Crystals on Change of Temperature. 87 



in rectangular-parallelepipedal order, the edges of an elemen- 

 tary parallelepiped having absolute lengths a, b, c respectively; 

 and, as usual, suppose that all the planes through molecular 

 mass-centres are crystalloid planes : it follows from the above 

 that such a set of planes will possess the symmetry character- 

 istic of the rhombic system so long as the ratios T > -•> - are all 

 J to b c a 



irrational, but the symmetry of the tetragonal if one and only 

 one of them (say y) become rational; but it is clear that unless 



a is not only in a rational ratio to b, but actually equal to it, 

 the symmetry of disposition of the mass-centres themselves, 

 and therefore the symmetry of the physical properties, will 

 still be no higher than rhombic. But we may go still further, 

 and assert that even if a actually become equal to b, the phy- 

 sical properties of the crystal need only be symmetrical to 

 three perpendicular planes. For if the molecules themselves 

 "have sides," or different properties in different directions 

 (and no one has ventured to assume that they have not), it is 

 possible to imagine that each molecule has an internal sym- 

 metry, upon which, as well as upon the arrangement itself of 

 the molecules, the symmetry of the physical properties must 

 ultimately depend. If, then, in the case we are considering, 

 the internal symmetry of the molecule be only symmetry to 

 the above three planes, even though the symmetry of disposi- 

 tion both of the molecular mass-centres and of the molecular 

 planes be tetragonal, those physical properties (among which 

 we must include dilatation on change of temperature) which 

 depend on the internal symmetry of the molecules as well as 

 upon their grouping will still present only that symmetry 

 which characterizes the rhombic system. And we may further 

 observe that, as the dilatations along the directions perpendi- 

 cular to these planes are independent, j will again become 



irrational, and the crystalloid system itself once more pass to 

 rhombic symmetry. 



It might appear at first sight that, from the measurement 

 of the angles of a crystal at only one temperature, no safe con- 

 clusion could be arrived at as to the crystal-system to which it 

 must be referred, and that either the crystal must be measured 

 at a second temperature or some physical tests must be applied. 

 We must, however, remember that the faces of a crystal will 

 be in general called into existence in such a way as to accord 

 in their symmetry of disposition with that which is common 

 to the internal arrangement of the molecules and to their 



