James Clerk Maxwell, in his days of early development, made a practice of communicating his progress in ideas by informal letters to his scientific friends G. G. Stokes and W. Thomson, who were in the habit of preserving their correspondence. The record, so far as revealed in the letters to Stokes, has been published in volume 2 of Prof. Stokes' Scientific Correspondence. The letters which are here printed have emerged among Lord Kelvin's manuscript remains. They had been arranged apparently by Prof. S. P. Thompson when he was preparing his biography of Lord Kelvin's practical activities. I find that they had been examined by myself when a project of publishing Lord Kelvin's scientific correspondence was contemplated, after the manner of that of Stokes; which afterwards proved to be impracticable, as the material had largely been skimmed over.

According to Carnot's postulate heat can give rise to work only by falling to lower temperature. This negation ensures that at each temperature a definite physical system possesses a work-function A, named by W. Thomson its available, energy at that temperature. This aspect of Carnot's postulate was enforced especially in Thomson and Tait's Nat. Phil. (1867). These available energies at different temperatures combine into one more general function, the isothermal available energy, which is a function of temperature θ as well as configuration. (Cf. the Minkowski condensation of personal spaces and times into a single universal space-time.) Thus we are entitled to assert the equation

where Ψ1r is the force exerted by the coordinate ψr of configuration. The final term in δA though regular has not to do with ostensible work: and −η, as yet arbitrary, here equal to A/θ, may be described as the thermal capacity or specific heat of available energy.