106 MOLECULAR MOTION AND ITS ENERGY 46 



give for the expansion-coefficient defined by the formula 



v v n 

 a v = -- ^ 



M 



the value 



(p + ap 

 " 



In order to gain an insight into this complicated formula 

 let us apply it to extreme cases, and first of all to that, 

 approximately realised with hydrogen, in which a = or 

 the cohesion is vanishingly small. With this assumption 

 we have 



a v = (1 - bv Q ~ l )a, 

 so that 



a v <a f = a. 



Now, on the contrary, take the cohesion to be so great 

 that in comparison with it we may neglect the correction 

 that arises from the size of the molecules, or put 6 = 0; 

 then 



p av 



in this case therefore we have 



> a. 



Both of these conclusions from theory are in consonance 

 with experiment ; for according to Eegnault's observations 

 already mentioned in 40 we have for hydrogen 



a v = 0-003661, a p = G'003667 ; 



but for all other gases the relation between the values of 

 the coefficients required for the second case is fulfilled. 



Van der Waals's theory thus agrees in all points 

 with experiment in so far as it rightly expresses the general 

 laws. This agreement speaks for the fact that to a certain 

 degree the assumptions on which the theory rests correspond 

 to reality. If we should consider van der Waals's theory 

 also as probably not yet perfect, we are yet justified in the 

 view that in it the first step is taken along the path by which 

 we shall arrive at a completely satisfactory kinetic theory of 



