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XXVII.—On the Centrifugal Theory of Elasticity, and its Connection with the 
Theory of Heat. By Wituiam Jonn Macquorn Rankine, C.E., F.R.S.E., 
F.R.S.S.A., &. 
. (Read December 15, 1851.) 
; 
Section First.—felations between Heat and Expansive Pressure. 
(1.) In February 1850, I laid before the Royal Society of Edinburgh a paper, 
in which the laws of the pressure and expansion of gases and vapours were de- 
duced from the supposition, that that part of the elasticity of bodies which depends 
upon heat, arises from the centrifugal force of the revolutions of the particles of 
elastic atmospheres surrounding nuclei, or atomic centres. A summary of the 
results of this supposition, which I called the Hypothesis of Molecular Vortices, 
_ was printed in the Transactions of this Society, volume xx., as an introduction 
to a series of papers on the Mechanical Action of Heat; and the original paper 
has since appeared in detail in the Philosophical Magazine. 
In that paper, the bounding surfaces of atoms were defined to be imaginary 
surfaces, situated between and ‘enveloping the atomic nuclei, and symmetrically 
placed with respect to them, and having this property—that at these surfaces the 
attractive and repulsive actions of the atomic nuclei and atmospheres upon each 
particle of atomic atmosphere, balance each other. The pressure of the atomic 
atmospheres at those imaginary boundaries is the part of the total expansive 
pressure of the body which varies with heat; the effect of the centrifugal force of 
_ molecular vortices being to increase it. 
In the subsequent investigation it was assumed, that owing to the symmetrical 
action of the particles of gases in all directions, and the small amount of those 
attractive and repulsive forces which interfere with the elasticity of their atmo- 
_ spheres, no appreciable error would arise from treating the boundary of the atmo- 
sphere of a single atom, in calculation, as if it were spherical; an assumption 
_ which very much simplified the analysis. 
An effect, however, of this assumption was, to make it doubtful whether the 
conclusions deduced from the hypothesis were applicable to any substances except 
_ those nearly in the state of perfect gas. I have, therefore, in the present paper, 
investigated the subject anew, without making any assumption as to the arrange- 
- ment of the atomic centres, or the form of the boundaries of their atmospheres. 
The equations deduced from the hypothesis, between expansive pressure and heat, 
are therefore applicable to all substances in all conditions; and it will be seen 
_ that they are identical with those in the original paper; shewing that the assump- 
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