40 Allen, etc. — Diopside and its delations 



members. But in case the crystal miscibility is incomplete or 

 limited the term isomorphism has not yet been defined with 

 adequate precision nor the criteria therefor developed with 

 sufficient sharpness to permit one to state in every actual case 

 whether or not isomorphism does exist. It seems proper, how- 

 ever, to speak of the two compounds in the first case as com- 

 pletely isomorphous, while in other instances the isomorphism 

 is incomplete or limited. In the case of incomplete isomorphism, 

 criteria such as crystallography similarity, additive character of 

 certain physical properties in the intermediate mixtures, chem- 

 ical analogy are then relied on to prove isomorphism. 



In the present series, the diopside and /3-MgSi0 3 are of the 

 same crystal system and somewhat similar in crystallographic 

 properties. Limited miscibility has been shown to exist and 

 the physical properties prove that the two are incompletely 

 isomorphous. This being the case, it is reasonable to suppose 

 that their internal crystal structure is similar, that the distri- 

 bution of the effective crystallographic forces is analogous. 

 In the intermediate mixtures, therefore, the distribution of the 

 forces is represented, approximately at least, by the resultants 

 of the crystallographic forces of the end members in their proper 

 intensities. One of the best methods for studying the distribu- 

 tion and relative intensity of crystallographic forces is by means 

 of etch figures. On the above assumption, the etch figures of 

 the intermediate members should be intermediate in character 

 between those of the end members, diopside and /3-MgSi0 3 .* 



After considerable experimentation on the conditions best 

 suited to produce favorable results, both with respect to the 

 etch figures and the handling and photographing of the exceed- 

 ingly small crystals, this statement has been substantiated. The 

 etch figures on 110 were produced by immersing cleavage 

 pieces from the different preparations in hot commercial hydro- 

 fluoric acid (heated over a steam bath in a platinum crucible) 

 for 40 seconds and then stopping the reaction by plunging the 

 crystal into cold water. The crystal was then mounted on the 

 condenser lens attachment of the universal stagef and examined 

 in strong reflected arc light and turned until the proper cleavage 

 face, 110, was normal to the axis of the microscope. The etch 

 figures on 110 thus obtained were not of equal size or develop- 

 ment for the different members of the series- The largest and 

 best developed etch figures are those of diopside (Plate I, 

 photomicrographs a and h), while the least favorable are those 

 of /3-MgSi0 3 , which are exceedingly difficult to obtain under 



*The value of etch, figures in determining isomorphism has been strongly 

 advocated by Eetgers (Zeitschr. f. Phys.-Chem., xvi, 35, 1895) and notwith- 

 standing the objections which have been raised to this criterion, it does 

 apply in certain series. In the present case of limited isomorphism the etch 

 figures sustain the contention of Eetgers. 



f This Journal, xxiv, p. 342, and fig. 7, p. 332, 1907. 



