151 



_2;.«;.a_, /Err -(/.,, r,>+2t„,.vr,+..+?,,„r,') 



J' = 00 J- =; — 00 



To integrate in the first place over all the variables n: except 

 d'j and .VA- comes to the same thinn- as to drop the (;— 2 linear 



relations .i;/ = ^ aiiVi{i ^\=J,k). Thus we start, as it were, only from 

 1 *^ 



the two equations 



^V = ^ii^'i + ^J-i^-i + • • • + «i^tv, 



and find therefore 



X '■=: — 00 a:r= — 00 

 J k 



where 



2>' representing a determinant of the matrix 



M' 



oji , aj2 , . . . aj^ 



Besides 



hence 



D^' rr: aki , a/!;2 , . . . a^d , 



f'jk' = —E'SajiCikn 



% performing the integration we obtain for i;^^. 



kjk' _ ^ajiüki 



and similarly 



■00 — 00 



Now the correlation-coefficient rj^ of .tj and ,Vk is defined bv the 

 expression 



