Partial Differentiation, with Special Reference to Thermodynamics

Abstract

THE preceding communication shows that if the partial differential indicated by ∂z/∂x₁ is defined as the limiting value of the rate of change of z with respect to x₁, and if we include changes due to the variation of x₂ (which is dependent on x₁) then the result obtained depends on the relation between x₁ and x₂ and in particular if dx₁ = dx₂ the expression is: ∂z/∂x₁ = Z₁ + Z₂ This ‘definition’ is therefore quite useless, and on this point there is no dispute.