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PHILOSOPHICAL SOCIETY OF WASHINGTON. 
ing as it is unfavorable or favorable to deafness. In like manner 
the same discriminate association ratio is obtained for the phenomena 
Not-A and B, and for Not-A and Not-B. The logical relation be¬ 
tween sight and hearing is just as close as that between sight and 
deafness, as that between blindness and hearing, and as that be¬ 
tween blindness and deafness. It is in fact the same relation stated 
in different words. 
The sum of the four indiscriminate association ratios is 
& (a — c)^ (6 — c)'^ (s — a — h-{-cY _. (cs — ahY 
ah a{s — b) (s — a) b (s — a)(s — b) ah {s — a) (s — h') 
Hence the discriminate association ratio = the sum of the indis¬ 
criminate association ratios — 1. Since every instance of A or of 
Not-A is necessarily associated with an instance of B or of Not-B 
and every instance of B or of Not-B is necessarily associated with 
an instance of A or of Not-A, this alternative association is perfect, 
and its extent = 1 whatever A and B may denote. The excess of 
the sum of the indiscriminate association ratios above unity may, 
therefore, be taken as a measure of that portion of the aggregate 
which is peculiar to any special signification of A and B. Such 
association as belongs necessarily to any two classes of phenomena 
whatever having been eliminated, the discriminate association ratio 
measures that residue which indicates special relations. 
I call c — — the concurrence residual. If c is less than —, the 
s s 
concurrence residual is negative and indicates that special causes 
prevent oftener than they produce positive association between A 
and B. If c = 0 and a — s — 6, the negative association (or disso¬ 
ciation) is perfect, and the discriminate association ratio =1. These 
conditions signify that the two phenomena are never both present 
and are never both absent. 
Denoting the discriminate association ratio by y, the concurrence 
residual by x, and the class residuals ^ ^ respect¬ 
ively by a and /5, we have the equation 
y 
and regarding x and y as variables and a and (3 as constants this 
equation is represented in Cartesian co-ordinates by a parabola. 
