4 On certain kinds of Groups or Series. [CHAP. i. 



treating this element as one of primary importance, no 

 further allusion will be made to it here, but we will pass on 

 at once to a more minute investigation of that distinctive 

 characteristic of certain classes of things which was intro 

 duced to notice in the last section. 



In these classes of things, which are those with which 

 Probability is concerned, the fundamental conception which 

 the reader has to fix in his mind as clearly as possible, is, I 

 take it, that of a series. But it is a series of a peculiar kind, 

 one of which no better compendious description can be given 

 than that which is contained in the statement that it com 

 bines individual irregularity with aggregate regularity. This 

 is a statement which will probably need some explanation. 

 Let us recur to an example of the kind already alluded toj 

 selecting one which shall be in accordance with experience] 

 Some children will not live to thirty. Now if this propo 

 sition is to be regarded as a purely indefinite or, as it would 

 be termed in logic, particular proposition, no doubt the! 

 notion of a series does not obviously present itself in con-J 

 nection with it. It contains a statement about a certa 

 unknown proportion of the whole, and that is all. But it 

 not with these purely indefinite propositions that we sha 

 be concerned. Let us suppose the statement, on the co: 

 trary, to be of a numerical character, and to refer to a giv&amp;lt; 

 proportion of the whole, and we shall then find it difficult 

 exclude the notion of a series. We shall find it, I thin 

 impossible to do so as soon as we set before us the aim 

 obtaining accurate, or even moderately correct inference 

 What, for instance, is the meaning of the statement th 

 two new-born children in three fail to attain the age 

 sixty-three ? It certainly does not declare that in any give 

 batch of, say, thirty, we shall find just twenty that fai 

 whatever might be the strict meaning of the words, th 



