( 802 ) 



becomes then identical with the denominator of the fraction from (5). 

 In the denominator we get a correction for tlie part of the cyhndre 

 y, Avhich falls within more than one distance sphere, or as we maj 

 also say, for the part of a surface .4, which is found within more 

 than one distance sphere, if we define this surface ^4 bv the coniH- 

 tion, tliat it is found e^ervwhere at a distance .y from tlie outer 

 surface. We shall call tliis surface ^4 henceforth "surface of imi)act", 

 because the force wliich in a collision acts on the centres of the 

 molecules, acts in this surtace. The determiuMtion of the numerical 

 value of the further coefïicients seems an exceedingly elaborat(M\(»ik. 

 at least Boltzmann amiounced already in the Lorentz volume of tlie 

 Arch. Neerl. that he wouhl have this calculation carried out for ihe 

 next coeflicient, but this calculation has not yet 1)een pubUslied. It 

 seems, however not doubtful to me. that also the iiuuierical value 

 must be the same as the value found in other ways. At all events 

 the flnal form becomes also by this method 



17 6^ _ 6' 



c 



(lib' ^^ b" X 



b b' b^ ^•» I 



i-7 + '*7^ + V+^-^/ 



/' + 4 1 1 r ~ r, ^-77 I = «?■ ■ • m 



in which v represents a tinite number. 



Now it is not dithcult to show that the only remaining method 

 for deriving the equation of state, which led to the correction ^^'„2, 

 must lead to exactly the same equation as (9), when its principles 

 are consistently applied. As is known, this method assumes, that 

 the pressure is to be integrated not only oxer the volume i\ Init 

 also over half of that of the distance spheres: />, because a molecule 

 whose centre has got on a distance sphere, is sul)jected to exactly 

 the same force as when it has got on the surface of impact (the 

 volume enclosed l»y the surtace of iuipact may be put = r). The 

 volume of the distance spheres, however, is really smaller than b, 

 because some distance spheres coincide, and we get therefore ^) : 



,. + ^)(,.-6 + lI-^'....) = A'r . . . ,10) 



Now VAN DKK Waals Jr. (loc. cit.) has already pointed out. that 

 it is tacitly assumed here, that the surface of the distance sphere 

 which is found within another distance sphere ex[>eriences a pressure 

 = 0, and that therefore, for the sake of consequence, also the parts of 

 the surface of impact falling within distance spheres, must he supposed 



1) Continuitat 1899, p. (35. 



