OF TESTIMONIES OR JUDGMENTS. 641 
tended to alter that state. By the evidence I mean, of course, that which forms 
the basis of the judgments. 
Making, as before, 
L2=8 yast LYZ=V 
and determining v as a developed logical function of «, y, z, s, and t, we find 
vaxyzstt+ O(myzstt+auzsytt+yztastuyestt Yuust 
+enyst+ayust) 
: 1 
+terms whose coefficients are rp 
Hence, availing ourselves of the simplification of Art. 21, we have 
ayzst+aytanst+ae — axystataytylaty 
¢ . cl 
_avystz+ ase _ awystat+yta 
es cp > cq 
_ vystat ase ytete _ xcystz 
be r ee a, 
=arystat cy + aset+yteatatytezt+l 
If we equate the product of the third and fourth to that of the fifth and sixth 
members of the above system, we find 
Prob. ayz = me 
whence by symmetry, 
= ‘(l—p) (A- 
Prob. cyz = eee sre: (4) 
Substituting these values in (3), we have 
Prob. yz _ pg(1—r) [ ] (5) 
Prob. xy pq(i—r)+(1—p) d-—q)r 
Before proceeding further, it will be well to note that in this formula p and g 
represent, not the general probabilities which the testimonies or evidences 
upon which our judgments are founded would give to the event 2, but the proba- 
bilities which they would separately produce in a mind embued with a previous 
expectation of the event z, the strength of which is measured by r. And there 
are some curious confirmations of the truth of the theorem, two of which I shall 
notice. 
If we represent the a posteriori value of Prob. z by R, and accordingly make 
pg (1—r) é 
pope be 
we find, on solving the equation relatively to r, 
1—-R 
Pq a=ed=pa=pR" spin? Se 
VOL. XXI. PART Iv. 8K 
