ii2 PETER GUTHRIE TAIT 



The calculation referred to here was given in the first paper as Part v, 

 the earlier parts being concerned with the mean free path, the number of 

 collisions, and the general proof of Maxwell's theorem. Part vi is devoted 

 to the discussion of some definite integrals, and the remaining three parts 

 of the first paper take up the question of the mean free path in a mixture 

 of two systems, the pressure in a system of colliding spheres, and the effect 

 of external potential. In the second paper Tait proceeded to apply the 

 results of the first paper " to the question of the transference of momentum, 

 of energy, and of matter, in a gas or gaseous mixture ; still, however, on 

 the hypothesis of hard spherical particles, exerting no mutual forces except 

 those of impact." Before entering on this line of investigation, Tait took 

 occasion to answer certain criticisms which had been made^>f his methods 

 in the first paper, especially in regard to the number of assumptions necessary 

 for the proof of Maxwell's theorem concerning the distribution of energy 

 in a mixture of a gas. Tait contended however that all he demanded was " that 

 there is free access for collision between each pair of particles, whether of 

 the same kind or of different systems ; and that the number of particles of 

 one kind is not overwhelmingly greater than that of the other." In the third 

 paper, a special case of molecular attraction is dealt with. The particles 

 which are under molecular force are assumed to have a greater average 

 kinetic energy than the rest. In terms of this assumption the expression 

 for the virial is developed in the fourth paper, leading finally to Tail's form 

 of the isothermal equation 



C A-eE 



v + y v+a 



where C, A, e, y, a are constants, and E is a quantity which in the case of 

 vapour or gas of small density has the value ^2,mu*, where u is the speed 

 of the particle of mass m. This average kinetic energy is generally assumed 

 to be proportional to the absolute temperature ; but Tait had grave reasons 

 for not accepting this view. He said : 



" It appears to me that only if E above (with a constant added when required, 

 as will presently be shown) is regarded as proportional to the absolute temperature, 

 can the above equation be in any sense adequately considered as that of an Iso- 

 thermal. If the whole kinetic energy of the particles is treated as proportional to 

 the absolute temperature, the various stages of the gas as its volume changes with 

 E constant correspond to changes of temperature without direct loss or gain of heat, 

 and belong rather to a species of Adiabatic than to an Isothermal. Neither Van 

 der Waals nor Clausius, so far as I can see, calls attention to the fact that when 



