Probable in a Correlated System of Variables. 163 

 Similarly : 



'_ IV- 1 X ( m y_ 4. m »+? 

 Thus 



v 1; 1 + ^U N 



^ = - JfiL C ot 2 /3 P = cot 2 /3 5- (l + -^ ; 

 or from (vii.) 



R„ B 1 1 1 / ... , 



- = H — ■ ....... (xm.) 



R o p 2 m p m„ + l 

 Again : 



&*•='- cot/3, cot/3 y *f = cot/3, cot & j». 



and 



if 1 = (XIV.) 



H a- p (T q m n+l 



Thus by (ii.) : 



But 

 hence : 



X 



= S D <"■> 



where the summation is now to extend to all (n + 1) errors, 

 and not merely to the first n. 



(4) . This result is of very great simplicity, and very easily 

 applicable. The quaniity 



X 



=\A(£> 



is a measure of the goodness of fit, and the stages of our 



M 2 



