79 



commonly used in calculations, but rather their reciprocal values : 

 h = , k = , and / = . These numbers h, k, and / are called 



111 ti J3 



the indices of the crystal-face (Miller), and the plane itself is 

 usually denoted by the symbol (h k 1). As only the ratio: ma: nb: 

 pc is of interest for the determination of the direction of A'B'C' ', 

 these numbers h, k, and / are generally reduced to the most simple 

 integers. 



The law of Hauy may therefore be expressed as follows: 

 Only such faces can occur as limiting faces of a crystal, the indices 

 of which are (simple) rational numbers, if these faces are defined with 

 respect to four not parallel and suitably chosen planes of the crystal. l ) 

 3. It is this very important law, which determines the limits 

 within which the possible values of the periods of eventually occurring 

 symmetry-axes in the crystal must remain. These limits may be 

 fixed in two ways: either we can look upon the external form of 

 the crystal only, or we can try to explain Hauy's law by some 

 suitable hypothesis on the molecular structure of the crystal, and 

 see if this supposed structural image possess a special character, 

 from which the limits of the axial periods mentioned above follow 

 as a logical consequence. Indeed, Hauy's law has led to such sup- 

 positions about the intimate, molecular structure of crystals in gene- 

 ral, suppositions which have been of great value in the develop- 

 ment of our views on the true nature of crystalline matter. These 

 views have been strikingly confirmed by the results lately obtained in 

 the recent experiments of Von Laue, Bragg Sr. and Jr., Debye, and 

 others, who sent a narrow pencil of Rontgen-rays through a crystal, 

 and observed in such a way a diffraction-phenomenon which is 

 closely related to the said molecular structure. Although the fun- 

 damental correctness of the above mentioned ideas regarding the 

 molecular structure of crystals has thereby become highly probable, 

 it is, however, better to postpone the demonstration based upon these 

 views till we are dealing in detail with the indicated systems of 

 molecules regularly distributed in space. With respect to our previous 



*) Although the condition of simplicity of the indices considered is not an 

 essential one, it may be clear that in practice the law of Hauy can be of 

 value only if these numbers are really simple ones. For the ratio of the inter- 

 cepted segments on the coordinate-axes, with respect to those of the primarily 

 chosen fourth plane, can be always reduced to a set of rational numbers, if 

 only we are free to multiply the observed ratio by any suitably chosen 

 factor, whatever may be the magnitude of the last. 



