162 Prof. Karl Pearson on Deviations from the 



Hence the problem reduces to the evaluation of the deter- 

 minant J and its minors. 

 If we write 



N 



7) =cot 2 /S ? = 1 



m n 



(«•) 



J = 



Clearly. 



-Vi 

 1 

 1 



Vs 



1 

 1 



~Vn 



Jio — — 



1 1 



— Vs 1 



1 —97 4 



—v* 



= (-l) a - 1 ('/3+l)(%+l)...(% + l). 



Generally, if X^fo + 1)(% + 1) (*fc + l) . . . (i?» + l), 



J ""<- 1 ^ 1 « + i)(, t+ D - • • (*> 



Bllt Jll — %Jl2 + Jl3 + J]4+ • • • +Jl« = 0. 



Hence Jn = (l + %)Ji2— J i2 — Jis— J^ • • • —Jin 



1 + ^ V 1 + % 1+% 1 + %" 1-Hw" 



Whence, comparing J with J u , it is clear that : 



J=( _Wi, * » _ il_i :... _ i y 



v ' V 1+77! 1+t; 2 1+173 1 + % 1+W 



Now 



Thus: 



= 1 





