296 
Proceedings of the Royal Society of Edinburgh. [Sessi 
The total discharge of water from the oritice is 
2 J2g j Jh { H - h){ I) - (H - h )\ . dh cubic feet per second, 
= 12 '05 1 Jh { H - h){ D — (H — /&)} . dh gallons per minute, 
if D, H, and h, in the last expression, are measured in inches ; these are the 
units most commonly used in practice. In fig. 1 the water surface, AB, lias 
been taken between the centre and the bottom of the hole, but the form 
of the expression for the discharge remains the same whatever the position 
of this surface. 
The integral is elliptic, and does not admit of a direct solution, but the 
result may be obtained by a graphical method, as follows. A definite value 
of H, in terms of D, is taken, and numerical solutions of the expression 
Jh(K-h)\D-(K-h)} 
are found by giving to h various values between zero and H, again in terms 
