Ill 



Sven Wicksell 



Differentiating this equation with regard to one of the parameters in the 

 exponent and multiplying with A' /2 we obtain the moments. We then rind, for 

 instance, differentiating with regard to A, 



-MS- 



dxdydzx- e h 3 



1_ 8A 

 A dA 



(10) 



, _ _ d A J_ 



SOO — V 200 - d J 



In a similar way we find the other moments of the second order 



_ sA_ 1_ 

 2nu dA A 



aA_ J_ 



»20 8jB A 



_ aA i 



m ~ dC A 



8A 1 

 8F, A 



8A J_ 

 dE, A 



8A J_ 

 dD, A' 



Using well known theorems it may now be shown that 



(10*) 



and that we have 

 (11) 



A = 



dM 



1 



^ V 200 



IT 



B = 



dM 



1 



^ V 020 



M ; 



G~ 



dM 



1 



^ V 002 





9Jf\ 



1 



^ V 01l/ 



Jf 





1 



8 v i o i / 



M 



dM\ 



1 



8 v iJ 



M' 



where the brackets denote that the differentiation is to he performed only for one 

 of the places where the moments occur in the determinant M. 

 Finally we now have 



1 



(12) 



II 



and as a check to the computations 



(13) 4v m H-Bv M0 +(7v 001 + 2Z) 



+ 2£v 101 + 2Fi 



Through the formulas (11) and (12) all the parameters of the generating 

 function <p are expressed in terms of the moments. 



4. To obtain the higher coefficients Biß expressed in a similar way we use 

 the formula (4*). Then we first have to determine the moments \ rj ^ expressed in 

 terms of the moments v a ß„ = X a ^ (a -f ß -f- 7 = 2). 



