A. Ritchie-Scott 
101 
It will be shown in a later paper that the coefficients of the cell frequencies are 
functions of moments of the frequencies about the mean. 
If any relation between h^, h.^, k\, makes 
Xn - Xi2 - X21 + X22 = 
while the right side of the a^^ equation remains finite the value of the expression for 
CTy^ will become infinite. X\i ~ X12 X21 + X22 obviously vanishes (1) when /i, = or 
= when either of bhe central categories becomes vanishingly small, and 
(2) when hi= — k^, = — A'a and r = 0, i.e. when both sets of the extreme 
categories have equal frequencies and the correlation is very small. 
(1) When = h^. Then Xii = Xn^ X21 = X22. ai2 = = a say, = ^.^^ = 0. 
Then ' m = ^i^:^) = 
and the right side of the ct^^ equation reduces to zero giving the indeterminate form 
(2) When = — h.^, = — Jc^ and r — 0. This case will be discussed in the 
next section. 
§ 5. Standard Deviation of Enneachoric r in Special Cases. 
Two particular cases are of interest, (1) when r = 0, (2) when the table de- 
generates into a 2 X 2 table. 
(1) Whenr = 0 A,, ^ <&. (kt) = , 
Hence a,, = .4oo — A„ = - 
— -^12 -^11 — 
Similarly ^22 = ^21 — ^ » 
N N 
m.2 — m.^ n.2 
^ 'N 
Ho. 
_ P12 ~^ ^22 
' N 
N ^ N N 
