x.] THE THEORY OF PROBABILITY. 217 



of time prove, perhaps the most fruitful branch of mathe- 

 matical science. It is the very guide of life, and hardly 

 can we take a step or make a decision of any kind without 

 correctly or incorrectly making an estimation of proba- 

 bilities. In the next chapter we proceed to consider how 

 the whole cogency of inductive reasoning rests upon pro- 

 babilities. The truth or untruth of a natural law, when 

 carefully investigated, resolves itself into a high or low 

 degree of probability, and this is the case whether or not 

 we are capable of producing precise numerical data. 



