THE BEHAVIOR OF INCLUSIONS IN IGNEOUS MAGMAS 517 



interest from the present point of view but from them the so-called 

 integral heats can be calculated by a graphical method. Rooze- 

 boom^ shows that if the curve of integral heats of mixing is plotted 

 against mol fractions of the components then the intercept on 

 the heat axis of the tangent to the curve gives the differential heat 

 of mixing for the composition represented by the point. Thus in 

 Figure 3 if the curve ABC represents the heats of mixing of diopside 

 liquid and anorthite liquid in various proportions to form one mol 

 of mixture, then the differential heat of mixing of one mol of 



CaMi/Si^Of 



mo/ percent 



CaAI^Si^Og 



Fig. 3. — Curve of integral mixing heats of diopside and anorthite liquids {ABC). 

 Showing graphical method of determining integral mixing heats from differential mixing 

 heats. 



anorthite in a large amount of liquid of the mol fraction x is 

 given by the intercept on CE of the tangent at x. Also the differ- 

 ential heat of solution of diopside in this same mixture is given by 

 the intercept on ^D of the same tangent. Now in our particular 

 case we have determined the differential heats by calculation from 

 the freezing-point curves and we wish to know the integral heat. 

 This is the reverse of the above problem and while not as straightfor- 

 ward can nevertheless be solved in the same way. We have, 

 fortunately, for the composition of the eutectic, the differential 

 heats of mixing for both diopside and anorthite which completely 

 fixes the tangent at the composition of the eutectic. Figure 3, 

 which has been referred to for purposes of illustration, is also the 

 actual figure for diopside and anorthite determined graphically from 



' Die Heterogenen Gleichgewichte, Zweiter Heft, Erster Teil (1904), pp. 287-90. 



