( 463 ) 

 If we equate this to the correspond iujs: expression for 



uiiieli is ohtaiiiod i)v changing ?^ into ti, we ;!;et, dividing? hy »/ : 

 27 63 3 



+ 1 (2 y' - 3 x') i;" I - (y' - x') ^- .^' - 18 (y' - x') r" .." + 



+ ^(3y'-2x')7i'y'-4rr„.7,-"§-4^,.;"'z=:0 (85) 



At first approximation this yiekls : 



§ = ^(2y'-3x').^•". 



Tliis relation is, liowever, identical with the relation (60) which is 

 derived from the first connodal relation. So we cannot (huw any 

 fnrther conclnsion from eqnation (85) withont brin^inji; it into con- 

 nection with the first connodal relation; hnt for this it is rcqnired 

 to introduce a further approximation for the latter. 



Second approximation of the first connodal relation. 



25. From the first connodal relation in connection with the equation 



dip' 



-£-=zl+«'+(14-0%.r+X: + 2x,.r4- (86) 



the following relation may easily be derived, if we take into account 

 the terms up to the order t!^ or if : 



1+J 

 (1 + 0% 'I |-(2y'-3x>^-3yV-f9(/-x')r'\- "^ (3y'-2x') i^» -| 



+ 4(T„§7j + 4<T,7].r" = (87) 



Within the same order of approximation we have however-. 



^ x" 2%ri 2§V 



^ _ ^ .v" ' 3.v"' 



.V 



In the second term of the second member of this equation, however, 

 we may safely make use of the first api)roximation furnished by 

 equation (69). Taking this into account (87) passes aftei- muHiplication 

 with u)" and division by ?j into ; 



