LAGRANGE'S EQUATIONS 343 



Since r- is a function of lt 2 , , we have 



_ = _, _, 

 dt(ddj del dt 20^ dt 



while, by differentiation of equation (178), 

 dx &x * d*x 





The right-hand members of equations (181) and (182) are seen 

 to be identical, so that 



dx 



and the last line of equation (180) transforms into 



/ . dx . dy . dz 

 I l_ ni iL _i_ 2 



of which the value is 



d 



dT 

 or 



1 



Equation (180) now becomes 



CC/tX/C "^"^7 ~^7 | *" - - 



Cc-6 

 | 



From the equations of motion, 



X=W ^ 7 " V ^ 

 so that this again becomes 



d/d_T\_dT_^/ v ix^ v <ly^ l7 te 

 dt\x 



