as applied to Gases and Vapours, 513 



of each atom, it must be supposed that the force acthig on each 

 particle of atomic atmosphere is centripetal towards the nearest 

 nucleus or centre. 



The variation of that force in the state of perfect fluidity must 

 be so extremely small in the neighbourhood of those surfaces, that 

 no appreciable error can arise, if, for the purpose of facilitating 

 the calculation of the elasticity of the atmosphere of an atom at 

 its bounding surface, the form of that surface is treated as if it 

 were a sphere, of a capacity equal to that of the rhombic dode- 

 cahedron. 



(9.) If the several atoms exercised no mutual attractions nor 

 repulsions, the total elasticity of a body would be equal to the 

 elasticity of the atomic atmospheres at their bounding surfaces. 

 Supposing such attractions and repulsions to exist, they will 

 produce an effect, which, in the state of perfect fluidity, will be 

 a function of the mean density of the body ; and which, for the 

 gaseous state, will be very small as compared with the total 

 elasticity. Therefore \i p be taken to represent the superficial 

 elasticity of the atomic atmospheres, P the actual or total elasti- 

 city of the fluid, and D its general density, 



P=;,+/(D), (1) 



w^here/(D) is a function of the density, which may be positive 

 or negative according to the nature of the forces operating be- 

 tween distinct atoms. 



(10.) The following relations must subsist between the masses 

 of the atmosphere and nucleus, and the density and volume of 

 each atom. 



Let R represent the radius of the sphere already mentioned, 

 whose capacity is equal to the volume of an atom, that volume 



being equal to — - R^. 

 o 



Let jju denote the mass of the atmosphere of an atom, m that 

 of the nucleus, and M = //- + m the whole mass of the atom (so 

 that if there is no real nucleus, but merely a centre of conden- 

 sation, m=0, and M=/t). 



Then D being the general density of the body, =^ I^ is the 



mean density of the atomic atmosphere, and M = -^ WJ). 



If wR be taken to denote the distance of any spherical layer 

 of the atmosphere from the nucleus, the density of the layer may 

 be represented by 



and the function -^u will be subject to this equation of condition, 



