Law of Molecular Force. 125 



new constants added to widen its scope. In this formula 



Clausius regards 777=^7 7^ as representing the virial of the 



zl^v + p)' x ° 



internal forces, and considers that Yan der Waals's formula is 

 defective because it fails to take account of the dependence 

 of the virial of the molecular forces on temperature. He 

 draws a contrast between the perfect gaseous state and the 

 liquid state : in the former the molecules are under one 

 another's influence during only a short time compared to the 

 time of traversing the free path, while in the latter it is only 

 exceptionally that a molecule escapes from the influence of its 

 neighbours. The state of an actual gas is supposed to lie 

 between these two extremes ; and Clausius contemplates in an 

 actual gas the occurrence of collisions, after which the pair of 

 colliding molecules do not separate but travel along together, 

 oscillating opposite one another. The lower the temperature 

 the larger will be the number of such pairs, and the greater 

 will be the mean value of the attractions, seeing that the 

 molecules which remain together attract one another more 

 powerfully on account of their greater proximity. Accord- 

 ingly, the term which in the characteristic equation represents 

 the mutual attractions must be assumed to increase with 

 falling temperature. This is Clausius's argument for showing 

 that the variation of the internal virial inversely as the tem- 

 perature is not merely a matter of pure convenience in his 

 empirical formula, but is probably a fact in nature. I have 

 reproduced it at some length, because not only has he applied 

 his formula to C0 2 , but also Sarrau (Comptes Renclus, xciv.) 

 has shown that it can represent well the behaviour of H, N, 

 0, CH 4 , C 2 H 4 in Amagat's experiments within certain limits. 

 Now, while Clausius's argument can readily be admitted as 

 showing the possibility of a certain dependence of the internal 

 virial on temperature, it gives no clue to what we may call the 

 amount of that dependence. It seems to me that it must 

 really be negligible, or, at all events,, if we regard the molecular 

 attractions of gaseous C0 2 as the residuum at comparatively 

 great molecular distances of the forces which constitute the 

 cohesion of liquid and solid C0 2 , we can hardly, from what we 

 know of the molecular forces involved in elasticity, imagine that 

 their effect in the virial should be so profoundly dependent on 

 temperature as it would be if the forces themselves actually 

 varied inversely as the temperature. In a subsequent attempt* 

 to apply his form to ether and water, Clausius has found it 



necessary to replace ™ in the virial term of the above equation 



* Wiedemann's Ann. xiv. 1881, and Ann. de Ch. et de Ph. 5 sene, xxx. 1883 



