364 SCIENCE PROGRESS 



This constant extension of the crystal structure in one direc- 

 tion with each addition of MgiSiO^ indicates that the increment 

 takes up its position as it were in the form of a slab on one 

 end of the unit of which the equivalence parameters as they 

 stand prior to the addition are the dimensions. But this is not 

 all. A mineral is known — forsterite — having the composition of 

 the increment under consideration, the crystals of which have 

 been examined. A possible set of equivalence parameters for 

 this mineral would be such that x and y were the same (say the 

 mean of) those above, while the 2 would be equal to the con- 

 stant increment on the z axis above. It is interesting to compare 

 the axial ratios and equivalence parameters thus calculated with 

 those obtained by direct measurement. The agreement is seen 

 to be remarkably close : 



The relation between all five minerals is admirably displayed 

 by a series of models of which a photograph is reproduced 

 in fig. I. Rectangular blocks having as horizontal dimensions 

 the X and y values and as a vertical dimension the z value for 

 forsterite, when superposed upon a similar set of blocks having 

 the corresponding dimensions of prolectite, form a stack ex- 

 hibiting the equivalence parameters of chondrodite ; a second 

 superposition of forsterite blocks gives a stack corresponding 

 to humite; another forsterite block on the humite stack gives 

 a representation of clinohumite. 



After considering the numerical data and the figure shown, 

 no one will be prepared to deny the utility of equivalence para- 

 meters as throwing light on obscure morphotropic relationships ; 

 many other instances could be quoted but for these the reader 

 should consult the original memoirs of Barlow and Pope. 



Before proceeding to demonstrate the lines on which the new 

 theory has been developed and to show how it has been applied 

 to the discussion of the crystalline form of a large number of 

 substances both elementary and compound, we would call atten- 

 tion to a confirmation which has been put forward by Le Bas^ 

 of the new idea respecting the relation between valency and 

 atomic volume. From a consideration of the molecular volumes, 



' J.C.S. Trans. 1907, 112. 



