1921.] COMPARISON OF THE TWO METHODS. 17 



which the solution of the Eulerian equations appears corresponds, 

 in many cases, more nearly to what we wish to know as to the 

 motion of a fluid, our object being, in general, to gain a knowledge 

 of the state of motion of the fluid mass at any instant, rather than 

 to trace the career of individual particles. 



* On the other hand, whenever the fluid is bounded by a 

 moving surface, the Lagrangian method possesses certain theoreti 

 cal advantages. In the Eulerian method the functions u, v, w 

 have no existence beyond this surface, and hence the range of 

 values of x, y, z for which these functions exist varies in conse 

 quence of the motion which we have to investigate. In the other 

 method, on the contrary, the range of values of the independent 

 variables a, b, c is given once for all by the initial conditions. 



The difficulty, however, of integrating the Lagrangian equa 

 tions has hitherto prevented their application except in certain 

 very special cases. According!} 7 in this treatise we deal almost 

 exclusively with the Eulerian equations. The integration and 

 simplification of these in certain cases form the subject of the 

 following chapter. 



* H. Weber, Crelle, t. 68. 



L. 



