12 ESSAY ON PROBABILITIES. 



attack, so as to wait until he can take advantage of the 

 length of a deduction, or of the mathematical character 

 of the steps. Do you admit, 1. That a certainty, if you 

 have it, of drawing a 10/. prize in a lottery, is precisely 

 the same thing whether there be 100 or 1000 tickets? 

 and 2. That if there be 3 white balls and 17 black in a 

 lottery, of which either white ball is to be a prize, you 

 are compelled to regard your chances of success and 

 failure with impressions of which it is reasonable to 

 suppose the force to be as 3 to 17; or to say, (C the 

 degree in which I fear failure is, to my degree of hope 

 of success, in the proportion of 17 to 3." If you say 

 this, it matters nothing whether you say it because you 

 feel the correctness of the proposition, or because you 

 feel a want of data to deny it in one way more than in 

 the opposite. Provided only that you do not deny it, 

 your occupation of opponent is gone ; for all that suc- 

 ceeds is merely a mathematical use of this mathematical 

 definition. In the words of the ritual, Speak now, or 

 ever after hold your tongue. 



But it may be asked, with regard to the mathematical 

 part of this subject, What is the province of the science 

 of calculation ? Are we, because we reject the higher 

 mathematics, entirely without evidence; or can we ob- 

 tain any thing like conviction of the truth of our me- 

 thods ? Now it happens unluckily for objectors, that 

 the duty of mathematics in this science is very much 

 more simple in character than the same in astronomy, 

 mechanics, optics, music, or any other part of mathe- 

 matical physics. For in the whole of these sciences, 

 we have principles, as well as results, deduced by long 

 trains of mathematical reasoning ; whereas, in the 

 science before us, we ask nothing of mathematics but the 

 abbreviation of long numerical operations. For in- 

 stance : " If bodies move round another body, circu- 

 Jarly, and so that each body, in its own circle, describes 

 equal lengths in equal times, and if, moreover, the 

 squares of the times of revolution are in the same 

 proportion as the cubes of the distances, then it follows 

 that the cause of motion can be nothing but an attractive 



