580 Prof. R. C. Tolman on the Relativity Theory : 

 Consider now a function T' defined by the equation 



T'=W! + W,+ . .. -T; . . . (15) 

 differentiating, we have 



dT = ^ i d<j> l 4- ■^ 2 d<j> 2 + . . . 

 -\-fad-ty-i -f- <£ 2 <fy- 2 + . . . 



and this by the introduction of relation (14) becomes 

 dT' = fadfr + <f> 2 df 2 + . . . - ^ <ty, - |^<ty 2 - . . . (16) 

 Examining this equation, we have 



d<£i~ B>i' ' ' ' * 



=*i (18) 



(17) 



Now Lagrange's equations give us 

 oft 



ll^-M-^-^ - 



But since U is independent of <£ l5 we have 



and furthermore by (17) we have 



Substituting in Lagrange's equations, we obtain 



^ti = _ B(T' + U ) 

 dt " B</>i 



Writing T'+U = E we have 



djn _ _dE 



(19) 



