PHILOSOPHICAL TRANSACTIONS. 
I. On the Physics of Media that are Composed of Free and Perfectly Elastic 
Molecules in a State of Motion. 
By J. J. Waterston. 
Communicated by Captain Beaufort, R.N., F.R.S., etc. 
Received December 11, 1845,—Read March 5, 1846. 
[Plates 1, 2.] 
Introduction by Lord Rayleigh, Sec.R.S. 
The publication of this paper after nearly half a century demands a word of 
explanation; and the opportunity may be taken to point out in what respects the 
received theory of gases had been anticipated by AVaterston, and to offer some 
suggestions as to the origin of certain errors and deficiencies in his views. 
So far as I am aware, the paper, though always accessible in the Archives of the 
Royal Society, has remained absolutely unnoticed. Most unfortunately the abstract 
printed at the time (‘Roy. Soc. Proc.,’ 1846, vol. 5, p. 604; here reprinted as 
Appendix I.), gave no adequate idea of the scope of the memoir, and still less of the 
nature of the results arrived at. The deficiency was in some degree supplied by a 
short account in the ‘Report of the British Association’ for 1851 (here reprinted 
as Appendix II.), where is distinctly stated the law, which was afterwards to become 
so famous, of the equality of the kinetic energies of different molecules at the same 
temperature. 
My own attention was attracted in the first instance to Waterston’s work upon 
the connection between molecular forces and the latent heat of evaporation, and 
thence to a paper in the ‘Philosophical Magazine’ for 1858, “On the Theory of 
Sound.” He there alludes to the theory of gases under consideration as having been 
started by Herapath in 1821, and he proceeds : — 
“ Mr. Herapath unfortunately assumed heat or temperature to be represented by 
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