MAGMATIC DIFFERENTIATION OF IGNEOUS ROCKS 617 



(pn) as at a low one (pi). This is also verified by petrographic 

 experience. Thus in effusives and dike-rocks with a proportion 

 Ab:An, fixed from the analysis of the whole rock, the mix-crystal 

 first separated had nearly exactly the same composition as in a 

 melt of Ab -j-An crystallizing at a pressure of one atmosphere/ 



B 



The formula of Clausius-Chapeyron quoted (p. 611) is to be 

 applied also to the dislocation, at uniform (hydrostatic) pressure, 

 of the inversion point between two reversible solid phases of one 

 and the same substance. 



The volume difference Vj— Va, in this case, involves the difference 

 between the solid phases stable at higher and lower temperature, 

 and the melting heat must be replaced by the inversion heat. 



Also here Vi— Vj is in most cases positive, and only exceptionally 

 negative.^ 



The inversion heat between two solid phases of one and the same 

 substance is, so far as we now know, always positive and generally 

 very small, sometimes low even almost to zero, and in most cases it 

 amounts only to a small fraction of the melting heat.^ 



For metals, sulphides, silicates, etc., the divisor of the tempera- 

 ture : pressure formula thus becomes, as a general rule, very small, 



' I refer, on this subject, to a comparison between my accoimt in Tscherm. 

 Milt., (1905), of the mix-crystal system Ab:An in igneous rocks and the diagram of 

 Bowen (cf. Fig. 2, dating from 1912-13) for the Ab:An melt at the pressure of one 

 atmosphere. The analyses of the plagioclase first separated in the rocks concern partly 

 • plagioclase somewhat zonally constructed, and partly plagioclase that has grown a little 

 poorer in An and richer in Ab on account of partial equilibrium of the solid and the 

 liquid phase. The plagioclase mix-crystal first separated in andesites, dacites, etc., 

 wiU, accordingly, have been somewhat richer in An and poorer in Ab than is indicated in 

 the analysis tables on pages 503 and 51 2 in my publication in Tscherm. Mitt. , XXN (igos). 



^ As an instance of negative Vi — V2 is mentioned : The density of the three modi- 

 fications of Ca2Si04 amoimts to: of a (at a high temperature) = 3.27, of /3 = 3.28, and 

 of y (at a low temperature) = 2.97. The density of common stannum is = 7.3, that of 

 the gray tin formed at a low temperature (undercooled much below -|-2o°) is only =5.8. 

 Both in the passage from jS to 7-Ca2Si04, and from the common white stannum to the 

 gray one, so great an increase of volume takes place that the substance is disintegrated 

 by itself. 



3 However, to this rule also there are some exceptions. The most striking instance 

 is formed by lithiumsulphate having an inversion heat even five times greater than the 

 melting heat (Hiittner und Tammann, Zeit. f. anorg., Ch. 43 [1903]). 



