SirW. Thomson on Thermodynamic Motivity. 349 



for publication in the' Proceedings of the Royal Society of 

 Edinburgh and in the Philosophical Magazine, the following 

 short abstract of the substance of that communication. 



In my paper on the Restoration of Energy from an Un- 

 equally Heated Space, published in the Philosophical Maga- 

 zine in 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 

 equalization of the temperature throughout to one common 

 temperature* T, by means of perfect thermodynamic engines, 



W = J (((dxdyclzVcd^l-e-^T^), . . (1) 



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 /j, 

 Carnot's function of the temperature t. 



Further on in the same paper a simplification is introduced 

 thus : — 



" Let the temperature of the body be measured according to 

 " an absolute scale, founded on the values of Carnot's function, 

 " and expressed by the following equation, 



" where a is a constant which may have any value, but ought 

 " to have for its value the reciprocal of the expansibility of air, 



* In the present article I suppose this temperature to be the given tem- 

 perature of the medium in which B is placed ; and thermodynamic engines 

 to work with their recipient and rejectant organs respectively in connexion 

 with some part of B at temperature t, 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 which the solution gave for T is substituted in the formula of the 



text it reduces to J i ( ( civ dy ch \* c dt, which was not instantly 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 ' (first and second edi- 

 tions). It does not, however, affect the subordinate problem of the original 

 paper, which is the main problem of this one. 



Pldl. Mag. S. 5. Vol. 7. No. 44. May 1879. 2 E 



