(257 ) 



X. — On the Foundations oj the Kinetic Theory of Gases. IV. By Prof. Tait. 



(Read Jan. 21, 1889, and April 6, 1891.) 



INDEX TO CONTENTS. 



PAGE 



Preliminary, 260 



Part XIX. The Isothermal Equations of Van der 



Waals and Clausius, . . . 260 

 „ XX. The Virial Equation for attracting Spheri- 

 cal Particles, 263 



PAGE 



Part XXI. Eelation between Kinetic Energy and 



Temperature, 266 



„ XXII. The Equation of Isothermals, . . 268 



„ XXIII. Comparison with Experiment, . . 269 



[A few words are necessary to explain why the present paper has hitherto been printed 

 in Abstract only, and to show what modifications it has undergone since it was read more 

 than two years ago. 



In the paper, as it was first presented to the Society, I contented myself with the usual 



practice of extracting from the virial a negative term {—ftp) to represent at least a 



portion of the part due to the molecular repulsion at impact. But, as will be seen by 



the Abstract printed at the time (Proc. Roy. Soc. Edin., 21/1/89), I stated that though 



this procedure is correct when molecular attraction is not taken into account, it requires 



considerable modification when such attractions are introduced. I also stated that its 



main effect would be to alter one of the disposable quantities (A) in my equation. I 



have since seen that the definition, of what we are now to understand by " temperature," 



which I then introduced, leads naturally and directly to the writing of a part of A in the 



form 



-e(E+C/(v+j)), 



where E is proportional to the absolute temperature and to the average energy of a free 

 particle. This remark really substitutes the new undetermined quantity e for the /3 

 which occurred in my former expression. But the equation in its new form, though 

 containing as many arbitrary constants as before, is considerably more simple to deal 

 with, as p occurs only in the term pv, in which both factors are directly given by 

 experiment. The term p(v — fi) was a source of great trouble in the attempt to deter- 

 mine the proper values of the constants. It was recognised by Van der Waals, even 

 in his earliest paper, that the quantity fi suffers large changes of value, with changes 

 of volume of the gas, so that no formula in which it is treated as a constant could 

 suffice to represent more than a moderate volume-range of the isothermals with any 

 consistent degree of accuracy. 



When I first read my paper, I had made no serious attempt to attack the formidable 



VOL. XXXVI. PART II. (NO. 10.) 2 R 



