OF TESTIMONIES OR JUDGMENTS. 607 
the only condition connecting a and } which they establish is, 
as b. 
Applying this principle to (5), we have 
= = -1 
Hate esr) 
= = -—1 
Fag ity Seth. 
r=0. r= pee. 
These may be reduced to the somewhat simpler form 
P=) sited. 40=0 
p>=qtr-1 
eh APY Ties wis ov tay 
r=pt+q—-l 
Such are the conditions of possible experience in the data. 
Suppose, for instance, it was affirmed as a result of medical statistics, that in 
two-fifths of a number of cases of disease of a certain character, two symptoms, x 
and y, were observed ; in two-thirds of all the cases, the symptoms y and z were 
observed ; and in four-fifths of all the cases, the symptoms wz and y were observed ; 
so that the number of cases observed being large, we might, on a future outbreak 
of the disease, consider the fractions two-fifths, two-thirds, and four-fifths, as the 
probabilities of recurrence of the particular combinations of the symptoms z, y, 
and z, observed. The above formulze would show that the evidence was contra- 
dictory. For representing the respective fractions by p, g, and 7, the condition 
p=qtr-l 
is not satisfied. 
It is an evident consequence of the principle enunciated in Art. 11, that in 
determining the conditions of possible experience and of limitation, we may employ 
any translated form of the problem, just as well as the form in which it is originally 
expressed. Thus, if we take the translated form of the problem of that article, 
and represent sleet by s, drift by ¢, storm by w, we shall have as the data 
Prob. s=p, Prob. t=q, Prob. u=r 
with the conditions 
stu=0, uts=0, ust=0 . 4 2 : (7) 
the queesitum being Prob. stw, which, as before, we shall represent by w. 
Now if we write 
Prob. stu=u, Prob. stu=0, Prob. s ui=0, Prob. sut=A 
Prob. tus=0, Prob.tus=p, Prob. ust=y AY fad te: 2if 1 (8) 
