EUTECTICS IN COMPLICATED MIXTURES 171 



A compound must be separated for purposes of definition. Xew com- 

 pounds are not uncommon products of the laboratory study of minerals at 

 their formation temperatures. Many of these are high-temperature min- 

 erals (like pseudo-wollastonite) which have no counterpart in the natural 

 rocks. Had the natural rocks crystallized without water or low-melting 

 alkalies, we should no doubt have had them, for some of them crystallize 

 with great promptness from appropriate compositions, and are perfectly 

 stable over considerable ranges of (usually high) temperature. 



ECJTECTICS IN COMPLICATED MIXTURES 



We have no trustworthy examples of the behavior of complicated min- 

 eral mixtures in eutectic relations under known formation conditions, but 

 a brief consideration of the subject from the theoretical standpoint indi- 

 cates the probability of certain complications in the consideration of two 

 or three component eutectics in the presence of other soluble minerals. 

 With but two pure minerals present, the eutectic appears as the intersec- 

 tion of two curves, and is a point (B, figure 7) — a single mixture in defi- 

 nite proportions. With another mineral present which is soluble in all 

 proportions in both, the eutectic point (with its two minerals separating 

 side by side) becomes a line along which the concentration varies, and 

 (presumably) the structure also. If a fourth mineral is added, its geo- 

 metrical representation in three-dimensional space becomes difficult, but 

 it is easy to see that the system must have received another degree of 

 -freedom, and that the eutectic (still considered as between the two orig- 

 inal minerals, but in the presence of two others) is now freely variable in 

 its own composition. In a four-component system, we may have two 

 minerals separating side by side over a range of concentrations and tem- 

 peratures. It is, of course, conceivable that this divariant system might 

 look more or less like the so-called ( ! ) eutectic structure, though it might 

 separate from very different initial concentrations. To ascribe particular 

 structures to the influence of two or three component eutectics in rocks 

 which contain other minerals, and which very probably contained more 

 volatile constituents during formation, is therefore a somewhat hazardous 

 undertaking at the present stage of development of the subject. 



An Illustration of a cooling Mixture 



Suppose we now examine the behavior of a cooling mineral mixture in 

 a simple actual case.^* If we take the mixture of calcium and magne- 



2* We have encountered no actual case in which no undercooling occurs ; all the tem- 

 peratures here given were, therefore, determined from melting material which is simply 

 the converse case of the one here described. The description of the order of phenomena 

 is somewhat clearer in this form. 



