77 



nmnionly n-ed in calculations, but rather their reciprocal valuer 

 ' it . A- ,' , and / = ' t . These numbers //, k, and / are called 

 H- indices of the crystal-lace (Miller), and tin- plum- iNelf U 

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

 i- oi' int. rest for the determination of the direction of A'J: 

 numbers //, k. and / arc ^ciu-rally reduced to the most simple 

 rs. 



The law of Hauy may therefore be expressed as follows: 

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

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

 >v.s/V(7 to lour not parallel and suitably chosen planes of the crystal. 1 ) 

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

 , ithin which the possible values of the periods of eventually occurring 

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

 !i\ed in two ways: either we can look upon the external form of 

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

 suitable hypothesis on the molecular structure of the crystal, and 

 if this supposed structural image possess a special character 

 rom which the limits of the axial periods mentioned above follow 

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

 >sitions about the intimate, molecular structure of crystals in 

 ncral, a theory which has been of great value in the development 

 )f our views on the true nature of crystalline matter. These views 

 iavc been strikingly confirmed by the results lately obtained in 

 ie recent expejiments of Von Laue, Bragg Sr. and Jr., and 

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

 md obtained in such a way a diffraction-pattern which is closely 

 slated to the said molecular structure. Although the fundamental 

 )irectness of the above mentioned ideas regarding the molecular 

 tructure of the crystals has thereby become highly probable, it 

 however better to postpone the demonstration based upon these 

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

 lolecules regularly distributed in space. With respect to our previous 



1) 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 be really simple ones too. 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. 



