O ESSAY ON PROBABILITIES. 



/ 



probable the assertion will be true of one or other out of 

 1, 000; 000 as of one alone. The method of measuring 

 is wrong, but that is here immaterial; suffice it 

 that, come how it may, the multiplication of the degree 

 of assent implied in ff there is a remote chance of it" 

 is found to give that which is conveyed in fc we are 

 quite sure of it." We have thus a sort of freezing and 

 boiling point of our scale of assent and dissent, namely, 

 absolute certainty against on the one hand, absolute 

 certainty for on the other hand, with every description 

 of intermediate state. 



Thirdly, we have proposed two ascending scales of 

 assertions, in both of which first impressions would 

 make us suppose the probability of the second is double 

 that of the first, that of the third treble, and so on, as 

 follows : 



A child born will die aged fifty. 

 Of two children born, one or 



other will die aged fifty. 

 Of three children born, one or 



other will die aged fifty. 

 &c. &c. &c. 



a must be drawn, 

 a or b must be drawn. 



a, or b, or c must be drawn. 

 &c. &c. &c. 



Now it will hereafter be positively proved that our 

 notion is correct in the second case, but incorrect in the 

 first ; or at least that it cannot be correct in both. 

 Even then, if we should fail in assigning positive mea- 

 surements, we may succeed in drawing useful distinctions. 

 When we imagine two things to have a point of re- 

 semblance which they have not, it is worth while to in- 

 vestigate methods of correction, even though we cannot 

 assign how much the two properties differ which we 

 supposed were alike. 



The quantities which we propose to compare are the 

 forces of the different impressions produced by different 

 circumstances. The phraseology of mechanics is here 

 extended : by force, we merely mean cause of action, 

 considered with reference to its magnitude, so that it is 

 more or less according as it produces greater or smaller 

 effect. It is one of the most essential points of the 



