Canon Moseley on the steady Flow of a Liquid. 355 



Also 



(weight CcD)/i = work actually done by weight of efflux 

 per unit of time, 

 — TT*- 



.-. U 3 =w7rR 2 i/A-U + U 4 (22) 



But 



U l +U 2 +U 3 +U 4 =Ut; 



.*. adding and striking out common terms, 



U 1 + \J 2 + 2U 3 =w7rWvh (23) 



But 



v — \J2gh %> 



by equation (5), 



U 3 =27rR/(/^ 1 +X l V 2 jV; 

 by equation (4), 



U,= — | v 3 ?'dr; 

 9 Jo 



TrwC* - 



••• — l v 3 rdr + U2 + 4 ! TrW(fM l + \ l V 2 )V = WTrK*h \/2ffh. . (24) 



y jo 



Now v=y Q e-f r , 



,. U 1= ™f Wr=^f B £ -3v^= ^[1- (1 +3 7 R) £ -vH]. 

 1 ^ Jo y J. W / J 



But since V=r e~v R , ,\ v =Ve YR , 



.\ by equation (24), 



7rwY 3 



-^-[eW-SyK-l] + U 2 + 47rR/( / u 1 + \ 1 V 2 )V=W7rR 2 A i/fyA. (26), 



If /Xj be exceedingly small as compared with X X V 2 , and U 2 be 

 neglected, 



irwV 3 _ 3 



-— r [ 6 3yR _ 3 7 R _ X\ + 47TR/X! V 3 = 7TW v/2^R 2 /4 ; 



• y- ^(2#RtM 



& (€3yR ~ 3yR " 1)+4m, J 



* Phil. Mag. September 1871, p. 186. 

 t Ibid. p. 186, equation (2). 

 % Ibid. p. 188, equation (8). 



2 A 2 



Ui=& e3yR - 3 rft-ij; - • • (25) 



