102 MOLECULAR MOTION AND ITS ENERGY 44 



permissible, namely, that the forces acting between the 

 molecules drive two encountering molecules away from each 

 other even before the moment of an actual contact. We 

 should then have to consider not the actual space occupied 

 by the molecules, but the sum of larger spaces which sur- 

 round the molecules ; and since we might picture these 

 envelopes as spherical, we might justify the name mole- 

 cular sphere, which we will retain until in our investiga- 

 tion of the free path ( 63) we introduce the term sphere 

 of action, used by Clausius, for a sphere with a similar 

 meaning. 



One is tempted to take the magnitude b that occurs in 

 the formula simply as the sum of the molecular spheres ; 

 but this conclusion could be unhesitatingly pronounced right 

 only if the molecules could be supposed at rest. But as 

 they move about they mutually obstruct each other by their 

 motion in greater proportion than if they were partly at 

 rest ; it consequently follows that we shall have to under- 

 stand by b a multiple of the sum of the molecular spheres. 

 The more exact determination of this w^e shall leave for 

 Part III. ( 117) ; at present the remark is sufficient that, 

 excepting perhaps the most extreme cases, we have to re- 

 present by b a magnitude which, as well as the molecular 

 sphere, is independent of the pressure and volume. 



The second magnitude ( contained in the corrected 

 formula, viz. the pressure which results from the forces of 

 cohesion, is determined by van der Waals in the same 

 way as Laplace calculated, in his theory of capillarity, a 

 magnitude of similar meaning, which he denoted by K, viz. 

 the pressure against a flat bounding surface. Since each 

 of these pressures, both & and K, arises from the mutual 

 actions of attracting and attracted particles, it is propor- 

 tional to the number of attracting particles on the one hand, 

 and of attracted particles on the other ; and it is conse- 

 quently proportional to the square of the number of particles 

 present, and thus increases in proportion to the square of 

 the density. If we refer all magnitudes varying with the 

 expansion of the gas to the volume, as in last formula, 



and not to the density, we have to introduce @ * a magni- 



