88 PROFESSOR TAIT ON THE 



of them are moving in directions inclined /3 to /3 + cZ/3 to the axis of x. Of 

 these the fraction 



—ex gee 8 



(where x is to be regarded as signless) reach the plane of yz, and each brings 



momentum 



Vv cos /5 



perpendicular to that plane. Hence the whole momentum which reaches unit 

 area of the plane is 



2x 



i r r> r 



^nV/ vv 2 I cos /3 sin /3 d/3 J cdxe- exaecfi 



vv 2 I ' 



c/0 



cos 2 /3 sin /3r?/3, 



the same expression as before. 



(c) Clausius' method of the virial, as usually applied, also gives the same 

 result. 



30. But this result is approximate only, for a reason pointed out in § 6 

 above. To obtain a more exact result, let us take the virial expression itself. 

 It is, in this case, if N be the number of particles in volume V, 



^N^^V + I^Rr), 



where R is the mutual action between two particles whose centres are ;* apart, 

 and is positive when the action is a stress tending to bring them nearer to one 

 another. Hence, omitting the last term, we have approximately 



which we may employ for the purpose of interpreting the value of the term 

 omitted. 



[It is commonly stated (see, for instance Clekk-Maxwell's Lecture to the 

 Chemical Society *) that, when the term ^(Rr) is negative, the action between 

 the particles is in the main repulsive : — "a repulsion so great that no attainable 

 force can reduce the distance of the particles to zero." There are grave 

 objections to the assumption of molecular repulsion ; and therefore it is well to 

 inquire whether the mere impacts, which must exist if the kinetic theory be 

 true, are not of themselves sufficient to explain the experimental results which 

 have been attributed to such repulsion. The experiments of Regnault on 

 hydrogen first showed a deviation from Boyle's Law in the direction of loss 



* Cfiem. Soc. Jour., xiii. (1875), p. 4'J3. 



