APPLICATIONS OF CRYSTALLOGRAPHY, ETC. 573 



by using- this mean refractive index to calculate a molecular 

 refraction by the formula quoted above, it is demonstrated 

 by taking- many examples that the molecular refractions of 

 crystalline salts are, like those of organic liquids, additive 

 quantities within the limits of experimental error, that is to 

 say, the molecular refractions are the sums of the equivalent 

 refractions of the atoms or groups of atoms (radicles) com- 

 posing the molecules. 



Evidently, in the foregoing case, the differentiated 

 structure of crystalline substances prevents the immediate 

 application to them of a law governing liquids and gases 

 although the hindrance so introduced can be put aside by 

 a comparatively simple operation. In the case of other 

 properties of crystalline substances, however, so simple a 

 method of eliminating the complication introduced by the 

 structure will scarcely avail, although the method adopted 

 above for maintaining the analogy 'by a process of averaging 

 will doubtless be ultimately found applicable to a large 

 number of properties. 



Thus the famous law of Dulong and Petit which states 

 that the product of the specific heat and atomic weight of 

 an element is a constant, is only a very rough approxima- 

 tion to truth. This is doubtless due to the fact that the 

 specific heat is not wholly dependent on the nature of the 

 element but partially also upon the crystalline form of the 

 element ; we know that two different crystalline forms of 

 the same chemical substance possess different specific heats 

 as in the case of diamond and graphite or of crystalline and 

 amorphous selenium. This quite apart from the apparent 

 necessity of obtaining data, not at the same temperature but 

 at equivalent temperatures, namely, at equal distances from 

 the critical temperatures of the substances concerned, is a 

 sufficient reason for the failure to so modify the law as to 

 make it exact ; since the specific heats are measured on 

 elements the crystalline forms of which are totally dissimilar, 

 the influence of the crystalline structure on the specific heat 

 is wholly irregular and consequently no simple law could 

 govern the data with rigid accuracy. Only after the specific 

 heats of the elements have been calculated from the specific 



