78 



PROFESSOR A. R. FORSYTE ON THE INTEGRATION OF 



X- - 9. P, 



I "V ' ; d \ 



ii = (1, 0, 1 ft T ' T 



\ ' .A.&; dy 



\ 2 



manifestly < is an arbitrary function ot x, y, u. 



To deduce the value of v so far as concerns variations of x and y, we have 



( Jv 



fi 



- = I -f- np 



and 



- = w -f 



therefore 



where thus far V is any arbitrary function of u alone. 



48. As yet no account has heen taken of derivatives with regard to u ; but the 

 whole of the equations are subsidiary to the construction of an integral of the original 

 equation. 



The part of the value of v given by V (u) can be dropped, as it has been considered 

 in the earlier stage, or it can be regarded as absorbed in the other part of the value, 

 all that is necessary for this purpose being that the function < should have a different 

 form. 



Assuming this done, the function < must be such as, first, to satisfy the equation 



= n = 

 du an 



with the preceding notation. Now 



