le eeE—EEeE——e— ee el 
OF TESTIMONIES OR JUDGMENTS. 617 
of the events # and y is known. Symbolically expressed, it is the value of the 
fraction. 
Prob. x y z 
Prob. zy 
or, as it may, by resolving the denominator, be written, 
Prob. 7 y z 
Prob. zy 2+ Prob. a yz at ge : epee) 
To effect this object, we shall determine the value of Prob. x yxand Prob. #yz 
separately. 
Collecting the elements furnished by the preceding analysis, the first of the 
partial problems herein involved may be thus stated :— 
Given Prob. z=, Prob. y=a, 
Prob. w=a,¢, Prob. v=a,c, (11) 
Prob. wz=4a,¢,p, Prob. vz=a,c,p, 
with the conditions, wz=0, vy=0, wv=0, th iene, fe ame me OS 
Required w, the value of Prob. xyz. 
In selecting the above, I have chosen to employ (3) in place of (1), and (6) in 
place of (4). It makes no difference in the final result. 
In accordance with the rule, let us write 
we=s, w=t, ayz=P 4 : y (18) 
we must then from (12) and (13) determine ¢ as a developed logical function of x, 
Y, W, 0, S, and t. 
This problem admits of perfectly definite solution on the principles of the cal- 
culus of Logic. Ishall here merely give the result, and point out a method by 
which it may be independently verified. We find 
p=cywsvttayvtws+0(ewsyutt+yvt2ws+acywust 
+ oe ywus t + terms whose coefficient is - Prtiet eM ay h- hese Ss) 
We may verify this expansion by substituting for s and ¢ their values wz and 
vz, paying attention to the conditions (12), and then comparing the result with 
the value of ¢, viz., xyz. 
Thus the term xyw svt becomes, on substitution 
cywuxwex(l-vzj=ayzwy 
by the calculus of Logic. Now this represents a class entirely included in the 
class wyz, whence the coefficient of the term is unity. 
The term x wsyv ¢ reduces to x wz y v, and represents a class no part of which 
is included in xyz, whence the coefficient is 0. 
VOL. XXI. PART IV. 8D 
