SECT. 6.] On certain kinds of Groups or Series. 9 



this, if we are to be in a position to justify our inferences. 

 The force of these considerations will come out in the course 

 of the investigation in Chapter VI. 



The late Leslie Ellis 1 has expressed what seems to me 

 a substantially similar view in terms of genus and species, 

 instead of speaking of a series. He says, &quot; When individual 

 cases are considered, we have no conviction that the ratios of 

 frequency of occurrence depend on the circumstances common 

 to all the trials. On the contrary, we recognize in the de 

 termining circumstances of their occurrence an extraneous 

 element, an element, that is, extraneous to the idea of the 

 genus and species. Contingency and limitation come in (so 

 to speak) together ; and both alike disappear when we con 

 sider the genus in its entirety, or (which is the same thing) 

 in what may be called an ideal and practically impossible 

 realization of all which it potentially contains. If this be 

 granted, it seems to follow that the fundamental principle 

 of the Theory of Probabilities may be regarded as included 

 in the following statement, The conception of a genus 

 implies that of numerical relations among the species sub 

 ordinated to it.&quot; As remarked above, this appears a sub 

 stantially similar doctrine to that explained in this chapter, 

 but I do not think that the terms genus and species are by 

 any means so well fitted to bring out the conception of a 

 tendency or limit as when we speak of a series, and I there 

 fore much prefer the latter expression. 



6. The reader will now have in his mind the conception 

 of a series or group of things or events, about the individuals 

 of which we know but little, at least in certain respects, 

 whilst we find a continually increasing uniformity as we 

 take larger numbers under our notice. This is definite 



1 Transactions of the Cambridge Beprinted in the collected edition of 

 Philosophical Society, Vol. ix. p. 605. his writings, p. 50. 



