OF NATURAL PHILOSOPHY. 219 



where all come within limits, some wide, some 

 close, what have we to guide us when we would 

 make up our minds what to conclude respecting 

 them ? It is evident that any system of calcula- 

 tion that can be shown to lead of necessity to the 

 most probable conclusion where certainty is not 

 to be had must be valuable. However, as this doc- 

 trine is one of the most difficult and delicate among 

 the applications of mathematics to natural philo- 

 sophy, this slight mention of it must suffice at 

 present. 



(231.) In the foregoing pages we have endea- 

 voured to explain the spirit of the methods to which, 

 since the revival of philosophy, natural science has 

 been indebted for the great and splendid advances 

 it has made. What we have all along most earnestly 

 desired to impress on the student is, that natural 

 philosophy is essentially united in all its depart- 

 ments, through all which one spirit reigns and one 

 method of enquiry applies. In cannot, however, be 

 studied as a whole, without subdivision into parts ; 

 and, in the remainder of this discourse, we shall 

 therefore take a summary view of the progress 

 which has been made in the different branches into 

 which it may be most advantageously so subdivided, 

 and endeavour to give a general idea of the nature 

 of each, and of its relations to the rest. In the 

 course of this, we shall have frequent opportunity 

 to point out the influence of those general principles 

 we have above endeavoured to explain, on the pro- 

 gress of discovery. But this we shall only do as 

 cases arise, without entering into any regular 

 analysis of the history of each department with that 



