132 INDUCTION*. 



in two different ways. In the one, each proposition is sepa 

 rately applicable to the case in hand, and our object in com 

 bining them is to give to the conclusion in that particular case 

 the double probability arising from the two propositions 

 separately. This may be called joining two probabilities by 

 way of Addition ; and the result is a probability greater than 

 either. The other mode is, when only one of the propositions 

 is directly applicable to the case, the second being only appli 

 cable to it by virtue of the application of the first. This is 

 joining two probabilities by way of Katiocination or Deduction ; 

 the result of which is a less probability than either. The type 

 of the first argument is, Most A are B ; most C are B ; this 

 thing is both an A and a C ; therefore it is probably a B. The 

 type of the second is, Most A are B ; most C are A ; this is a 

 C ; therefore it is probably an A, therefore it is probably a B. 

 The first is exemplified when we prove a fact by the testimony 

 of two unconnected witnesses ; the second, when we adduce 

 only the testimony of one witness that he has heard the thing 

 asserted by another. Or again, in the first mode it may be 

 argued that the accused committed the crime, because he con 

 cealed himself, and because his clothes were stained with blood ; 

 in the second, that he committed it because he washed or 

 destroyed his clothes, which is supposed to render it probable 

 that they were stained with blood. Instead of only two links, 

 as in these instances, we may suppose chains of any length. 

 A chain of the former kind was termed by Bentham* a self- 

 corroborative chain of evidence ; the second, a self-infirmative 

 chain. 



When approximate generalizations are joined by way of 

 addition, we may deduce from the theory of probabilities laid 

 down in a former chapter, in what manner each of them adds 

 to the probability of a conclusion which has the warrant of 

 them all. 



In the early editions of this treatise, the joint probability 

 arising from the sum of two independent probabilities was 

 estimated in the following manner. If, on an average, two of 



* Rationale of Judicial Evidence, vol. iii. p. 224. 



