We may have parallel valleys of greater or less magnitude drained by streams and tributaries, and of which the conformation at the surface and the geological configuration underneath may be such that one valley may, as it were, completely rob the other, both as regards rainfall and discharge of water absorbed; but the extent to which this may occur can only be ascertained by careful gauging, both of streams and rainfall. This fetching of water by one valley from another often takes place for great distances and far beyond the apparently legitimate range of any particular gathering ground.

In the chalk, unless where the sides of the hills are steep, a large proportion of the rainfall is absorbed, and carried down to flint beds, where it is stored in large sheets of water; in this formation, also, water is often fetched from great distances by a flat underlie. The water is hard, though a most agreeable drinking water.

The Silurian formations, the granites and the older rocks generally, as well as volcanic districts, throw off water very rapidly; these and the millstone-grit formation are all favourable for giving fine soft water.

Sandstones and shales form excellent filters, and the water flowing from them is always very pure, and generally of one or two degrees of hardness.

The Old and New Red Standstone formations have great powers of storing water, as exhibited by the numerous wells formed in these formations.

It often occurs that in gathering grounds, otherwise excellent, there may be portions yielding water of an inferior character, such as that flowing from decomposing peat, or from a tract of land highly manured, or from a metalliferous district; the quantities of water discharged from such districts have generally to be ascertained. Similar observations may have to be made as to quantities of hard and soft waters, and of the purest, flowing from one gathering ground. Such may be required for dye, print, and chemical works; we may have to ascertain the quantities of water discharged by streams appropriated by existing mills or other interests, and also of such waters which it may be desired to substitute for them.

Enough, we suppose, has now been said to explain the importance of careful examination of extensive gathering grounds, not only as regards formation and configuration, but also as regards the position of stream and rain gauges. Where a number of rain gauges are used it is more than desirable that they should all be of exactly the same diameter; this may be from 6 to 12 inches, at the option of the observer; their being all of one size obviates the necessity of there being more than one graduated measuring glass; and, as this is an important though very simple instrument, we will say a few words about it because, unless care be taken, it is very likely to get broken.

The area of the rain gauge funnel, multiplied by 252-458, the weight in grains of a cubic inch of distilled water, and the product divided by 437-5, the number of grains in one oz. avoirdupois, gives the weight in ounces of one inch depth of rain over the area of the rain gauge; then the depth of any cylindrical glass, containing such quantity of water and graduated into tenths and hundredths, will give the depth of rain over the area of the gauge. If, for instance, the diameter of the rain gauge is 7 inches, then the area will be 38.4846 inches, and we shall have

Then any glass containing 22.205 ounces of water, and graduated as above, will give the means of measuring the depth of rain which has fallen on the gauge.

The above calculations are shortened by using the constant 0-577; thus 38-4846 × 0.577 equal to 22.205, and the same for any other area of gauge; then as a general rule we have the square of the diameter of the area of gauge x 0.7854 x 0.577, which gives the weight in ounces of one inch depth of rain over the gauge. result will of course be obtained by simply multiplying the square of the diameter by the constant 0·45317.

The same

Where we have any glass of a given diameter, and we wish to find the depth that shall contain a quantity of water equal to 1 inch distributed over the area of the rain

gauge, divide the weight in ounces of such inch of water by the square of the diameter of the glass multiplied by the above constant 0.45317; the quotient will be the depth of the glass, which, divided in tenths and hundredths, gives the graduations required. For instance, let the glass be 4 inches in diameter, and the diameter of the gauge 7 inches as above, then

The hydraulic inclination of streams and rivers is found practically by dividing the head of water by the length. The hydraulic mean depth is the sectional area of water divided by the wetted border or perimeter.

The mean velocity is found approximately by multiplying the maximum velocity, which is at the surface and centre of a current, by the following co-efficients :

0.81 for small channels

0.835 for larger channels, but not irregular rivers. For crooked channels, with shallow streams over beds of stones and weeds, the above co-efficients may be reduced to 0.7.

The surface velocity of streams may be measured by floats; where we have nothing better at hand, a slice of apple makes a very good float; the velocity with which this flows over a hundred feet of the stream should be ascertained by repeated experiments.

To measure the discharge of rivers by mean velocities, we should have a section across the breadth, and, according to inequalities in the bed, this breadth should be divided into sections, and mean velocities obtained for each of these.

The current meter is a useful instrument for measuring the velocity of streams at any depth of water; we here give a figure of this instrument. A is a rod to sink it to

any required depth; c is a vane or 'fly,' the axle of which carries an endless screw turning a graduated wheel B, which indicates the velocity; r is a plate which steadies the instrument, and keeps it vertical.

VELOCITIES OF STREAMS AND RIVERS.

209

By giving a slight pull to the line D, the instrument is released. The velocity of a stream may be ascertained at

any depth, and a suitable average velocity may be taken to ascertain the discharge. The current meter is useful also to ascertain the velocity of under currents.

The constant for every current meter must be ascertained by experiment.

P

CHAPTER XII.

OFFICE WORK.

LAND QUANTITIES-PLANIMETER-REDUCING PLANS-PANTAGRAPH

EIDOGRAPH.

ASCERTAINING land quantities from plots, or scaling, as it is termed sometimes, is a most tedious operation, when we have any large quantity to deal with; the method almost always adopted in practice is to reduce the figure to be scaled to some parallelogram, or divide it into triangles. The planimeter of Messrs. Elliot, here illustrated, shortens this very tedious operation. E and F are two points at the ends of the movable arms, A and B ; when in use the

B

the paper.

less screw,

E

instrument rests on these two points, and on a third, being that part of the graduated wheel D which is tangent to G is a graduated disc connected with an endand H is a vernier to the wheel D. In the operation of computing with the planimeter, place the point E conveniently on the paper, so that the tracer F may be in a position to be run over the greatest possible portion of the periphery of the figure to be