8 Mr. W. J. M. Raukine on the Mechanical Action of Heat. 



The additional elasticity -^, being that which is due to the 



motion, is independent of the diameter. The divisor^ (the force 

 of gravity) is inti'oduced, on the supposition of the density /> 

 being measured by weight. 



Supposing the atmosphere of an atom to be divided into con- 

 centric spherical layers, it may be shown that the effect of the 

 coexistence of a great number of small vortices in one of those 

 layers whose radius is ?', and mean density p, is to give it a cen- 

 trifugal force, expressed by 



^, (V.) 



which tends to increase the density and elasticity of the atmo- 

 sphere at the surface, which I have called the boundary of the 

 atom. The layer is also acted upon by the difference between 

 the mean elasticities at its two surfaces, and by the attraction 

 towards the atomic centre ; and these three forces must balance 

 each other. 



I have integrated the differential equation which results from 

 this condition, for substances in the gaseous state, in which the 

 forces that interfere with the centrifugal force and atmospheric 

 elasticity are comparatively small ; and the result is 



P is the entire elasticity of the gas, and D its mean density. 

 M represents the total mass of an atom, measured by weight, 



and fM that of its atmospheric part ; so that ~D is the mean 



density of the atomic atmospheres*. 



/(D) denotes the effect of the mutual actions of separate atoms. 



The first term represents the superficial-atomic elasticity. F de- 

 notes the effect of the attraction of the nucleus in modifying that 

 elasticity, and can be represented approximately by a converging 



series, m terms of the negative powers of 5— y-f-l, commencing 



with the inverse square, the coefficients being functions of the 

 density D. 



By using the first term of such a series, and determining its 

 coefficient, and the quantity /(D) empirically, I have obtained 

 formulae agreeing closely with the results of M. Regnault's ex- 



* The corresponding differential equation for substances in any state 

 whatsoever is integrated in a paper on the Centrifugal Theory of Elasticity, 

 published in the Transactions of the Royal Society of Edinburgh, vol. xx. 

 pnrt 3. 



