26 DISCOURSE ON THE STUDY 



are deduced, and the essential bearings and con- 

 nections of the several parts of natural philosophy. 

 There are whole branches too and very extensive 

 and important ones, to which mathematical reasoning 

 has never been at all applied ; such as chemistry, 

 geology, and natural history in general, and many 

 others, in which it plays a very subordinate part, and 

 of which the essential principles, and the grounds of 

 application to useful purposes, may be perfectly well 

 understood by a student who possesses no more 

 mathematical knowledge than the rules of arith- 

 metic ; so that no one need be deterred from the 

 acquisition of knowledge, or even from active origi- 

 nal research in such subjects, by a want of mathe- 

 matical information. Even in those branches which, 

 like astronomy, optics, and dynamics, are almost ex- 

 clusively under the dominion of mathematics, and in 

 which no effectual progress can be made without 

 some acquaintance with geometry, the principal 

 results may be perfectly understood without it. To 

 one incapable of following out the intricacies of 

 mathematical demonstration, the conviction afforded 

 by verified predictions must stand in the place of 

 that purer and more satisfactory reliance which a 

 verification of every step in the process of reasoning 

 can alone afford, since every one will acknowledge 

 the validity of pretensions which he is in the daily 

 habit of seeing brought to the test of practice. 



(21.) Among the verifications of this practical 

 kind which abound in every department of physics, 

 there are none more imposing than the precise pre- 

 diction of the greater phenomena of astronomy; 

 none, certainly, which carry a broader conviction 



