An important part of Jevons's economic theory was his theory of exchange of commodities. For justification he drew upon several aspects of differential equations and their applications, especially a principle in mechanics associated with equilibrium. Unfortunately his use of the principle was faulty. The error is analyzed here, along with his handling of differential equations in general, and the reactions to these aspects of his economic theory made by contemporaries, especially Marshall, Walras, and Edgeworth. These were often critical, though not over his misuse of the mechanical principle!