( 141 ) 



l)ut tlio systems arc supposcfl to he liinitod by a splioiical surface, 

 described with a radius, which has twice the length of the radius 

 of the systems themselves. Let us call these larger spheres: distance- 

 spheres. 



All these distance-spheres are supposed to lie quite outside one 

 another and to have no points in common. As the volume of all 

 these spheres together is 8 times as great as the volume of the 

 molecules, the case that all these spheres lie outside one another is 

 by no means possible, if tlie volume is smaller than 2 b. 



But even if the vohune is so large, that the distance-spheres 

 would lie quite outside one another, if the molecules are supposed 

 to be spread in the space at regular distances, a great number of 

 distance- spheres are sure to cover one another in consequence of the 

 fact they are spread quite irregularly. Now the question is, in how 

 far the computation of the value of the virial of the pressure 

 N -\- N^ is to be modified in conseiiuence of this fact. If we have 

 some molecules, lying in such a way that the distance-spheres inter- 

 sect, we have not two entire spherical surfaces on which pressure 

 is exercised but a surface consisting of two parts of spherical sur- 

 faces. The pressure within the space enclosed by them, is the same, 

 as if it consisted of two separate parts, but the value ot the virial 

 of the pressure for the two molecules together amounts to twice 

 ^/z (^ + A^i) (^- 'S') , if 5 is the volume of a distance-sphere and S 

 the volume of the segment which is cut off from a distance-sphere 

 by the plane of ' their intersection. In other words, we must take 

 into account only that part of the distance-sphere that reaches up 

 to the plane of the intersection, instead of the whole distance-sphere. 



We come, accordingly, to the same result wliich I had obtained 

 in another way before (Verslag Kon. Ak. van Wetenschappen Am- 

 sterdam, 31 October 189G). 



A second approximation is also mentioned there, and though tlic 

 determination of the value of that correction leads to such long 

 calculations, that as yet I have not brought them to an end, yet I 

 will make some remarks on the way in which this value might be 

 obtained. 



K Aj B and C are taken for the instantaneous position of the 

 three centres of the distance-spheres and M for the centre of the 

 circumscribed circle, the mean value of the volume limited by the 

 surface of the distance-sphere A and the two planes FM and 

 A M D, will represent the second correction. 



If we put AM=a and LAMG — C^ and the radius of the 

 distance-sphere = R, the value of the vohinic F.UD will be 



