476 INDUCTION. 



aptness of the examples by -which I have attempted to illus 

 trate them. His words are these: * 



&quot;Upon these methods, the obvious thing to remark is, 

 that they take for granted the very thing which is most 

 difficult to discover, the reduction of the phenomena to 

 formulae such as are here presented to us. When we have 

 any set of complex facts offered to us ; for instance, those 

 which were offered in the cases of discovery which I have 

 mentioned, the facts of the planetary paths, of falling 

 bodies, of refracted rays, of cosmical motions, of chemical 

 analysis ; and when, in any of these cases, we would discover 

 the law of nature which governs them, or, if any one chooses 

 so to term it, the feature in which all the cases agree, where 

 are we to look for our A, B, C, and a, b, c ? Nature does 

 not present to us the cases in this form ; and how are we to 

 reduce them to this form ? You say, when we find the com 

 bination of A B C with a b c and A B D with a b d, then 

 we may draw our inference. Granted; but when and where 

 are we to find such combinations ? Even now that the dis 

 coveries are made, who will point out to us what are the 

 A, B, C, and a, b, c elements of the cases which have just 

 been enumerated ? Who will tell us which of the methods 

 of inquiry those historically real and successful inquiries 

 exemplify ? Who will carry these formulas through the 

 history of the sciences, as they have really grown up ; and 

 show us that these four methods have been operative in their 

 formation; or that any light is thrown upon the steps of 

 their progress by reference to these formulse ?&quot; 



He adds that, in this work, the methods have not been 

 applied &quot; to a large body of conspicuous and undoubted ex 

 amples of discovery, extending along the whole history of 

 science ;&quot; which ought to have been done in order that the 

 methods might be shown to possess the &quot; advantage&quot; (which 

 he claims as belonging to his own) of being those &quot; by which 

 all great discoveries in science have really been made.&quot; 

 (p. 277.) 



* Philosophy of Discovery, pp. 263, 264. 



