132 SCIENCE PROGRESS. 



a result practically identical with that of Fedorow and 

 Schonflies ; namely, that there are 229 possible varieties of 

 homogeneous structures, and that these present exactly the 

 same thirty-two types of symmetry which are to be found 

 in crystals, and no others. 



The conclusion of the whole matter is, then, that the 

 peculiar symmetry of crystals can be fully explained as 

 resulting from their homogeneity. That they are homo- 

 geneous structures we are bound to believe from the fact 

 that, so far as our observation goes, a crystal is the same at 

 every point within its mass ; it is impossible to distinguish 

 one internal part from another ; and this character can 

 scarcely be attributed to anything else than the juxta- 

 position of identical parts or particles. 



The geometrical principle of homogeneity with its 

 resulting symmetry is one of the very greatest importance, 

 and must be taken into account jn any theory of the con- 

 stitution of solid matter ; no theory of crystalline structure 

 which ignores it deserves serious consideration, and any 

 theory which is antagonistic to it may be at once dismissed. 



Lord Kelvin, in his interesting Boyle Lecture, delivered 

 at Oxford in 1893, nas shown how the same problem may 

 be regarded in three different ways. In the first place, it is 

 possible to consider, as has been done above, the regular 

 arrangement of a number of identical figures or units of anv 

 sort ; secondly, one may imagine them to be so arranged that 

 they are all in contact, the problem then becomes one 

 concerning the close packing of bodies of a given shape 

 (for example, a pile of cannon balls) ; or, thirdly, these may 

 be imagined to increase in size until they are all in complete 

 contact over their whole surface, the problem then becomes 

 one of the partitioning of space into cells. 



But, in any case, corresponding parts of the. structure, 

 that is to say, parts which are either identical or inverted 

 (in the sense described above), must conform to one of the 

 229 types now established, and the nature of such structures 

 is limited by this condition. 



