316 Mr J. Brill, Note on the Steady Motion [May 27, 



and (8) will cause the bulk of the terms under the integral sign 

 to vanish. If we seek to determine the condition that the re- 

 mainder may vanish also, we find either that ni is a function of %, 

 which leads to the case we have just considered, or that the form 

 of the stream-lines is not to be varied. 



In connection with the above special case, it is interesting to 

 note the case in which, the motion not being steady, the vorticity 

 is distributed so as to obey the law 



3M_r=„vMogf. 



This equation may be written in the form 



^^ l;-r-il(i)^(i) 



and, combining it witii the equation 



we have .„| + „| = -^j(|y+ (|)] , 



or 



dlogJ\ d^ / _ 9 log ^\ 95 _ 



dec J dx \ dy J By 



dy Jdy 

 Adopting the same notation as before, we have 



d(oe, y) 



or ^ a function of % and t, so that at any instant ^ is constant along 

 any of the curves ;)^ = const., as in the above special case of steady 

 motion. 



3. We now pass on to discuss the case of steady motion sym- 

 metrical about an axis. In this case the equations of motion 

 assume the form 



cr oz 



dz 

 In addition to these we have 



\dr r) 



.(9). 



or r oz 



A dV dU . 



and ^5 -^ =■ 2&). 



or oz 



