to Calcium and Magnesium Metasilicates. 25 



magnesium vary comparatively little from the compositions 

 CaSi0 3 , MgSi0 3 and CaMgSi 2 6 ; and the second, that the 

 specific volume of diopside could not be calculated additively 

 from the volumes of the constituents. Retgers's method of 

 solving the question of isomorphism or isodimorphism between 

 two substances is well known. It consists in the preparation 

 of a suitable series of mix-crystals of the two substances and a 

 study of the relation which their specific volumes bear to one 

 another. He proved by many examples that the specific vol- 

 umes of isomorphous mixtures (as he defined them), when 

 plotted as a function of the composition, form a straight line. 

 In the paper quoted above, Retgers said that this would be 

 the best way to prove whether calcium and magnesium sili- 

 cates form a double salt or are isodimorphous, if their mixtures 

 could only be crystallized in sufficiently large individuals for 

 specific gravity determinations. He used the floating method, 

 which is not adapted for very small particles, and he empha- 

 sized the importance of making sure that the material is both 

 physically and chemically homogeneous. He therefore used 

 only transparent individuals for fear that aggregates might 

 contain some foreign material which would escape optical 

 detection. It has been shown in this laboratory that the spe- 

 cific gravities of mineral powders, if not too fine (100-120 mesh), 

 can be determined with a degree of accuracy (±001 for 

 substances of the gravity of 3) very nearly as great as those 

 obtained by Retgers's method. Of course, the particles should 

 be free from air bubbles or vacua, and it must be admitted 

 that powders require a very careful microscopic investigation 

 to decide this point. Mixtures of calcium and magnesium 

 silicate generally show a certain amount of " dustiness" due 

 to very minute inclusions, or more probably to vacua. These 

 are more numerous in the mixtures which are rich in mag- 

 nesia (70-97 per cent), but not in the pure magnesium 

 silicate itself. When large masses of material (100 grams) are 

 crystallized slowly, the density is greater and the microscope 

 shows that the vacua are fewer and smaller. Although the 

 specific gravities of the mixtures crystallized in this way are 

 still too low, we judged that they would probably be approx- 

 imately comparable among themselves, and this conviction 

 has been justified by experiment. 



The specific- volume curve (fig. 9) plainly consists of three 

 branches. AJB is the locus of the volumes of mechanical mix- 

 tures of the pseudo-wollastonite and diopside (leaving out of 

 the question the small mutual solubility). Independently of 

 microscopic or thermal evidence, it would, of course, be 

 impossible to say whether this line indicated a series of 

 mechanical mixtures or a series of mix-crystals between two 



