[ 424 ] 



LXVII. On the Dynamical Theory of Heat. By William 

 Thomson, M.A., Felloio of St. Peter's College, Cambridge, 

 and Professor of Natural Philosophy in the tfniversity of 

 Glasgozv*. 



[Continued fiom p. 176.] 



Pakt IV. — On a Method of discovering experimentally the Rela- 

 tion between the Mechanical JJ'ork spent, and the Heat jjroduced 

 by the Compression of a Gaseous Fluid. 



61. rilHE important researches of Joule on the thermal cir- 

 -i- cumstances connected wath the expansion and com- 

 pression of air, and the admii-able reasoning upon them expressed 

 in his papert " On the Changes of Temperatui-e produced by the 

 Rarefaction and Condensation of Air/' especially the way in 

 which he takes into account any mechanical effect that may be 

 externally produced, or internally lost, in fluid friction, have in- 

 troduced an eutu'cly new method of treating questions regarding 

 the physical propeiiies of fluids. The object of the present 

 paper is to show how, by the use of this new method, in con- 

 nexion with the pi-inciples explained in my preceding paper, a 

 complete theoretical view may be obtained of the phsenomena 

 experimented on by Joule; and to point out some of the objects 

 to be attained by a continuation and extension of his experi- 

 mental researches. 



62. The Appendix to my Account of Carnot's TheoiyJ con- 

 tains a theoretical investigation of the heat developed by the 

 compression of any fluid fulfilling the laws § of Boyle and Ma- 

 riotte and of Dalton and Gay-Lussac. It has since been shown 

 that that investigation requires no modification when the dyna- 

 mical Theory is adopted, and therefore the formula obtained as 

 the result may be regarded as being established for a fluid of the 

 kind assumed, independently of any hypothesis whatever. We 

 may obtain a corresponding formula applicable to a fluid not 

 fulfilling the gaseous laws of density, or to a solid pressed uni- 

 formly on all sides, in the follo\vdng manner. 



63. Let Mdv be the quantity of heat absorbed by a body kept 

 at a constant temperatm-e t, when its volume is increased from 

 V to v + dv; hip be the uniform pressure which it experiences 

 from without, when its volume is v and its temperature t ; and 



let ^ + -J- dt denote the value p would acquire if the temperatui'e 



* From the Transactions of the Royal Society of Edinbui-gh, vol. xx. 

 part 2. April 17, 1851. 



t Philosophical Maffazine, May 1845, vol. xxvi. p. 369. 



:J: Transactions, vol. xvi. part 5. 



§ To avoid circumlocution, these laws will, in what follows, be called 

 simply the yaseoi/s laws, or the gaseous laws of density. 



