as ae 
XXXI.—On Thermodynamic Motivity. By Sir W. Tuomson, F.R.S. 
(Read April 3, 1876. Received for publication April 12, 1879.) 
After having for many years felt with Professor Tart 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 Dzssipation,”* 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 Maguzine 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 T, by 
means of perfect thermodynamic engines,— 
Wad fifdady de frcdt(ie“Yaee) - . . . (a); 
where ¢ denotes the temperature of any point 2, y, z of the body; ¢ the thermal 
capacity of the body’s substance at that point and that temperature ; J, JouLE’s 
equivalent ; and », CARNoT’s function of the temperature ¢. Farther on in the 
same paper a simplification is introduced thus— 
“ Let the temperature of the body be measured according to an absolute 
* Tait’s “Thermodynamics,” First Edition (1868), § 178. 
+ In the present article I suppose this temperature to be 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 ¢, and the endless surrounding matter at 
temperature T. In the original paper this supposition is introduced subordinately 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 
. é . 5 = 2 t 
which the solution gave for T is substituted in the formula of the text, it reduces to Vf da dy def, edt, 
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. 
VOL. XXVIII. PART 1II. 9H 
