MOLECULAR CONSTITUTION OF BODIES. 423 



If M is the mass of the whole quantity of gas, and c is the mean square of 

 the velocity of a particle, we may write the equation 



or in words, the product of the volume and the pressure is one-third of the 

 mass multiplied by the mean square of the velocity. If we now assume, what 

 we shall afterwards prove by an independent process, that the mean square of 

 the velocity depends only on the temperature, this equation exactly represents 

 Boyle's Law. 



But we know that most ordinary gases deviate from Boyle's Law, especially 

 at low temperatures and great densities. Let us see whether the hypothesis 

 of forces between the particles, which we rejected when brought forward as the 

 sole cause of gaseous pressure, may not be consistent with experiment when 

 considered as the cause of this deviation from Boyle's Law. 



When a gas is in an extremely rarefied condition, the number of particles 

 within a given distance of any one particle will be proportional to the density 

 of the gas. Hence the virial arising from the action of one particle on the 

 rest will vary as the density, and the whole virial in unit of volume will vary 

 as the square of the density. 



Calling the density p, and dividing the equation by V, we get 



where A is a quantity which is nearly constant for small densities. 



Now, the experiments of Regnault shew that in most gases, as the density 

 increases the pressure falls below the value calculated by Boyle's Law. Hence 

 the virial must be positive ; that is to say, the mutual action of the particles 

 must be in the main attractive, and the effect of this action in diminishing 

 the pressure must be at first very nearly as the square of the density. 



On the other hand, when the pressure is made still greater the substance 

 at length reaches a state in which an enormous increase of pressure produces 

 but a very small increase of density. This indicates that the virial is now 

 negative, or, in other words, the action between the particles is now, in the 

 main, repulsive. We may therefore conclude that the action between two par- 

 ticles at any sensible distance is quite insensible. As the particles approach 

 each other the action first shews itself as an attraction, which reaches a maxi- 

 mum, then diminishes, and at length becomes a repulsion so great that no 

 attainable force can reduce the distance of the particles to zero. 



