ON THE GAUGING OF WATER BY TRIANGULAR NOTCHES. 155 



zon. I therefore made numerous experiments to determine what might be 

 the amount of the ordinary or of the greatest effect due to the diminution 

 of pressure of the air within the bell. I usually failed to meet with any per- 

 ceptible alteration in the quantity flowing due to this cause, but sometimes 

 the quantity seemed to be increased by some small fraction, such as one, or 

 perhaps two, per cent. On the whole, then, I do not think that this circum- 

 stance need prevent the use, for many practical purposes, of notches of any 

 desired width for a given depth. 



My experiments give as the formula for the notch, with slopes of two 

 horizontal to one vertical, and without the floor, 



Q=0-636 H^ 

 and for the same notch, with the horizontal floor at the level of its vertex, 



Q=0-628 nt 

 In all the experiments from which these formulas are derived, the bell of 

 falling water was kept open by the insertion of a knife or strip of iron, so 

 as to admit the atmospheric pressure to the interior. The quantity flowing 

 at various depths was not far from being proportional to the f power of the 

 depth, but it appeared that the coefficient in the formula increased slightly 

 for very small depths, such as one or two inches. For instance, in the notch 

 with slopes 2 to 1 without the floor, the coefficient for the depth of two 

 inches came out experimentally O-G^Q, instead of 0'636, which appeared to 

 be very correctly its amount for four inches' depth. It is possible that the 

 deviation from proportionality to the f power of the depth, which in this 

 notch has appeared to be greater than in the right-angled notch, may be 

 due partly to small errors in the experiments on this notch, and partly to the 

 clinging of the falling vein of water to the outside of the notch, which would 

 evidently produce a much greater proportionate eff'ect on the very small 

 flows than on great flows. The special purpose for which the wide notches 

 have been proposed is to serve for the measurement of wide rivers or streams 

 in cases in which it would be inconvenient or impracticable to dam them up 

 deep enough to effect their flow through a right-angled notch. In such 

 cases I would now further propose that, instead of a single wide notch, two, 

 three, or more right-angled notches might be formed side by side in the 

 same weir-board, with their vertices at the same level, as shown in the an- 



nexed figure. In cases in which this method may be selected, the personsr 

 using It, or making comparisons of gaugings obtained by it, will have the 

 satisfaction of being concerned with only a single standard form of gauge- 

 fiotch throughout the investigation in which they may be engaged. 



By comparison of the formulas given above for the flows through the two 

 notches experimented on, of which one is twice as wide for a given depth 

 as the other, it will be seen that in the formula for the wider notch the co- 

 efficient -636 is rather more than double the coefficient -305 in the other. 

 Ihis indicates that as the width of a notch, considered as variable, increases 

 trom that of a right-angled notch upwards, the quantity of water flowing 



