CHAPTER IV. 



ON THE MODES OF ESTABLISHING AND DETERMINING THE 

 EXISTENCE AND NUMERICAL PROPORTIONS OF THE CHA 

 RACTERISTIC PROPERTIES OF OUR SERIES OR GROUPS. 



1. AT the point which we have now reached, we are 

 supposed to be in possession of series or groups of a certain 

 kind, lying at the bottom, as one may say, and forming the 

 foundation on which the Science of Probability is to be 

 erected. We have described with sufficient particularity the 

 characteristics of such a series, and have indicated the pro 

 cess by which it is, as a rule, actually brought about in 

 nature. The next enquiries which have to be successively 

 made are, how in any particular case we are to establish 

 their existence and determine their special character and 

 properties ? and secondly 1 , when we have obtained them, in 

 what mode are they to be employed for logical purposes ? 



The answer to the former enquiry does not seem difficult 

 Experience is our sole guide. If we want to discover what is 

 in reality a series of things, not a series of our own concep 

 tions, we must appeal to the things themselves to obtain it 

 for we cannot find much help elsewhere. We cannot tel 

 how many persons will be born or die in a year, or how 

 many houses will be burnt or ships wrecked, without actually 

 counting them. When we thus speak of experience we 



1 This latter enquiry belongs to logical part of this volume, and is 

 what may be termed the more purely entered on in the course of Chapter vi 



