Manchester Memoirs, Vol. xliv. (1900}, No. 10. 



X. On the Motion of the Fluid Particles in a Class of 

 Cases of Steady Motion. 



By R. F. GWYTHER, M.A. 



• Recch'ed and read February 6th, iqoo. 



Although the most interesting cases of fluid motion 

 depend upon the general motion of the fluid and not upon 

 the motion of individual particles, it is desirable to obtain, 

 if possible, a few cases in which the motion of a particle is 

 determined without approximation and satisfying abso- 

 lutely the surface conditions. Such a case can be found 

 for standing waves in a channel, but no case of steady 

 motion has been obtained. This paper shows how far we 

 can proceed in what would seem the most simple class of 

 cases, and shows what are the difficulties still remaining. 



I deal with that class of cases of steady m.otion where 



can be found to represent explicitly the Eulerian relation. 

 When this can be done it is probably the most 

 useful form possible, as it allows the lines of motion to be 

 readily drawn on a diagram. It is also very convenient 

 when surface-tension has to be taken into account, since 

 the measure of curvature of any line of motion is 

 given by 



/ {/" (,/, + i^)f (^ - i^) -f" {<p - iW (<P + i4^) } 



and even if the surface-tension has not been accounted 

 May 4th, igoo. 



