a magnet, respectively as the body is magnetic or diamagnetic. Further questions arise if we apply pressure to crystals. Thus doubly refracting crystals with one principal axis acquire two axes when the pressure is perpendicular in direction to the principal axis.
All the phenomena peculiar to crystalline bodies are thus closely correlated with the formation of the crystal, or will almost certainly be found to be so as investigation proceeds. It is upon empirical observation indeed that the laws of connexion are in the first place founded, but the simple hypothesis that the elasticity and approximation 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 verified 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 attempts at so-called natural classification are really attempts at perfect induction, it follows that they are subject to the remarks which were made upon the inverse character of the inductive process, and upon the difficulty of every inverse operation (pp. 11, 12, 122, &c.). There will be no royal road to the discovery of the best system, and it will even be impossible to lay down rules of procedure to assist those who are in search of a good arrangement. The only logical rule 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 correlation 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 in the classes varying from three to twenty elements. Now if we were to calculate the whole number of ways in which sixty-three objects can be arranged in six groups, we should find the number to be so great that the life of the longest lived man would be wholly inadequate to enable him to go through these possible groupings. The rule of exhaustive arrangement, then, is absolutely impracticable. It follows that mere haphazard trial cannot as a general rule give any useful result. If we were to write the names of the elements in succession upon sixty-three cards, throw them into a ballot-box, and draw them out haphazard in six handfuls time after time, the probability is excessively small that we should take them out in a specified order, that for instance at present adopted by chemists.
The usual mode in which an investigator proceeds to form a classification of a new group of objects seems to consist in tentatively arranging them according to their most obvious similarities. Any two objects which present a close resemblance to each other will be joined and formed into the rudiment of a class, the definition of which will at first include all the apparent points of resemblance. Other objects as they come to our notice will be gradually assigned to those groups with which they present the greatest number of points of resemblance, and the definition of a class will often have to be altered in order to admit them. The early chemists could hardly avoid classing together the common metals, gold, silver, copper, lead, and iron, which present such conspicuous points of similarity as regards density, metallic lustre, malleability, &c. With the progress of discovery, however, difficulties