82 



A. Mukliopddhyay — Remarhs on Monqes Eqtiatiori. 



[Feb. 



wliere K^, Kg are any two constants is a second integral of the Mongian 

 equation. From this we have 



d_ 

 dx 



\dx )\dxV 



dx^ 



= 0. 



Taking the logarithmic differential, we get 

 d^y dhj d^y 



dx^ 



^_p 



dx 



4 dx^ dx^ _ 



3 ^"'^~ 



dx^ dx^ 



which gives 



Let, 



Now as 



we have 



dx dx^ dx"^ dx \dx^/ \dx^/ dx^ 



dx^ dx^ \dx^) 



^~ dx'^ dx^ \dxy 

 dx^ dx^ \dxy 



dx \dx^/ \dx^/ dx^ dx dx^ dx'^ 



\dx^) dx^ dx 



-4 



h w 



h 



y = ^3, say. 



But, we have shewn that 



whence. 



h^ 



Co2 "■ &2 h' 



^=.„2-a. 





Therefore, the equation for the eccentricity becomes 



(2-62)' 



(i-)" I 







)2 



