268 PROFESSOR TAIT ON THE 



free), we see that the state of aggregation which we call liquid is such that, as it is made 

 colder and colder, a particle which can escape from it requires to have more and more 

 than its average share of the non-molecular part of the energy. 



We might be tempted to generalise further, and to speculate on the limiting condi- 

 tions between the liquid and the solid states. But these, and a host of other curious 

 and important matters suggested by the present speculation, prominent among which 

 is the question of the density of saturated vapour at different temperatures (with the 

 mechanism of the equilibrium of temperature between the liquid and the vapour), must 

 be deferred to the next part of this paper. It is sufficient to point out here how 

 satisfactorily the present mode of regarding the subject fits itself to the grand facts 

 regarding latent heat, and to its steady diminution as the pressure under which ebulli- 

 tion takes place is gradually raised to the critical value. What we are called upon to do 

 now is to justify, by comparison with experiment, the hypothesis which we have adopted 

 as to the proper physical definition of temperature, and the form of the virial equation to 

 which it has led us. If we have any measure of success in this, we may regard the 

 main difficulty of at least the elements of these further problems as having been to 

 some extent removed. 



What has been said above leads us, in the succeeding developments, to write (so long 

 at least as we are dealing with vapour or gas) 



where t is the absolute temperature, and R (whose employment is now totally changed) 

 is practically the rate of increase of pressure with temperature at unit volume, under 

 ordinary conditions. 



XXIL — The Equation of Isothermals. 



72. Assuming the definition of temperature given in last section, the virial equation 

 of § 70 becomes 



1w =r(i+^->+4- — A_. 



\ v + a/ v + y v + a 



For the minimax, which occurs at the critical point, we must have simultaneously 



dv ' dv' 2 

 But 



dp _ A-~Re t C 

 V dv +P ~(v + af (v+y) 2 ' 



A o.o#_ gA-R e ; 2C 

 dv 2 ^ dv (v + o) s " r («+7) s 



