! SECT. 2.] Modes of establishing the Groups or Series. 75 



mean to employ the term in its widest signification; we 

 mean experience supplemented by all the aids which in 

 ductive or deductive logic can afford. When, for instance, 

 we have found the series which comprises the numbers of 

 persons of any assigned class who die in successive years, we 

 have no hesitation in extending it some way into the future 

 as well as into the past. The justification of such a proce 

 dure must be sought in the ordinary canons of Induction. 

 As a special discussion will be given upon the connection 

 between Probability and Induction, no more need be said 

 upon this subject here; but nothing will be found there at 

 variance with the assertion just made, that the series we 

 employ are ultimately obtained by experience only. 



2. In many cases it is undoubtedly true that we do not 

 resort to direct experience at all. If I want to know what is 

 my chance of holding ten trumps in a game of whist, I do 

 not enquire how often such a thing has occurred before. If 

 all the inhabitants of the globe were to divide themselves up 

 into whist parties they would have to keep on at it for a 

 great many years, if they wanted to settle the question 

 satisfactorily in that way. What we do of course is to cal 

 culate algebraically the proportion of possible combinations 

 in which ten trumps can occur, and take this as the answer 

 to our problem. So again, if I wanted to know the chance 

 of throwing six with a die whose faces were unequal, it 

 would be a question if my best way would not be to calculate 

 geometrically the solid angle subtended at the centre of 

 gravity by the opposite face, and the ratio of this to the 

 whole surface of a sphere would represent sufficiently closely 

 the chance required. 



It is quite true that in such examples as the above, espe 

 cially the former one, nobody would ever think of appealing 

 to statistics. This would be a tedious process to adopt when, 



