52 Proceedings of the Royal Irish Academy. 



Hence, confining ourselves to principal term, 

 energy = —^-. 



Equation of Pressure. 



We have 



p = -\^'-^^^^m■^9^' (71) 



To determine F(f)^ consider centre of upper surface. For this point 

 evidently v = U. Also 



where 



d<j> 2 j,du ^ ^ Y,nP 2 ^du 

 '^'^ ~ T ^ cos nl — — = J P~ .y, 

 at I dt nR I dt ' 



y = — ^i-r - — ^1 -J- ■ ' • 



t I 

 We have, then, n denoting atmospheric pressure, 



which determines F{f). Assuming the same equation to hold for a 

 distance below the orifice, small compared with the height I of the 

 cylinder, but large compared with radius of orifice, we have 



whence 

 where 



1 2 (Jy 



1 ^ du . ,^ , 



\ Rir 1 2i?7r 

 J-i —J- . J-i — • 



I 



This gives the equation determining the law of variation of u 



R 



till steady motion is attained. When is small, y' - y is proportional 



v 



I"" Y (x) dx 



to We may evidently write on the left-hand side 



for ^2-^72. 



