60 INDUCTION. 



number of instances smaller than that required for striking 

 a fair average ? It is not only to be considered what is the 

 general result of the chances in the long run, but also what 

 are the extreme limits of variation from the general result, 

 which may occasionally be expected as the result of some 

 smaller number of instances. 



The consideration of the latter question, and any con- 

 sideration of the former beyond that already given to it, 

 belong to what mathematicians term the doctrine of chances, 

 or, in a phrase of greater pretension, the Theory of Proba- 

 bilities. 



