﻿358 Dr. G. Bakker on the 



which they should yield lead to the following differential 

 equation : — 



B 2 V 7s 2 Y d 2 V 



b + b + h=^ +i ^- ••••■<» 



Now t I have demonstrated the following theorem *: — 



" If V and p are functions of x, y, and z, V satisfying the 

 three following conditions : — 



1st. V and its first derivatives with respect to a, y, and z 

 are continuous everywhere: 



2nd. Some isolated points, lines, and surfaces excepted, V 

 fulfils in an acyclic region the equation 



3rd. The products xY, yY, zY, x^, f^ , and z 2 ^ 



become nowhere infinite : then the potential of an agent, the 

 density of which is p, is for that region V, meanwhile the 

 potential function is 



<K'-)=-/^ (*) 



It is interesting to remark that van der Waals in his 

 beautiful thermodynamic theory of capillarity has demon- 

 strated that the potential function (4) indicates the continuity 

 between the liquid and gaseous states, no matter what the 

 temperature. 1 therefore adopt as the potential function of 

 the forces between the parts of the liquid (the cohesion- 

 forces) : — 



p-or 



~\ 



Observation. — C. Neumann pointed out a remarkable 

 property of that function. He found that if a coefficient 

 depending on the radius is left out of account, in consequence 

 of this function the potential of a homogenic sphere for an 

 exterior point is determined in the same way as if the whole 

 mass were concentrated in the centre. 



On account of the great importance, practical as well as 

 theoretical, of such a function for a theory of gases and 

 liquids, I examined the question whether there are other 

 potential functions which possess this property f. I have 

 found two solutions : — 



1st, ^)-^ + — +0 



* Koninkl. AJcad. v. Wetensch. at Amsterdam. Proceedings of the 

 Meeting of Saturday Nov. 25th, 1899. 



t Koninkl. Akad v. Wetensch. at Amsterdam. Proceedings of th» 

 Meeting of Saturday Oct. 28th, 1899. 



