THE CURRENT METER. 261 also averages of the areas due to the sections into which each cross section is divided. From the cross sections on paper the lengths of the divisions a, b, c, d, and e, are taken, and these are , staked off in the river ; iron-shod poles about 10 or 12 feet long are used for this purpose, which a boatman will soon drive into the ground; midway between these the surface velocities are taken, by means of white tin balls, as we have just mentioned as regards streams, only rather larger in diameter, about three inches, so that they may be readily seen. We have thus the surface velocities for each of the sections into which each cross line is divided; with regard to the coefficients by which each of these is to be multiplied to obtain the mean velocities, it is to be observed of the coefficients 81 V, and 835 V, mentioned above, that they are due for the surface velocities in the centre of the stream, and those by which the mean velocity of the whole of a stream, from the surface water to the bottom, and from the centre to the sides or banks, is to be obtained where applicable. The greatest coefficient will have to be applied to the surface velocity of the section d, a smaller one for c, and less again for b, and the least for a and e, where the friction will in every way be more marked in its effects. We prefer obtaining our mean velocities by direct experiments in the following manner, supposing we are still adopting floats, of which we take a couple, connected together by eyes and a cord long enough to reach from the surface to near the bottom of the water; one of these we load sufficiently to sink nearly to the bottom, and to draw down the other, left quite empty, so that it is just perceptible on the surface; the velocities thus obtained we take for mean velocities. The advantage of having one float loaded and the other unloaded, is, that the slightest obstruction on the lower float, or on the line, becomes quite perceptible on the upper one, in which case we reject the trial thus made; after taking half a dozen satisfactory experiments, we take the mean for the mean velocity. Elliott's Current Meter, Fig. 129A, is a most useful instrument for ascertaining velocities, either a few inches below the surface, at the bottom, or at any depth between. A is a rod, by means of which the instrument is sunk to any required depth ; C, a vane consisting of four spiral wings, called the rotator or fly, the axle of which carries an endless screw which turns a toothed and graduated wheel, B, by which the velocity is indicated ; F is a portion of a plate by wbich the instrument is steadied in the course of the current.* The constant due to each instrument must * The “Fly” is brought into action on the wheel by tightening the line which acts on the spiral spring, and the action ceases as soon as it is loosened. be ascertained by direct experiment, by drawing it through still water a certain number of feet per minute, or submitting it to the action of a current, the velocity of which has been carefully ascertained. Massey's Patent Log, for measuring velocities at sea, is constructed on a similar principle ; the whole is contained within a brass wedge-shaped box; there are three cogged wheels instead of one, acting on each other in such proportion that a total revolution of one completes a division of the next, or to, a revolution of the next ), registering thus from 160 miles to tenths and decimal parts. It is towed astern by a stout lead line of 60 fathoms. Mr. Beardmore says that he has had a current meter constructed with two wheels, the second having one tooth less than the first, and showing in its revolution about 11 28 turns of the first; this gives the power of leaving the instrument a considerable time under water, which is very desirable to obtain a good mean velocity. There are two or three other instruments made for measuring velocities, but the current meter above described is now in general use in preference to any other. In connexion with stream gauging, it is generally of the greatest importance to ascertain the effect of rain on the discharge of streams, both as regards depth of rain and time. Where there are many overfalls and rain-gauges, and consequently a great number of observations to make during the day, the operation of gauging the depth of rain fallen by means of the glass we have described becomes troublesome, and takes up a good deal of time. At Fig. 129 is shown an addition to the rain-gauge, by which the depths of rain falling during a wet day may be ascertained with great facility; it will be perceived that leading from the funnel to the reservoir R is a tube containing an inner one, the space between the two conveying the water from the funnel to the reservoir; to the upper part of the inner one is fixed a glass tube T; the dimensions of the reservoir are made according to what we have already said about the gauge glass, so that any defined rise in the reservoir gives a corresponding depth of rain ; at the bottom of the reservoir is a float, which rises as the rain falls, and carries with it a very slender rod rising up through the inner pipe into the glass tube, which is graduated; the depth of rain falling is thus ascertained at a glance on the graduations above zero, with which the top of the rod coincides when the reservoir is empty. When the float is not in use, the inner pipe may be stopped up by means of a cork, so that there is but little room for the action of evaporation. It is generally also very desirable to distinguish the average flow of a stream from the flood streams, which is often difficult to do. Mr. Leslie has proposed the following method : USEFUL MEMORANDA. 263 Tabulate the gaugings in the order of their quantities, and divide the number of observations into four equal parts, and take the least fourth for droughts and the highest for floods, the average of the middle half is then obtained, and all quantities in the whole table above that average are set down as flood water; next, all the gaugings not exceeding the average of the middle half are tabulated at their actual quantity ; but all that are above the average are put down as equal to that average quantity; the mean of the whole of the new table is to be considered as a fair average of the water flowing in the stream, exclusive of floods. Mr. Leslie gives a table of a stream thus treated, a which varied in its run from 1902 to 59,861 cubic feet per minute. Average of the whole was 10,231 cubic feet per minute; the average of the middle half was 7,234 cubic feet per minute; and the average quantity, exclusive of floods, was 5,830 cubic feet per minute. Having the depth of Rainfall in inches, to ascertain the number of cubic feet per acre.- Multiply the constant, 363, by the depth of rain in tenths of inches; the product gives the cubic feet per square acre. Examples.—Depth of rain 4 inches, required the number of cubic feet per acre. 363 x 40 = 14520 cubic feet per acre. Depth of rain 54 inches, required the number of cubic feet per acre. 363 x 55.0 = 19965 cubic feet per acre. Having the depth of Rainfall in inches, to find the number of cubic feet per square mole.—Multiply the constant, 23232, by the depth of rain in tenths of inches; the product is the number of cubic feet per square mile. With the depth of Rainfall in inches, to find the weight in tons per square acre.-Multiply the constant, 10128, by the depth in tenths of inches; the product is the weight required nearly, with three places of decimals. To find the weight in tons per square mile from the depth of Rain in inches.-Multiply the constant, 64821, by the depth of rain in tenths of inches; the product is the weight required nearly, with two places of decimals. To find the power of a Fall in Mill-work.—Multiply the discharge in cubic feet per minute by the height of the fall in feet, and by 62-5, and divide the product by 42000; the quotient is the amount of horse power. "In practice, a discharge of twelve cubic feet per second, with a fall of one foot, is taken as equal to a one-horse power; therefore the number of cubic feet discharge per second, divided by 12, and multiplied by the fall in feet, is equal to one-horse power. Example.—130 cubic feet discharge per second, with a fall of 48.75 feet = 528 horse power. In the ordinary state of works the wheels are about filled to two-thirds, that is, two-thirds of the bucket are considered as filled to produce a useful effect; and in the above, two-thirds of 528 = 352 horse power is about the useful effect. CHAPTER XV. LEVELLING. Curvature. - The Dumpy Level.-- Adjustments. - Levelling Staves.—The Dumpy Level.—Levelling Staves. If the earth were a perfect sphere covered with water, unaffected by wind or tide, the surface of the water would trace a surface parallel to the horizon in every direction, which surface would consist of an infinite number of level lines, all of which would intersect the radii drawn from the earth's centre at equal distances, and at right angles to them. The tracing of such a line of any length on the earth's surface, or at any given distance from it, would be setting out level lines. The practice of levelling, in the engineering or surveying application of the term, consists of the ascertaining of the difference of level between any two places, or the differences of level between any number of places, whether in a straight line, or situated in any other manner on the earth's surface. Let A E B, Fig. 130, be a portion of the surface of the earth, with its centre at C; let an observer be supposed standing at E, with a spirit-level in adjustment; t t will be the line coinciding with the axis of the telescope ; this line would be parallel to TET, at right angles to E C, a line supposed to be dropped from the station E' to C, the centre of the earth; the true level line would be the curve a E'b, parallel to AEB; t E'ť is the apparent level, and a El the true level line; and the difference equal to at, b ť', E't or Eť is the sensible horizon, a E or Eb, the real horizon; but the visual line along the axis of the telescope produced is distorted by the effect of refraction, and both these circumstances have been alluded to under the head of "Survey. ing Instruments.” If the level between E' and b, instead of being set out at once from E', had been set out, say at 10,000 stations, each time gradually nearing b, then the apparent levels would have so nearly coincided with the true levels, that the differences would not have been worthy of consideration. |