114 BEPOET— 1891. 



distribution of energy between the two velocity components of the par- 

 ticles, and it seems reasonable to draw the following inferences regarding 

 the more general case : — 



(i.) If the molecules are very few and far between, impacts will 

 seldom occur, and the distribution will approximate to what it would be 

 if there were no impacts, as in the case considered by Thomson. 



(ii.) If the molecules are densely distributed, impacts will be nume- 

 rous, so that the distribution of speed will depend mainly on these impacts, 

 and will approximate to that investigated by Tait for a uniform field. 



(iii.) In intermediate cases the distribution of speed_ will be deter- 

 mined partly by the impacts and partly by the variations in the field. lb 

 -will, therefore, be intermediate between those investigated by the method 

 of Thomson and that of Tait. A complete investigation of such a case 

 would probably be one of great difiBculty. 



43. The third case — namely, that in which the intermolecular forces 

 are other than those due to impacis — presents a new feature of difficulty : 

 it now becomes necessary to take account of the possibility that three 

 or more particles may be simultaneously within mutual influence of one 

 another ; for the probability of this is no longer infinitely small, as it is in 

 the case of simple impacts. 



In his recent paper already alluded to, Thomson considers this point, 

 more especially with reference to a system composed of double molecules 

 or ' doublets.' ' A compound gas is an example of such a system. Here a 

 complete collision may consist of a large number of impacts, and the 

 author reoiarks that ' it seems exceedingly difficult to find how to cal- 

 culate true statistics of these chattei'ing collisions and arrive at sound 

 conclusions as to the iiltimate distribution of enei'gy in any of the very 

 simplest cases other than Maxwell's original case of I860.' ' 



It seems, however, unnecessary to consider multiple collisions if either 

 of the following conditions is satisfied: — 



(a) If the I'ange of molecular action lies between narrow limits, so 

 that the collision is approximately of the nature of a simple impact. 



(b) If the intermolecular force only acts when the particles are at a 

 considerable distance apart. The 'radius of encounter,' as it maybe 

 called, being thus very great, we may safely assume that the aggregate 

 effect on any molecule of such a system of distant molecules is constant, 

 and therefore equivalent to that of a field of external force. Unfor- 

 tunately, hoAvever, this case is of little interest. 



A difficulty of a different kind has been indicated by Tait - — ■ 

 namely, that of giving a satisfactory answer to the question, ' What is to 

 be taken as the measure of the temperature ? ' According to the views 

 of Clausius, Van der Waals, and others, the whole average kinetic energy 

 per molecule measures the temperature ; but Tait gives reasons for be- 

 lieving that the temperature depends on the mean squai*e speed of the 

 free paths of the molecules, and is therefore measured by the value of 

 the average kinetic energy when (with the same mean square speed of 

 free path) the volume is infinite. In other words, Tait supposes the 

 temperature measured by the average kinetic energy per free molecule. 

 If the mean square speed be kept constant, the whole kinetic energy will 

 vary with the volume of the gas, and thus on the hypothesis of Clausius 



> Nature, August 13, 1891, § 8. 



- ' On the Virial Equation for Molecular Forces, being Part IV. of a paper on the 

 Foundations of the Kinetic Theory of Qasep,' Froc. H.S.E. 1890. 



