442 SCIENTIFIC THOUGHT. 



sons. They seemed to afford a practical means of recog- 

 nising and obtaining in the laboratory substances in 

 their qualitative or chemical purity, if they were ele- 

 ments, or in identical chemical combinations, if they 

 were compounds. And secondly, these regular, recur- 

 ring forms, which, in many cases, exhibited characteristic 

 and geometrically fixed arrangements of plane surfaces, 

 appeared the only means by which we could gain an 

 insight into the grouping and the shape of the ultimate 

 particles, out of which, according to the atomic view, 

 molar substances were constituted. If the particles of 

 any substance, when set free to follow their most natural 

 movements by solution, by fusion, or by volatilisation, 

 meet again during the process of solidification in definite, 

 always recurring forms, the conclusion seems obvious 

 that the individual and ultimate particles possess 

 marked peculiarities in the different directions of space. 

 And it is almost inconceivable that these peculiarities 

 should consist in anything else than in distinct primitive 

 forms, arranged in varying, but geometrically definable, 

 meshes of a network. Accordingly, different systems 

 have been elaborated ever since the age of Haliy, which 

 have the object of easily classifying, recognising, and 

 measuring crystalline structures, or, more ambitiously, 

 of discovering the number of simple forms and arrange- 

 ments of networks of which our spatial conceptions 

 admit. It is satisfactory to be able to state that 

 investigations of the latter kind, carried on from 

 seemingly different beginnings, have resulted in the 

 recognition of a certain limited number of forms of 

 symmetry. This symmetry is referred to points, called 



