297 
1908-9.] Discharge of Water from Circular Weirs. 
of D. Thus the discharge is calculated for a number of layers between the 
water surface and the bottom of the orifice, each result being in the form 
of a product of D 3/2 and a number. The values of these elementary dis- 
charges are then plotted as abscissae, with the corresponding values of li as 
ordinates, and a curve is obtained which shows the variation in the dis- 
charge from the bottom of the aperture to the water surface. The area 
under this curve, divided by the scale of the drawing, gives the value of 
the integral for the particular head chosen, in the form of a product of 
D 5/2 and a number. 
The values of H actually taken were OTD, 0*2D, and so on by tenths 
of D up to TOD. To obtain the total discharge for each definite head of 
water, the elementary discharges were calculated for layers at depths of 
005D, 0T0D, etc., from the water surface — that is, at every twentieth 
part of the diameter between the water surface and the bottom of the 
orifice. The curves obtained in this manner are shown in fig. 2. The 
area under each curve gives the total discharge of the weir for the corre- 
sponding head of water. For the original drawing the horizontal scale is : — 
1 inch — 005 D 3/2 , and the vertical scale is: — 1 inch = OTD, so that 1 square 
inch represents 0005 D 5/2 . By multiplying each area by 0’005D 5/2 , and then 
by the constant 1205, the corresponding discharge is obtained, as given in 
the second column of Table I. The discharge for any size of orifice can be 
