4 GWYTHER,i]/^//^« of tJie Fluid Particles in Steady Motion. 



are alike, and that when we form the necessary surface 

 conditions in either case, the results are, mutatis mutandis^ 

 applicable to the other. 



If then x-\-iy=f{<^-\-i'i/), is a solution of the Eulerian 

 equations which can be made to satisfy the surface 

 conditions, then 



X + iy =f{u + il>) , 

 where 



/^ 



/'(// + i/>)/ \u - ib)du -ct + a , 



is under the same circumstances the solution of the 

 Lagrangian equations. 



The character of the difficulties, supposing those 

 connected with the surface conditions to have been over- 

 come, are now obvious. To obtain the case of a simple, 

 compact solution, it is requisite that the integral must be 

 of such a character that u can be obtained from it as a 

 manaeeable function of ^ and b. 



