or Centrifugal Theory of Elasticity. 355 



be imaginary surfaces, situated between and enveloping tbe 

 atomic nuclei, and symmetrically placed with respect to them, 

 and ba\dug 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 bound- 

 aries is the part of the total expansive pressure of the body which 

 vai'ies 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 direc- 

 tions, and the small amount of those attractive and repulsive 

 forces which interfere with the elasticity of their atmospheres, 

 no appreciable error would arise from treating the boundary of 

 the atmosphere 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 doubt- 

 ful 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 

 arrangement of the atomic centres, or the form of the bound- 

 aries 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 ; showing 

 that the assumption, that the atomic atmospheres might be 

 treated in calculation as if spherical, did not give rise to any 

 error. 



By the aid of certain transformations in those equations, I 

 have been enabled, in investigating the principles of the mutual 

 transformation of heat and expansive power, to deduce Joule^s 

 law of the equivalence of heat and mechanical power directly 

 from them, instead of taking it (as I did in my previous papers) 

 as a consequence of the principle of vis viva. Carnot's law is 

 also deduced directly from the hypothesis, as in one of the pre- 

 vious papers. 



(2.) Classification of Elastic Pressures. — The pressures con- 

 sidered in the present paper are those only which depend on the 

 volume occupied by a given weight of the substance ; not those 

 which resist change of figure in solids and viscous liquids. Cer- 

 tain mathematical relations exist between those two classes of 

 pressures, but they do not affect the present investigation. 



To illustrate this symbolically, let V represent the volume 



occupied by unity of weight of the substance, so that ==• is the 



