Mr. R. A. Sampson. 



[Dec. 11, 



Therefore 





 ad 



Whence 



disregarding a constant. 



But By = V 



and clearly, ^ (- m , 



= 2m . . 

 r 



= 2.IH . B\nO . 

 . cos 0, 



Hence 



= - V- (, 

 + (m, ) - ^ (n, ?) + 



c 



Therefore 



and 

 where 



= 2mr 



(1), 



disregarding a constant. 



Thus if m =/(f) d, we may, by properly choosing the function/, 

 write 



(2), 



where YT is the current function for any irrotational motion in a 

 liquid, symmetrical about the axis of z. 



Again, if r = ^{^+(2-?)"}, 



dr w dr _ z 



dv ~ V dz ~ r 



d*r 1 tr 3 d*r 1 (z r) 3 



Therefore J^+^ = 



1 



r 



dw 



