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



disorder, though durable is not everlasting. Keep on watch 

 ing it long enough, and it will be found almost invariably to 

 fluctuate, and in time may prove as utterly irreducible to 

 rule, and therefore as incapable of prediction, as the indi 

 vidual cases themselves. The full bearing of this fact upon 

 the theory of the subject, and upon certain common modes 

 of calculation connected with it, will appear more fully in 

 some of the following chapters ; at present we will confine 

 ourselves to very briefly establishing and illustrating it. 



Let us take, for example, the average duration of life. 

 This, provided our data are sufficiently extensive, is known to 

 be tolerably regular and uniform. This fact has been already 

 indicated in the preceding sections, and is a truth indeed 

 of which the popular mind has a tolerably clear grasp at the 

 present day. But a very little consideration will show that 

 there may be a superior as well as an inferior limit to 

 the extent within which this uniformity can be observed; 

 in other words whilst we may fall into error by taking too 

 few instances we may also fail in our aim, though in a very 

 different way and from quite different reasons, by taking too 

 many. At the present time the average duration of life in 

 England may be, say, forty years; but a century ago it was 

 decidedly less ; several centuries ago it was presumably very 

 much less; whilst if we possessed statistics referring to a still 

 earlier population of the country we should probably find that 

 there has been since that time a still more marked improve 

 ment. What may be the future tendency no man can say for 

 certain. It may be, and we hope that it will be the case, 

 that owing to sanitary and other improvements, the duration 

 of life will go on increasing steadily ; it is at least conceivable, 

 though doubtless incredible, that it should do so without 

 limit. On the other hand, and with much more likelihood, 

 this duration might gradually tend towards some fixed 



