Chemistry and Physics. 321 



6. Relations between the Geometric constants of a Crystal 

 and the Molecular Weight of its Substance ; by Professor G. 

 Linck. (Abstract of a paper published in vol. xxvi of Groth's 

 Zeitschrift fur Krystallographie.) — The author has already called 

 attention* to the fact that the characteristics of crystals, i. e. their 

 geometric and optical constants, stand in direct relation to the 

 atomic or molecular weight of the elements contained in them. 

 This is most clearly shown in the eutropic series : a eutropic 

 series being defined as a series of substances, crystallizing simi- 

 larly, but differing, only in that they each contain a different 

 element, though the elements are yet similar according to the 

 periodic system of Mendeleeff. If such a series is arranged 

 according to increasing molecular or atomic weight, then the 

 series, for all characteristics of the crystal, remains unchanged. 

 The fundamental law of these phenomena the author has desig- 

 nated " Eutropy." 



For the present investigation it was necessary to know the 

 system to which the crystal belonged, its axial relations, the 

 specific gravity and the atomic weight. Of these, the atomic 

 weights were taken exclusively from Krafft's Lehrbuch der 

 Chemie. The specific gravities were taken from one or the other 

 of the three books of Dana (1893), Rammelsberg (1881), or 

 Websky (1868). So far as it was possible to decide, only such 

 values were used as belonged to chemically homogenous material. 

 In like manner the geometric constants, the axial ratios, were for 

 the most part, and wherever possible, taken from a single author 

 (Groth, Tab. Uebersicht, 1889). 



The method employed is stated by the author as follows : If 

 we assume with Fock, that the smallest conceivable crystal is 

 identical with the molecule, — although this is not an essential 

 condition for the further development of the subject here dis- 

 cussed — then the relative size of the molecule may be computed 

 from the volume. This is not the molecular volume, as defined in 

 terms of molecular weight, M, and specific gravity, d, according 



M 



to the formula —= t but the volume of the smallest crystal expressed 

 a 



as a product in terms of its geometric constants. As represent- 

 ing the smallest crystal, instead of the hypothetical actual poly- 

 hedron, the author assumes (after Schrauf) an ellipsoid whose 

 volume is proportional to that of the fundamental form. This 

 ellipsoid, designated as the crystal-volume, CV, is therefore re- 

 garded as the extreme case of a combination. 



The crystal-volume is computed from the crystallographic axes 

 of the fundamental form. These divide the fundamental form 

 into eight irregular tetrahedra of equal volume. Of each one of 

 these we know the length of the three edges corresponding to 

 the axes, and also the three angles a, /?, y, which these axes i'orm 



* Zeitschrift fur physikalische Chemie, xix, 193. 



Am. Jour. Sol— Fourth Series, Vol. IV, No. 22.— Oct., 1897. 

 22 



