1030 PROFESSOR TAIT ON THE 



ascribed to it could be explained by the mere resilience involved in the conception of 

 impacts. 



The present paper consists of instalments read to the Society at intervals during the 

 years 1887, 8. The first of these, which is also the earliest in point of date, deals with 

 a special case of molecular attraction, on which, of course, depends the critical tempera- 

 ture, and the distinction between gases and vapours. Here the particles which, at any 

 time, are under molecular force have a greater average kinetic energy than the rest. 

 Mathematical, or rather numerical, difficulties of a somewhat formidable nature inter- 

 fered with the exact development of these inquiries. I found, for instance, that in spite 

 of the extreme simplicity of the special assumption made as to the molecular force, 

 the investigation of the average time between the encounter of two particles and their 

 final disengagement from one another involves a quadrature of a very laborious kind. 

 Thus the correction of the number of impacts could not easily be made except by 

 some graphic process. 



One reason for the postponement of publication of the present part was the hope that 

 I might be enabled to append tables of the numerical values of the chief integrals which 

 it involves, especially the peculiarly interesting one 





X i x -dx . 



Want of time, however, forced me to substitute for complete tables mere graphical re- 

 presentations of the corresponding curves, drawn from a few carefully calculated values. 

 These are not fitted for publication, though they were quite sufficient to give a general 

 notion of the numerical values of the various results of the investigation; and enabled 

 me to take the next step : — viz. the approximate determination of the form of the Virial 

 equation when molecular attraction is taken account of. Part IV. of this investigation, 

 containing this application, was read to the Society on Jan. 21, 1889, and an Abstract 

 has appeared in the Proceedings. It appears that the difference of average kinetic 

 energy between a free, and an entangled, particle is of special importance in the physical 

 interpretation of the Virial Equation. 



An Appendix is devoted to the consideration of the modification which the previous 

 results undergo when the coefficient of restitution is supposed to be less than 1. This 

 extension of the investigation was intended as an approximation to the case of radiation 

 from the particles of a gas, and the consequent loss of energy. But, so far as I have 

 developed it, no results of any consequence were obtained. I met with difficulties of a 

 very formidable order, arising mainly from the fact that the particles after impact do not 

 always separate from one another. The full treatment of the impact of a single particle 

 with a double one is very tedious ; and the conditions of impact of two double particles 

 are so complex as to be totally unfit for an elementary investigation like the present. 



The remainder of the Appendix is devoted to two points, raised by Professors 

 Newcomb and Boltzmann, respectively : — the first being the problem of distribution of 



