98 DISCOURSE ON THE STUDY 



in Fresnel's a priori discovery of the extraordinary 

 refraction of both rays in a doubly refracting medium. 

 To give another example : The law of gravitation 

 is a physical axiom of a very high and universal 

 kind, and has been raised by a succession of induc- 

 tions and abstractions drawn from the observation of 

 numerous facts and subordinate laws in the planetary 

 system. When this law is taken for granted, and 

 laid down as a basis of reasoning, and applied to 

 the actual condition of our own planet, one of the 

 consequences to which it leads is, that the earth* 

 instead of being an exact sphere, must be compressed 

 or flattened in the direction of its polar diameter, 

 the one diameter being about thirty miles shorter 

 than the other ; and this conclusion, deduced at 

 first by mere reasoning, has been since found to be 

 true in fact. All astronomical predictions are 

 examples of the same thing. 



(89.) In the important business of raising these 

 axioms of nature, we are not, as in the analysis of 

 phenomena, left wholly without a guide. The na- 

 ture of abstract or general reasoning points out in 

 a great measure the course we must pursue. A 

 law of nature, being the statement of what will 

 happen in certain general contingencies, may be 

 regarded as the announcement, in the same words, 

 of a whole group or class of phenomena. When- 

 ever, therefore, we perceive that two or more phe- 

 nomena agree in so many or so remarkable points, as 

 to lead us to regard them as forming a class or group, 

 if we lay out of consideration, or abstract, all the cir- 

 cumstances in which they disagree, and retain in 

 our minds those only in which they agree, and 



