76 Modes of establishing the Groups or Series. [CHAP. iv. 



as here, the mechanical and other conditions upon which the 

 production of the events depend are comparatively few, de 

 terminate, and admit of isolated consideration, whilst the 

 enormous number of combinations which can be constructed 

 out of them causes an enormous consequent multiplicity of 

 ways in which the events can possibly happen. Hence, in 

 practice, a priori determination is often easy, whilst a poste 

 riori appeal to experience would be not merely tedious but 

 utterly impracticable. This, combined with the frequent 

 simplicity and attractiveness of such examples when deduct 

 ively treated, has made them very popular, and produced the 

 impression in many quarters that they are the proper typical 

 instances to illustrate the theory of chance. Whereas, had 

 the science been concerned with those kinds of events only 

 which in practice are commonly made subjects of insurance, 

 probably no other view would ever have been taken than 

 that it was based upon direct appeal to experience. 



3. When, however, we look a little closer, we find that 

 there is no occasion for such a sharp distinction as that ap 

 parently implied between the two classes of examples just 

 indicated. In such cases as those of dice and cards, even, in 

 which we appear to reason directly from the determining 

 conditions, or possible variety of the events, rather thai from 

 actual observation of their occ rrence, we shall find that this 

 procedure is only valid by the &quot;help of a tacit assumption 

 which can never be determined otherwise than by direct 

 experience. It is, no doubt, an exceedingly natural and 

 obvious assumption, and one which is continually deriving 

 fresh weight from every-day observation, but it is one which 

 ought not to be admitted without consideration. As this is a 

 very important matter, not so much in itself as in connection 

 with the light which it throws upon the theory of the subject, 

 we will enter into a somewhat detailed examination of it. 



