( 462 ) 

 It is now easy to find : 



either by paying? attention to the fact that we liavc in Vifj;. d, § 12 

 (see the first descriptive part), if applied to the (r', ,p)-diagrani, with a 

 suflicient degree of approximation : 



RQ^PQ. iff RPQ = FQ.tfj — ix= — .PQ. i.j (i z= ~ . PQ . 7n, 



or by application of the formnlae (13) and (14), observing that 



This yields by substitution in (78) : 



^J^^^(^- 0^' -f J (2y'-3x;)V-^-12(y'-K')..^.y^ -r'^p. (80) 



or tinaiiy substituting for /' its value from (47): 



^^' = ~ ~(2-/-3-T-,('V-'-y.t==-4^(2r'-:''=')'.v( v,,).(8i) 



from which we immediately derive formula (20), applying (18). 



T/u' third connodal relation. 



24. We have now obtained the principal formulae. For the sake 

 of completeness, however, we shall treat here also tiie third coimodal 

 relation, the more so as this leads to a new determination of the 

 formulae (47) and (48), which puts the former to the test. 



This third relation reads : 



Ö.6-J Or, d.i\ or J 



dxp' dx^' 



We first transform rp'—-c- v' —; . uitli the aid of (32). It proves 



0.1' ov 



to be necessary to keep all terms up to the order t'^ or tj'. So we 

 find: 



From this follows : 



v'>'^-,^^--^^=-(i+OG'-''+§'])-a+o?oa2^-^-^^ 



Oa-j ov ^ o o 



Q 27 63 3 



4 o4 40 4 



