SECT. 8.] Credibility of Extraordinary Stories. 413 



7. We will now take the case in which the witness 

 has many ways of going wrong, instead of merely one. Sup 

 pose that the balls were all numbered, from 1 to 1,000, and 

 the witness knows this fact. A ball is drawn, and he tells 

 me that it was numbered 25, what are the odds that he is 

 right ? Proceeding as before, in 10,000 drawings this ball 

 would be obtained 10 times, and correctly named 9 times. 

 But on the 9990 occasions on which it was not drawn there 

 would be a difference, for the witness has now many open 

 ings for error before him. It is, however, generally considered 

 reasonable to assume that his errors will all take the form of 

 announcing wrong numbers; and that, there being no apparent 

 reason why he should choose one number rather than another, 

 he will be likely to announce all the wrong ones equally 

 often. Hence his 999 errors, instead of all leading him now 

 back again to one spot, will be uniformly spread over as 

 many distinct ways of going wrong. On one only of these 

 occasions, therefore, will he mention 25 as having been 

 drawn. It follows therefore that out of every 10 times that 

 he names 25 he is right 9 times ; so that in this case his 

 average or general truthfulness applies equally well to the 

 special case in point. 



8. With regard to the truth of these conclusions, it 

 must of course be admitted that if we grant the validity of 

 the assumptions about the limits within which the blunder 

 ing or mendacity of the witness are confined, and the com 

 plete impartiality with which his answers are disposed within 

 those limits, the reasoning is perfectly sound. But are not 

 these assumptions extremely arbitrary, that is, are not our 

 lotteries and bags of balls rendered perfectly precise in many 

 respects in which, in ordinary life, the conditions supposed to 

 correspond to them are so vague and uncertain that no such 

 method of reasoning becomes practically available ? Suppose 



