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Published online by Cambridge University Press: 14 March 2016
After having for many years felt with Professor Tait the want of a word “to express the Availability for work of the heat in a given magazine, a term for that possession the waste of which is called Dissipation” I now suggest the word Motivity to supply this want.
In my paper on the “Restoration of Energy from an Unequally Heated Space,” published in the Philosophical Magazine for January 1853, I gave the following expression for the amount of “mechanical energy” derivable from a body B, given with its different parts at different temperatures, by the equalisation of its temperature throughout to one common temperature T, by means of perfect thermodynamic engines,—
where t denotes the temperature of any point x, y, z of the body; c the thermal capacity of the body's substance at that point and that temperature; J, Joule's equivalent; and μ, Carnot's function of the temperature t.
page 741 note * Tait's “Thermodynamics,” First Edition (1868), § 178.
page 741 note † In the present article I suppose this temperature to he the given temperature of the medium in which B is placed; and thermodynamic engines to work with their recipient and rejectant organs respectively in connection with some part of B at temperature t, and the endless surrounding matter at temperature T. In the original paper this supposition is introduced suhordinately at the conclusion. The chief purpose of the paper was the solution of a more difficult problem, that of finding the value of T,—a kind of average temperature of B to fulfil the condition that the quantities of heat rejected and taken in by organs of the thermodynamic engines at temperature T are equal. The burden of the problem was the evaluation of this thermodynamic average; and I failed to remark that when the value which the solution gave for T is substituted in the formula of the text, it reduces to 
, which was not very obvious from the analytical form of my solution, but which we immediately see must be the case by thinking of the physical meaning of the result; for, the sum of the excesses of the heats taken in above those rejected by all the engines must, by the first law of thermodynamics, be equal to the work gained by the supposed process. This important simplification was first given by Professor Tait in his “Thermodynamics.” It does not, however, affect the subordinate problem of the original paper, which is the main problem of this one.
