A third transform with the same criticalpoint placement as in the previous ternary example but with the butane chemical potential held constant instead of the pressure. The tangent line is drawn at a fixed value of
it has a slope equal to the local pressure, and it gives the value of common to the red and green states through its intercept on the (imaginary) wall at V_{N} = 0. While in the previous image (the conventional Gibbs energy, a second transform) the blue and yellow surfaces were biconvex and the red region saddleshaped, those curvatures are reversed in this drawing. The Legendre transform causes that reversal.
The symbol A^{++} represents a modified Helmholtz energy with the general independent variable set
Legendre transforms with respect to mole numbers in this set are designated by +, ++, etc.
