450 Prof. S. D. Wicksell on the Normal Correlation 



The moments of the variates expressed in any units 

 being denoted by vj* j~ %m w© have further 



f*A . . . . k n = *!*!*!** .... <r n ** m hK . _ kn , 



where a u o" 2 , . . . . a n are the respective dispersions of the 

 variates. 



On account of the reciprocity of the determinants S and A 

 we have finally, putting 



&P2 — n • A — I ai1 ' ai2 ' • • • • a ln A _ d^ 



— &pq > ^ — ' \) />q — ^ 



«21, «22, .... a2« oapq 



<*>nli &n%i 



and 



^ /- ^ / : j = K W> ^ O ^ " A 



the general formula 



VA 



9^\«/2 



(27T) 



f°° /''oo /-»GO 



j -oo i -ao ,/— oo 



& 2 /fc H - -^SSr/^aj^r^ 



^ + ^ 2 + +fo t 



= (-i) 2 fi(o,o,....o). 



n l k 2 . . . . J; n 



Here a^ may be any real quantities, and up to the 

 sixth order the value of the integral is obtained if in 

 the respective equations (6) and ($) r pq is exchanged 



for *&. 

 A 



Appendix. 



In order to prove equation (2) we put, using the theorem 

 of Fourier, 



<£Ol> ** In) = 7Z-- dw, \ dl0 2 .... dW***** 



(27T) W J-oo J -oo J_oo 



d\, dX 2 j d\»0(Xi, X 2 . . . . X*) ***■>**. 



— CO ^/ _ 00 »— «o 



