THE VALIDITY OF THE LAW OF RATIONAL INDICES, 

 AND THE ANALOGY BETWEEN THE FUNDA- 

 MENTAL LAWS OF CHEMISTRY AND 

 CRYSTALLOGRAPHY. 



By AUSTIN F. ROGERS. 

 (Read March i, 19 12.) 



Some fundamental law of nature governs the position of the 

 faces of a crystal and limits in number the faces which occur on the 

 crystals of any one substance. Crystal faces are designated by 

 intercepts on coordinate axes, which are chosen so as to yield simple 

 relations. Now it is found that the intercepts of the various crystal 

 faces of a given substance, on each coordinate axis taken separately, 



Fig. I. The coordinate axes of a crystal. 



usually bear a simple ratio to each other such as i : co , 1:2, 1:3,2:3, 

 3:1, etc. A selected face chosen because of its prominence is taken as 

 a standard and the other faces are expressed in terms of it. The 

 selected face is called the unit face, as its intercepts on the three 

 axes establish a unit which, in general, is different for each axis, as 

 represented in Fig. i. The intercepts of the unit face which are, in 



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