244 OF THE THEORY OF PROBABILITIES. [CHAP. XVI. 



" The probability of an event is the reason we have to believe 

 that it has taken place, or that it will take place." 



" The measure of the probability of an event is the ratio of 

 the number of cases favourable to that event, to the total num- 

 ber of cases favourable or contrary, and all equally possible" 

 (equally likely to happen). 



From these definitions it follows that the word probability, in 

 its mathematical acceptation, has reference to the state of our 

 knowledge of the circumstances under which an event may hap- 

 pen or fail. With the degree of information which we possess 

 concerning the circumstances of an event, the reason we have to 

 think that it will occur, or, to use a single term, our expectation of 

 it, will vary. Probability is expectation founded upon partial 

 knowledge. A perfect acquaintance with all the circumstances 

 affecting the occurrence of an event would change expectation 

 into certainty, and leave neither room nor demand for a theory 

 of probabilities. 



3. Though our expectation of an event grows stronger with 

 the increase of the ratio of the number of the known cases fa- 

 vourable to its occurrence to the whole number of equally pos- 

 sible cases, favourable or unfavourable, it would be unphilosophical 

 to affirm that the strength of that expectation, viewed as an 

 emotion of the mind, is capable of being referred to any numerical 

 standard. The man of sanguine temperament builds high hopes 

 where the timid despair, and the irresolute are lost in doubt. 

 As subjects of scientific inquiry, there is some analogy between 

 opinion and sensation. The thermometer and the carefully pre- 

 pared photographic plate indicate, not the intensity of the sen- 

 sations of heat and light, but certain physical circumstances 

 which accompany the production of those sensations. So also 

 the theory of probabilities contemplates the numerical measure 

 of the circumstances upon which expectation is founded ; and this 

 object embraces the whole range of its legitimate applications. 

 The rules which we ehiploy in life-assurance, and in the other 

 statistical applications of the theory of probabilities, are altogether 

 independent of the mental phenomena of expectation. They are 

 founded upon the assumption that the future will bear a resem- 



