Temperature and Molecular Attraction. Ill 



condensation, if the pressure were suddenly released. This 

 point would mark the change from elliptical to hyperbolic 

 orbits among the particles. From section 9, for two particles, 

 the relations between the molecular velocity r, the absolute 

 force between the molecules which I will here call //-, and the 

 distance apart of the molecules s, is given by the relation 



v 2 ^ (20) 



For a system of n particles, in accordance with the ideas 

 expressed in section 20, I believe the same relation would 

 hold. 



Now it is a common idea that at the critical temperature 

 the kinetic energy of Hie molecules of a liquid (gas) under 

 the critical pressure just balances the attraction. The idea 

 rests on the diminution and final disappearance of surface 

 tension at the critical temperature, and the fact that a liquid 

 at its critical temperature may be changed to a gas without 

 the addition of external energy, that is by an infinitesimal 

 change in pressure, the heat of vaporization being zero. It 

 must, then, be at this point that equation 20 will hold good. 

 If we proceed on the supposition that the total molecular 

 velocity at the critical temperature can be calculated as for a 



perfectgas, then the velocity vis equal to c\\/ — , where c x is a 

 constant. The distance apart of the molecules s is equal to 



Co \ / -y , where c 2 is a constant. The absolute force /x 

 V d c 



between the molecules can be obtained from equation 1, and 



is, as I have shown in the papers cited, equal to c 3 V mp* 



Substituting these values in equation 20 we have 



Cl m= ' ,,- -« °" -A~ Y -= constant. . (21) 



c - 2 vz 



This equation is tested for the substances under examina- 

 tion and the results of the test are shown in Table III. The 

 data for the twenty-six substances shown were obtained from 

 the excellent measurements by Young already cited. The 

 approximate truth of equation 21 is abundantly confirmed, 

 although the variations in the constant shown are con- 

 siderably greater than can be attributed to the error of the 

 measurements used. 



