278 Prof. M. J. M. Hill. Motion of Fluid, part of [Feb. 7, 



With, notation similar to that in the pre ceding case, the equation in 

 X is — 





'dx\ 







dt 



n 





dX 







[do j 





The current function is 



Bt J 



=H 



( dx\ 



< sx 



rSr i 



de 



For a vortex of invariable form rotating about the origin with 

 angular velocity ~ , this equation becomes 



V drS r r2 #A St 2 dt ) \ 1 ~SX J j> | , 



and the current function is 



SF(X,t) _r* da 

 St 2 dt' 



(3.) Motion symmetrical with regard to the axis of z in planes 

 passing through it, referred to cylindric co-ordinates r, z. 

 The equation in X is — 



/dxV 



rAjr* r dr dz*)\ St 



+ jVcr 



dt_ 

 dX 

 K dz , 



L 



fs¥(X,t) 



■h 



rSr 



SX ifdXV: 



The current function is 



st 



+ I rSr 



/ dxY 



dJ 

 dX 

 \ dz 



