VELOCITY OF A FLUID UNDER CONSERVATIVE FORCES. 169 



•which Ave do not at present understand ; and it is possible 

 that the sun may have a similar influence. 



Since writing the above, I have learned that Mr. Baxen- 

 dell made use of the method of mean departures described 

 in this communication in one of a remarkable series of 

 papers which he presented to this Society on March 8th, 

 1864. But I have no reason for supposing that he was 

 aware of the peculiar characteristics of the method de- 

 vised by Mr. Dodgson and myself, in virtue of which we 

 can, with comparatively little trouble, ascertain the exact 

 periods of inequalities which are crowded very near to- 

 gether in the time-scale. 



XIX. On a Form of representing the Velocity at any 

 Point of an Incompressible Fluid under Conservative 

 Forces. By R. F. Gwyther, M.A. 



Read February 24tb, 1880. 



I . The velocity at any point of a fluid may be repre- 

 sented in other forms than the usual velocity potential or 

 the vector potential of Helmholtz. 



The form o-= v^ corresponds to the case when SctSt is 

 a complete differential without a factor ; let us imagine it 

 to be made a complete differential by a factor — that is, a 

 to be of the form 



or to be a combination of the two, thus, 



cr=:V^ + A;v^ (!•) 



