140 SCIENCE PROGRESS. 



parallelepiped ; it is by no means certain that the crystallo- 

 graphic or topic axes represent molecular intervals ; and 

 there is no direct evidence to show that the symmetry of 

 the crystal molecule (whatever that may be) is the same as 

 that of the crystal itself. 



ADDITIVE RELATIONS OF CHONDRODITE. 



Another important contribution to the subject is one in 

 which the crystals compared are not isomorphous, but bear 

 an additive relation to one another ; it is a case in which 

 the substances differ not by the replacement of one element 

 or radicle by another, but by the addition or subtraction of 

 the same radicle. 



By careful analysis of the minerals of the chondrodite 

 group Penfield [Amer. Journ. Science, xlvii., p. 1 88) has 

 proved that there are three compounds having the com- 

 position — 



(A) Mg 3 [Mg (F. OH)] 2 (Si 4 ) 3 No. of Mg atoms 5 



(B) Mg 5 [Mg (F. OHft (Si 4 ) 3 „ „ 7 



(C) Mg y [Mg (F. OH)l (Si 4 ) 4 „ „ 9 



Each of these is derived from the preceding one by the 

 addition of the olivine radicle Mg 2 Si 4 . 



The three minerals have almost the same form, but 

 differ only in the length of one crystallographic axis. The 

 lengths of this axis in the three minerals are in the ratio 

 5:7:9. Thus the addition of the olivine radicle Mg 2 Si 4 

 exerts a so-called " morphotropic " action along one definite 

 axis, and causes a certain constant increase in the length of 

 this axis. 



Penfield himself does not draw any conclusion re- 

 garding the structure of the crystal, but, obviously, it 

 might be suggested with as much reason as in any of the 

 previous cases that the olivine radicle is situated on the 

 variable axis. It is further a curious fact that the length of 

 this axis varies directly as the number of magnesium atoms 

 in the compound. 



