504 Lord Rayleigh on the Pressure of 



and neither 6 in (31) nor the virial has a finite value. The 

 like remains true when fju>h 2 . 



In the above example Pr <3 remains constant, and the pre- 

 ponderance of attraction over repulsion depends upon the 

 greater vectorial angle in the former case. If Pr 3 , instead 

 of remaining constant, continually increases with diminishing 

 ?', the preponderance of attraction follows a fortiori. 



A particular case of (32) which arises when fi=h 2 should 

 be singled out for especial notice, i. e. the case of circular 

 motion for which u = constant. The attracting particles then 

 revolve round one another in perpetuity, and the virial is 

 infinite in comparison with that of an ordinary encounter. 

 It is this possible occurrence of re-entrant orbits which causes 

 hesitation as to the accuracy with which we may assume the 

 virial of a rare gas to be inversely as the volume. It seems 

 to be generally supposed (see, for example, Meyer's ' Kinetic 

 Theory of Gases/ § 4) that if a gas be rare enough no 

 appreciable pairing can occur. But the question is not as 

 to the frequency with which new pairs may form, but as to 

 the relative number of them in existence at any time. It is 

 easy to recognize that the coupling or the severance of a pair 

 of particles cannot occur of itself, but requires always the 

 cooperation of a third particle. If the gas is very rare, no 

 doubt there are few opportunities for the formation of fresh 

 pairs, but for the same reason t^iose already formed have a 

 higher degree of permanence. On the whole it would 

 appear that the number of pairs in existence at any moment 

 is independent of the volume v of a rare gas, and the same 

 would be true of the corresponding virial. At this rate we 

 should have terms in the virial which by (20) come under 

 the form , , x 



T.F(^) (37) 



It will be remarked that if these terms in the virial. 

 independent of v, are sensible, the density of the gas will 

 depart from Avogadro's rule, however greatly it may be 

 rarefied. In the case of elastic spheres, which come into 

 collision when their centres approach to a certain distance, 

 there is naturally a limit to the magnitude of the attraction, 

 and then pairing becomes impossible if the velocity be suffi- 

 ciently great. Any departure from Avogadro's rule at high 

 rarefactions would thus tend to disappear as the temperature 

 rises. 



The behaviour of mere centres of force, which may 

 approach one another without limit, appears to follow a 

 different course. Taking for example the power law of (10), 



