26 Arrangement and Formation of the Series. [CHAP. n. 



they depart from that mean, we shall find that this di 

 minution of frequency takes place according to one in 

 variable law, whatever may be the nature of these mag 

 nitudes, and whatever the process by which they may have 

 been obtained. 



That such a uniformity as this should prevail amongst 

 many and various classes of phenomena would probably seem 

 surprising in any case. But the full significance of such a 

 fact as this (if indeed it were a fact) only becomes apparent 

 when attention is directed to the profound distinctions in the 

 nature and origin of the phenomena which are thus supposed 

 to be harmonized by being brought under one comprehensive 

 principle. This will be better appreciated if we take a brief 

 glance at some of the principal classes into which the things 

 with which Probability is chiefly concerned may be divided. 

 These are of a three-fold kind. 



4. In the first place there are the various combina 

 tions, and runs of luck, afforded by games of chance. Sup 

 pose a handful, consisting of ten coins, were tossed up a 

 great many times in succession, and the results were tabu 

 lated. What we should obtain would be something of the 

 following kind. In a certain proportion of cases, and these 

 the most -numerous of all, we should find that we got five 

 heads and five tails ; in a somewhat less proportion of cases 

 we should have, as equally frequent results, four heads six 

 tails, and four tails six heads ; and so on in a continually 

 diminishing proportion until at length we came down, in a 

 very small relative number of cases, to nine heads one tail, 

 and nine tails one head ; whilst the least frequent results 

 possible would be those which gave all heads or all tails 1 . 



1 As every mathematician knows, cessive terms of the expansion of 

 the relative numbers of each of these (l + l) 10 , viz. 1, 10, 45, 120, 210, 252, 

 possible throws are given by the sue- 210, 120, 45, 10, 1. 



