364 THE PRINCIPLES OF SCIENCE. 



the simple hypothesis that the elasticity and approxima- 

 tion of the particles vary in the directions of the crystalline 

 axes allows of the application of deductive reasoning. 

 The whole of the phenomena are gradually being proved 

 to be consistent with this hypothesis, so that we have in 

 this subject of crystallography a beautiful instance of 

 successful classification, connected with a nearly perfect 

 physical hypothesis. Moreover this hypothesis was veri- 

 fied experimentally as regards the mechanical vibrations 

 of sound by Savart, who found that the vibrations in a 

 plate of biaxial crystal indicated the existence of varying 

 elasticity in varying directions. 



Classification an Inverse and Tentative Operation. 



If all attempts at so-called natural classification be 

 really attempts at perfect induction, it follows that they 

 are all subject to the remarks which were made upon the 

 inverse character of the inductive process, and upon the 

 difficulty of every inverse operation (vol. i. pp. 14, 15, 

 140, &c.). There will of necessity be no royal road to the 

 discovery of the best system, and it will even be im- 

 possible to lay down any series of rules of procedure to 

 assist those who are in search of a good arrangement. 

 The only invariable logical rule which could be stated 

 would be as follows : Having given certain objects, group 

 them in every way in which they can be grouped, and 

 then observe in which method of grouping the coincidence 

 of properties is most conspicuously manifested. But this 

 method of exhaustive classification will in almost every 

 case be impracticable, owing to the immensely great 

 number of modes in which a comparatively small number 

 of objects may be grouped together. About sixty-three 

 elements have been classified by chemists in six principal 

 groups as Monad, Dyad, Triad, &c. elements, the numbers 



