102 Prof. Thomson on the Restoration of Mechanical Energy 



than I can command, to pursue the subject further. WTiilst I 

 admit that I have had occasion from time to time to modify my 

 first ideas, I must be allowed to express my conviction that these 

 last results are in all essential respects correct, and that the pro- 

 positions which I have succeeded in establishing will eventually 

 be regarded as standard propositions in this department of 

 applied mathematics. Not knowing to what extent they may at 

 present receive the assent of mathematicians, I have preferred 

 the Philosophical Magazine to any other medium of communi- 

 cation, for the purpose of affording an opportunity for any dis- 

 cussion or elucidation which the novelty of the views may call 

 for. The obvious and important application of these hydrody- 

 namical theorems in the undulatory theory of light I need not 

 now insist upon. 



Cambridge Observatory, 

 December 30, 1852. 



XVII. On the Restoration of Mechanical Energy from an unequally 

 heated space. By Prof. W. Thomson*. 



WHEN heat is diffused by conduction from one part to 

 another of an unequally heated body, the body is put 

 into such a state that it is impossible to derive as much mecha- 

 nical effect of a non-thermal kindf from it as could have been 

 derived from the body in its given state J. Hence, if a body be 

 given in an envelope impermeable to heat, with its different parts 

 at different temperatures, a dissipation of mechanical energy 

 within it, going on until the temperatures of all its parts become 

 the same, can only be avoided by immediately restoring a por- 

 tion of its mechanical energy from the state of heat, and equali- 

 zing the temperature of all its parts, wholly by the operation of 

 perfect thermo -dynamic engines. Let T be the uniform tempe- 



* Communicated b]"^ the Author. 



t [Note added Jan. 14, 1853.] Instead of " mechanical effect of a non- 

 thermal kind," I should have said simply potential energy, had I at the 

 time of writing this paper learned the use of the admirable terms "poten- 

 tial " and '* actual mtroduced by Mr. Rankine in his paper " On the 

 Transformation of Energy " (communicated to the Glasgow Philosophical 

 Society at its last meeting, Jan. 5, and published in the present number of 

 the Philosophical Magazine), to designate the two kinds of energy which I 

 had previously distinguished by the inconvenient adjectives of '* statical '* 

 and "dynamical." (See Proc. Roy. Soc. Edinb. Feb. 16. 1852; or Phil. 

 Mag. Oct. 1852, p. 304.) 



X Proceedings of the Royal Society of Edinburgh for Feb. 16, 1852, 

 (p. 139), or p. 305 of the last Volume of this Journal. The formulae given 

 in that paper which have reference to the subject of the present communi- 

 cation, require corrections, which are indicated in "Errata'* published in the 

 last Number. 



