88 Method of Integration. 



let the auxiliary equation be 



dh _ dh 

 dxdy dydx 



c being some undetermined quantity, if these equations be 

 added the result may be put in the form 



d /dz ^ ^ ^ d^/dz ^ ^ dz\ 

 dx\dx dy) dy\ dy dxp 



or in the form 



d ( dz dz\ ,, d / a dz dz\ ,„„ 



Now let c be so determined that the coefficients of -r 



dy 



on both sides are equal ; this implies the equation 



hence if for c we substitute its two values we shall have two 

 equations and two arbitrary functions, hence from these 



the values of ~r and 7^ may be determined, and the inte- 

 gration completed. 



