126 
MR. G. UDXY YULE ON THE THEORY OF CONSISTENCE 
The Limits to Associations given by Conditions of Consistence. 
§ 32—§ 37. 
§ 32, The general conditions of consistence give limits to the frequencies of any 
one aggregate in terms of the frequencies of two or more given aggregates of the 
same congruence. Hence they give limits also to the possible associations between 
attriljutes in the unknown aggregate. 
Thus, to take an imaginary example, suppose we have 
(AB) 
11 
(AC) 
8 
(A/3) 
22 
(Ay) 
25 
(aB) 
39 
(aC) 
52 
(a^) 
28 
(«y) 
15 
lUO 
100. 
allies 
of the 
BC aggregate. 
From 
sistence, § 5, we liave 
(BC) < 33 + 5U + GO 
100 
1 - 8 
< 24 
< 11 + 8 - 33 < - 14 
> GO + 11 — 8 > G3 
> 50 - 11 + 8 > 47. 
Therefore the limiting values to (BC) are 24 and 47. But we know (B) —■ 50, (C) 
= GO, (U) = 100, tlierefore the limiting values to the frequencies of the aggregate 
are 
(BC) 
24 
47 
(/3y) 
2G 
3 
m 
3G 
13 
m 
14 
37 
100 
100. 
Hence we may calculate, if desired, the limiting values to the association |BC^|. 
For the association coefficient suggested in my })revious memoir the values are 
— 0'47 and —O'OG. The values of [ AB | and [AC'I are —0'47 and —0'83 respectively. 
For the great majority of cases occurring in ])ractice the limits thus inferred from 
knovm associations are, as in the imaginary exanq)le, pretty wide. Very high values 
must he assigned to the two given associations l)efore it is possible to infer even the 
sign of the third. Arguments of the vague type, “ so many A’s are B, and so many 
A’s are also C, that clearly we must ex])ect to find B and C fre(-[uently occurring 
