178 INDUCTION. 



two cases, as in Laplace's example; yet he surely would 

 not say that if the witness answered 79, the assertion would be 

 in an enormous proportion less credible, than if he made the 

 ;same answer to the same question asked in the other way. 

 If, for instance, (to put a case supposed by Laplace himself,) 

 he has staked a large sum on one of the chances, and thinks 

 that by announcing its occurrence he shall increase his credit ; 

 he is equally likely to have betted on any one of the 999 

 numbers which are attached to black balls, and so far as the 

 chances of mendacity from this cause are concerned, there 

 will be 999 times as many chances of his announcing black 

 falsely, as white. 



Or suppose a regiment of 1000 men, 999 Englishmen and 

 one Frenchman, and that of these one man has been killed, 

 and it is not known which. I ask the question, and the 

 witness answers, the Frenchman. This was not only as impro- 

 bable ci priori, but is in itself as singular a circumstance, as 

 remarkable a coincidence, as the drawing of the white ball : 

 yet we should believe the statement as readily, as if the 

 answer had been John Thompson. Because though the 999 

 Englishmen were all alike in the point in which they differed 

 from the Frenchman, they were not, like the 999 black 

 balls, undistinguishable in every other respect; but being 

 all different, they admitted as many chances of interest or 

 error, as if each man had been of a different nation ; and if 

 a lie was told or a mistake made, the misstatement was as 

 likely to fall on any Jones or Thompson of the set, as on the 

 Frenchman. 



The example of a coincidence selected by D'Alembert, that 

 of sixes thrown on a pair of dice ten times in succession, belongs 

 to this sort of cases rather than to such as Laplace's. The 

 coincidence is here far more remarkable, because of far rarer 

 occurrence, than the drawing of the white ball. But though 

 the improbability of its really occurring is greater, the superior 

 probability of its being announced falsely cannot be established 

 with the same evidence. The announcement "black" repre- 

 sented 999 cases, but the witness may not have known this, 

 and if he did, the 999 cases are so exactly alike, that there is 



