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 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 area. |
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
