CHANCE, AND ITS ELIMINATION. 69 



tutes 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 that general result, which may occasionally be 

 expected as the result of some smaller number of 

 instances. 



The consideration of the latter question, and any 

 consideration of the former beyond that already given 

 to it, belong to what mathematicians term the doc- 

 trine of chances, or, in a phrase of greater pretension, 

 the Theory of Probabilities. An attempt at a philo- 

 sophical appreciation of that doctrine is, therefore, a 

 necessary portion of our task. 



