1912.] THE LAW OF RATIONAL INDICES. 115 



For the crystals of any one substance the angles between corre- 

 sponding faces are constant. This law is known as the law of 

 constancy of interfacial angles. It corresponds to the law of defi- 

 nite proportions in chemistry. 



The proportions in which two elements combine determines the 

 atomic weight of the elements. In an analogous way the intercepts, 

 which are determined by certain constant interfacial angles, establish 

 the axial ratio which, like the atomic weight, is a constant. 



Crystal measurement corresponds to quantitative analysis in 

 chemistry. Exact measurements establish the axial ratio of a crys- 

 tal just as exact analyses establish the atomic weight of an element. 



Two chemical elements A and B unite not only to form the com- 

 pound AB but also the compounds ABr,, A.Mz> A^B, etc. This fact 

 is known as the law of multiple proportions. These proportions for 

 most chemical compounds are usually simple but in many com- 

 pounds, especially those containing silicon or carbon, they are often 

 far from simple. Among silicate minerals we have such compounds 

 as MggAljjSi^OoT and H^oMg^^^AlgSieO^^. Among organic com- 

 pounds we have C6oHi22> C17H23NO3, Co^¥{^QO^^, and many others 

 with fifty or more carbon atoms in the molecule. In spite of these 

 complex formulje all chemists accept the law of multiple propor- 

 tions as an established fact. Without it chemistry would scarcely 

 deserve to be called a science. The law of rational indices in 

 crystallography corresponds to the law of multiple proportions in 

 chemistry. The same difificulties are encountered in crystal meas- 

 urement as in quantitative analysis. That is, there are certain errors 

 which usually render it impossible to prove absolutely the law of 

 rational indices or the law of multiple proportions.-*' According to 

 Jaquet the formula of hemoglobin (of the dog) is C-5SH1003N195- 

 S3FeOois- This formula can hardly be regarded as established. It 

 may be a little different but it is very probable that these elements 

 unite in definite proportions. This is exactly analogous to vicinal 

 faces such as (251 •250-250) observed on alum by Miers. 



The law of multiple proportions was deduced by Dalton from 

 his atomic theory before there were accurate analyses to prove it, 



■" Organic chemistry has an advantage over inorganic chemistry in that 

 the formulse may usually be determined by the method of formation. 



