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at a given temperature, is simply proportional to the density. This 

 is therefore assumed to be the law of the elasticity of the atomic at- 

 mosphere of any given substance; so that the superficial atomic 

 elasticity is held to be pi'oportional to the density of the atomic 

 atmosphere, at its bounding surface. 



It is shewn, that although the form of such bounding surfaces in 

 a perfect fluid is a rhombic dodecahedron, it may be treated without 

 sensible error, in calculation, as if it were spherical, and the atmo- 

 sphere of each atom may be conceived to be composed of concentric 

 spherical layers, the density being uniform for each layer, but 

 varying for different layers. 



An oscillatory movement is supposed to be propagated from the 

 nucleus or atomic centre in an inappreciably short time, to every 

 pai't of the atmosphere, so that the mean velocity of movement is 

 uniform throughout. The quantity of heat in one atom, or any 

 other mass of matter, is expressed in terms of the force of gravity, 

 by the weight of that mass, multiplied by the height through which 

 it must fall at the earth's surface, in order to acquire that velocity. 

 This oscillatoi-y movement is conceived to be resolved into two com- 

 ponents, one in the direction of radii passing through the atomic centre, 

 the other performed in spherical surfaces described round that centre. 

 The latter component alone produces centrifugal force ; and it is 

 afterwards shewn to be probable, that the ratio which the vis viva of 

 this latter component bears to the whole vis inva of the oscillations, 

 depends on the chemical constitution of the substance. The centri- 

 fugal force thus arising, has a tendency to increase the superficial 

 density and elasticity of the atomic atmosphere, and must, at each 

 layer of that atmosphere, be in equilibrio with the forces arising from 

 the elastic pressure of the adjacent layers, and from the attraction 

 towards the nucleus or centre. The condition of this equilibrium 

 is expressed by a differential equation, which at the same time shews 

 it to be stable. By the integration of that equation, there is ob- 

 tained a general expression for the elasticity of a gas, in terms of 

 its density and heat. 



The first and largest term is simply proportional to the density of 

 the gas, multiplied by a function, which varies as a certain fraction 

 of the heat increased by a constant. In a perfect gas, this term 

 constitutes the whole elasticity. 



It is followed by an approximative converging series, chiefly ne- 



