SECT. 35.] Measurement of Belief. 163 



terms presuppose a series ; within the indefinitely numerous 

 class which composes this series a smaller class is distin 

 guished by the presence or absence of some attribute or 

 attributes, as was fully illustrated and explained in a pre 

 vious chapter. These larger and smaller classes respectively 

 are commonly spoken of as instances of the event, and of 

 its happening in a given particular way. Adopting this 

 phraseology, which with proper explanations is suitable 

 enough, we may define the probability or chance (the terms 

 are here regarded as synonymous) of the event happening 

 in that particular way as the numerical fraction which repre 

 sents the proportion between the two different classes in the 

 long run. Thus, for example, let the probability be that 

 of a given infant living to be eighty years of age. The 

 larger series will comprise all infants, the smaller all who live 

 to eighty. Let the proportion of the former to the latter be 

 J) to 1 ; in other words, suppose that one infant in ten lives 

 to eighty. Then the chance or probability that any given 

 infant will live to eighty is the numerical fraction ^. This 

 assumes that the series are of indefinite extent, and of the 

 kind which we have described as possessing a fixed type. 

 If this be not the case, but the series be supposed termi 

 nable, or regularly or irregularly fluctuating, as might be the 

 case, for instance, in a society where owing to sanitary or 

 other causes the average longevity was steadily undergoing 

 a change, then in so far as this is the case the series ceases 

 to be a subject of science. What we have to do under these 

 circumstances, is to substitute a series of the right kind for 

 the inappropriate one presented by nature, choosing it, of 

 course, with as little deflection as possible from the observed 

 facts. This is nothing more than has to be done, and in 

 variably is done, whenever natural objects are made subjects 

 of strict science. 



112 



