354 SCIENCE PROGRESS 



graphers and for which neither Sohncke's conception as 

 ultimately modified by himself nor the later mathematical 

 developments which followed give any adequate explanation. 

 An interesting example of such a morphotropic relationship 

 occurs amongst a group of minerals comprising chondrodite, 

 humite and clinohumite. The axial ratios of these minerals 



The axial ratio a:b is practically the same for each mineral, 

 whilst a constant increment to the ratio c : b accompanies each 

 addition of the group MgiSiOi. The need of an explanation of 

 this and of many other similar relationships between crystal- 



line substances has long been felt. 



Topic Parameters or Molecular Distance Ratios 



With the object of attempting to explain such relationships 

 as have been shown to exist between the crystalline forms of 

 chemically related substances, a new method of investigating 

 crystal structure was suggested simultaneously by Becke and 

 Muthmann. The method consists in attempting to determine 

 the dimensions of the space-lattice which can be regarded as 

 the fundamental basis of the crystal structure. It was expected 

 that interesting information would be obtained by comparing 

 these dimensions for different allied substances. The axial 

 ratios give only the relative dimensions of the particular space- 

 lattice which is indicated by the principal faces of the crystal. 

 The crystal structure being imagined divided into units, so that 

 each unit contains a chemical molecule, the centres of gravity 

 of these units are taken to form the points of a space-lattice 

 which is the fundamental lattice. The volume of each parallel- 

 opipedal cell of this space-lattice can be expressed numerically 

 by the molecular volume of the substance and is obtained by 

 dividing the molecular weight by the density. The volume 

 of the parallelopipedal cell, its relative dimensions and the 

 angles between its sides (the interaxial angles of the crystal) 

 being known, the absolute dimensions of the cell can be readily 

 calculated. These dimensions are called " Topic Parameters " 



