Sub-system indifferent

It may happen that in the state considered, the sub-system is indifferent. Then all the determinants of order (< s + r ) formed with the lines of the following indifference matrix (29.96) are zero (c/. 29.19) ... 

If 8sP is the increase in pressure which accompanies an increase in temperature 8T in the sub-system along the indifferent line, then we have at the point considered (c/. 29.77)... 

Morey has shown that on the monovariant line of this system (or more correctly on the metastable extension of this line), there is a point where the sub-system liquid + solid 1 +solid 2 is indifferent. This is a kind of eutectic where the liquid can, without altering its composition precipitate both crystals of K2O. 2Si02 and K2O. SiO 2. H20. The line of indifference of this sub-system, and the monovariant line of the parent system are, at this point, tangential when projected on the (T, p) plane. 

This follows immediately since all the projections of mono variant lines must, because of the theorem proved in 17, be tangents at the same point to the same lines of indifference, corresponding to the common sub-system. 

If the sub-system also is monovariant, then it is indifferent in all its states and the indifferent line of the sub-system is also its equilibrium line. It then follows from the theorem of 17 that the projection of the mono variant line of the parent system on the T,p) plane is coincident with the projection of the monovariant line of the sub-system. 

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