88 Mr. L. Fletcher on the Dilatation of 



grouping, even if the crystal is formed at some temperature at 

 which the latter possesses a symmetry corresponding to a 

 higher type. 



In what follows, it will be assumed that in a crystal there 

 is an extremely large number of points arranged in parallele- 

 pipedal order, and that at each of these points there is a centre 

 of mass of a molecule or molecular group — all these groups 

 being equal and parallel in orientation. For brevity, such a 

 molecular group will be spoken of as a molecule. 



We infer from the above, that the only symmetry-planes 

 which are permanent on change of temperature are those 

 which are at once planes of symmetry to the molecules them- 

 selves and to the molecular grouping, and also that it would 

 be possible for a single crystal to determine at each of six dif- 

 ferent temperatures a crystalloid system presenting symmetry 

 corresponding to a different crystal-system. 



Now nothing in the above would conflict with the possibi- 

 lity of new planes of symmetry common to the molecules and 

 their arrangement starting into existence. All we can say is 

 that, if they do come into existence, they must do so symme- 

 trically to the preexisting common symmetry-planes ; but 

 once in existence, they cannot be made to disappear again by 

 any cause which would produce internal reactions symmetrical 

 to these common symmetry-planes. Even if the molecules 

 explode, they must do so simultaneously and symmetrically 

 to these planes, and the products of these explosions must 

 therefore also be symmetrical to them. As a crude illustra- 

 tion of the way in which such planes might come into exist- 

 ence, take the previous example of a rhombic arrangement of 

 molecules themselves possessing rhombic symmetry, and let 

 the temperature change to that at which the arrangement of 

 the molecules is tetragonal. It is quite conceivable that at 

 this temperature the internal equilibrium of the molecules 

 might become unstable, and that each molecule might rear- 

 range itself in such a way as to be still symmetrical to the old 

 planes of symmetry, but also at the same time to the two ad- 

 ditional planes requisite for tetragonal symmetry. From this 

 instant the whole system, including the arrangement and the 

 internal constitution of the molecules, would present a sym- 

 metry corresponding to the tetragonal type ; in fact, the 

 crystal would henceforth be tetragonal. 



But this symmetrical state could only be so permanent in a 

 space where no disturbing force could enter. We know from 

 experiment that the cohesion of a body diminishes as the tem- 

 perature increases, and that in general the body may come 

 to find itself in a fluid condition, a state in which the slightest 

 exertion of force will disturb the general arrangement of the 



