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



We also have, from the same equations combined with the 

 equation of continuity, 



ld(mr, X) , fd' Id d'\, 



or — ^ ^ + v[^, + -:^ +:^A\ogr(o = 0. 



r d {r, z) \dr^ r dr dz J ° 



This last equation may be written 



^^+vrVnogro. = 0, 

 d (r, z) ° . 



but since V'' log r = 0, 



it reduces to the form 



d(r, z) 



'•'' ^-J^^+^r[^nogf{x)-Vnogm] = (16). 



The motion is therefore given by equations (14), (15), (16). 



4. For the special case of motion symmetrical about an axis 

 in which the vorticity is distributed according to the law 



Vnoga) = 0, 



we have mr a function of ^, and (14) and (15) reduce to the 

 forms 



^+F+1^^^ +/(%)= const., 



S-,7l? + l^H-.y'(x) = 0. 



dr^ r dr dz 



or the theorem takes the same form as in the case of the perfect 

 fluid. We have also 2&) = rf^ (;y)- 



We will now consider the case in which, the motion not being 

 steady, the vorticity is distributed according to the law expressed 

 by the equation 



aiogw (d"- Id d^\ , 



This equation may be written in the form 



dt~''\di'''^ rdr^ dz'J ft)|Uv """U^/r 



