5i8 N. L. BOW EN 



the calculated differential heats of Table I. Thus FG is the tan- 

 gent at the composition of the eutectic joining the value of the dif- 

 ferential heat of mixing for diopside liquid in the eutectic with the 

 differential heat of mixing for anorthite liquid in the eutectic liquid. 

 This fixes immediately that the integral heat of formation of one 

 mol of the eutectic liquid from its liquid components is 650 cal. 

 Knowing that the curve of integral heats is tangent to this line at 

 a: = 0.65, we may readily draw a complete curve (the envelope of 

 the family of tangents) that satisfies the known values of the differ- 

 ential heats. When this is done we get the curve A BC. This curve, 

 then, gives us directly the amount of heat evolved when liquid 

 anorthite and liquid diopside are mixed in any proportion. Thus 

 when \ mol diopside liquid is mixed with f mol anorthite liquid 

 500 calories are evolved. The maximum amount of heat per mole- 

 cule of mixture (720 cal.) is evolved when about .047 mol of anorth- 

 ite liquid is mixed with 0.53 mol of diopside. This happens to be 

 about equal weights, so that the maximum amount of heat is evolved 

 when about equal weights are mixed and is equal to about 3 cal. 

 per gram of mixture. This heat is sufficient to heat the mixture 

 about 10°. 



If now we turn to the equilibrium diagram of diopside and albite 

 and calculate a curve of freezing-point depression for diopside, using 

 the value of the latent heat found from the anorthite diagram, we 

 find again that the calculated curve coincides with the observed 

 curve in its upper portion and then deviates from it (Fig. 4) , but in 

 this case in the opposite direction to that found for the other dia- 

 gram. Again, this deviation can be interpreted as due to a heat of 

 mixing of the liquid but now of the opposite sign. If we apply the 

 Van Laar equation we can calculate the differential heats and from 

 these determine graphically as before the integral heats of mixing. 

 Thus we get Figure 5. 



We find, then, that albite Hquid and diopside Hquid mix with 

 absorption of heat, the maximum absorption (790 cal.) taking place 

 when 0.48 mol albite is mixed with 0.52 mol diopside. This also 

 is about equal to 3 cal. per gram of mixture. 



Assuming that the theoretical basis of our calculations is to be 

 relied upon we have proved that anorthite and diopside, both 



