OF LOGICAL CLASS-FEEQUENCIES, ETC. 
129 
Congruence. 11. Girls. 
ABD =: 0 .Tg = 0 cc- = 0 
= 0-0682 = 0*0682 = 0-0689 
[x^ -j- 0:3 + a-g = — 0*7779) 
a^i + ajg + ^5 = 0-0682 
-~ ^3 + ^5 — '0-0850 
— a;i + ^3 + ^5 0-0689 
ACD a;^ = 0 a;g = 0 Xg = 0 
X 3 = 0-0325 Xg = 0-0682 Xg r- 0-0325 
{x .2 + + a;g = — 0*8304) 
a^ + Xg — Xg = 0-0682 
Xo — ajg + ^^6 — 0-0325 
— Xj + Xg + Xg = 0*0689 
BCD x^ = 0 Xg — 0 Xg — 0 
x^ = 0-0325 Xg = 0*0689 a-g = 0*0325 
K + ‘^5 + ^6 = - 0-8136) 
Xj, + ^*^5 — ^6 = 0*0850 
x_,, — Xg + Xg = 0*0325 
— x^ -}- Xg + — 0*0689. 
§ 35. If the limits to each class frequency given by these relations be worked out 
it will be found that the lower limit to every class, in terms of the others, is zero 
without exception. That is to say, any pair whatever of the given defects might 
exhibit complete “ disassociation ” (association coefficient = — 1 ), without this being 
in any way inconsistent with the high associations exhibited by other pairs. In two 
cases for the boys and three for the girls ujiper limits could, however, be inferred, 
as given below. 
Group. 
1 
1 
Limit given 
by 
congruence. 
Limits. 
Corresponding 
y associations. 
Boys. 
Girls. 
Boys. 
Girls. 
(AB) . . 
ABC 
870 
643 
0-9996 
0-9972 
(AD) . . 
ABD 
630 
574 
0-9861 
0-9953 
ACD 
— 
634 
-- 
0-9991 
(BD) . . 
ABD 
— 
630 
— 
0 - 9955 
Thus our imaginary “ hasty arguer,” if he attempted to infer from the given values 
of (BC) and (AC) that “ some A’s must be B ” or, worse still, that “ A and B must be 
VOL. CXCVII.—A. 
s 
