Polyphase systems with two phases of uniform composition

Polyphase Systems with Two Phases of Uniform Composition. 

We now proceed to prove that any polyphase system containing two phases of the same composition is in an indifferent state. 

If a and j8 are the two phases with the same composition, then by hypothesis, 

The matrix (29.19) has two identical columns and thus all determinants of order ( + r ) formed from this matrix must be zero hence the system is in an indifferent state. 

The inverse of this theorem is clearly not true, for in 5 we have already seen examples of indifferent systems in which no pair of phases has the same composition. In two-phase non-reacting systems all indifferent states are states of uniform composition, for in the case of only two phases (29.19) reduces to 

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