1125 



W 

 in which 





i/=^,§r + 26,,§,£, -f-.... + />,,§/• 

 The aim of tliis paper is : 



1. to express the eoefiicieiits hjk of the fjiiadratic expression // 

 and the quantity E in the coefficients «^v , 



2. to ehicidate the notion of a coefficient of correlation by means 

 of the expressions found. 



The probability of the simultaneous occurrence of the values 

 u^, u^, . .Mcr is 



(7 



ÖW=- — e ' nöui. 



_p 1 



We begin by writing 



hiui= vi (i := 1,2, . . . (j) 



and 



aji = hi aji {j =1,2, ... q; i z= 1,2, . . . o). 



Thus we get 



-^ — 2 Vi a 



dW = — e ' növi 



— 1 



^ 2 



and 



A'l =: aiiui -|- a\2V2, + • • • + a^v^, 



X^ =: a^\V\ -|- a22U2 + •••"!" <^27Vff, 

 Av = «51^1 + ao'iv-i \ . . . -\- ap.jV^. 



For the present we shall continue working with the coefficients 

 nji only in the final result. 



Like Bravais we moreover introduce (J — q auxiliary variables, viz, 



Xp-\-i = -2" cip^i^i v; 

 : 1 



A'cr =: ^ (-Ini Vi 

 I 



. /.Cj, .i-j, . . . .r^.'N . 

 The determinant of substitution ot is then 



\v^, I'j, . . . tvy 



