60 Mr Darwin, Lagrangian Methods for High Speed Motion 



grangian form. The solution will usually depend on finding integrals 

 corresponding to coordinates which do not occur explicitly in L 

 and if cj) and A do not involve the time explicitly there is also the 

 energy integral. This has the form 



^^^r/+2.,<^+SS^?^^ 



Simfi^ + Sf '-^l r/ + 2ei</. + SS -^-^ 



This completes the development of the method. Its direct applica- 

 tions are naturally somewhat limited, since, even with the large 

 order terms only, there are comparatively few problems that are 

 soluble. A problem of some interest that can be solved completely 

 is the motion of two attracting particles, where their masses have a 

 finite ratio*. 



* A discussion of this problem by the present writer will be found in Phil. Mag. , 

 Vol. 39, p. 537 (1920), together with a somewhat fuller account of the general theory. 



