APPLICATIONS OF CRYSTALLOGRAPHY, ETC. S77 



suggested by the idea of physical molecules ; we may, 

 however, take a step beyond this and point out that so 

 far as our present knowledge goes there is litde foundation 

 for the view that amongst polymorphous substances the 

 units of which the crystalline structure is built up are other 

 than simple chemical molecule. 



Barlow has shown that by distributing an infinite number 

 of bodies in space in such a way that the arrangement 

 around each is in all respects similar, a number of arrange- 

 ments are obtained each of which has exactly the symmetry 

 of one or other of the thirty-two crystalline systems ; it is 

 obvious that no direct relation exists a priori between the 

 symmetry of the system of bodies and that of the com- 

 ponent bodies or figures themselves. We must conclude 

 from Barlow's work that a crystal is simply a system 

 built up of particles which do not in general possess the 

 same symmetry as the system itself, and which we may 

 suppose to be the so-called physical molecules. Now in 

 the case of a substance like calcium carbonate which exists 

 in two polymorphous forms, namely as the hexagonal 

 mineral calcite and the orthorhombic aragonite, it seems to 

 demand fewer assumptions to suppose that the physical 

 molecules are the same in the two minerals, the only dif- 

 ferences lying in the nature of the mode of distribution 

 of the molecules, than to assume that the units of which 

 the crystalline structure is built up are of different com- 

 plexity in the two cases. Many substances, like am- 

 monium nitrate, exist in several forms, each of which is 

 stable within certain limits of temperature but changes into 

 another polymorphous modification so soon as those limits 

 are exceeded ; in these cases also it is only natural to sup- 

 pose from our present knowledge that at a certain tempera- 

 ture one crystalline modification exists, the molecules of 

 which are arranged in a certain definite manner, and 

 that as the temperature drops the structure contracts, the 

 molecules shrink nearer together, until ultimately when the 

 temperature of change is reached, the structure jams and the 

 same molecules arrange themselves anew in quite a dif- 

 ferent manner. When one polymorph changes into another 



