66 INDUCTION. 



It is obvious, too, that even when the probabilities are 

 derived from observation and experiment, a very slight im 

 provement in the data, by better observations, or by taking 

 into fuller consideration the special circumstances of the case, 

 is of more use than the most elaborate application of the 

 calculus to probabilities founded on the data in their previous 

 state of inferiority. The neglect of this obvious reflection has 

 given rise to misapplications of the calculus of probabilities 

 which have made it the real opprobrium of mathematics. It 

 is sufficient to refer to the applications made of it to the credi 

 bility of witnesses, and to the correctness of the verdicts of 

 juries. In regard to the first, common sense would dictate 

 that it is impossible to strike a general average of the veracity, 

 and other qualifications for true testimony, of mankind, or of 

 any class of them ; and even if it were possible, the employ 

 ment of it for such a purpose implies a misapprehension of 

 the use of averages : which serve indeed to protect those whose 

 interest is at stake, against mistaking the general result of 

 large masses of instances, but are of extremely small value as 

 grounds of expectation in any one individual instance, unless 

 the case be one of those in which the great majority of indi 

 vidual instances do not differ much from the average. In the 

 case of a witness, persons of common sense would draw their 

 conclusions from the degree of consistency of his statements, 

 his conduct under cross-examination, and the relation of the 

 case itself to his interests, his partialities, and his mental 



the enumeration, because we ourselves determine what the possibilities shall 

 be. But suppose a case more analogous to those which occur in nature : instead 

 of three colours, let there be in the box all possible colours : we being supposed 

 ignorant of the comparative frequency with which different colours occur in 

 nature, or in the productions of art. How is the list of cases to be made out ? 

 Is every distinct shade to count as a colour? If so, is the test to be a common 

 eye, or an educated eye, a painter s for instance ? On the answer to these 

 questions would depend whether the chances against some particular colour 

 would be estimated at ten, twenty, or perhaps five hundred to one. While 

 if we knew from experience that the particular colour occurs on an average a 

 certain number of times in every hundred or thousand, we should not require 

 to know anything either of the frequency or of the number of the other pos 

 sibilities. 



