OF TESTIMONIES OR JUDGMENTS. 633 
we find, by the calculus of logic, 
paeayst+O(asytt+ytastaystt+avyst+yastt+xyst) 
+ terms whose coeficients are 2 Fe, Pao detealine 
a result which may be verified by the method applied to (14) in Art. 23. 
Hence we find, adopting the simplification of Art. 21, 
V=ayst+ust+yt+ayt+ae+y+l, 
and since we haye 
Prob. e=c, Prob. y=c’, Prob. s=cp, Prob. t=c'g 
Prob. xyz=u, 
(5) 
we find, as an algebraic system of equations, 
ayst+aus+ay+n _— axystt+yt+ay+y 
c c 
— vyst + vs is avyst + yt ‘ : : (6) 
ep cg 
_ ryst 
FF =aryst+ust+yit+aytu+ytl 
This system is easily reduced to the form 
vw yt ty taetytl 
cp—u —s ¢q—u——s il +u—ep—ceg 
a+1 * yt _ axsyt 
~I+u—cp-¢  I+u—c—cq wu 
(7) 
And if we equate the respective products of the first three and of the last three 
members of the above, we find 
(cp—u) (¢q—u) (L+u—ep—cg)=(1+u—e¢—ep) (ltu-e-egu ss 8) 
a quadratic equation by which the value of w must be determined. 
If, in like manner, we assume 
Prob. xyz=t 
we shall find 
(cl—p—t) (¢1—g—#) (1+ t—cl —p—c1—q) = (1+ t—¢’—el—p) (1+ t-—c—cl—qg)t (9) 
From these equations the values of ~ and ¢ being determined, we have finally 
Prob. xyz u 
= ‘ : c - - 1 
Prob. zy Uutt ‘ (10) 
Before we can apply this solution, we must determine the conditions of pos- 
sible experience, and the conditions limiting the values of w and z. For this pur- 
pose writing 
Prob. ayz=u, Prob. vyz=t, Prob. wzy=. Prob. ayz=y, 
Prob. yea =0, Prob, yxz =, 
VOL. XXI. PART IV. 8H 
