SECT. 7.] On certain kinds of Groups or Series. 11 



common, without this they would not be classed together. 

 But there is also a distinction existing amongst them ; a 

 certain number of other attributes are to be found in some 

 and are not to be found in others. In other words, the 

 individuals which form the series are compound, each being 

 made up of a collection of things or attributes ; some of 

 these things exist in all the members of the series, others 

 are found in some only. So far there is nothing peculiar 

 to the science of Probability ; that in which the distinctive 

 characteristic consists is this ; that the occasional attri 

 butes, as distinguished from the permanent, are found on 

 an extended examination to tend to exist in a certain definite 

 proportion of the whole number of cases. We cannot tell in 

 any given instance whether they will be found or not, but 

 as we go on examining more cases we find a growing uni 

 formity. We find that the proportion of instances in which 

 they are found to instances in which they are wanting, is 

 gradually subject to less and less comparative variation, and 

 approaches continually towards some apparently fixed value. 



The above is the most comprehensive form of description ; 

 as a matter of fact the groups will in many cases take a 

 far simpler form ; they may appear, e.g. simply as a suc 

 cession of things of the same kind, say human beings, with 

 or without an occasional attribute, say that of being left- 

 handed. We are using the word attribute, of course, in its 

 widest sense, intending it to include every distinctive feature 

 that can be observed in a thing, from essential qualities 

 down to the merest accidents of time and place. 



7. On examining our series, therefore, we shall find 

 that it may best be conceived, not necessarily as a succession 

 of events happening in different ways, but as a succession 

 of groups of things. These groups, on being analysed, are 

 found in every case to be resolvable into collections of sub- 



