Polyphase systems having a pair of indifferent phases

Polyphase Systems having a pair of Indifferent Phases. 

Two phases are said to be indifferent with respect to one another if a system limited to these two phases is indifferent. 

In the complete system containing (/ phases, let us suppose that phases 1 and 2 are indifferent with respect to one another. Suppose that the number of chemical reactions occurring in these two phases, apart from transfers from one phase to the other, is 6. This is the number of reactions which can occur in a system limited to two portions of these phases in contact. If these phases are indifferent, then from (29.19) the composition of the phases must be such that all determinants of order (b 4-2) formed from the lines of the matrix (here abbreviated to the first line) 

We see immediately that all determinants of order ( + r ) formed from the lines of this table must be zero, since any such determinant can be developed in terms of a series of minors formed from the elements of the first b +2) columns. All these minors are zero because of (29.26) hence all the determinants are zero and the whole system is indifferent. 

We may note that if phases 1 and 2 form, when alone, a system with a variance of one or less, then they must always be indifferent, and there is no further condition of indifference. The above theorem remains valid however, for in order to construct determinants of order (6+2) from (29.27) we must include one or more lines consisting only of zeros and any such determinant must be zero. 

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