Law of Molecular Force. 179 



due to this cause that almost exactly neutralizes the cooling- 

 effect, oA log — , within the range of the actual experiments ; 



so that the part of the total cooling-effect not due to external 

 work reduces, on numerical substitution, almost exactly to the 



value of the term l( V Thus, then, we see that the 



general discussion of the characteristic equation in the light 

 of Thomson's equation for the cooling-effect shows that the 

 potential energy of the molecules of a kilogramme of C0 2 may 



be taken as represented by — , and is therefore § of the virial 



of their mutual attractions. Whence, in view of the general 

 considerations adduced at the commencement of this paper, 

 we may consider the law of the inverse fourth power to be 

 established. 



We will now proceed to calculate the total cooling-effects S, 

 and compare them with those obtained experimentally for C0 2 

 by Thomson and Joule (" Fluids in Motion/' part ii., Phil. 

 Trans. 1854 ; part iv., 1862 ; also ' Mathematical and Phy- 

 sical Papers of Sir William Thomson,' vol. i.; and Joule's 

 Scientific Papers, vol. ii. pp. 247, 342) and by Regnault 

 (" Sur la detente des Gaz," Mdm. de V Acad, des Sciences, 

 xxxvii.). 



Making the same approximations as previously, we get 



«-™KHK ! -(-vt + «)4 



We see that, except for the small term a A log— , o is pro- 



11 r i 



portional to , or within the limits of pressure employed 



by Thomson and Joule to pi—p2- This was the first result 

 discovered by Thomson and Joule ; and, in accordance with 

 it, they reduced their determinations to the one standard of 

 the cooling-effect experienced by the gas in escaping through 

 a porous plug into the atmosphere under a pressure in excess 

 of the atmospheric by that of 100 English inches, or 2*54 metres 

 of mercury. 



In the following Table the numbers taken from Thomson 

 and Joule's " Fluids in Motion," part ii. 5 are marked II.; 

 the others are from part iv. The values of K p at differ- 

 ent temperatures have been obtained by interpolating from 



N2 



