If for a binary solution one starts with an expression for M (or M^R or M^E) as a function of x₁ and applies Eqs. (10.15) and (10.16) to find M̅₁ and M̅₂ (or M̅^R₁and M̅^R₂ or M̅^E₁ and M̅^E₂) and then combines these expressions by Eq. (10.11), the initial expression for M is regenerated. On the other hand, if one starts with expressions for M̅₁ and M̅₂, combines them in accord with Eq. (10.11), and then applies Eqs. (10.15) and (10.16), the initial expressions for M̅₁ and M̅₂ are regenerated if and only if the initial expressions for these quantities meet a specific condition. What is the condition?

Eq.(10.15) and (10.16)

Eq.(10.11)

Eq.(10.15) and (10.16)

Eq.(10.11)

dM dM M1 = M +X2 dx (10.15) M2 = M X1 I dxI (10.16)