176 CHANGE OF THE INDEPENDENT VARIABLE. 



and thus -~ = -*- , 



dx dx 



dy 



d*y _ d 

 ~ ~ 



' 



dx d*x _ 

 ~ s 



198. The formulae of Art. 197 may also be obtained 

 directly thus : 



^ = J_. 



dx dx' 



dy 



,, f d^v d 1 



therefore ^ = - -- 

 ax* dx dx 



d I dy 

 ~ dy dx' dx 

 dy 



d?x 



_ 



dtf dy _ dy* 



~ fdx\ ' ~dx /dx\* ' 



W \dy) 



d'*x d*x 



d*y_ d _~djf__ d Jdj_ _ 



dx 3 dx fdx\*~~ dy /dx\*' dx 

 (dy) 



