426 Credibility of Extraordinary Stories. [CHAP. xvu. 



sionally happen. It is true that we shall thus go constantly 

 astray, and may do so to a great extent, so that if there 

 were any rational and precise method of specializing his 

 trustworthiness, according to the nature of his story, we 

 should be on much firmer ground. But at least we may 

 thus know what to expect on the average. Provided we 

 have a sufficient number and variety of statements from 

 him, and always take them at the same constant rate or 

 degree of trustworthiness, we may succeed in balancing and 

 correcting our conduct in the long run so as to avoid any 

 ruinous error. 



19. A few words may now be added about the combi 

 nation of testimony. No new principles are introduced here, 

 though the consequent complication is naturally greater. Let 

 us suppose two witnesses, the veracity of each being $. 

 Now suppose 100 statements made by the pair ; according to 

 the plan of proceeding adopted before, we should have them 

 both right 81 times and both wrong once, in the remaining 

 18 cases one being right and the other wrong. But since 

 they are both supposed to give the same account, what we 

 have to compare together are the number of occasions on 

 which they agree and are right, and the total number on which 

 they agree whether right or wrong. The ratio of the former 

 to the latter is the fraction which expresses the trustworthi 

 ness of their combination of testimony in the case in question. 



In attempting to decide this point the only difficulty is 

 in determining how often they will be found to agree when 

 they are both wrong, for clearly they must agree when they 

 are both right. This enquiry turns of course upon the num 

 ber of ways in which they can succeed in going wrong. 

 Suppose first the case of a simple yes or no (as in 6), and 

 take the same example, of a bag with 1000 balls, in which 

 one only is white. Proceeding as before, we should find that 



