function in the two-dimensional motion. They are defined by the relation 

 with the velocity of the double body flow as follows. 



3$ 1 dV ,,.. 



dx h 9y 



9$ 1 9^ ,,,v 



9y h dx 



If the double body is the body of revolution, then h is the radial length. 

 In general cases, it is determined by the partial differential equation 



3h + 3h + , ( 9U . 3v , , 



If we change the independent variables of Equation (58) from x,y to $,¥, 

 there is a relation 



l o "&T + v o 37" = q o W (67) 



Because of the fact that differentiation of the perturbation potential 



reduces the order of magnitude, the order of 3<J)../3$ and 3(f> -./Sf are higher 



2 2-1 

 than that of 3 <f>, /3$ by Y n • Differentiating the above equation again 



and omitting higher order terms, one obtains from Equation (57) 



2 

 , 3 <f>, 34>, 



% -T + ^0 3^ = ^o D(x ^> (68) 



Next, the independent variables are transformed again to new variables £, 

 n, ^ by the following relations. 



= kl e ° 



dC (69) 



29 



