204 Penfielcl and Howe — Chemical Composition- 



Conclusions. — Iq the preceding pages we have shown that 

 the minerals of the humite group are not identical with each 

 other in chemical composition and that they can be expressed 

 by the following formulae, constructed on two, three and four 

 molecules of ortho silicic acid, in which two hydrogen atoms 

 are replaced by the univalent radical [Mg(F . OH)] and the re- 

 maining ones by magnesium : 



Chondrodite Mg 3 



Humite . Mg 6 



Clinohumite Mg 7 



Mg(F.OH)l t [Si0 4 ] f 

 Mg(F.OH)] 2 [SiOJ s 

 Mg(F.OH)] t [SiOJ 4 



These form a chemical series, varying progressively from 

 chondrodite to clinohumite by an increase of one molecule of 

 Mg 2 Si0 4 . This variation in chemical composition is intimately 

 connected with the crystallization. Thus on page 188 it was 

 mentioned that the three minerals form a crystallographic 

 series in which the vertical axes increase from chondrodite to 

 clinohumite. It was also shown that by dividing the vertical 

 axes by 5, 7 and 9 respectively the quotients become practi- 

 cally identical and it is a very interesting and remarkable fact 

 that these divisors 5, 7 and 9 correspond to the number of 

 magnesium atoms in the formulas deduced by us. Groth* has 

 shown that in certain organic compounds the substitution of 

 one hydrogen atom by another atom or radical causes a change 

 in one of the crystallographic axes, the other two and the sym- 

 metry remaining essentially unchanged. Such a crystallo- 

 graphic series he calls a " Morphotropisch* Reihe." In the 

 humite group we evidently have a kind of morphotropic series, 

 but not exactly analogous to that cited by Groth as in the 

 present case we have a change brought about by the addition 

 of a molecule of Mg 2 Si0 4 , instead of the substitution of a 

 radical. This addition of Mg 2 Si0 4 causes the vertical axis to 

 increase by about 1*2575, or \ of the vertical axis of clino- 

 humite, while the other two axes and the inclination ft remain 

 the same. The symmetry, however, changes so that the first 

 and last members of the series are monoclinic. In the whole 

 range of chemical crystallography there is no series of com- 

 pounds known to the authors that can be compared to the 

 humite group. It is reasonable to expect that other members 

 of this series will be found. Thus Mg[Mg(F . OH)] 2 Si0 4 is 

 a possible and a most likely compound to occur. This should 

 crystallize either orthorhombic or monoclinic with ft = 90° 

 and should have the axial ratio a\~b\c— 1-086 : 1 : l - 887. The 

 member next beyond clinohumite would be Mg 9 [Mg(F. OH)] 2 

 [Si0 4 ] 6 but, owing to its more complicated composition, it 

 would seem less apt to occur. Chrysolite, Mg 2 Si0 4 , is closely 



*Mocatsber. Berlin Akad., 1870, p. 247. 



