amongst the Molecules of a Gas. 89 



then allowed to expand might possess. For in view of the 

 facts that at 0° C. C0 2 liquefies under a pressure of about 40 

 atmospheres, Avhile at 45° there is required 100 atmospheres to 

 liquefy it, and that the pressure on the high-pressure side of 

 the plug, in the experiments from which the above numbers 

 were derived, reached 6 atmospheres, it becomes apparent 

 that at the low temperatures the forces which are ultimately to 

 produce cohesion in the liquid are hardly likelv to be so closely 



A 



represented by the monomial expression - ± as at the high 



temperatures. In fact, regarding the ultimate law of the action 

 of one particle on another at any distance as a function of r 



of the form /(-) or/ ( - 2 ), and considering the law of gravi- 

 tation as simply the first term of the expansion of the latter in 

 ascending powers of — 2 , which expresses the action accurately 



enough within the limits of astronomical distances, we may 

 look upon Thomson and Joule's experiments on air as 

 showing how the second term, involving the inverse fourth 

 power of r y becomes appreciable at very small distances ; in 

 the case of C0 2 we may regard the above table as showing 



how the term -g may begin to be appreciable, and how perhaps 



at still smaller distances still higher terms may appear and 

 become predominant in producing cohesion and elasticity. 



There remains one application of our theory which throws 

 an interesting light on a fact to which Thomson and Joule drew 

 attention more than once as being very remarkable. When 

 a mixture of the two gases, C0 2 and air, is expanded through 

 a plug, it might be expected that each would contribute its 

 proportion of cooling effect according to its own amount and 

 its thermal capacity. But such is far from being the case. 

 Indeed, experiment showed that the cooling effect for pure 

 is greater than for pure N, and yet in air and other mixtures 

 of the two gases the cooling effect is less than in either of the 

 constituents under the same circumstances. 



Let Vj be the volume of a mixture of two gases before ex- 

 pansion, V 2 the volume after. Let V Ai , V Bl , be the volumes 

 of the two constituent gases A and B before expansion ; Va 2 , 

 Yb 2 , the volumes after. Suppose that there are a molecules 

 of A and b molecules of B in the mass under consideration. 

 We must first make a hypothesis as to the action of a molecule 

 of A on a molecule of B. If the mutual potential of two 



