consequent length and tediousness of the necessary 

 operations,, would have formed as effectual a barrier to 

 the attainment of a result, as difficulty of principle, or 

 want of clear perception. 



There was also another circumstance which stood in 

 the way of the first investigators, namely, the not hav- 

 ing considered, or, at least, not having discovered, the 

 method of reasoning from the happening of an event to 

 the probability of one or another cause. The questions 

 treated in the third chapter of this work could not 

 therefore be attempted by them. Given an hypothesis 

 presenting the necessity of one or another out of a 

 certain, and not very large, number of consequences, 

 they could determine the chance that any given one or 

 other of those consequences should arrive ; but given an 

 event as having happened, and which might have been 

 the consequence of either of several different causes, or 

 explicable by either of several different hypotheses, 

 they could not infer the probability with which the 

 happening of the event should cause the different hypo- 

 theses to be viewed. But, just as in natural philosophy 

 the selection of an hypothesis by means of observed 

 facts is always preliminary to any attempt at deductive 

 discovery ; so in the application of the notion of proba- 

 bility to the actual affairs of life, the process of reasoning 

 from observed events to their most probable antecedents 

 must go before the direct use of any such antecedent, 

 cause, hypothesis, or whatever it may be correctly 

 termed. These two obstacles, therefore, the mathema- 

 tical difficulty, and the want of an inverse method, pre- 

 vented the science from extending its views beyond 

 problems of that simple nature which games of chance 

 present. In the mean time, it was judged by its fruits; 



