1888.] A. Mukhopadhyay — BemarTcs on Monges Equation. 83 



To get the actual equation for the eccentricity, we have now simply to 

 substitute for c^, Cg, c^ the differential expressions to which they are 

 equivalent. For this purpose, we recall that the two first integrals 



-^d^z - 8 



^ S"^-^^ 



' ^S-^ ^^^^'t:^) = ^^2 



(I) = --. 

 •'(1)"= 



lead to the relations 



which give 



dhj d^y .(dW_ (dhjJ 



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



Hence, we have 



and 



W^ W3 + Y3 



c,Hl + c,^) = 



Y2 ya 



Therefore, 



» (S) 



C2» (1+0/)- ci= i-^ + -, 



sU^'V ,m 



\dx^/ 

 TV 



/d^V' 

 \dx^) 



„ . 3 



81 



where 



\dx^) 



