110 ROGERS— THE VALIDITY OF [March i, 



have been found either among minerals or prepared compounds. 

 Moreover, every crystal that has been carefully investigated can be 

 assigned to one of thirty-one out of the thirty-two possible crystal 

 classes. 



Physicists in general assume the coarse-grainedness of matter.^^ 

 It is only fair to assume that in crystals the molecules or particles 

 are arranged in a definite and regular manner. The most compre- 

 hensive definition of a crystal is the following: "A crystal is a 

 homogeneous solid, the physical properties of which are the same in 

 parallel directions but, in general, are different in non-parallel 

 directions." 



It is necessary to assume a regular arrangement of particles in 

 order to explain many of the physical properties of crystals. On 

 account of the correlation between the geometrical and physical 

 (especially the optical) properties of crystals it is practically certain 

 that the crystal form is an outward expression of a regular internal 

 structure. A regular internal structure accounts at the same time 

 for the constancy of interfacial angles and for diversity in crystal 

 habit. It also seems impossible to explain cleavage in any other 

 way. 



If crystals are made up of regularly arranged particles, '^^ the 

 centers of which are at small, finite distances apart, all crystal faces 

 necessarily have rational indices for the faces are due to the align- 

 ment of particles in parallel position but with the omission of par- 

 ticles in step-like arrangement. A whole number of particles is 

 always omitted. 



The indices are not necessarily small numbers hut may often he 

 large numhers. Even the highest indices ever assigned to crystal 

 faces such as the vicinal faces of adularia (5oo-527-o), (250-249-o), 

 and (20O- 157-0) are simple compared with the number of particles 

 or molecules in a crystal. 



" Riicker, Report British Association for the Advancement of Science, 

 1901, p. 12. 



" The size, shape, and nature of the particles are immaterial. It is also 

 immaterial whether they are contact as Haiiy believed or widely spaced as 

 modern physicists are inclined to believe. So stripped is the structure-theory 

 of all hypothesis that it becomes a mere geometrical abstraction. It is only 

 necessary to assume that crystals are made up of parts. 



