1 06 SCIENCE PROGRESS 



No definite success, however, attended these efforts ; and in 

 a memoir on The Nature of the Structural Unit, in 1896, 

 the writer proved that for the series in question the structural 

 unit was simply the chemical molecule, thus clearing the ground 

 of all further complication. 



The structural units (chemical molecules) of the various 

 members of isomorphous series are obviously built up into 

 crystals according to the same plan, and the " elements " of the 

 crystals — that is, the relative lengths of the crystallographical 

 axes a, b, and c, cut off by the primary faces, and the three 

 mutual inclinations of the axes a, ft, and 7 — are relative measures 

 of the sides and also the angles of the elementary parallelo- 

 pipedon of the structure. The axial ratio a : b : c is usualfy 

 expressed so that b = 1. Hence it only affords the mutual 

 relation of the three axes to each other in that particular 

 substance, and gives no idea of the relations between the 

 dimensions of the elementary parallelopipeda of different 

 members of the series. But if we take the relative volumes of 

 the molecules into consideration, by combining the molecular 

 volume (molecular weight divided by density) of each salt 

 with the crystallographical axial ratios and axial angles, we 

 at once obtain the relative dimensions of the elementary paral- 

 lelopipeda of the various members of the isomorphous series. 

 These new axial dimensions expressing the true relations in 

 space are termed the topic parameters or axes, and are repre- 

 sented by %, -ty, co. They were employed simultaneously by 

 Muthmann in Germany and by the writer, in the year 1894; 

 and the latter was indebted for the idea _ to Prof. Becke of 

 Prague. They are expressed by simple mathematical for- 

 mulae involving only the crystallographical axial values a, b, c, 

 the axial angles a, ft, 7, the density of the crystals, and the 

 molecular weight of the salt. 



If the whole space of the elementary parallelopipedon were 

 filled with the matter of the molecule, the topic parameters 

 of the members of isomorphous series would indicate the 

 relative sizes of the chemical molecules. But the writer has 

 shown that the space is by no means filled with matter; 

 hence they do not represent the sizes of the molecules, but 

 the relative distances apart of the centres of gravity of con- 

 tiguous molecules along the directions of the three crystallo- 

 graphic axes. In other words, a point within the molecule, 



