216 SCIENCE PROGRESS. 



of Amagat. The results obtained by Amagat for C0 2 are 

 discussed at length by Tait. 



25. Our kinetic theory of gases is bound, if it aspires to 

 be complete, to give some account of these phenomena. 

 The first object to which physicists have turned their atten- 

 tion has been to invent a modified form of the virial equa- 

 tion which should express the properties of an actual gas, as 

 determined by Andrews or Amagat, in the same con- 

 venient w r ay in which the equation pv = Qt expresses the 

 properties of the ideal perfect gas. For this purpose it is 

 necessary to introduce into the virial equation certain con- 



stants. Van der Waals proposed the equation [p + ~ 2 \ 



(v — ft) = |-2j (mu 2 ) in which a and ft are two disposable con- 

 stants, but Tait shows that at least three are neces- 



sary. Clausius proposed/* = ,— —/ — ~\l m which we 



have three disposable constants a, ft and a (for ex- 

 planation of k see Tait, part iv., p. 261). Finally Tait 



C A - Rte _ . u . c 

 gives us t>v = R/ + — - - • 1 take his form 



& r v + y v -f a 



given, part iv., p. 265, and subsequently modified in nota- 

 tion only. In this R/ is the mean kinetic energy during 



dp 

 free path, and, as stated below, R = -,,- 



26. If such an equation can be found, it will be very 

 valuable, perhaps more valuable than a complete kinetic 

 theory. But for a kinetic theory — and that is now our object 

 — we require not only a modified formula accurately express- 

 ing the observed facts, but some hypothesis concerning the 

 nature and constitution of gas molecules which shall explain 

 and justify the modified formula. Such a hypothesis Tait 

 has given us, and so far as I know no one else has yet 

 worked out any in detail. 



27. His hypothesis is that the molecules behave indeed 

 like conventional elastic spheres when they actually collide 

 with each other, but in addition attract each other with 

 finite force. He assumes further that the effect of that 

 finite force may be approximately represented as follows, 

 dealing with equal spheres only : When two molecules 



