411 Mr. S. H. Burbury on Boltzmann's Law of 



whence 



A = 6- 2 *2MX, (6) 



if D/» / i^)ii=A t i? &c. 



This differs from Boltzmann's result by the factor /u, in the 

 index. If all the molecuies are similar, fi is a constant and, 

 in the limiting case of an infinitely rare medium, unity. The 

 physical result is of the same general character as Boltzmann's. 

 In what follows I shall use Boltzmann's own form e~ 2h X unless 

 my proposed modification of it requires special notice. 



18. I ask now, Is not the law, whether in Boltzmann's, or 

 in the modified form, the characteristic of gas, as distinguished 

 from other states of matter ? This question leads to 



Van der Waals' Theory. 



It may be said that the hypothesis here suggested cannot 

 be reconciled with van der Waals' theory, which purports to 

 prove the continuity of the gaseous and liquid states. I reply 

 that the law e _2A x, and the theory of van der Waals', though 

 both doubtless true, cannot be both true of the same substance 

 in the same state. For that van der Waals' theory is of 

 necessity based on assumptions which are inconsistent with 

 Boltzmann's law, whether modified as I propose or not. 



19. In van der Waals' theory we suppose a gas contained 

 in a cylinder, in which works an air-tight piston, and the gas 

 is compressed slowly, so that stationary motion is always 

 attained. If p be the pressure on the piston, a) the volume 

 within the cylinder, Clausius' equation gives 



-|^ = T+U, (7) 



where T is the kinetic energy of the gas, U the virial of the 

 intermolecular forces, which, for the attractive forces alone sup- 

 posed to act, is negative. It is now assumed that the density 

 is always the same at every point within the gas, and may, 



therefore, be represented by — . Also that the resultant of 



all the intermolecular forces is at any point, not very 

 near the boundary, zero. On these assumptions U varies as 



— ? . Hence is derived the factor Ip + -y J in van der Waals' 



equation 



V a,_Z>) = rT (8) 



0+s> 



Now if the law e~ 2h X prevails, this uniform distribution is 

 impossible, except perhaps in the limiting case considered in 



