﻿Steady Motion of a Viscous Fluid. 457 



Hence 



v'HSNIf) 2 } { -^(iog/'w) + F"(«)}= /w . 



Using a welhknown property of conjugate functions this 

 may be written 



so that we have to determine a function of a-f iff such that 

 the square of its modulus is linear in ff. Mr. Gr. N. Watson, 

 to whom I submitted this problem, has supplied me with the 

 complete solution. If 



| tfa+i/3) I 2 =A/3+B, 



where A, B are real functions of a, then 



0(a + t£) = *«*<•+*>, 



where X is real but k may be complex. In this case 



A = 0, B= | tc | 2 e 2 *«. 



Applying this result to the problem in hand 



d(x + iy ) 

 d(* + iff) 



-fce x(a+i P\ 



Hence 



/(<0=f< 



The constants «:, A, merely determine the scales of measure- 

 ment in the different systems of coordinates, and we have 

 only two distinct solutions (1) k = 1, \=0j (2) « = 1, X=l. 



The first case gives 



u + i/3 = x + h/ } 

 and we have a solution in Cartesian coordinates 



yjr= — y//(2a,i' + b)+ ill e oaa + te + c (^o;) 3 . 



