184 Mr. W. Sutherland on the 



pv = aO. The import of the term a A log— is therefore 



thermodynamical, and cannot at present be explained on 

 purely molecular grounds. Its relative importance in the 

 case of air is much greater than in that of C0 2 ; for at 0° 0. 



its value is t 3 q of that of It ), and at 100° it is f of it. 



Taking account of the fact, then, that a A log— has nothing 



to do directly with the forces acting between the molecules, 

 we find, in the purely thermodynamic estimate of the energy 

 imparted to the expanding gas to keep its temperature con- 

 stant, the term /( ). But this is the term which our 



theory of molecular force would lead us to expect as repre- 

 senting the change of kinetic energy due to increase of 

 potential energy. Hence we may consider it as proved that 

 the molecular potential energy of a kilogramme of air occu- 

 pying a volume v is — . 



For the total cooling effect we get, on substituting for 

 P2 v 2~Pi v i its value, 



K^=«AlogJ+(i -I) {2 ;-ao(T-A)}. 



As v 1 and v 2 are directly proportional to T, if p x and p 2 have 

 always the same values at different temperatures, the term 



acTl ) is constant, and when evaluated numerically is 



almost equal to a A log — , within the range of Thomson and 

 Joule's experiments; so that K^S reduces nearly, but not quite, 

 to 21 1 ) ; whence we find the cooling-effect propor- 

 tional to pi—p 2 , which is the experimental result. 



Cooling-effects for Air escaping at different temperatures 

 through porous plugs into the atmosphere under an excess 

 of pressure of 100 English inches, or 2*54 metres of 

 mercury. 





Temperature C 



7°1. 



17°. 



39°-5. 



92° -8. 



Observed by Thomson "1 

 and Joule J 



•88 

 •96 



•86 II. 

 •93 



•75 

 •86 



51 



•72 



Calculated from equation 



