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 cd-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 cd of the cumulative flow below the cumulative demand, plus the greatest excess ef of the cumulative flow over the cumulative demand. This capacity is represented by the height of the line a'a' (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

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 be 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 streamflow 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.

JUNE JULY

Ave SEP OCT NOT

FIG. 3.

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.

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 be 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 be determined by examination of the variation of the actual from a constant demand.

180

119

100

M

DEC

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 chor c'h', whichever, in the particular case under investigation, is the greater. In the illustration the c'h' is a little greater, measuring 47% 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. 3representing, 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. 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 daily 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 daily 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 arca) and corresponding ratios:

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 mainApplied 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

tained and no foul water may be drawn off.

Mediterranean coast, is often concentrated into shorter periods. evaporation for the time; but gaugings made by the writer in the Morcover, it often falls upon sun-heated rocks, thus increasing 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.

Springs and shallow wells.

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 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."

Deep Wells.

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 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.

sand.

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 Wells in of sand also increases. In sand below water there are, of course, no open fissures, and even if adits could be 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 interspaces; 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

increase of

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 onlyin. 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 enormous increase of yield of such a well, if, by any means, we can get rid of the frictional sand, even from Artificial within the 16 in. radius. We cannot do this, but yield. 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

Pumps in

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 suction pipe only is below water. Pumps, however, may be (and have been) placed deep down in boreholes, 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 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.

Air-lift.

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.

Saline

water

below

ground.

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 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 marks of the formation, and has never been washed out. It is now worked as an important industry in Cheshire.

Wells in

Perhaps the most instructive cases of nearly uniform percola. tion 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 sand. be drawn off by wells or borings. On such an island, 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 saltwater 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. Vertical scale 13 times longitudinal scale

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, how ever, 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