7i] Solution of Equations 



We find, on differentiating and simplifying, 



71 



T V ^(J "-j~ *x ( Yl 



so that, on substituting the assumed value (162) for v, 



dv 



00 0V OV\ 



2 T ^- + ,- 

 ^ S^ 3X/ 



-f . . . 



f -, x dw dw 



4 S- + r- 



3X- 



) ............... (163). 



Let us now assume w, w^w" ... to be successively determined by equations 

 of the form 



(166), 



where 6 is as yet undetermined. With the help of these assumed relations, 

 equation (163) becomes 



---) ..-(167). 



A 



Clearly equation (161) will be satisfied if the quantity in square brackets 

 on the right of equation (167) satisfies the conditions which must be satisfied 

 by <r in equation (161). It must therefore be made to vanish when X = 

 and when X = X'. 



To satisfy this condition, let us now choose for 6 the value 



...] ...(168), 



then the expression in square brackets on the right of equation (167) 

 reduces to 



