a single day on a saturated mountain area will nearly all reach the rivers, but if it falls during a drought seven-eighths may be lost so far as the period of the drought is concerned. In such a case most of the water is absorbed by the few upper inches of soil, only to be re-evaporated during the next few days, and the small proportion which sinks into the ground probably issues in springs many months later. Thus the actual yield of rainfall to the streams depends largely upon the mode of its time-distribution, and without a knowledge of this it is impossible to anticipate the yield of a particular rainfall. In estimating the evaporation to be deducted from the rainfall for the purpose of determining the flow into a reservoir, it is important to bear in mind that the loss from a constant water surface is nearly one and a half times as great as from the intermittently saturated land surface. Even neglecting the isolated and local discharges due to excessive and generally unrecorded rainfall, the variation in the discharge of all streams, and especially of mountain streams, is very great. We have seen that the average flow from mountain areas in Great Britain towards the end of a dry season does not exceed one-fifth of a cubic foot per second per 1000 acres. Adopting this general minimum as the unit, we find that the flow from such areas up to about 5000 acres, whose mean annual rainfall exceeds 50 in., may be expected occasionally to reach 300 cub. ft., or 1500 such units; while from similar areas of 20,000 or 30,000 acres with the same mean rainfall the discharge sometimes reaches 1200 or 1300 such units. It is well to compare these results with those obtained from much larger areas but with lower mean rainfall. The Thames at Teddington has been continuously gauged by the Thames Conservators since 1883, and the Severn at Worcester by the writer, on behalf of the corporation of Liverpool, during the 10 years 1881 to 1890 inclusive. The highest flood, common to the two periods, was that which occurred in the middle of February 1883. On that occasion the Thames records gave a discharge of 7·6 cub. ft. per second per 1000 acres, and the Severn records a discharge of 8·6 cub. ft. per second per 1000 acres, or 38 and 43 respectively of the above units; while in February 1881, before the Thames gaugings were commenced, the Severn had risen to 47 of such units, and subsequently in May 1886 rose to 50 such units, though the Thames about the same time only rose to 13. But in November 1894 the Thames rose to about 80 such units, and old records on the Severn bridges show that that river must on many occasions have risen to considerably over 100 units. In both these cases the natural maximum discharge is somewhat diminished by the storage produced by artificial canalization of the rivers.

These illustrations of the enormous variability of discharge serve to explain what is popularly so little understood, namely, the advantage which riparian owners, or other persons interested in a given stream, may derive from works constructed primarily for the purpose of diverting Compensation water.the water of that stream—it may be to a totally different watershed—for the purposes of a town supply. Under modern legislation no such abstraction of water is usually allowed, even if limited to times of flood, except on condition of an augmentation of the natural dry-weather flow, and this condition at once involves the construction of a reservoir. The water supplied to the stream from such a reservoir is known as “compensation water,” and is generally a first charge upon the works. This water is usually given as a continuous and uniform flow, but in special cases, for the convenience of mill-owners, as an intermittent one.[2] In the manufacturing districts of Lancashire and Yorkshire it generally amounts to one-third of the whole so-called “available supply.” In Wales it is usually about one-fourth, and elsewhere still less; but in any case it amounts to many times the above unit of one-fifth of a cubic foot per second per 1000 acres. Thus the benefit to the fisheries and to the riparian owners generally is beyond all question; but the cost to the water authority of conferring that benefit is also very great—commonly (according to the proportion of the natural flow intended to be rendered uniform) 20 to 35% of the whole expenditure upon the reservoir works. Down to the middle of the 19th century, the proportioning of the size of a Yield of stream
with reservoir.
reservoir to its work was a very rough operation. There were few rainfall statistics, little was known of the total loss by evaporation, and still less of its distribution over the different periods of dry and wet weather. Certain general principles have since been laid down, and within the proper limits of their application have proved excellent guides. In conformity with the above-mentioned convention (by which compensation water is determined as a certain fraction of the average flow during the three driest consecutive years) the available supply or flow from a given area is still understood to be the average annual rainfall during those years, less the corresponding evaporation and absorption by vegetation. But this is evidently only the case when the reservoir impounding the water from such an area is of just sufficient capacity to equalize that flow without possible exhaustion in any one of the three summers. If the reservoir were larger it might equalize the flow of the four or more driest consecutive years, which would be somewhat greater than that of the three; if smaller, we might only be able to count upon the average of the flow of the two driest consecutive years, and there are many reservoirs which will not yield continuously the average flow of the stream even in the single driest year. With further experience it has become obvious that very few reservoirs are capable of equalizing the full flow of the three consecutive driest years, and each engineer, in estimating the yield of such reservoirs, has deducted from the quantity ascertained on the assumption that they do so, a certain quantity representing, according to his judgment, the overflow which in one or more of such years might be lost from the reservoir. The actual size of the reservoir which would certainly yield the assumed supply throughout the driest periods has therefore been largely a matter of judgment. Empirical rules have grown up assigning to each district, according to its average rainfall, a particular number of days’ supply, independently of any inflow, as the contents of the reservoir necessary to secure a given yield throughout the driest seasons. But any such generalizations are dangerous and have frequently led to disappointment and sometimes to needless expenditure. The exercise of sound judgment in such matters will always be necessary, but it is nevertheless important to formulate, so far as possible, the conditions upon which that judgment should be based. Thus in order to determine truly the continuously available discharge of any stream, it is necessary to know not only the mean flow of the stream, as represented by the rainfall less the evaporation, but also the least favourable distribution of that flow throughout any year.

The most trying time-distribution of which the author has had experience in the United Kingdom, or which he has been able to discover from a comparison of rainfalls upon nearly impermeable areas exceeding 1000 acres, is graphically represented by the thick irregular line in the left-hand half of fig. 3, where the total flow for the driest year measures 100 on the vertical percentage scale; the horizontal time scale being divided into calendar months.

The diagram applies to ordinary areas suitable for reservoir construction and in which the minimum flow of the stream reaches about one-fifth of a cubic foot per second per 1000 acres. Correspondingly, the straight line a a represents uniformly distributed supply, also cumulatively recorded, of the same quantity of water over the same period. But, apart from the diurnal fluctuations of consumption which may be equalized by local “service reservoirs,” uniform distribution of supply throughout twelve months is rarely what we require; and to represent the demand in most towns correctly, we should increase the angle of this line to the horizontal during the summer and diminish it during the winter months, as indicated by the dotted lines b b. The most notable features of this particular diagram are as follows: Up to the end of 59 days (to the 28th February) the rate of flow is shown, by the greater steepness of the thick line, to be greater than the mean for the year, and the surplus water—about 11% of the flow during the year—must be stored; but during the 184 days between this and the end of the 243rd day (31st August) the rate of flow is generally below the mean, while from that day to the end of the year it is again for the most part above the mean. Now, in order that a reservoir may enable the varying flow, represented cumulatively by the irregular line, to be discharged in a continuous and uniform flow to satisfy a demand represented cumulatively by the straight line a a, its capacity must be such that it will hold not only the 11 % surplus of the same year, but that, on June 10th, when this surplus has been used to satisfy the demand, it will still contain the water c d—19%—stored from a previous year; otherwise between June 10th and August 31st the reservoir will be empty and only the dry weather flow of the stream will be available for supply. In short, if the reservoir is to equalize the whole flow of this year, it must have a capacity equal to the greatest deficiency c d of the cumulative flow below the cumulative demand, plus the greatest excess e f of the cumulative flow over the cumulative demand. This capacity is represented by the height of the line aa′ (drawn parallel to a a from the point of maximum surplus f) vertically above the point of greatest deficiency c, and equal, on the vertical scale, to the difference between the height c = 48% and g = 78% or 30% of the stream-flow during the driest year. A reservoir so proportioned to the stream-flow with a proper addition to avoid drawing off the bottom water, would probably be safe in Great Britain in any year for a uniform demand equal to the cumulative stream-flow; or, if it failed, that failure would be of very short duration, and would probably only occur once in 50 years.

Fig. 3.

It may be at first sight objected that a case is assumed in which there is no overflow before the reservoir begins to fall, and therefore no such loss as generally occurs from that cause. This is true, but it is only so because we have made our reservoir large enough to contain in addition to its stock of 19% at the beginning of the year, all the surplus water that passes during the earlier months in this driest year with its least favourable time-distribution of flow. Experience shows, in fact, that if a different distribution of the assumed rainfall occurs, that distribution will not try the reservoir more severely while the hitherto assumed uniform rate of demand is maintained. But, as above stated, the time-distribution of demand is never quite uniform. The particular drought shown on the diagram is the result of an exceptionally early deficiency of rainfall which, in conjunction with the variation of demand shown by the dotted line b b, is the most trying condition. The reservoir begins to fall at the end of February, and continues to do so with few and short exceptions until the end of August, and it so happens that about the end of August this dotted line, b b representing actual cumulative demand, crosses the straight line a a of uniform demand, so that the excess of demand, represented by the slope from June to September, is balanced by the deficiency of demand, represented by the flatter slope in the first five months, except as regards the small quantity b e near the end of February, which, not having been drawn off during January and February, must overflow before the end of February. To avoid this loss the 11% is in this case to be increased by the small quantity b e determined by examination of the variation of the actual from a constant demand. After the reservoir begins to fall—in this case at the end of February—no ordinary change in the variation of demand can affect the question, subject of course to the cumulative demand not exceeding the reservoir yield for the assumed year of minimum rainfall. In assuming a demand at the beginning of the year below the mean, resulting in an overflow equal in this case to b e at the end of February and increasing our reservoir to meet it, we assume also that some additional supply to that reservoir beyond the 11% of the stream-flow from the driest year can be obtained from the previous year. In relation to this supply from the previous year the most trying assumption is that the rainfall of that year, together with that of the driest year, will be the rainfall of the two driest consecutive years. We have already seen that while the rainfall of the driest of 50 years is about 63% of the mean, that of the driest two consecutive years is about 75% of the mean. It follows, therefore, that the year immediately preceding the driest cannot have a rainfall less than about 87% of the mean. As the loss by evaporation is a deduction lying between a constant figure and a direct proportional to the rainfall, we should err on the safe side in assuming the flow in the second driest year to be increased proportionally to the rainfall, or by the difference between 63 and 87 equal to 24% of the mean of 50 years. This 24% of the 50 years’ mean flow is 38% of the driest year’s flow in fig. 3, and is therefore much more than sufficient to ensure the reservoir beginning the driest year with a stock equal to the greatest deficiency—19%—of the cumulative flow of that year beyond the cumulative demand.

But in determining the capacity of reservoirs intended to yield a supply of water equal to the mean flow of two, three or more years, the error, though on the safe side, caused by assuming the evaporation to be proportional to the rainfall, is too great to be neglected. The evaporation slightly increases as the rainfall increases, but at nothing like so high a rate. Having determined this evaporation for the second driest consecutive year and deducted it from the rainfall—which, as above stated, cannot be less than 87% of the mean of 50 years—we may, as shown on fig. 3, extend our cumulative diagram of demand and flow into the reservoir from one to two years.

The whole diagram shows, by the greater gradient of the unbroken straight lines, the greater demand which can be satisfied by the enlargement of the reservoir to the extent necessary to equalize the flow of the two driest consecutive years. The new capacity is either c h or ch′, whichever, in the particular case under investigation, is the greater. In the illustration the ch′ is a little greater, measuring 47 1/2% of the flow of the driest year. In the same way we may group in a single diagram any number of consecutive driest years, and either ascertain the reservoir capacity necessary for a given uniform yield (represented cumulatively by a straight line corresponding with a′ a′ , but drawn over all the years instead of one), or conversely, having set up a vertical from the most trying point in the line of cumulative flow (c or c′ in fig. 3—representing, in percentage of the total annual flow of the driest year, the capacity of reservoir which it may be convenient to provide) we may draw a straight line a′′′ a′′′ of uniform yield from the head of that vertical to the previous point of maximum excess of cumulative flow. The line a′′ a′′ drawn from zero parallel to the first line, produced to the boundaries of the diagram, will cut the vertical at the end of the first year at the percentage of the driest year’s flow which may be safely drawn continuously from the reservoir throughout the two years. It is to be observed that any irregularity in the rate of supply from the reservoir may occur between the critical periods of maximum excess of cumulative flow and maximum deficiency of cumulative flow (f and c respectively, in the one year diagram) which does not increase the aggregate cumulative supply between those points, or cause the line of cumulative supply from the reservoir to cut the line of cumulative flow into it.

Note.—The figures in the right-hand column at the ends of the curved lines are inches of mean annual rainfall over a period of 50 years.

The co-ordinates to any point upon any curved line give respectively the required reservoir capacity and daily yield in gallons per acre of drainage area, corresponding with the mean annual rainfall represented by that curved line.

The curves have been drawn for a mean annual evaporation of 14 in. For any increased rate of evaporation 1¼ in. are to be subtracted from the rainfall for each inch of evaporation above 14 in. For any decreased rate of evaporation 1¼ in. are to be added to the rainfall for each inch of evaporation below 14 in.

Any excess of evaporation from the water surface and allowance for bottom water are to be added to the storage so found.

The period over which the reservoir equalizes the flow is shown by the number of years marked on the straight radial lines.

Where the absolute minimum stream flow is known to be greater than the minimum of 15 cubic foot per second per 1000 acres (108 gallons per acre per day) assumed in the diagram, the capacity of the reservoir as taken from the diagram may be reduced by the amount corresponding to that minimum flow for the particular rainfall and evaporation.

Fig. 4.

From diagrams constructed upon these principles, the general diagram (fig. 4) has been produced. To illustrate its use, assume the case of a mean rainfall of 50 in., figured in the right-hand column at the end of a curved line, and of 14 in. of evaporation and absorption by vegetation as stated in the note on the diagram. The ordinate to any point upon this curved line then represents on the left-hand scale the maximum continuous yield per day for each acre of drainage area, from a reservoir whose capacity is equal to the corresponding abscissa. As an example, assume that we can conveniently construct a reservoir to contain, in addition to bottom water not to be used, 200,000 gallons for each acre of the watershed above the point of interception by the proposed dam. We find on the left-hand scale of yield that the height of the ordinate drawn to the 50-inch mean rainfall curve from 200,000 on the capacity scale, is 1457 gallons per day per acre; and the straight radial line, which cuts the point of intersection of the curved line and the co-ordinates, tells us that this reservoir will equalize the flow of the two driest consecutive years. Similarly, if we wish to equalize the flow of the three driest consecutive years we change the co-ordinates to the radial line figured 3, and thus find that the available capacity of the reservoir must be 276,000 gallons per acre, and that In consideration of the additional expense of such a reservoir we shall increase the dally yield to 1612 gallons per acre. In the same manner it will be found that by means of a reservoir having an available capacity of only 118,000 gallons per acre of the watershed, we may with the same rainfall and evaporation secure a dally supply of 1085 gallons per acre. In this case the left-hand radial line passes through the point at which the coordinates meet, showing that the reservoir will just equalize the flow of the driest year. Similarly, the yield from any given reservoir, or the capacity required for any yield, corresponding with any mean rainfall from 30 to 100 in., and with the flow over any period, from the driest year to the six or more consecutive driest years, may be determined from the diagram.

It is instructive to note the ratio of increase of reservoir capacity and yield respectively for any given rainfall. Thus, assuming a mean rainfall of 60 in. during 50 years, subject to evaporation and absorption equal to 14 in. throughout the dry period under consideration, we find from the diagram the following quantities (in gallons per acre of drainage area) and corresponding ratios:—

Net Capacity of Reservoir. Yield of Reservoir.
Number of driest
consecutive years,
the flow of which
is equalized.

In gallons per
acre of drainage
In terms of
Reservoir equaliz-
ing one year’s
flow = 100.

Increase per cent
on each step.
Gallons per day.
In terms of yield
per driest year
= 100.

Increase per cent
on each step.
(1) (2) (3) (4) (5) (6) (7)
1 162,000 100 0  1475 100 0
2 256,000 158.0 58.0 1922 130.3 30.3
3 352,000 217.3 37.5 2108 142.9  9.7
4 416,000 256.8 18.2 2220 150.5  5.3
5 466,000 287.7 12.0 2294 155.5  3.3
6 504,000 311.1  8.1 2350 159.3  2.4

On comparing columns 3 and 6 or 4 and 7 it appears that so great is the increase required in the size of a reservoir in relation to its increased yield, that only in the most favourable places for reservoir construction, or under the most pressing need, can it be worth while to go beyond the capacity necessary to render uniform the flow of the two or three driest consecutive years.

It must be clearly understood that the diagram fig. 4 does not relieve the reader from any exercise of judgment, except as regards the net capacity of reservoirs when the necessary data have been obtained. It Is merely a geometrical determination of the conditions necessarily consequent in England, Scotland and Wales, upon a given mean rainfall over many years, upon evaporation and absorption in particular years (both of which he must judge or determine for himself), and upon certain limiting variations of the rainfall, already stated to be the result of numerous records maintained in Great Britain for more than 50 years. It must also be remembered that the total capacity of a reservoir must be greater than its net available capacity, in order that in the driest seasons fish life may be maintained and no foul water may be drawn off.

Applied to most parts of Ireland and some parts of Great Britain, the diagram will give results rather unduly on the safe side, as the extreme annual variations of rainfall are less than in most parts of Great Britain. Throughout Europe the annual variations follow nearly the same law as in Great Britain, but in some parts the distribution of rainfall in a single year is often more trying. The droughts are longer, and the rain, when it falls, especially along the Mediterranean coast, is often concentrated into shorter periods. Moreover, it often falls upon sun-heated rocks, thus increasing the evaporation for the time; but gaugings made by the writer in the northern Apennines indicate that this loss is more than compensated by the greater rapidity of the fall and of the consequent flow. In such regions, therefore, for reservoirs equalizing the flow of 2 or more years, the capacity necessary does not materially differ from that required in Great Britain. As the tropics are approached, even in mountain districts, the irregularities become greater, and occasionally the rainy season is entirely absent for a single year, though the mean rainfall is considerable.

We have hitherto dealt only with the collection and storage of that portion of the rainfall which flows over the surface of nearly impermeable areas. Upon such areas the loss by percolation into the ground, not retrieved in the form of springs above the point of interception Springs and
shallow wells.
may be neglected, and the only loss to the stream is that already considered of re-evaporation into the air and of absorption by vegetation. But the crust of the earth varies from almost complete impermeability to almost complete permeability. Among the sedimentary rocks we have, for example, in the clay slates of the Silurian formations, rocks no less cracked and fissured than others, but generally quite impermeable by reason of the joints being packed with the very fine clay resulting from the rubbing of slate upon slate in the earth movements to which the cracks are due. In the New Red Sandstone, the Greensand and the upper Chalk, we find the opposite extremes; while the igneous rocks are for the most part only permeable in virtue of the open fissures they contain. Wherever, below the surface, there are pores or open fissures, water derived from rainfall is (except in the rare cases of displacement by gas) found at levels above the sea determined by the resistance of solids to its passage towards some neighbouring sea, lake or watercourse. Any such level is commonly known as the level of saturation. The positions of springs are determined by permeable depressions in the surface of the ground below the general level of saturation, and frequently also by the holding up of that level locally by comparatively impermeable strata, sometimes combined with a fault or a synclinal fold of the strata, forming the more permeable portion into an underground basin or channel lying within comparatively impermeable boundaries. At the lower lips or at the most permeable parts of these basins or channels such rainfall as does not flow over the surface, or is not evaporated or absorbed by vegetation, and does not, while still below ground reach the level of the sea, issues as springs, and is the cause of the continued flow of rivers and streams during prolonged droughts. The average volume in dry weather, of such flow, generally reduced to terms of the fraction of a cubic foot per second, per thousand acres of the contributing area, is commonly known in water engineering as the “dry weather flow” and its volume at the end of the dry season as the “extreme dry weather flow.”

Perennial springs of large volume rarely occur in Great Britain at a sufficient height to afford supplies by gravitation; but from the limestones of Italy and many other parts of the world very considerable volumes issue far above the sea-level, and are thus available, without Deep Wells. pumping, for the supply of distant towns. On a small scale, however, springs are fairly distributed over the United Kingdom, for there are no formations, except perhaps blown sand, which do not vary greatly in their resistance to the percolation of water, and therefore tend to produce overflow from underground at some points above the valley levels. But even the rural populations have generally found surface springs insufficiently constant for their use and have adopted the obvious remedy of sinking wells. Hence, throughout the world we find the shallow well still very common in rural districts. The shallow well, however, rarely supplies enough water for more than a few houses, and being commonly situated near to those houses the water is often seriously polluted. Deep wells owe their comparative immunity from pollution to the circumstances that the larger quantity of water yielded renders it worth while to pump that water and convey it by pipes from comparatively unpolluted areas; and that any impurities in the water must have passed through a considerable depth, and by far the larger part of them through a great length of filtering material, and must have taken so long a time to reach the well that their organic character has disappeared. The principal water-bearing formations, utilized in Great Britain by means of deep wells, are the Chalk and the New Red Sandstone. The Upper and Middle Chalk are permeable almost through their mass. They hold water like a sponge, but part with it under pressure to fissures by which they are intersected, and, in the case of the Upper Chalk, to ducts following beds of flints. A well sunk in these formations without striking any fissure or water-bearing flint bed, receives water only at a very slow rate; but if, on the other hand, it strikes one or more of the natural water-ways, the quantity of water capable of being drawn from it will be greatly increased.

It is a notable peculiarity of the Upper and Middle Chalk formations that below their present valleys the underground water passes more freely than elsewhere. This is explained by the fact that the Chalk fissures are almost invariably rounded and enlarged by the erosion of carbonic acid carried from the surface by the water passing through them. These fissures take the place of the streams in an impermeable area, and those beneath the valleys must obviously be called upon to discharge more water from the surface, and thus be brought in contact with more carbonic acid, than similar fissures elsewhere. Hence the best position for a well in the Chalk is generally that over which, if the strata were impermeable, the largest quantity of surface water would flow. The Lower Chalk formation is for the most part impermeable, though it contains many ruptures and dislocations or smashes, in the interstices of which large bodies of water, received from the Upper and Middle Chalk, may be naturally stored, or which may merely form passages for water derived from the Upper Chalk. Thus despite the impermeability of its mass large springs are occasionally found to issue from the Lower Chalk. A striking example is that known as Lydden Spout, under Abbot’s Cliff, near Dover. In practice it is usual in chalk formations to imitate artificially the action of such underground watercourses, by driving from the well small tunnels, or “adits” as they are called, below the water-level, to intercept fissures and water-bearing beds, and thus to extend the collecting area.

Next in importance to the Chalk formations as a source of underground water supply comes the Trias or New Red Sandstone, consisting in Great Britain of two main divisions, the Keuper above and the Bunter below. With the exception of the Red Marls forming the upper part of the Keuper, most of the New Red Sandstone is permeable, and some parts contain, when saturated, even more water than solid chalk; but, just as in the case of the chalk, a well or borehole in the sandstone yields very little water unless it strikes a fissure; hence, in New Red Sandstone, also, it is a common thing to form underground chambers or adits in search of additional fissures, and sometimes to sink many vertical boreholes with the same object in view.

As the formation approaches the condition of pure sand, the water-bearing property of any given mass increases, but the difficulty of drawing water from it without admixture of sand also increases. In sand below water there are, of course, no open fissures, and even if adits could be Wells in sand. usefully employed, the cost of constructing and lining them through the loose sand would be prohibitive. The well itself must be lined; and its yield is therefore confined to such water as can be drawn through the sides or the bottom of the lining without setting up a sufficient velocity to cause any sand to flow with the water. Hence it arises that, in sand formations, only shallow wells or small boreholes are commonly found. Imagine for a moment that the sand grains were by any means rendered immobile without change in the permeability of their inter spaces; we could then dispense with the iron or brickwork lining of the well; but as there would still be no cracks or fissures to extend the area of percolating water exposed to the open well, the yield would be very small. Obviously, it must be very much smaller when the lining necessary to hold up loose sand is used. Uncemented brickwork, or perforated ironwork, are the usual materials employed for lining the well and holding up the sand, and the quantity of water drawn is kept below the comparatively small quantity necessary to produce a velocity, through the joints or orifices, capable of disturbing the sand. The rate of increase of velocity towards any isolated aperture through which water passes into the side of a well sunk in a deep bed of sand is, in the neighbourhood of that aperture, inversely proportional to the square of the distance therefrom. Thus, the velocity across a little hemisphere of sand only 1/2 in. radius covering a 1-in. orifice in the lining is more than 1000 times the mean velocity of the same water approaching the orifice radially when 16 in. therefrom. This illustration gives some idea of the Artificial increase
of yield.
enormous increase of yield of such a well, if, by any means, we can get rid of the frictional sand, even from within the 16 in. radius. We cannot do this, but happily the grains in a sand formation differ very widely in diameter, and if, from the interstices between the larger grains in the neighbourhood of an orifice, we can remove the finer grains, the resistance to flow of water is at once enormously reduced. This was for the first time successfully done in a well, constructed by the Biggleswade Water Board in 1902, and now supplying water over a large area of North Bedfordshire. This well, 10 ft. diameter, was sunk through about 110 ft. of surface soil, glacial drift and impermeable gault clay and thence passed for a further depth of 70 ft. into the Lower Greensand formation, the outcrop of which, emerging on the south-eastern shore of the Wash, passes south-westwards, and in Bedfordshire attains a thickness exceeding 250 ft. The formation is probably more or less permeable throughout; it consists largely of loose sand and takes the general south-easterly dip of British strata. The Biggleswade well was sunk by processes better known in connexion with the sinking of mine shafts and foundations of bridges across the deep sands or gravels of bays, estuaries and great rivers. Its full capacity has not been ascertained; it much exceeds the present pumping power, and is probably greater than that of any other single well unassisted by adits or boreholes. This result is mainly due to the reduction of frictional resistance to the passage of water through the sand in the immediate neighbourhood of the well, by washing out the finer particles of sand and leaving only the coarser particles. For this purpose the lower 45 ft. of the cast-iron cylinders forming the well was provided with about 660 small orifices lined with gun-metal tubes or rings, each armed with numerous thicknesses of copper wire gauze, and temporarily closed with screwed plugs. On the removal of any plug, this wire gauze prevented the sand from flowing with the water into the well; but while the finer particles of sand remained in the neighbourhood of the orifice, the flow of water through the contracted area was very small. To remove this obstruction the water was pumped out while the plugs kept the orifices closed. A flexible pipe, brought down from a steam boiler above, was then connected with any opened orifice. This pipe was provided, close to the orifice, with a three-way cock, by means of which the steam might be first discharged into the sand, and the current between the cock and the well then suddenly reversed and diverted into the well. The effect of thus alternately forcing high-pressure steam among the sand, and of discharging high-pressure water contained in the sand into the well, is to break up any cohesion of the sand, and to allow all the finer particles in the neighbourhood of the orifice to rush out with the water through the wire gauze into the well. This process, in effect, leaves each orifice surrounded by a hemisphere of coarse sand across which the water flows with comparative freedom from a larger hemisphere where the corresponding velocity is very slow, and where the presence of finer and more obstructive particles is therefore unimportant. Many orifices through which water at first only dribbled were thus caused to discharge water with great force, and entirely free from sand, against the opposite side of the well, while the general result was to increase the inflow of water many times, and to entirely prevent the intrusion of sand. Where, however, a firm rock of any kind is encountered, the yield of a well (under a given head of water) can only be increased by enlargement of the main well in depth or diameter, or by boreholes or adits. No rule as to the adoption of any one of these courses can be laid down, nor is it possible, without examination of each particular case, to decide whether it is better to attempt to increase the yield of the well or to construct an additional well some distance away. By lowering the head of water in any well which draws its supply from porous rock, the yield is always temporarily increased. Every well has its own particular level of water while steady pumping at a given rate is going on, and if that level is lowered by harder pumping, it may take months, or even years, for the water in the interstices of the rock to accommodate itself to the new conditions; but the permanent yield after such lowering will always be less than the quantity capable of being pumped shortly after the change. We have hitherto supposed the pumps for drawing the water to have been placed in the well at such a level as to be accessible, while the Pumps in boreholes. suction pipe only is below water. Pumps, however, may be (and and have been) placed deep down in boreholes, so that water may be pumped from much greater depths. By this means the head of pressure in the boreholes tending to hold the water back in the rock is reduced, and the supply consequently increased; but when the cost of maintenance is included, the increased supply from the adoption of this method rarely justifies expectations. When the water has been drawn down by pumping to a lower level its passage through the sandstone or chalk in the neighbourhood of the borehole is further resisted by the smaller length of borehole below the water; and there are many instances in which repeated lowering and increased pumping, both from wells and boreholes, have had the result of reducing the water available, after a few years, nearly to the original quantity. One other method—the Air-lift. use of the so-called “air-lift”—should be mentioned. This ingenious device originated in America. The object attained by the air-lift is precisely the same as that attained by putting a pump some distance down a borehole; but instead of the head being reduced, by means of the pump, it is reduced by mixing the water with air. A pipe is passed down the borehole to the desired depth, and connected with air-compressors at the surface. The compressors being set to work, the air is caused to issue from the lower end of the pipe and to mix in fine bubbles with the rising column of water, sometimes several hundred feet in height. The weight of the column of water, or rather of water and air mixed, is thus greatly reduced. The method will therefore always increase the yield for the time, and it may do so permanently, though to a very much smaller extent than at first; but its economy must always be less than that of direct pumping.

In considering the principles of well supplies it is important to bear the following facts in mind. The crust of the earth, so far as it is permeable and above the sea-level, receives from rainfall its supply of fresh water. That supply, so far as it is not evaporated or absorbed by vegetation, passes away by the streams or rivers, or sinks into the ground. If the strata were uniformly porous the water would lie in the rock at different depths below the surface according to the previous quantity and distribution of the rainfall. It would slowly, but constantly, percolate downwards and towards the sea, and would ooze out at or below the sea-level, rarely regaining the earth’s surface earlier except in deep valleys. Precisely the same thing happens in the actual crust of the earth, except that, in the formations usually met with, the strata are so irregularly permeable that no such uniform percolation occurs, and most of the water, instead of oozing out near the sea-level, meets with obstructions which cause it to issue, sometimes below the sea-level and sometimes above it, in the form of concentrated springs. After prolonged and heavy rainfall the upper boundary of the sub-soil water is, except in high ground, nearly coincident with the surface. After prolonged droughts it still retains more or less the same figure as the surface, but at lower depths and always with less pronounced differences of level.

Sedimentary rocks, formed below the sea or salt lagoons, must originally have contained salt water in their interstices. On the upheaval of such rocks above the sea-level, fresh water from rainfall began to flow over their exposed surfaces, and, so far as the strata were permeable, to lie in their Saline water below ground. interstices upon the salt water. The weight of the original salt water above the sea-level, and of the fresh water so superimposed upon it, caused an overflow towards the sea. A hill, as it were, of fresh water rested in the interstices of the rock upon the salt water, and continuing to press downwards, forced out the salt water even below the level of the sea. Subject to the rock being porous this process would be continued until the greater column of the lighter fresh water balanced the smaller head of sea water. It would conceivably take but a small fraction of the period that has in most cases elapsed since such upheavals occurred for the salt water to be thus displaced by fresh water, and for the condition to be attained as regards saturation with fresh water, in which with few exceptions we now find the porous portions of the earth’s crust wherever the rainfall exceeds the evaporation. There are cases, however, as in the valley of the Jordan, where the ground is actually below the sea-level, and where, as the total evaporation is equal to or exceeds the rainfall, the lake surfaces also are below the sea-level. Thus, if there is any percolation between the Mediterranean and the Dead Sea, it must be towards the latter. There are cases also where sedimentary rocks, formed below the sea or salt lagoons, are almost impermeable: thus the salt deposited in parts of the Upper Keuper of the New Red Sandstone, is protected by the red marls of the formation, and has never been washed out. It is now worked as an important industry in Cheshire.

Perhaps the most instructive cases of nearly uniform percolation in nature are those which occur in some islands or peninsulas formed wholly of sea sand. Here water is maintained above the sea-level by the annual rainfall, and may be drawn off by wells or borings. On such an island, Wells in sand. in the centre of which a borehole is put down, brackish water may be reached far below the sea-level; the salt water forming a saucer, as it were, in which the fresh water lies. Such a salt-water saucer of fresh water is maintained full to overflowing by the rainfall, and owing to the frictional resistance of the sand and to capillary action and the fact that a given column of fresh water is balanced by a shorter column of sea water, the fresh water never sinks to the mean sea-level unless artificially abstracted.

Although such uniformly permeable sand is rarely met with in great masses, it is useful to consider in greater detail so simple a case. Let the irregular thick line in fig. 5 be the section of a circular island a mile and a quarter in diameter, of uniformly permeable sand.

Fig. 5.

The mean sea-level is shown by the horizontal line aa, dotted where it passes through the land, and the natural mean level of saturation bb, above the sea-level, by a curved dot and dash line. The water, contained in the interstices of the sand above the mean sea-level, would (except in so far as a film, coating the sand particles, is held up by capillary attraction) gradually sink to the sea-level if there were no rainfall. The resistance to its passage through the sand is, however, sufficiently great to prevent this from occurring while percolation of annual rainfall takes place.

Hence we may suppose that a condition has been attained in which the denser salt water below and around the saucer CC (greatly exaggerated in vertical scale) balances the less dense, but deeper fresh water within it. Next suppose a well to be sunk in the middle of the island, and a certain quantity of water to be drawn therefrom daily. For small supplies such a well may be perfectly successful; but however small the quantity drawn, it must obviously have the effect of diminishing the volume of fresh water, which contributes to the maintenance of the level of saturation above the sea-level; and with further pumping the fresh water would be so far drawn upon that the mean level of saturation would sink, first to a curved figure—a cone of depression—such as that represented by the new level of saturation dd, and later to the figure represented by the lines ee, in which the level of saturation has everywhere been drawn below the mean sea-level. Before this stage the converse process begins, the reduced column of fresh water is no longer capable of balancing the sea water in the sand, inflow occurs at c and e, resulting finally in the well water becoming saline. The figure, in this case of uniform percolation, assumed by the water in the neighbourhood of a deep well is a surface of revolution, and, however irregular the percolation and the consequent shape of the figure, it is commonly, but somewhat incorrectly, called the “cone of depression.” It cannot have straight, or approximately straight, sides in any vertical plane, but in nature is an exceedingly irregular figure drawn about curves—not unlike those in fig. 5. In this case, as in that of a level plane of uniformly porous sand, the vertical section of the figure is tangential to the vertical well and to the natural level of the subsoil water.

The importance of this illustration is to be found elsewhere than in islands, or peninsulas, or in uniformly porous sand. Where the strata are not uniformly porous, they may resist the passage of water from the direction of the sea or they may assist it; and round the whole coast of England, in the Magnesian limestone to the north-east, in the Chalk and Greensand to the east and south, and in the New Red Sandstone to the west, the number of wells which have been abandoned as sources of potable supply, owing to the percolation of sea water, is very great. Perhaps the first important cases occurred in the earlier part of the 19th century on the Lancashire shore of the Mersey estuary, where, one after another, deep wells in the New Red Sandstone had to be abandoned for most purposes. On the opposite side, in the Cheshire peninsula, the total quantity of water drawn has been much less, but even here serious warnings have been received. In 1895 the single well then supplying Eastbourne was almost suddenly rendered unfit for use, and few years pass without some similar occurrence of a more or less serious kind. The remarkable suddenness with which such changes are brought about is not to be wondered at when the true cause is considered. The action of sandstone in filtering salt waters was investigated in 1878 by Dr Isaac Roberts, F.R.S., who showed that when salt water was allowed to percolate blocks of sandstone, the effluent was at first nearly fresh, the salt being filtered out and crystallized for the most part near the surface of ingress to the sandstone. As the process continued the salt-saturated layer, incapable of further effective filtration, grew in thickness downwards, until in the process of time it filled the whole mass of sandstone. But before this was accomplished the filtration of the effluent became defective, and brackish water was received, which rapidly increased nearly to the saltness of the inflow. Into such blocks, charged with salt crystals and thoroughly dried, fresh water was then passed, and precisely the converse process took place. A thickness of only 12 in. of Bunter sandstone proved at first to be capable of removing more than 80% of the chlorides from sea water; but, after the slow passage of only 0·6 gallon through 1 cub. ft. of stone, the proportion removed fell to 8·51%. The general lesson to be learned from these facts is, that if the purity of the water of any well not far removed from the sea is to be maintained, that water must not be pumped down much below the sea-level. In short, the quantity of water drawn must in no case be allowed to exceed the quantity capable of being supplied to the well through the medium of the surrounding soil and rock, by rain falling upon the surface of the land. If it exceeds this, the stock of fresh water held in the interstices of the rock, and capable of flowing towards the well, must disappear; and the deficit between the supply and demand can only be made up by water filtering from the sea and reaching the well at first quite free from salt, but sooner or later in a condition unfit for use.


Any well-made earthen embankment of moderate height, and of such thickness and uniformity of construction as to ensure freedom from excessive percolation at any point, will in the course of time become almost impermeable to surface water standing Earthen dams. against it; and when permeable rocks are covered with many feet of soil, the leakage through such soil from standing water newly placed above it generally diminishes rapidly, and in process of time often ceases entirely. Even the beds of sluggish rivers flowing over porous strata generally become so impermeable that excavations made in their neighbourhood, though freely collecting the subsoil water, receive no river water whatever. Thus natural or artificial surfaces which are completely permeable to rainfall may become almost impermeable when protected by surface water from drought and frost, and from earth-worms, vegetation and artificial disturbance. The cause of this choking of the pores is precisely the same as that described below in the case of sand filters. But in order that the action may be complete the initial resistance to percolation of water at every part of the soil must be such that the motion of the water through it shall be insufficient to disturb the water-borne mineral and organic particles lodged on the surface or in the interstices of the soil. If, therefore, a reservoir so formed survives the first few years without serious leakage, it is not likely, in the absence of artificial disturbance, to succumb owing to leakage at a later period. Hence, as the survival of the fittest, there are many artificial waters, with low dams consisting exclusively of earth—and sometimes very sandy earth—satisfactorily performing their functions with no visible leakage. But it is never advisable to rely upon this action, where, as in the case of a reservoir for water supply, large portions of naturally permeable bottom are liable to be uncovered and exposed to the weather.

The most important dams are those which close the outlets of existing valleys, but a dam may be wholly below ground, and according to the commoner method of construction in Great Britain, wherever sufficiently impermeable rising ground is not met with at the intended boundary Construction. of a reservoir, a trench is cut along such portion, and carried down to rock or such other formation as, in the engineer’s opinion, forms a sufficiently impermeable sheet beneath the whole surface to be covered with water. Into this trench so called “puddled clay,” that is, clay rendered plastic by kneading with water, is filled and thoroughly worked with special tools, and trodden in layers. In this manner an underground compartment is formed, the bottom of which is natural, and the sides partly natural and partly artificial, both offering high resistance to the passage of water. Above ground, if the water level is to be higher than the natural boundary, the same puddle walls or cores are carried up to the required level, and are supported as they rise by embankments of earth on either side.

Fig. 6 is a typical section of a low dam of this class, impounding water upon gravel overlying impermeable clay. In such a structure the whole attention as regards water-tightness should be concentrated upon the puddle wall or core. When, as may happen in dry seasons, the puddle wall remains long above the water level, it parts with moisture and contracts. It is essential that this contraction shall not proceed to such an extent as may possibly produce cracking. Drying is retarded, and the contraction due to a given degree of drying is greatly reduced, by the presence of sand and small stones among the clay. Nearly all clays, notably those from the Glacial deposits, naturally contain sand and stones, 40 to 50% by weight of which is not too much if uniformly distributed and if the clay is otherwise good.

Fig. 6.—Section of Typical Low Earth Embankment in Flat Plain.

But in the lower parts of the trench, where the clay can never become dry, plasticity and ductility are, for reasons to be explained below, the first consideration, and there the proportion of grit should be lower. The resistance of clay to percolation by water depends chiefly upon the density of the clay, while that density is rapidly reduced if the clay is permitted to absorb water. Thus, if dry clay is prevented from expanding, and one side be subjected to water pressure while the other side is held up by a completely porous medium, the percolation will be exceedingly small; but if the pressure preventing the expansion is reduced the clay will swell, and the percolation will increase. On the restoration of the pressure, the density will be again increased by the reduction of the water-filled interstices, and the percolation will be correspondingly checked. Hence the extreme importance in high dams with clay cores of loading the clay well for some time before water pressure is brought against it. If this is done, the largest possible quantity of clay will be slowly but surely forced into any space, and, being prevented from expanding, it will be unable subsequently to absorb more water. The percolation will then be very small, and the risk of disintegration will be reduced to a minimum. The embankments on either side of the puddle wall are merely to support the puddle and to keep it moist above the ground level when the reservoir is low. They may be quite permeable, but to prevent undue settlement and distortion they must, like the puddle, be well consolidated. In order to prevent a tendency to slip, due to sudden and partial changes of saturation, the outer embankment should always be permeable, and well drained at the base except close to the puddle. The less permeable materials should be confined to the inner parts of the embankments; this is especially important in the case of the inner embankment in order that, when the water level falls, they may remain moist without becoming liable to slip. The inner slope should be protected from the action of waves by so-called “hand-pitching,” consisting of roughly squared stonework, bedded upon a layer of broken stone to prevent local disturbance of the embankment by action of the water between the joints of the larger stones.

In mountain valleys, rock or shale, commonly the most impermeable materials met with in such positions, are sometimes not reached till considerable depths are attained. There are several cases in Great Britain where it has been necessary to carry down the puddle trench to about 200 ft. below the surface of the ground vertically above those parts. The highest dams of this class in the British islands impound water to a level of about 110 ft. above the bottom of the valley. Such great works have generally been well constructed, and there are many which after fifty years of use are perfectly sound and water-tight, and afford no evidence of deterioration. On the other hand, the partial or total failure of smaller dams of this description, to retain the reservoir water, has been much more common in the past than is generally supposed. Throughout Great Britain there are still many reservoirs, with earthen dams, which cannot safely be filled; and others which, after remaining for years in this condition, have been repaired. From such cases and their successful repair valuable experience of the causes of failure may be derived.

Most of these causes are perfectly well understood by experienced engineers, but instances of malconstruction of recent date are still met with. A few such cases will now be mentioned. The base of a puddle trench is often found to have been placed Erosion by leakage. upon rock, perfectly sound in itself, but having joints which are not impermeable. The loss of water by leakage through such joints or fissures below the puddle wall may or may not be a serious matter in itself; but if at any point there is sufficient movement of water across the base of the trench to produce the slightest erosion of the clay above it, that movement almost invariably increases. The finer particles of clay in the line of the joint are washed away, while the sandy particles, which nearly all natural clays contain, remain behind and form a constantly deepening porous vein of sand crossing the base of the puddle.

Fig. 7.—Earth Embankment, with stone toe and concrete trench.

Percolation through this sand is thus added to the original leakage. Having passed through the puddle core the leaking water sometimes rises to the surface of the ground, producing a visibly turbid spring. As erosion proceeds, the contraction of the space from which the clay is washed continues, chiefly by the sinking down of the clay above the sand. Thus the permeable vein grows vertically rather than horizontally, and ultimately assumes the form of a thin vertical sheet traversing the puddle wall, often diagonally in plan, and having a thickness which has varied in different cases from a few inches to a couple of feet or more, of almost clean sand rising to an observed height of 30 or 40 ft., and only arrested in its upward growth by the necessary lowering of the reservoir water to avoid serious danger. The settlement of the plastic clay above the eroded portion soon produces a surface depression at the top of the embankment over or nearly over the leakage, and thus sometimes gives the first warning of impending danger. It is not always possible to prevent any leakage whatever through the strata below the bottom or beyond the ends of the trench, but it is always possible to render such leakage entirely harmless to the work above it, and to carry the water by relief-pipes to visible points at the lower toe of the dam. Wherever the base of a puddle wall cannot be worked into a continuous bed of clay or shale, or tied into a groove cut in sound rock free from water-bearing fissures, the safest course is to base it on an artificial material at once impermeable and incapable of erosion, interposed between the rock and the puddled clay. Water-tight concrete is a suitable material for the purpose; it need not be made so thick as the puddle core, and is therefore sometimes used with considerable advantage in lieu of the puddle for the whole depth below ground. In fig. 7 a case is shown to be so treated. Obviously, the junction between the puddle and the concrete might have been made at any lower level.

Fig. 8.—Leakage due to improperly formed discharge
culvert through puddle wall of reservoir.

However well the work may be done, the lower part of a mass of puddled clay invariably settles into a denser mass when weighted with the clay above. If, therefore, one part is held up, by unyielding rock for example, while an Unequal settlement. adjoining part has no support but the clay beneath it, a fracture—not unlike a geological fault—must result. Fig. 8 is a part longitudinal section through the puddle wall of an earthen embankment. The puddle wall is crossed by a pedestal of concrete carrying the brick discharge culvert. The puddle at a was originally held up by the flat head of this pedestal; not so the puddle at b, which under the superincumbent weight settled down and produced the fault bc. accompanied with a shearing or tangential strain or, less probably, with actual fracture in the direction bd. Serious leakage at once began between c and b and washed out the clay, particle by particle, but did not wash out the sand associated with it, which remained behind in the crevice. The clay roof, rather than the walls of this crevice of sand, gave way and pressed down to fill the vacancy, and the leakage worked up along the weakened plane of tangential strain bd. On the appearance of serious leakage the overflow level of the water originally at ef was lowered for safety to gh; and for many years the reservoir was worked with its general level much below gh. The sand-filled vein, several inches in width, was found, on taking out the puddle, to have terminated near the highest level to which the water was allowed to rise, but not to have worked downwards. There can be little doubt that the puddle at the right-hand angle j was also strained, but not to the point of rupture, as owing to the rise of the sandstone base there was comparatively little room for settlement on that side. In repairing this work the perfectly safe
Fig. 9.—Overhanging Rock Leakage
form shown by the dotted lines ka, kj was substituted for the flat surface aj, and this alone, if originally adopted, would have prevented dangerous shearing strains. As an additional precaution, however, deep tongues of concrete like those in fig. 7 were built in the rock throughout the length of the trench, and carried up the sides and over the top of the pedestal. The puddle was then replaced, and remains sensibly watertight. The lesson taught by fig. 8 applies also to the ends of puddle walls where they abut against steep faces of rock. Unless such faces are so far below the surface of the puddle, and so related to the lower parts of the trench, that no tension, and consequent tendency to separation of the puddle from the rock, can possibly take place, and unless abundant time is given, before the reservoir is charged, for the settlement and compression of the puddle to be completed, leakage with disastrous results may occur.

In other cases leakage and failure have arisen from allowing a part of the rock bottom or end of a puddle trench to overhang, as in fig. 9. Here the straining of the original horizontal puddle in settling down is indicated in a purposely exaggerated way by the curved lines. There is considerable distortion of the clay, resulting from combined shearing and tensile stress, above each of the steps of rock, and reaching its maximum at and above the highest rise ab, where it has proved sufficient to produce a dangerous line of weakness ac, the tension at a either causing actual rupture, or such increased porosity as to permit of percolation capable of keeping open the wound. In such cases as are shown in figs. 8 and 9 the growth of the sand vein is not vertical, but inclined towards the plane of maximum shearing strain. Fig. 9 also illustrates a weak place at b where the clay either never pressed hard against the overhanging rock or has actually drawn away therefrom in the process of settling towards the lower part to the left. When it is considered that a parting of the clay, sufficient to allow the thinnest film of water to pass, may start the formation of a vein of porous sand in the manner above explained, it will be readily seen how great must be the attention to details, in unpleasant places below ground, and below the water level of the surrounding area, if safety is to be secured. In cases like fig. 9 the rock should always be cut away to a slope, such as that shown in fig. 10.

If no considerable difference of water-pressure had been allowed between the two sides of the puddle trench in figs. 8 or 9 until the clay
Fig. 10.—Proper figure for Rock Slope
had ceased to settle down, it is probable that the interstices, at first formed between the puddle and the concrete or rock, would have been sufficiently filled to prevent injurious percolation at any future time. Hence it is always a safe precaution to afford plenty of time for such settlement before a reservoir is charged with water. But to all such precautions should be added the use of concrete or brickwork tongues running longitudinally at the bottom of the trench, such as those shown at a higher level in fig. 7.

In addition to defects arising out of the condition or figure of the rock or of artificial work upon which the puddle clay rests, the puddle wall itself is often defective. The original material may have been perfectly satisfactory, but if, for example, in the progress of the work a stream of water is allowed to Defects in puddle wall flow across it, fine clay is sometimes washed away, and the gravel or sand associated with it left to a sufficient extent to permit of future percolation. Unless such places are carefully dug out or re-puddled before the work of filling is resumed, the percolation may increase along the vertical plane where it is greatest, by the erosion and falling in of the clay roof, as in the other cases cited. Two instances probably originating in some such cause are shown in fig. 11 in the relative positions in which they were found, and carefully measured, as the puddle was removed from a crippled reservoir dam. These fissures are in vertical planes stretching entirely across the puddle trench, and reaching in one case, aa, nearly to the highest level at which the reservoir had been worked for seventeen years after the leakage had been discovered. The larger and older of these veins was 441/2 ft. high, of which 14 ft. was above the original ground level, and it is interesting to note that this portion, owing probably to easier access for the water from the reservoir and reduced compression of the puddle, was much wider than below. The little vein to the left marked bb. about 31/2 ft. deep, is curious. It looks like the beginning of success of an effort made by a slight percolation during the whole life of the reservoir to increase itself materially by erosion.

Fig. 11.—Vertical Vein of Leakage

There is no reason to believe that the initial cause of such a leakage could be developed except during construction, and it is certain that once begun it must increase. Only a knowledge of the great loss of capital that has resulted from abortive reservoir construction justifies this notice of defects which can always be avoided, and are too often the direct result, not of design, but of parsimony in providing during the execution of such works, and especially below ground, a sufficiency of intelligent, experienced and conscientious supervision.

In some cases, as, for example, when a high earthen embankment crosses a gorge, and there is plenty of stone to be had, it is desirable to place the outer bank upon a toe or platform of rubble stonework, as in fig. 7, by which means the height of the earthen portion is reduced and complete drainage secured. But here again great care must be exercised in the packing and consolidation of the stones, which will otherwise crack and settle.

As with many other engineering works, the tendency to slipping either of the sides of the valley or of the reservoir embankment itself has often given trouble, and has sometimes led to serious disaster. This, however, is a kind of failure not always attributable to want of proper supervision during construction, but rather to improper choice of the site, or treatment of the case, by those primarily responsible.

In countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted with more or less success. In the mining districts of America, for example, where timber is cheap, rough stone embankments have been lined on the water face Dams with diaphragms of wood, steel, concrete, &c. with timber to form the water-tight septum. In such position, even if the timber can be made sufficiently water-tight to begin with, the alternate immersion and exposure to air and sunshine promotes expansion and contraction, and induces rapid disintegration, leakage and decay. Such an expedient may be justified by the doubtful future of mining centres, but would be out of the question for permanent water supply. Riveted sheets of steel have been occasionally used, and, where bedded in a sufficient thickness of concrete, with success. At the East Cañon Creek dam, Utah, the height of which is about 61 ft. above the stream, the trench below ground was filled with concrete much in the usual way, while above ground the water-tight diaphragm consists of a riveted steel plate varying in thickness from 5/16 in. to 3/16 in. This steel septum was protected on either side by a thin wall of asphaltic concrete supported by rubble stone embankments, and owing to irregular settling of the embankments became greatly distorted, apparently, however, without causing leakage. Asphalt, whether a natural product or artificially obtained, as, for example, in some chemical manufactures, is a most useful material if properly employed in connexion with reservoir dams. Under sudden impact it is brittle, and has a conchoidal fracture like glass; but under continued pressure it has the properties of a viscous fluid. The rate of flow is largely dependent upon the proportion of bitumen it contains, and is of course retarded by mixing it with sand and stone to form what is commonly called asphalt concrete. But given time, all such compounds, if they contain enough bitumen to render them water-tight, appear to settle down even at ordinary temperatures as heavy viscous fluids, retaining their fluidity permanently if not exposed to the air. Thus they not only penetrate all cavities in an exceedingly intrusive manner, but exert pressures in all. directions, which, owing to the density of the asphalt, are more than 40% greater than would be produced by a corresponding depth of water. From the neglect of these considerations numerous failures have occurred.

Elsewhere, a simple concrete or masonry wall or core has been used above as well as below ground, being carried up between embankments either of earth or rubble stone. This construction has received its highest development in America. On the Titicus, a tributary of the Croton river, an earthen dam was completed in 1895, with a concrete core wall 100 ft. high—almost wholly above the original ground level, which is said to be impermeable; but other dams of the same system, with core walls of less than 100 ft. in height, are apparently in their present condition not impermeable. Reservoir No. 4 of the Boston waterworks, completed in 1885, has a concrete core wall. The embankment is 1800 ft. long and 60 ft. high. The core wall is about 8 ft. thick at the bottom and 4 ft. thick at the top, and in the middle of the valley nearly 100 ft. in height. At irregular intervals of 150 ft. or more buttresses 3 ft. wide and 1 ft. thick break the continuity on the water side. That this work has been regarded as successful is shown by the fact that Reservoir No. 6 of the same waterworks was subsequently constructed and completed in 1894 with a similar core wall. There is no serious difficulty in so constructing walls of this kind as to be practically water-tight while they remain unbroken; but owing to the settlement of the earthen embankments and the changing level of saturation they are undoubtedly subject to irregular stresses which cannot be calculated, and under which, speaking generally, plastic materials are much safer. In Great Britain masonry or concrete core wails have been generally confined to positions below ground. Thus placed, no serious strains are caused either by changes of temperature or of moisture or by movements of the lateral supports, and with proper ingredients and care a very thin wall wholly below ground may be made watertight.

The next class of dam to be considered is that in which the structure as a whole is so bound together that, with certain reservations, it may be considered as a monolith subject chiefly to the overturning tendency of water pressure resisted by the weight of the structure itself Masonry dams. and the supporting pressure of the foundation. Masonry dams are, for the most part, merely retaining walls of exceptional size, in which the overturning pressure is water. If such a dam is sufficiently strong, and is built upon sound and moderately rough rock, it will always be incapable of sliding. Assuming also that it is incapable of crushing under its own weight and the pressure of the water, it must, in order to fail entirely, turn over on its outer toe, or upon the outer face at some higher level. It may do this in virtue of horizontal water-pressure alone, or of such pressure combined with upward pressure from intrusive water at its base or in any higher horizontal plane. Assume first, however, that there is no uplift from intrusive water. As the pressure of water is nil at the surface and increases in direct proportion to the depth, the overturning moment is as the cube of the depth; and the only figure which has a moment of resistance due to gravity, varying also as the cube of its depth, is a triangle. The form of stability having the least sectional area is therefore a triangle. It is obvious that the angles at the base of such a hypothetical dam must depend upon the relation between its density and that of the water. It can be shown, for example, that for masonry having a density of 3, water being 1, the figure of minimum section is a right-angled triangle, with the water against its vertical face; while for a greater density the water face must lean towards the water, and for a less density away from the water, so that the water may he upon it. For the sections of masonry dams actually used in practice, if designed on the condition that the centre of all vertical pressures when the reservoir is full shall be, as hereafter provided, at two-thirds the width of the base from the inner toe, the least sectional area for a density of 2 also has a vertical water face. As the density of the heaviest rocks is only 3, that of a masonry dam must be below 3, and in practice such works if well constructed vary from 2⋅2 to 2⋅6 . For these densities, the deviation of the water face from the vertical in the figure of least sectional area is, however, so trifling that, so far as this consideration is concerned, it may be neglected.

Fig. 12.—Diagram of Right-Angled Triangle Dam.

If the right-angled triangle abc, fig. 12, be a profile 1 ft. thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab = d in feet, the horizontal pressure of water against the section of the dam, increasing uniformly with the depth, is properly represented by the isosceles right-angled triangle abe, in which be is the maximum water-pressure due to the full depth d, while the area abe = d2/2 is the total horizontal pressure against the dam, generally stated in cubic feet of water, acting at one-third its depth above the base. Then d2/2 is the resultant horizontal pressure with an overturning moment of


If x be the width of the base, and ρ the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be ρxd/2 at its centre of gravity g, situated at 2/3x from the outer toe, and the moment of resistance to overturning on the outer toe,


Equating the moment of resistance (2) to the overturning moment (1), we have


That, is to say, for such a monolith to be on the point of overturning under the horizontal pressure due to the full depth of water, its base must be equal to that depth divided by the square root of twice the density of the monolith. For a density of 2⋅5 the base would therefore be 44⋅7% of the height.

We have now to consider what are the necessary factors of safety, and the modes of their application. In the first place, it is out of the question to allow the water to rise to the vertex a of such a masonry triangle. A minimum thickness must be adopted to give substance to the upper part; and where Factors of safety. the dam is not used as a weir it must necessarily rise several feet above the water, and may in either event have to carry a roadway. Moreover, considerable mass is required to reduce the internal strains caused by changes of temperature. In the next place, it is necessary to confine the pressure, at every point of the masonry, to an intensity which will give a sufficient factor of safety against crushing. The upper part of the dam having been designed in the light of these conditions, the whole process of completing the design is simple enough when certain hypotheses have been adopted, though somewhat laborious in its more obvious form. It is clear that the greatest crushing pressure must occur, either, with the reservoir empty, near the lower part of the water face ab, or with the reservoir full, near the lower part of the outer face ac. The principles hitherto adopted in designing masonry dams, in which the moment of resistance depends upon the figure and weight of the masonry, involve certain assumptions, which, although not quite true, have proved useful and harmless, and are so convenient that they may be continued with due regard to the modifications which recent investigations have suggested. One such assumption is that, if the dam is well built, the intensity of vertical pressure will (neglecting local irregularities) vary nearly uniformly from face to face along any horizontal plane. Thus, to take the simplest case, if abce (fig. 13) represents a rectangular mass already designed for the superstructure of the dam, and g its centre of gravity, the centre of pressure upon the base will be vertically under g, that is, at the centre of the base, and the load will be properly represented by the rectangle bfgc, of which the area represents the total load and the uniform depth of its uniform intensity.

Fig. 13.—Factor of Safety Diagram.

At this high part of the structure the intensity of pressure will of course be much less than its permissible intensity. If now we assume the water to have a depth d above the base, the total water pressure represented by the triangle kbh will have its centre at d/3 from the base, and by the parallelogram of forces, assuming the density of the masonry to be 2⋅5, we find that the centre of pressure upon the base bc is shifted from the centre of the base to a point i nearer to the outer toe c, and adopting our assumption of uniformly varying intensity of stress, the rectangular diagram of pressures will thus be distorted from the figure bfgc to the figure of equal area bjlc, having its centre o vertically under the point at which the resultant of all the forces cuts the base bc. For any lower level the same treatment may, step by step, be adopted, until the maximum intensity of pressure cl exceeds the assumed permissible maximum, or the centre of pressure reaches an assigned distance from the outer toe c, when the base must be widened until the maximum intensity of pressure or the centre of pressure, as the case may be, is brought within the prescribed limit. The resultant profile is of the kind shown in fig. 14.

Having thus determined the outer profile under the conditions hitherto assumed, it must be similarly ascertained that the water
Fig. 14.—Diagram showing lines of pressure in Masonry Dam.
face is everywhere capable of resisting the vertical pressure of the masonry when the reservoir is empty, and the base of each compartment must be widened if necessary in that direction also. Hence in dams above 100 ft. in height, further adjustment of the outer profile may be required by reason of the deviation of the inner profile from the vertical. The effect of this process is to give a series of points in the horizontal planes at which the resultants of all forces above those planes respectively cut the planes. Curved lines, as dotted in fig. 14, drawn through these points give the centre of pressure, for the reservoir full and empty respectively, at any horizontal plane. These general principles were recognized by Messrs Graeff and Delocre of the Fonts et Chaussées, and about the year 1866 were put into practice in the Furens dam near St Etienne. In 1871 the late Professor Rankine, F.R.S., whose remarkable perception of the practical fitness or unfitness of purely theoretical deductions gives his writings exceptional value, received from Major Tulloch, R.E., on behalf of the municipality of Bombay, a request to consider the subject generally, and with special reference to very high dams, such as have since been constructed in India. Rankine pointed out that before the vertical pressure reached the maximum pressure permissible, the pressure tangential to the slope might do so. Thus conditions of stress are conceivable in which the maximum would be tangential to the slope or nearly so, and would therefore increase the vertical stress in proportion to the cosecant squared of the slope. It is very doubtful whether this pressure is ever reached, but such a lim.it rather than that of the vertical stress must be considered when the height of a dam demands it. Next, Rankine pointed out that, in a structure exposed to the overturning action of forces which fluctuate in amount and direction, there should be no appreciable tension at any point of the masonry. But there is a still more important reason why this condition should be strictly adhered to as regards the inner face. We have hitherto considered only the horizontal overturning pressure of the water; but if from originally defective construction, or from the absence of vertical pressure due to weight of masonry towards the water edge of any horizontal bed, as at ab in fig. 14, water intrudes beneath that part of the masonry more readily than it can obtain egress along bc, or in any other direction towards the outer face, we shall have the uplifting and overturning pressure due to the full depth of water in the reservoir over the width ab added to the horizontal pressure, in which case all our previous calculations would be futile. The condition, therefore, that there shall be no tension is important as an element of design; but when we come to construction, we must be careful also that no part of the wall shall be less permeable than the water face. In fig. 13 we have seen that the varying depth of the area bjlc approximately represents the varying distribution of the vertical stress. If, therefore, the centre of that became so far removed to the right as to make j coincident with b, the diagram of stresses would become the triangle j ′l ′c′, and the vertical pressure at the inner face would be nil. This will evidently happen when the centre of pressure i′ is two-thirds from the inner toe b′ and one-third from the outer toe c′; and if we displace the centre of pressure still further to the right, the condition that the centre of figure of the diagram shall be vertically under that centre of pressure can only be fulfilled by allowing the point j ′ to cross the base to j ′′ thus giving a negative pressure or tension at the inner toe. Hence it follows that on the assumption of uniformly varying stress the line of pressures, when the reservoir is full, should not at any horizontal plane fall outside the middle third of the width of that plane.

Rankine in his report adopted the prudent course of taking as the safe limits certain pressures to which, at that time, such structures were known to be subject. Thus for the inner face he took, as the limiting vertical pressure, 320 ft. of water, or nearly 9 tons per sq. ft., and for the outer face 250 ft. of water, or about 7 tons per sq. ft.

For simplicity of calculation Rankine chose logarithmic curves for both the inner and outer faces, and they fit very well with the conditions. With one exception, however—the Beetaloo dam in Australia 110 ft. high—there are no practical examples of dams with logarithmically curved faces.

After Rankine, a French engineer, Bouvier, gave the ratio of the maximum stress in a dam to the maximum vertical stress as 1 to the cosine squared of the angle between the vertical and the resultant which, in dams of the usual form, is about as 13 is to 9.

During the last few years attention has been directed to the stresses—including shearing stresses—on planes other than horizontal. M. Levy contributed various papers on the subject which will be found in the Comptes rendus de l’Académie des Sciences (1895 and 1898) and in the Annales des Ponts et Chaussées (1897). He investigated the problem by means of the general differential equations of static equilibrium for dams of triangular and rectangular form considered as isotropic elastic solids. In one of these papers Levy formulated the requirement now generally adopted in France that the vertical pressure at the upstream end of any joint, calculated by the law of uniformly varying stress, should not be less than that of the water pressure at the level of that joint in order to prevent intrusive water getting into the structure.

These researches were followed by those of Messrs L. W. Atcherley and Karl Pearson, F. R.S.,[3] and by an approximate graphical treatment by Dr W. C. Unwin, F.R.S.[4] Dr Unwin took two horizontal planes, one close above the other, and calculated the vertical stresses on each by the law of uniformly varying stresses. Then the difference between the normal pressure on a rectangular element in the lower plane and that on the upper plane is the weight of the element and the difference between the shears on the vertical faces of that element. The weights being known, the principal stresses may be determined. These researches led to a wide discussion of the sufficiency of the law of uniformly varying stress when applied to horizontal joints as a test of the stability of dams. Professor Karl Pearson showed that the results are dependent upon the assumption that the distribution of the vertical stresses on the base of the structure also followed the law of uniformly varying stress. In view of the irregular forms and the uncertainties of the nature of the materials at the foundation, the law of uniformly varying stress was not applicable to the base of the dam. He stated that it was practically impossible to determine the stresses by purely mathematical means. The late Sir Benjamin Baker, F.R.S., suggested that the stresses might be measured by experiments with elastic models, and among others, experiments were carried out by Messrs Wilson and Gore[5] with indiarubber models of plane sections of dams (including the foundations) who applied forces to represent the gravity and water pressures in such a manner that the virtual density of the rubber was increased many times without interfering with the proper ratio between gravity and water pressure, and by this means the strains produced were of sufficient magnitude to be easily measured.

The more important of their results are shown graphically in figs. 15 and 16, and prove that the law of uniformly varying stress is generally applicable to the upper two-thirds of a dam, but that at parts in or near the foundations that law is departed from in a way which will be best understood from the diagrams.

Fig. 15 shows a section of the model dam. The maximum principal stresses are represented by the directions and thicknesses of the two systems of intersecting lines mutually at right angles.

Tensile stresses (indicated by broken lines on the diagram) are shown at the upstream toe notwithstanding that the line of resistance is well within the middle third of the section. It is important to notice that the maximum value of the tension at the toe lies in a direction approximately at 45° to the vertical, but at points lower down in the foundation this tension, while less in magnitude, becomes much more horizontal. This feature indicates that in the event of a crack occurring at the upstream toe, its extension would tend to turn downwards and follow a direction nearly parallel with the maximum pressure lines, in which direction it would not materially affect the stability of the structure.

As a matter of fact, the foundations of most dams are carried down in vertical trenches, the lower part only being in sound materials so that actual separation almost corresponding with the hypothetical crack is allowed in the first instance with no harmful effects. Similar experiments upon models with rounded toes but otherwise of the same form showed a considerable reduction in the magnitude of the tensile stresses.

On examining the diagram it will be observed that the maximum compressive stresses are parallel to and near to the down stream face of the section, which values are approximately equal to the maximum value of the vertical stress determined by the law of uniformly varying stress divided by the cosine squared of the angle between the vertical and the resultant.

The distributions of stress on the base line of the model for “reservoir empty” and “reservoir full” are shown in fig. 16 by ellipses of stress and by diagrams of stress on vertical and horizontal sections.

Arrow heads at the ends of an axis of an ellipse indicate tension as distinct from compression, and the semi-axes in magnitude and direction represent the principal stresses.

It is obvious that experiments of the kind referred to cannot take into account all the conditions of the problem met with in actual practice, such as the effect of the rock at the sides of the valley and variations of temperature, &c., but deviations in practice from the conditions which mathematical analyses or experiments assume are nearly always present. Such analyses and experiments are not on that account the less important and useful.

So far we have only considered water-pressure against the reservoir side of the dam; but it sometimes happens that the water and earth pressure against the outer face is considerable enough to modify the lower part of the section. In dams of moderate height above ground and considerable depth below ground there is, moreover, no reason why advantage should not be taken of the earth resistance due either to the downstream face of the trench against which the foundations are built, or to the materials excavated and properly embanked against that face above the ground level or to both. We do not always know the least resistance which it is safe to give to a retaining wall subject to the pressure of earth, or conversely, the maximum resistance to side-thrust which natural or embanked earth will afford, because we wisely neglect the important but very variable element of adhesion between the particles. It is notorious among engineers that retaining walls designed in accordance with the well-known theory of conjugate pressures in earth are unnecessarily strong, and this arises mainly from the assumption that the earth is merely a loose granular mass without any such adhesion. As a result of this theory, in the case of a retaining wall supporting a vertical face of earth beneath an extended horizontal plane level with the top of the wall, we get

where P is the horizontal pressure of the earth against the wall

exerted at one-third its height, w the weight of unit volume of the material, x the height of the wall, and the angle of repose of the material.

That the pressure so given exceeds the maximum possible pressure we do not doubt; and, conversely, if we put

we may have equal confidence that P′ will be less than the maximum pressure which, if exerted by the wall against the earth, will be borne without disturbance. But like every pure theory the principles of conjugate pressures in earth may lead to danger if not applied with due consideration for the angle of repose of the material, the modifications brought about by the limited width of artificial embankments, the possible contraction away from the masonry, of clayey materials during dry weather for some feet in depth and the tendency of surface waters to produce scour between the wall and the embankment. Both the Neuadd and the Fisher Tarn dams are largely dependent upon the support of earthen embankments with much economy and with perfectly satisfactory results.

Fig. 16.—Showing Stresses at base of model dam determined experimentally.

In the construction of the Vyrnwy masonry dam Portland cement concrete was used in the joints. When more than six months old, 9 in. cubes of this material never failed under compression below 111 tons per sq. ft. with an average of 167 tons; and the mean resistance of all the blocks tested between two and three years after moulding exceeded 215 tons per sq. ft., while blocks cut from the concrete of the dam gave from 181 to 329 tons per sq. ft. It has been shown that the best hydraulic lime, or volcanic puzzuolana and lime, if properly ground while slaking, and otherwise treated in the best-known manner, as well as some of the so-called natural (calcareous) cements, will yield results certainly not inferior to those obtained from Portland cement. The only objection that can in any case be urged against most of the natural products is that a longer time is required for induration; but in the case of masonry dams sufficient time necessarily passes before any load, beyond that of the very gradually increasing masonry, is brought upon the structure. The result of using properly treated natural limes is not to be judged from the careless manner in which such limes have often been used in the past. Any stone of which it is desirable to build a masonry dam would certainly possess an average strength at least as great as the above figures for concrete; the clay slate of the Lower Silurian formation, used in the case of the Vyrnwy dam, had an ultimate crushing strength of from 700 to 1000 tons per sq. ft. If, therefore, with such materials the work is well done, and is not subsequently liable to be wasted or disintegrated by expansion or contraction or other actions which in the process of time affect all exposed surfaces, it is clear that 15 to 20 tons per sq. ft. must be a perfectly safe load. There are many structures at present in existence bearing considerably greater loads than this, and the granite ashlar masonry of at least one, the Bear Valley dam in California, is subject to compressive stresses, reaching, when the reservoir is full, at least 40 to 50 tons per sq. ft., while certain brickwork linings in mining shafts are subject to very high circumferential stresses, due to known water-pressures. In one case which has been investigated this circumferential pressure exceeds 26 tons per sq. ft., and the brickwork, which is 18 in. thick and 20 ft. internal diameter, is perfectly sound and water-tight. In portions of the structure liable to important changes of pressure from the rise and fall of the water and subject to the additional stresses which expansion and contraction by changes of temperature and of moisture induce, and in view of the great difficulty of securing that the average modulus of elasticity in all parts of the structure shall be approximately the same, it is probably desirable to limit the calculated load upon any external work, even of the best kind, to 15 or 20 tons per sq. ft. It is clear that the material upon which any high masonry dam is founded must also have a large factor of safety against crushing under the greatest load that the dam can impose upon it, and this consideration unfits any site for the construction of a masonry dam where sound rock, or at least a material equal in strength to the strongest shale, cannot be had; even in the case of such a material as shale the foundation must be well below the ground.

The actual construction of successful masonry dams has varied from the roughest rubble masonry to ashlar work. It probable, however, that, all things considered, random rubble in which the flattest side of each block of stone is dressed to a fairly uniform surface, so that it Materials. may be bedded as it were in a tray of mortar, secures the nearest approach to uniform elasticity. Such stones may be of any size subject to each of them covering only a small proportion of the width of the structure (in the Vyrnwy dam they reached 8 or 10 tons each), and the spaces between them, where large enough, must be similarly built in with smaller, but always the largest possible, stones; spaces too small for this treatment must be filled and rammed with concrete. All stones must be beaten down into their beds until the mortar squeezes up into the joints around them. The faces of the work may be of squared masonry, thoroughly tied into the hearting; but, in view of the expansion and contraction mentioned below, it is better that the face masonry should not be coursed. Generally speaking, in the excavations for the foundations springs are met with; these may be only sufficient to indicate a continuous dampness at certain beds or joints of the rock, but all such places should be connected by relief drains carried to visible points at the back of the dam. It should be impossible, in short, for any part of the rock beneath the dam to become charged with water under pressure, either directly from, the water in the reservoir or from higher places in the mountain sides. For similar reasons care must be taken to ensure that the structure of the water face of the dam shall be the least permeable of any part. In the best examples this has been secured by bedding the stones near to the water face in somewhat finer mortar than the rest, and sometimes also by placing pads to fill the joints for several inches from the water face, so that the mortar was kept away from the face and was well held up to its work. On the removal of the pads, or the cutting out of the face of the mortar where pads were not used, the vacant joint was gradually filled with almost dry mortar, a hammer and caulking tool being used to consolidate it. By these means practical impermeability was obtained. If the pores of the water face are thus rendered extremely fine, the surface water, carrying more or less fine detritus and organic matter, will soon close them entirely and assist in making that face the least permeable portion of the structure.

But no care in construction can prevent the compression of the mass as the superincumbent weight comes upon it. Any given yard of height measured during construction, or at any time after construction, will be less than a yard when additional weight has been placed upon it; hence the ends of such dams placed against rock surfaces must move with respect to those surfaces when the superincumbent load comes upon them. This action is obviously much reduced where the rock sides of the valley rise slowly; but in cases where the rock is very steep, the safest course is to face the facts, and not to depend for water-tightness upon the cementing of the masonry to the rock, but rather to provide a vertical key, or dowel joint, of some material like asphalt, which will always remain water-tight. So far as the writer has been able to observe or ascertain, there are very few masonry dams in Europe or America which have not been cracked transversely in their higher parts. They generally leak a little near the junction with the rock, and at some other joints in intermediate positions. In the case of the Neuadd dam this difficulty was met by deliberately omitting the mortar in transverse joints at regular intervals near the top of the dam, except just at their faces, where it of course cracks harmlessly, and by filling the rest with asphalt. Serious movement from expansion and contraction does not usually extend to levels which are kept moderately damp, or to the greater mass of the dam, many feet below high-water level.

The first masonry dam of importance constructed in Great Britain was that upon the river Vyrnwy, a tributary of the Severn, in connexion with the Liverpool water-supply (Plate I.). Its height, subject to water-pressure, is about 134 ft., and a carriage-way is carried on arches at an elevation of about 18 ft. higher. As this dam is about 1180 ft. in length from rock to rock, it receives practically no support from the sides of the valley. Its construction drew much attention to the subject of masonry dams in England—where the earthwork dam, with a wall of puddled clay, had hitherto been almost universal—and since its completion nine more masonry dams of smaller size have been completed. In connexion with the Elan and Claerwen works, in Mid-Wales, for the supply of Birmingham, six masonry dams were projected, three of which are completed, including the Caban Goch dam, 590 ft. long at the water level, and subject to a water-pressure of 152 ft. above the rock foundations and of 122 ft. above the river bed, and the Craig-yr-allt Goch dam, subject to a head of 133 ft. The latter dam is curved in plan, the radius being 740 ft. and the chord of the arc 515 ft. In the Derwent Valley scheme, in connexion with the water supplies of Derby, Leicester, Nottingham and Sheffield, six more masonry dams have received parliamentary sanction. Of these the highest is the Hagglee, on the Ashop, a tributary of the Derwent, which will impound water to about 136 ft. above the river bed, the length from rock to rock being 980 ft. Two of these dams are now in course of construction, one of which, the Howden, will be 1080 ft. in length and will impound water to a depth of 114 ft. above the river bed. In 1892 the excavation was begun for the foundations of a masonry dam across the Croton river, in connexion with the supply of New York. The length of this dam from rock to rock at the overflow level is about 1500 ft. The water face, over the maximum depth at which that face cuts the rock foundations, is subject to a water-pressure of about 260 ft., while the height of the dam above the river bed is 163 ft. The section, shown in fig. 17, has been well considered. The hearting is of rubble masonry, and the faces are coursed ashlar. So-called “natural cement” has been used, except during frosty weather, when Portland cement was substituted on account of its more rapid setting. An important feature in connexion with this dam is the nature of the foundation upon which it stands. Part of the rock is schist, but the greater portion limestone, similar in physical qualities to the Carboniferous limestone of Great Britain. The lowest part of the surface of this rock was reached after excavating through alluvial deposits to a depth of about 70 ft., but owing to its fissured and cavernous nature it became necessary to excavate to much greater depths, reaching in places more than 120 ft. below the original bottom of the valley. Great pains appear to have been taken to ascertain that the cavernous portions of the rock had been cut out and built up before the building was begun.

Fig. 17.—Section of Croton Dam.

The Furens dam, already referred to as the earliest type of a scientifically designed structure of the kind, is subject to a pressure of about 166 ft. of water; the valley it crosses is only about 300 ft. wide at the water level, and the dam is curved in plan to a radius of 828 ft. Much discussion has taken place as to the utility of such curvature. The recent investigations already referred to indicate the desirability of curving dams in plan in order to reduce the possibility of tension and infiltration of water at the upstream face. In narrow rock gorges extremely interesting and complex problems relating to the combined action of horizontal and vertical stresses arise, and in some such cases it is evident that much may be done by means of horizontal curvature to reduce the quantity of masonry without reduction of strength. The Bear Valley dam, California, is the most daring example in existence of the employment of the arch principle. Its height from the rock bed is 64 ft., and it is subject during floods to a head of water not much less. The length of the chord of the arc across the valley is about 250 ft. and the radius 335 ft. The dam was begun in 1883, with a base 20 ft. thick, narrowing to 13 ft. at a height of 16 ft. The cost of this thickness being regarded as too great, it was abruptly reduced to 8 ft. 6 in., and for the remaining 48 ft. it was tapered up to a final width of about 3 ft. The masonry is described by Mr Schuyler as “a rough uncut granite ashlar, with a hearting of rough rubble all laid in cement mortar and gravel.” This dam has been in satisfactory use since 1885, and the slight filtration through the masonry which occurred at first is said to have almost entirely ceased.

In New South Wales thirteen thin concrete dams, dependent upon horizontal curvature for their resistance to water pressure, have been constructed in narrow gorges at comparatively small cost to impound water for the use of villages. The depth of water varies from 18 ft. to 76 ft. and five of them have cracked vertically, owing apparently to the impossibility of the base of the dam partaking of the changes of curvature induced by changes of temperature and of moisture in the upper parts. It is stated, however, that these cracks close up and become practically water-tight as the water rises.

Fig. 18.—Section of Bouzey Dam.

Something has been said of the failures of earthen dams. Many masonry dams have also failed, but, speaking generally, we know less of the causes which have led to such failures. The examination of one case, however, namely, the bursting in 1895 of the Bouzey dam, near Épinal, in France, by which many Failures. lives were lost, has brought out several points of great interest. It is probably the only instance in which a masonry dam has slipped upon its foundations, and also the only case in which a masonry dam has actually overturned, while curiously enough there is every probability that the two circumstances had no connexion with each other. A short time after the occurrence of the catastrophe the dam was visited by Dr W. C. Unwin, F.R.S., and the writer, and a very careful examination of the work was made by them. Some of the blocks of rubble masonry carried down the stream weighed several hundred tons. The original section of the dam is shown by the continuous thick line in fig. 18, from which it appears that the work was subject to a pressure of only about 65 ft. of water. In the year 1884 a length of 450 ft. of the dam, out of a total length of 1706 ft., slipped upon its foundation of soft sandstone, and became slightly curved in plan as shown at a, b, fig. 19, the maximum movement from the original straight line being about 1 ft. Further sliding on the base was prevented by the construction of the cross-lined portions in the section (fig. 18). These precautions were perfectly effective in securing the safety of the dam up to the height to which the counter fort was carried. As a consequence of this horizontal bending of the dam the vertical cracks shown in fig. 19 appeared and were repaired. Eleven[6] years after this, and about fifteen years after the dam was first brought into use, it overturned on its outer edge, at about the level indicated by the dotted line just above the counterfort; and there is no good reason to attribute to the movement of 1884, or to the vertical cracks it caused, any influence in the overturning of 1895. Fig. 19.—Elevation and Plan of Bouzey Dam. Some of the worst cracks were, indeed, entirely beyond the portion overturned, which consisted of the mass 570 ft. long by 37 ft. in depth, and weighing about 20,000 tons, shown in elevation in fig. 19. The line of pressures as generally given for this dam with the reservoir full, on the hypothesis that the density of the masonry was a little over 2, is shown by long and short dots in fig. 18. Materials actually collected from the dam indicate that the mean density did not exceed 1⋅85 when dry and 2⋅07 when saturated, which would bring the line of pressures even closer to the outer face at the top of the counter fort. In any event it must have approached well within 31/2 ft. of the outer face, and was more nearly five-sixths than two-thirds of the width of the dam distant from the water face; there must, therefore, have been considerable vertical tension at the water face, variously computed according to the density assumed at from 11/4 to 13/4 ton per square foot. This, if the dam had been thoroughly well constructed, either with hydraulic lime or Portland cement mortar, would have been easily borne. The materials, however, were poor, and it is probable that rupture by tension in a roughly horizontal plane took place. Directly this occurred, the front part of the wall was subject to an additional overturning pressure of about 35 ft. of water acting upwards, equivalent to about a ton per square foot, which would certainly, if it occurred throughout any considerable length of the dam, have immediately overturned it. But, as a matter of fact, the dam actually stood for about fifteen years. Of this circumstance there are two possible explanations. It is known that more or less leakage took place through the dam, and to moderate this the water face was from time to time coated and repaired with cement. Any cracks were thus, no doubt, temporarily closed; and as the structure of the rest of the dam was porous, no opportunity was given for the percolating water to accumulate in the horizontal fissures to anything like the head in the reservoir. But in reservoir work such coatings are not to be trusted, and a single horizontal crack might admit sufficient water to cause an uplift. Then, again, it must be remembered that although the full consequences of the facts described might arise in a section of the dam 1 ft. thick (if that section were entirely isolated), they could not arise throughout the length unless the adjoining sections were subject to like conditions. Any horizontal fissure in a weak place would, in the nature of things, strike somewhere a stronger place, and the final failure would be deferred. Time would then become an element. By reason of the constantly changing temperatures and the frequent filling and emptying of the reservoir, expansion and contraction, which are always at work tending to produce relative movements wherever one portion of a structure is weaker than another, must have assisted the water-pressure in the extension of the horizontal cracks, which, growing slowly, during the fifteen years, provided at last the area required to enable the intrusive water to overbalance the little remaining stability of the dam.


From very ancient times in India, Ceylon and elsewhere, reservoirs of great area, but generally of small depth, have been built and used for the purposes of irrigation; and in modern times, especially in India and America, comparatively shallow reservoirs have been constructed of much greater area, and in some cases of greater capacity, than any in the United Kingdom. Yet the hilly parts of the last-named country are rich in magnificent sites at sufficient altitudes for the supply of any parts by gravitation, and capable, if properly laid out, of affording a volume of water, throughout the driest seasons, far in excess of the probable demand for a long future. Many of the great towns had already secured such sites within moderate distances, and had constructed reservoirs of considerable size, when, in 1879, 1880 and 1892 respectively, Manchester, Liverpool and Birmingham obtained statutory powers to draw water from relatively great distances, viz. from Thirlmere in Cumberland, in the case of Manchester; from the river Vyrnwy, Montgomeryshire, a tributary of the Severn, in the case of Liverpool; and from the rivers Elan and Claerwen in Radnorshire, tributaries of the Wye, in the case of Birmingham. Lake Vyrnwy, completed in 1889, includes a reservoir which is still by far the largest in Europe.

Plate I.
From Photographs by J. Maclardy.
LAKE VYRNWY, December 1889.

Fig. 20.—Welsh Reservoir Sites.

This reservoir is situated in a true Glacial lake-basin, and having therefore all the appearance of a natural lake, is commonly known as Lake Vyrnwy. It is 825 ft. above the sea, has an area of 1121 acres, an available capacity exceeding 12,000 million gallons, and a length of nearly 5 m. Its position Lake Vyrnwy. in North Wales is shown in black in fig. 20, and the two views on Plate I. show respectively the portion of the valley visible from the dam before impounding began, and the same portion as a lake on the completion of the work. Before the valves in the dam were closed, the village of Llanwddyn, the parish church, and many farmsteads were demolished. The church was rebuilt outside the watershed, and the remains from the old churchyard were removed to a new cemetery adjoining it. The fact that this valley is a post-Glacial lake-basin was attested by the borings and excavations made for the foundations of the dam. The trench in which the masonry was founded covered an area 120 ft. wide at the bottom, and extending for 1172 ft. across the valley. Its site had been determined by about 190 borings, probings and shafts, which, following upon the indications afforded by the rocks above ground, proved that the rock bed crossing the valley was higher at this point than elsewhere. Here then, buried in alluvium at a depth of 50 to 60 ft. from the surface, was found the rock bar of the post-Glacial lake; at points farther up the valley, borings nearly 100 ft. deep had failed to reach the rock. The Glacial striae, and the dislocated rocks—moved a few inches or feet from their places, and others, at greater distances, turned over, and beginning to assume the sub-angular form of Glacial boulders—were found precisely as the glacier, receding from the bar, and giving place to the ancient lake, had left them, covered and preserved by sand and gravel washed from the terminal morain. Later came the alluvial silting-up. Slowly, but surely, the deltas of the tributary streams advanced into the lake, floods deposited their burdens of detritus in the deeper places, the lake shallowed and shrank and in its turn yielded to the winding river of an alluvial strath, covered with peat, reeds and alders, and still liable to floods. It is interesting to record that during the construction of the works the implements of Neolithic man were found, near the margin of the modern lake, below the peat, and above the alluvial clay on which it rested. Several of the reservoir sites in Wales, shown by shaded lines in fig. 20, are in all probability similar post-Glacial lake-basins, and in the course of time some of them may contain still greater reservoirs. They are provided with well-proportioned watersheds and rainfall, and being nearly all more than 500 ft. above the sea, may be made available for the supply of pure water by gravitation to any part of England. In 1892 the Corporation of Birmingham obtained powers for the construction of six reservoirs on the rivers Elan and Claerwen, also shown in fig. 20, but the sites of these reservoirs are long narrow valleys, not lake-basins. The three reservoirs on the Elan were completed in 1904. Their joint capacity is 11,320 million gallons, and this will be increased to about 18,000 millions when the remaining three are built.

Of natural lakes in Great Britain raised above their ordinary levels that the upper portions may be utilized as reservoirs, Loch Katrine supplying Glasgow is well known. Whitehaven is similarly supplied from Ennerdale, and in the year 1894 Thirlmere in Cumberland was brought into use, as already mentioned, for the supply of Manchester. The corporation have statutory power to raise the lake 50 ft., at which level it will have an available capacity of about 8000 million gallons; to secure this a masonry dam has been constructed, though the lake is at present worked at a lower level.

It is obvious that the water of a reservoir must never be allowed to rise above a certain prescribed height at which the works will be perfectly safe. In all reservoirs impounding the natural flow of a stream, this involves the use of an overflow. Where the dam is of masonry it may be used as a weir; but where Overflow. earthwork is employed, the overflow, commonly known in such a case as the “bye-wash,” should be an entirely independent work, consisting of a low weir of sufficient length to prevent an unsafe rise of the water level, and of a narrow channel capable of easily carrying away any water that passes over the weir. The absence of one or both of these conditions has led to the failure of many dams.

Reservoirs unsafe from this cause still exist in the United Kingdom. Where the contributory drainage area exceeds 5000 acres, the discharge, even allowing for so-called “cloud-bursts,” rarely or never exceeds the rate of about 300 cub. ft. per second per 1000 acres, or 1500 times the minimum dry weather flow, taken as one-fifth of a cubic foot; and if we provide against such an occasional discharge, with a possible maximum of 400 cub. ft. at much more distant intervals, a proper factor of safety will be allowed. But when a reservoir is placed upon a smaller area the conditions are materially changed. The rainfall which produces, as the average of all the tributaries in the larger area, 300 cub. ft. per second per 1000 acres, is made up of groups of rainfall of very varying intensity, falling upon different portions of that area, so that upon any section of it the intensity of discharge may be much greater.

The height to which the water is permitted to rise above the sill of the overflow depends upon the height of the embankment above that level (in the United Kingdom commonly 6 or 7 ft.), and this again should be governed by the height of possible waves. In open places that height is seldom more than about one and a half times the square root of the “fetch” or greatest distance in nautical miles from which the wave has travelled to the point in question; but in narrow reaches or lakes it is relatively higher. In lengths not exceeding about 2 m., twice this height may be reached, giving for a 2-mile “fetch” about 31/2 ft., or 13/4 ft. above the mean level. Above this again, the height of the wave should be allowed for “wash,” making the embankment in such a case not less than 51/4 ft. above the highest water-level. If, then, we determine that the depth of overflow shall not exceed 11/2 ft., we arrive at 63/4 ft. as sufficient for the height of the embankment above the sill of the overflow. Obviously we may shorten the sill at the cost of extra height of embankment, but it is rarely wise to do so.

The overflow sill or weir should be a masonry structure of rounded vertical section raised a foot or more above the waste-water course, in which case for a depth of 11/2 ft. it will discharge, over every foot of length, about 6 cub. ft. per second. Thus, if the drainage area exceeds 5000 acres, and we provide for the passage of 300 cub. ft. per second per 1000 acres, such a weir will be 50 ft. long for every 1000 acres. But, as smaller areas are approached, the excessive local rainfalls of short duration must be provided for, and beyond these there are extraordinarily heavy discharges generally over and gone before any exact records can be made; hence we know very little of them beyond the bare fact that from 1000 acres the discharge may rise to two or three times 300 cub. ft. per second per 1000 acres. In the writer's experience at least one case has occurred where, from a mountain area of 1300 acres, the rate per 1000 was for a short time certainly not less than 1000 cub. ft. per second. Nothing but long observation and experience can help the hydraulic engineer to judge of the configuration of the ground favourable to such phenomena. It is only necessary, however, to provide for these exceptional discharges during very short periods, so that the rise in the water-level of the reservoir may be taken into consideration; but subject to this, provision must be made at the bye-wash for preventing such a flood, however rare, from filling the reservoir to a dangerous height.

From the overflow sill the bye-wash channel may be gradually narrowed as the crest of the embankment is passed, the water being prevented from attaining undue velocity by steps of heavy masonry, or, where the gradient is not very steep, by irregularly set masonry.


When surface waters began to be used for potable purposes, some mode of arresting suspended matter, whether living or dead, became necessary. In many cases gauze strainers were at first employed, and, as an improvement upon or addition to these, the water was caused Sand filtration. to pass through a bed of gravel or sand, which, like the gauze, was regarded merely as a strainer. As such strainers were further improved, by sorting the sand and gravel, and using the fine sand only at the surface, better clarification of the water was obtained; but chemical analysis indicated, or was at the time thought to indicate, that that improvement was practically confined to clarification, as the dissolved impurities in the water were certainly very little changed. Hence such filter beds, as they were even then called, were regarded as a luxury rather than as a necessity, and it was never suspected that, notwithstanding the absence of chemical improvement in the water, changes did take place of a most important kind. Following upon Dr Koch's discovery of a method of isolating bacteria, and of making approximate determinations of their number in any volume of water, a most remarkable diminution in the number of microbes contained in sand-filtered water was observed; and it is now well known that when a properly constructed sand-filter bed is in its best condition, and is worked in the best-known manner, nearly the whole of the microbes existing in the crude water will be arrested. The sand, which is nominally the filter, has interstices about thirty times as wide as the largest dimensions of the larger microbes; and the reason why these, and, still more, why organisms which were individually invisible under any magnifying power, and could only be detected as colonies, were arrested, was not understood. In process of time it became clear, however, that the worse the condition of a filter bed, in the then general acceptation of the term, the better it was as a microbe filter; that is to say, it was not until a fine film of mud and microbes had formed upon the surface of the sand that the best results were obtained.

Even yet medical science has not determined the effect upon the human system of water highly charged with bacteria which are not known to be individually pathogenic. In the case of the bacilli of typhoid and cholera, we know the direct effect; but apart altogether from the presence of such specific poisons, polluted water is undoubtedly injurious. Where, therefore, there is animal pollution of any kind, more especially where there is human pollution, generally indicated by the presence of bacillus coli communis, purification is of supreme importance, and no process has yet been devised which, except at extravagant cost, supersedes for public supplies that of properly-conducted sand filtration. Yet it cannot be too constantly urged that such filtration depends for its comparative perfection upon the surface film; that this surface film is not present when the filter is new, or when its materials have been recently washed; that it may be, and very often is, punctured by the actual working of the filters, or for the purpose of increasing their discharge; and that at the best it must be regarded as an exceedingly thin line of defence, not to be depended upon as a safeguard against highly polluted waters, if a purer source of supply can possibly be found. Such filters are not, and in the nature of things cannot be, worked with the precision and continuity of a laboratory experiment.

In fig. 21 a section is shown of an efficient sand-filter bed. The thickness of sand is 3 ft. 6 in. In the older filters it was usual to support Fig. 21.—Section of Sand-Filter Bed. this sand upon small gravel resting upon larger gravel, and so on until the material was sufficiently open to pass the water laterally to under-drains. But a much shallower and certainly not less efficient filter can be constructed by making the under-drains cover the whole bottom. In fig. 21 the sand rests on small gravel of such degree of coarseness that the whole of the grains would be retained on a sieve of ⅛-in. mesh and rejected by a sieve of ½-in. mesh in the clear, supported upon a 3-in. thickness of bricks laid close together, and constituting the roof of the under-drains, which are formed by other bricks laid on thin asphalt, upon a concrete floor. In this arrangement the whole of the materials may be readily removed for cleansing. In the best filters an automatic arrangement for the measurement of the supply to each separate filter, and for the regulation of the quantity within certain limits, is adopted, and the resistance at outflow is so arranged that not more than a certain head of pressure, about 2½ ft., can under any circumstances come upon the surface film, while a depth of several feet of water is maintained over the sand. It is essential that during the working of the filter the water should be so supplied that it will not disturb the surface of the sand. When a filter has been emptied, and is being re-charged, the water should be introduced from a neighbouring filter, and should pass upwards in the filter to be charged, until the surface of the sand has been covered. The unfiltered water may then be allowed to flow quietly and to fill the space above the sand to a depth of 2 or 3 ft. It would appear to be impossible with any water that requires filtration to secure that the first filtrate shall be satisfactory if filtration begins immediately after a filter is charged; and if the highest results are to be obtained, either the unfiltered water must be permitted to pass extremely slowly over the surface of the sand without passing through it, or to stand upon the sand until the surface film has formed. With waters giving little or no sediment, which are often the most dangerous, some change, as by the first method, is necessary. It has been proposed, on the other hand, to allow the filter to act slowly until the surface film is formed, and to discard the first effluent. This course can scarcely fail to introduce into the sand many bacteria, which may be washed through when the full working of the filters is begun; and it should not, therefore, be adopted when the source of the supply is known to be subject to human pollution. The time for the formation of an efficient surface films varies, according to the quality of the raw water, from a few hours to a few days. Judging from the best observations that have been made on a large scale, the highest rate of efficient filtration when the surface film is in good condition is about 4 in. downwards per hour of the water contained above the sand, equivalent to about 50 gallons per day from each square foot of sand. When the surface film has once been formed, and the filter has begun its work, it should continue without interruption until the resistance of that film becomes too great to permit of the necessary quantity of water being passed. That period will vary, according to the condition of the water, from eight or ten days to four weeks. The surface film, together with half an inch to an inch of sand, is then carefully scraped off and stored for subsequent washing and use. This process may be repeated many times until the thickness of the fine sand is reduced to about 18 in., when the filter bed should be restored to its full thickness.

A lately discovered effect of sand filtration is a matter of great importance in connexion with the subject of aqueducts. A brown slimy sediment, having the appearance of coffee grounds when placed in clear water, has been long observed in pipes conveying surface waters from mountain moorlands. The deposit grows on the sides of the pipes and accumulates at the bottom, and causes most serious obstruction to the flow of water. The chemists and bacteriologists do not appear to have finally determined the true nature and origin of this growth, but it is found in the impounded waters, and passes into the pipes, where it rapidly increases. It is checked even by fine copper wire-gauze strainers, and where the water passes through sand-filter beds in the course of an aqueduct, the growth, though very great between the reservoir and the filter beds, is almost absent between the filter beds and the town. Even the growth of the well-known nodular incrustations in iron pipes is much reduced by sand filtration. From these facts it is clear that, other things being the same, the best position for the strainers and filter beds is as close as possible to the reservoir.

Some surface waters dissolve lead when bright, but cease to do so when the lead becomes tarnished. More rarely the action is continuous, and the water after being passed through lead cisterns and pipes produces lead poisoning—so called “plumbism.” The liability to this appears to be entirely removed by efficient sand filtration.

Sand filtration, even when working in the best possible manner, falls short of the perfection necessary to prevent the passage of bacteria which may multiply after the filter is passed. Small, however, as the micro-organisms are, they are larger than the capillary passages in some materials through which water under pressure may be caused to percolate. It is therefore natural that attempts should have been made to construct filters which, while permitting the slow percolation of water, should preclude the passage of bacteria or their spores. In the laboratory of Pasteur probably the first filter which successfully accomplished this object was produced. In this apparatus, known as the Pasteur-Chamberland filter, the filtering medium is biscuit porcelain. It was followed by the Berkefield filter, constructed of baked infusorial earth. Both these filters arrest the organisms by purely mechanical action, and if the joints are water-tight and they receive proper attention and frequent sterilization, they both give satisfactory results on a small scale for domestic purposes. The cost, however—to say nothing of the uncertainty—where large volumes of water are concerned, much exceeds the cost of obtaining initially safe water. Moreover, if a natural water is so liable to pathogenic pollution as to demand filtration of this kind, it ought at once to be discarded for an initially pure supply; not necessarily pure in an apparent or even in a chemical sense, for water may be visibly coloured, or may contain considerable proportions both of organic and inorganic impurity, and yet be tasteless and free from pathogenic pollution.

There are several materials now in use possessing remarkable power to decolourize clarify, chemically purify and oxidize water; but they are too costly for use in connexion with public water supplies unless a rate of filtration is adopted quite inconsistent with the formation of a surface film capable of arresting micro-organisms. This fact does not render them less useful when applied to the arts in which they are successfully employed.

Attempts have been made, by adding certain coagulants to the water to be filtered, to increase the power of sand and other granular materials to arrest bacteria when passing through them at much higher velocities than are possible for successful filtration by means of the surface film upon sand. The effect is to produce between the sand or other grains a glutinous substance which does the work performed by the mud and microbes upon the surface of the sand filter. Elsewhere centrifugal force, acting somewhat after its manner in the cream separator, has been called in aid.

The sedimentation tank forms a very important help to filtration. In the case of river waters liable to turbidity the water should always be passed through such tanks before being placed in the filters. Sedimentation tanks. They form, moreover, additional safeguards against organic impurity. Sedimentation tanks on a sufficient scale may effect the purification of the water to almost any desired extent. This is shown to be the case by the purity of some lake waters; but the first cost of the works and the subsequent removal of the sediment are in some cases a serious matter, and any approach to the comparatively perfect action of lakes is out of the question. By the use of such tanks, however, when the condition of the water demands it, and by passing the effluent water through sand filters when in good condition, the number of microbes is found to be reduced by as much as 97 or even 99%. This, when attained, is undoubtedly a most important reduction in the chance of pathogenic bacteria passing into the filtered water; but much more must be done than has hitherto in most places been done to ensure the constancy of such a condition before it can be assumed to represent the degree of safety attained. No public supply should be open to any such doubt as ought to, or may, deter people from drinking the water without previous domestic filtration or boiling.


The earliest water supplies in Great Britain were generally distributed at low pressure by wooden pipes or stone or brick conduits. For special purposes the Romans introduced cast-lead pipes, but they were regarded as luxuries, not as necessaries, and gave way to cheaper conduits Intermittent supply. made, as pump barrels had long been made, by boring out tree trunks, which are occasionally dug up in a good state of preservation. This use of tree-trunks as pipes is still common in the wooded mountain districts of Europe. Within the 19th century, however, cast iron became general in the case of large towns; but following the precedent inseparable from, the use of weaker conduits, the water was still delivered under very low pressure, rarely more than sufficient to supply taps or tanks near the level of the ground, and generally for only a short period out of each twenty-four hours. On the introduction of the Waterworks Clauses Act 1847, an impetus was given to high-pressure supplies, and the same systems of distributing mains were frequently employed for the purpose; but with few exceptions the water continued to be supplied intermittently, and cisterns or tanks were necessary to store it for use during the periods of intermission. Thus it happened that pipes and joints intended for a low-pressure supply were subjected, not only to high pressure, but to the trying ordeal of suddenly varying pressures. As a rule such pipes were not renewed: the leakage was enormous, and the difficulty was met by the very inefficient method of reducing the period of supply still farther. But even in entirely new distributing systems the network is so extensive, and the number of joints so great, that the aggregate leakage is always considerable; the greatest loss being at the so-called “ferrules” connecting the mains with the house “communication” or “service” pipes, in the lead pipes, and in the household fittings. But a far greater evil than mere loss of water and inconvenience soon proved to be inseparable from intermittent supply. Imagine a hilly town with a high-pressure water supply, the water issuing at numerous points, sometimes only in exceedingly small veins, from the pipes into the sub-soil. In the ordinary course of intermittent supply or for the purpose of repairs, the water is cut off at some point in the main above the leakages; but this does not prevent the continuance of the discharge in the lower part of the town. In the upper part there is consequently a tendency to the formation of a vacuum, and some of the impure sub-soil water near the higher leakages is sucked into the mains, to be mixed with the supply when next turned on. We are indebted to the Local Government Board for having traced to such causes certain epidemics of typhoid, and there can be no manner of doubt that the evil has been very general. It is therefore of supreme importance that the pressure should be constantly maintained, and to that end, in the best-managed waterworks the supply is not now cut off even for the purpose of connecting house-service pipes, an apparatus being employed by which this is done under pressure. Constant pressure being granted, constant leakage is inevitable, and being constant it is not surprising that its total amount often exceeds the aggregate of the much greater, but shorter, draughts of water taken for various household purposes. There is therefore, even in the best cases, a wide field for the conservation and utilization of water hitherto entirely wasted.

Following upon the passing of the Waterworks Clauses Act 1847, a constant supply was attempted in many towns, with the result in some cases that, owing to the enormous loss arising from the prolongation of the period of leakage from a fraction of an hour to twenty-four hours, it was impossible to maintain the supply. Accordingly, in some places large sections of the mains and service pipes were entirely renewed, and the water consumers were put to great expense in Constant supply. changing their fittings to new and no doubt better types, though the old fittings were only in a fraction of the cases actually causing leakage. But whether or not such stringent methods were adopted, it was found necessary to organize a system of house-to-house visitation and constantly recurring inspection. In Manchester this was combined with a most careful examination, at a depôt of the Corporation, of all fittings intended to be used. Searching tests were applied to these fittings, and only those which complied in every respect with the prescribed regulations were stamped Detection of waste. and permitted to be fixed within the limits of the water supply. But this did not obviate the necessity for house-to-house inspection, and although the number of different points at which leakage occurred was still great, it was always small in relation to the number of houses which were necessarily entered by the inspector; moreover, when the best had been done that possibly could be done to suppress leakage due to domestic fittings, the leakage below ground in the mains, ferrules and service pipes still remained, and was often very great. It was clear, therefore, that in its very nature, house-to-house visitation was both wasteful and insufficient, and it remained for Liverpool to correct the difficulty by the application, in 1873, of the “Differentiating waste water meter,” which has since been extensively used for the same purpose in various countries. One such instrument was placed below the roadway upon each main supplying a population of generally between 1000 and 2000 persons.

Its action is based upon the following considerations: When water is passing through a main and supplying nothing but leakage the flow of that water is necessarily uniform, and any instrument which graphically represents that flow as a horizontal line conveys to the mind a full conception of the nature of the flow, and if by the position of that line between the bottom and the top of a diagram the quantity of water (in gallons per hour, for example) is recorded, we have a full statement, not only of the rate of flow, but of its nature. We know, in short, that the water is not being usefully employed. In the actual instrument, the paper diagram is mounted upon a drum caused by clockwork to revolve uniformly, and is ruled with vertical hour lines, and horizontal quantity lines representing gallons per hour. Thus, while nothing but leakage occurs the uniform horizontal line is continued. If now a tap is opened in any house connected with the main, the change of flow in the main will be represented by a vertical change of position of the horizontal line, and when the tap is turned off the pencil will resume its original vertical position, but the paper will have moved like the hands of a clock over the interval during which the tap was left open. If, on the other hand, water is suddenly drawn off from a cistern supplied through a ball-cock, the flow through the ball-cock will be recorded, and will be represented by a sudden rise to a maximum, followed by a gradual decrease as the ball rises and the cistern fills; the result being a curve having its asymptote in the original horizontal line. Now, all the uses of water, of whatever kind they may be, produce some such irregular diagrams as these, which can never be confused with the uniform horizontal line of leakage, but are always superimposed upon it. It is this leakage line that the waterworks engineer uses to ascertain the truth as to the leakage and to assist him in its suppression. In well-equipped waterworks each house service pipe is controlled by a stop-cock accessible from the footpath to the officials of the water authority, and the process of waste detection by this method depends upon the manipulation of such stop-cocks in conjunction with the differentiating meter. As an example of one mode of applying the system, suppose that a night inspector begins work at 11.30 p.m. in a certain district of 2000 persons, the meter of which records at the time a uniform flow of 2000 gallons an hour, showing the not uncommon rate of leakage of 24 gallons per head per day. The inspector proceeds along the footpath from house to house, and outside each house he closes the stop-cock, recording opposite the number of each house the exact time of each such operation. Having arrived at the end of the district he retraces his steps, reopens the whole of the stop-cocks, removes the meter diagram, takes it to the night complaint office, and enters in the “night inspection book” the records he has made. The next morning the diagram and the “night inspection book” are in the hands of the day inspector, who compares them. He finds, for example, from the diagram that the initial leakage of 2000 gallons an hour has in the course of a 41/2 hours’ night inspection fallen to 400 gallons an hour, and that the 1600 gallons an hour is accounted for by fifteen distinct drops of different amounts and at different times. Each of these drops is located by the time and place records in the book and the time records on the diagram as belonging to a particular service pipe; so that out of possibly 300 premises the bulk of the leakage has been localized in or just outside fifteen. To each of these premises he goes with the knowledge that a portion of the total leakage of 2000 gallons an hour is almost certainly there, and that it must be found, which is a very different thing from visiting three or four hundred houses, in not one of which he has any particular reason to expect to find leakage. Even when he enters a house with previous knowledge that there is leakage, its discovery may be difficult. It is often hidden, sometimes underground, and may only be brought to light by excavation. In these cases, without some such system of localization, the leakage might go on for years or for ever. There are many and obvious variations of the system. That described requires a diagram revolving once in a few hours, otherwise the time scale will be too close; but the ordinary diagram revolving once in 24 hours is often used quite effectively in night inspections by only closing those stop-cocks which are actually passing water. This method was also first introduced in Liverpool. The night inspector carries with him a stethoscope, often consisting merely of his steel turning-rod, with which he sounds the whole of the outside stop-cocks, but only closes those through which the sound of water is heard. An experienced man, or even a boy, if selected as possessing the necessary faculty (which is sometimes very strongly marked), can detect the smallest dribble when the stopcock is so far closed as to restrict the orifice. Similar examinations by means of the stop-valves on the mains are also made, and it often happens that the residual leakage (400 gallons an hour in the last case) recorded on the diagram, but not shut off by the house stopcocks, is mentioned by the inspector as an “outside waste,” and localized as having been heard at a stop-cock and traced by sounding the pavement to a particular position under a particular street. All leakages found on private property are duly notified to the water tenant in the usual way, and subsequent examinations are made to ascertain if such notices have been attended to. If this work is properly organized, nearly the whole of the leakage so detected is suppressed within a month. A record of the constantly fluctuating so-called “night readings” in a large town is most interesting and instructive. If, for example, in the case of a hundred such districts we watch the result of leaving them alone, a gradual growth of leakage common to most of the districts, but not to all, is observed, while here and there a sudden increase occurs, often doubling or trebling the total supply to the district. Upon the original installation of the system in any town, the rate of leakage and consequent total supply to the different districts is found to vary greatly, and in some districts it is usually many times as great per head as in others. An obvious and fruitful extension of the method is to employ the inspectors only in those districts which, for the time being, promise the most useful results.

In many European cities the supply of water, even for domestic purposes, is given through ordinary water meters, and paid for, according to the meter record, much in the same manner as a supply of gas or electricity. By the adoption of this method great reductions in the quantity of water Supply by meter. used and wasted are in some cases effected, and the water tenant pays for the leakage or waste he permits to take place, as well as for the water he uses. The system, however, does not assist in the detection of the leakage which inevitably occurs between the reservoir and the consumer’s meter; thus the whole of the mains, joints and ferrules connecting the service pipes with the mains, and the greater parts of the service pipes, are still exposed to leakage without any compensating return to the water authority. But the worst evil of the system, and one which must always prevent its introduction into the United Kingdom, is the circumstance that it treats water as an article of commerce, to be paid for according to the quantity taken. In the organization of the best municipal water undertakings in the United Kingdom the free use of water is encouraged, and it is only the leakage or occasional improper employment of the water that the water authority seeks, and that successfully, to suppress. The objection to the insanitary effect of the meter-payment system has, in some places, been sought to be removed by providing a fixed quantity of water, assumed to be sufficient, as the supply for a fixed minimum payment, and by using the meter records simply for the purpose of determining what additional payment, if any, becomes due from the water tenant. Clearly, if the excesses are frequent, the limit must be too low; if infrequent, all the physical and administrative complication involved in the system is employed to very little purpose.

The question of the distribution of water, rightly considered, resolves itself into a question of delivering water to the water tenant, without leakage on the way, and of securing that the fittings employed by the water tenant shall be such as to afford an ample and ready supply at all times of the day and night without leakage and without any unnecessary facilities for waste. If these conditions are complied with, it is probable that the total rate of supply will not exceed, even if it reaches, the rate necessary in any system, not being an oppressive and insanitary system, by which the water is paid for according to the quantity used.  (G. F. D.) 

  1. Since the above was written, this work has been taken over by the “British Rainfall Organization.”
  2. The volume of compensation water is usually fixed as a given fraction of the so-called “available supply” (which by a convention that has served its purpose well, is understood to be the average flow of the stream during the three consecutive driest years).
  3. On Some Disregarded Points in the Stability of Masonry Dams, Drapers’ Company Research Memoir (London, 1904).
  4. Engineering (May 12th, 1905).
  5. Proceedings of the Institution of Civil Engineers, vol. 172, p. 107.
  6. See Proc. Inst. C.E. vol. cxxvi. pp. 91-95.