400 Prof. R. Clausius on the Behaviour of Carbonic Acid 



homogeneity of the motion would be admissible in considering 

 only the ideal state, which we call the perfect state of a gas ; 

 but when we have to investigate the deviations of a gas 

 from the perfect state, that assumption appears to me to be 

 inadmissible. 



I will not here advance any definite theory about the way 

 in which the motion changes when a gas leaves the perfect 

 state ; but I will take leave to adduce a mode of alteration as 

 at least a possible one. For the perfect gaseous state it may 

 be assumed that every two molecules that rush together sepa- 

 rate again after the collision. On the contrary, when the gas 

 is condensed to liquidity, a quite different behaviour takes 

 place : namely, the molecules are in general held together by 

 their mutual attraction ; and only exceptionally, on a specially 

 favourable coincidence of the phases of motion, do individual 

 molecules separate themselves from the rest of the mass. Now, 

 between these two extreme cases one can well imagine an in- 

 termediate state of this kind: — As a rule, indeed, the molecules 

 separate again after the collision ; but it sometimes happens 

 that two molecules after meeting do not again separate, but 

 only oscillate about one another while carrying out the pro- 

 gressive motion in common, until, by the change that takes 

 place in the motion on further collision, the separation is again 

 occasioned. The number of such pairs of attached molecules 

 would then become so much the greater the lower the tempe- 

 rature (and hence the less the mean vis viva of the motion) 

 became ; and on a further fall of the temperature there might 

 supervene instances of not merely two, but several molecules 

 holding together and executing as groups the progressive 

 motion in common. 



If such a behaviour occurred, the mean strength of the mu- 

 tual attraction of the molecules would be thereby increased, 

 since the molecules remaining united would of course, on 

 account of the greater nearness, attract one another more 

 strongly ; and, accordingly, it would not be allowable to regard 

 the quantity which represents in the formula the mutual attrac- 

 tion of the molecules as independent of the temperature, but one 

 would be obliged to admit that it becomes greater with falling 

 temperature. 



Van der Waals has, further, from theoretical considerations, 

 drawn the conclusion, also already expressed by others in their 

 formulas, that the decrease of pressure conditioned by the 

 mutual attraction of the molecules is inversely proportional to 

 the square of the volume. It may be granted that for larger 

 volumes this conclusion is approximately correct ; and yet no 

 universal and rigorous validity need be ascribed to it, but one 



