80 Modes of establishing the Groups or Series. [CHAP. IV. 



number of cases favourable to the event bears to the total 

 number of cases which are possible. This seems a somewhat 

 loose and ambiguous way of speaking. It is clearly not 

 enough to count the number of cases merely, they must also 

 be valued, since it is not certain that each is equally potent 

 in producing the effect. This, of course, would never be 

 denied, but sufficient importance does not seem to be at 

 tached to the fact that we have really no other way of 

 valuing them except by estimating the effects which they 

 actually do, or would produce. Instead of thus appealing to 

 the proportion of cases favourable to the event, it is far better 

 (at least as regards the foundation of the science, for we are 

 not at this moment discussing the practical method of facili 

 tating our calculations) to appeal at once to the proportion 

 of cases in which the event actually occurs. 



6. The remarks above made will apply, of course, to 

 most of the other common examples of chance ; the throwing 

 of dice, drawing of cards, of balls from bags, &c. In the 

 last case, for instance, one would naturally be inclined to 

 suppose that a ball which had just been put back would 

 thereby have a better chance of coming out again next time, 

 since it will be more in the way for that purpose. How is 

 this to be prevented ? If we designedly thrust it to the 

 middle or bottom of the others, we may overdo the precau 

 tion ; and are in any case introducing human design, that 

 element so essentially hostile to all that we understand by 

 chance. If we were to trust to a good shake setting matters 

 right, we may easily be deceived ; for shaking the bag can 

 hardly do more than diminish the disposition of those balls 

 which were already in each other s neighbourhood, to remain 

 so. In the consequent interaction of each upon all, the 

 arrangement in which they start cannot but leave its impress 

 to some extent upon their final positions. In all such cases, 



