INTRODUCTORY EXPLANATIONS. 11 



or for its want of demonstrable inexactness one way 

 more than the other, it is still a principle of human 

 action, and as such is adopted. Many writers on pro- 

 bability speak of it as being a maxim which, if it were 

 not adopted, ought to be. Certainly, such an assertion 

 has some strong arguments in its favour ; but with me 

 they would not outweigh the importance I should attach 

 to exact deduction from the conceptions which actually 

 prevail. 



Let the prospect of drawing any given letter be 

 of a degree of force represented by 1, all the several 

 prospects being equal. Then 2 is the chance of draw- 

 ing one or other out of any given pair ; and so on 

 up to 26, which is here the representative of certainty. 

 But if the lottery had 50 letters, the prospect of draw- 

 ing a given letter would no longer be represented by 

 1 ; or if so, the certainty of drawing one out of 50 

 in the second would be represented by 50, while the 

 certainty of drawing one out of 26 in the first is repre- 

 sented by 26. Now certainty, absolute certainty, should 

 have the same representation whatever contingencies it 

 may be supposed to be compounded of. If a man be 

 sure of 100/., it matters nothing whether his certainty 

 arise from the announcement of a prize in a lottery of 

 1000 tickets, or of a legacy to which 20 other people 

 were looking forward. To use a common phrase, a man 

 can but be certain ; and therefore it would be desirable 

 to use the same symbol for certainty in all cases. Let 

 this symbol be unity or 1 ; then in the first lottery the 

 chance of any given letter is represented by -r^p and in 

 the second by -$ 1 J. Similarly the chance of 1 out of 10 

 given letters in the first lottery is -J-g, and in the se- 



Now I pause upon this result, which, in fact, con- 

 tains all the theory I shall be obliged to use ; grant 

 this, and you can be constrained, by demonstration, to 

 admit all the rest as simple logical consequences. A 

 writer on this subject, therefore, must take care not to 

 let an opponent of its principles choose his own ground of 



