RECENT ADVANCES IN SCIENCE 383 



co-ordinates are given for a number of substances including 

 calcite, dolomite, haematite, ilmenite, corundum, quartz, etc., 

 and in some cases the positions of certain atoms are deduced 

 from the already determined location of other atoms. The 

 above law is analogous to that of Haiiy, and the rationality 

 of co-ordinates to that of indices. 



The third paper deals with the effect of chemical similarity 

 on the distance between the atoms and with the relations 

 between the crystallographic unit and the chemical molecule. 

 The space between two adjacent atoms of the same kind is 

 greater than that between two dissimilar atoms, while in the 

 case of the latter the distance between the atoms varies inversely 

 as their chemical affinity. The rule has to be modified for 

 certain cases in which bivalent atoms are concerned. The 

 chemical molecule consists of one or more crystallographic 

 units except in the case of the diamond, where the elementary 

 parallelohedron includes two chemical molecules. 



The fourth paper discusses the determination of the 

 reticular density of atoms in the more important planes in a 

 crystal. In calculating the reticular density of a possible crystal 

 face the value taken is the maximum for all the planes parallel 

 to it. A distinction is made between principal and fundamental 

 parallelohedra, the former being those which canj by symmetry 

 operations, be brought into coincidence with themselves or with 

 congruent figures, while the latter are those which do not possess 

 ! this property. Seven cubic substances whose structure has 

 been determined are examined, and the fundamental parallelo- 

 hedra and the disposition of the atoms with respect thereto 

 determined. 



From the theoretical point of view, the results of the X-ray 

 analysis of crystals is discussed by Beckenkamp (Centr. Min. 

 I 9 l 7> 97, 353, 393) an d J- Stark (Jahrb. Rad. Elektr. 12, 280, 

 191 5), both of whom maintain that the individuality of the 

 atom persists in the crystalline state, and by F. Rinne (Zeit. 

 anorg. Chem. 96, 317, 191 6), who is of the same opinion, holding 

 i that the molecular structure is not necessarily derivable from 

 \ the elementary cell of the lattice. From a consideration of the 

 density and X-ray structure of the crystalline elements, C. W. 

 Kanolt {Science, 47, 123, 191 7) proposes to calculate the atomic 

 weights. 



The question of the existence of molecules in the crystalline 



