for a System of Correlated Variables. 

 write, using i\. . .r„ as any values of s v . .*», 



&c. = &c, 

 from which follow algebraically 



13 



Du 



D l; 



^ = T7 ri+ TT' 2 



+ ^r,+ &c= 



(19) 



in which D is the determinant of the quadratic function Q e , 

 namely, 



D = 



&12 ^n 



b n b S2 a 3 ••• 



or D = 2, + -T~ T~ ■••j 



du { du< 



and D n , D 22 , &c. are its coaxial minors obtained by erasing 

 the first, respective second, or nth row and column. Also 

 D pq is the anaxial minor obtained by erasing the pth row and 

 qth column, or vice versa. Since, by definition, b pq = b qp JoY 

 ^very p and q, it follows that V pq = D qp for every p and q. 

 The sio-ns of the anaxial minors are so taken that 

 D=a 1 D 11 + 6i 2 D 12 + &i 3 I>i3+ & c - 



23. Again, let 



D n Do, 



1) 



D 



= « 2 , &C, 



and 



Di2 _ ^ 



— Pi2 l\ 



>pq 



D _A " i2 D 



The r's and w's are then connected by the symmetrical 

 systems 



r l — a l u l -\-b u u 2 + &c, 



and 



&c, 



&c. = &c. 



(19a) 



(196) 



