8 On certain kinds of Groups or Series. [CHAP. I. 



universal and unlimited, it only prevails in certain directions 

 and up to certain points. 



5. In speaking as above of a series, it will hardly be 

 necessary to point out that we do not imply that the objects 

 themselves which compose the series must occur successively 

 in time; the series may be formed simply by their coming 

 in succession under our notice, which as a matter of fact 

 they may do in any order whatever. A register of mortality, 

 for instance, may be made up of deaths which took place 

 simultaneously or successively; or, we might if we pleased 

 arrange the deaths in an order quite distinct from either of 

 these. This is entirely a matter of indifference; in all these 

 cases the series, for any purposes which we need take into 

 account, may be regarded as being of precisely the same de 

 scription. The objects, be it remembered, are given to us in 

 nature ; the order under which we view them is our own pri 

 vate arrangement. This is mentioned here simply by way of 

 caution, the meaning of this assertion will become more plain 

 in the sequel. 



I am aware that the word series in the application with 

 which it is used here is liable to some misconstruction, but I 

 cannot find any better word, or indeed any as suitable in all 

 respects. As remarked above, the events need not neces 

 sarily have occurred in a regular sequence of time, though 

 they often will have done so. In many cases (for instance, 

 the throws of a penny or a die) they really do occur in suc 

 cession; in other cases (for instance, the heights of men, or 

 the duration of their lives), whatever may have been the 

 order of their actual occurrence, they are commonly brought 

 under our notice in succession by being arranged in statistical 

 tables. In all cases alike our processes of inference involve 

 the necessity of examining one after another of the members 

 which compose the group, or at least of being prepared to do 



