698 Dr. C. V. Burton on the Kinetic 



twice ; thus the conditions sought for, in addition to (9a), are 



SC W St.)- ' 2c (-p _ 5t) =0 '- 



(15) 



17. Special Class i. An interesting case is that in which 

 there is but a single working coordinate, say yjr; so that the 

 system, regarded from our standpoint, has only one degree 

 of freedom. In this case the sole equation of motion is 



which indicates that the energy K, due to the " ignored " 

 momenta, necessarily behaves as potential energy, without 

 any condition having to be satisfied beyond those expressed 

 by (9a). 



18. Returning now to (7) and making use of (8) and (13), 

 we see that 



+ C(M^+N^"+...)+C'(M'-f + W$+...) + ... 

 =T-c|g-C'|§-...-Cx l -C^'-... . (17) 



Remembering that K is a h.q.f. of C, C, . . ., we have 

 accordingly 



= C_K_Cx 1 -Cx 1 '-..., . . . (18) 



by (9). Thus the modified function T', from which the 

 equations of motion (11) are derived, becomes identical 

 with C— K provided 



OXi + C'x/ + ... = 0; (19) 



that is, provided 



2C(Mt + N<£ + ...) = 0, . . . . (19a) 

 a condition which is the same as 



^2CM+^2CN + ...=0. . . . (19b) 



