OF TESTIMONIES OR JUDGMENTS. 607 



the only condition connecting a and b which they establish is, 



a> b. 



Applying this principle to (5), we have 



= p+q+r—1 



P>0 . p 

 q>0 . q 



2 

 = p+q+r—1 



= n = p + q + r — 1 



These may be reduced to the somewhat simpler form 



P>0 <? >0 r > 

 p > q + r— 1 



q>r+p— 1 

 r>p+q— 1 



(6) 



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 x 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 x, y, 

 and z, observed. The above formulae would show that the evidence was contra- 

 dictory. For representing the respective fractions by p, q, and r, the condition 



p>q + r— 1 

 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 t, storm by u, we shall have as the data 



Prob. s=p, ~Pvo\).t = q, Prob. u = r 

 with the conditions 



stu=0, uts = 0, ust—0 .... (7) 



the quaesitum being Prob. stu, which, as before, we shall represent by u. 

 Now if we write 



Prob. stu=u, Prob. s t u = 0, Prob. sut=0, Prob. su t=\ 



Prob. tus = 0, Prob. tus=fJ. y Prob. ust~v ... (8) 



