CALCULATION OF CHANCES. 71 



as neither to be suggested to the reader, nor kept in 

 view by the writer himself. 



To a calculation of chances, according to Laplace, 

 two things are necessary: we must know that of 

 several events some one will certainly happen, and no 

 more than one ; and we must not know, nor have any 

 reason to expect, that it will be one of these events 

 rather than another. I contend that these are not the 

 only requisites, and that another supposition is neces- 

 sary. This supposition it might be imagined that 

 Laplace intended to indicate, by saying that all the 

 events must be equally possible (egalement possibles). 

 But his next sentence shows that, by this expression, 

 he did not mean to add anything to the two condi- 

 tions which he had already suggested. "The theory of 

 chances consists in reducing all events of the same 

 kind to a certain number of cases equally possible, that 

 is, such that we are equally undecided as to their exist- 

 ence ; and to determine the number of these cases which 

 are favourable to the event of which the probability is 

 sought." By " events equally possible," then, he 

 only means events " such that we are equally unde- 

 cided as to their existence ;" that we have no reason 

 to expect one rather than another ; which is not a 

 third condition, but the second of the two previously 

 specified. I, therefore, feel warranted in affirming 

 that Laplace has overlooked, in this general theoreti- 

 cal statement, a necessary part of the foundation of 

 the doctrine of chances. 



2. To be able to pronounce two events equally 

 probable, it is not enough that we should know that 

 one or the other must happen, and should have no 

 ground for conjecturing which. Experience must 

 have shown that the two events are of equally frequent 



