( 164 ) 
Some time later) Prof. van DER WAALS pointed out a remark- 
able 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 homogeneous sphere for an exterior 
point is determined by the distance between the point and the 
centre of the sphere in the same way as if the whole mass were 
concentrated in the centre. | 
On account of the great importance, practical as well as theore- 
tical, of such a function for a theory of gases and liquids, which 
assumes spherical molecules (by which the potentiat energy might 
be determined in a simple way by the configuration of the centres 
of the molecules), I examined the question whether there are more 
potential functions, which possess this property. As a solution I 
found the general function : 
p(r) = ; -— re tei ee ern 
in which A and B are arbitrary positive and negative constants. 
For a spherical shell the coefficient depends on the radius in the 
following manner: 
If however, we restrict ourselves to attractive forces, which 
decrease according to the distance, the most general function is that 
of VAN DER WAALS, viz: 
p(r) = C— B 
a 
If for this potential function a spherical (homogeneous) mass 
assumes this property, it will also be the case for a spherical shell 
and vice versa. 
Let & be the radius 
of a spherical shell 
which is thought 
infinitely thin, P the 
point on which the 
sheli acts, d the 
thickness and M the 
centre of the shell. 
Let us imagine a 
cone with an infini- 
Fig. 1. tely small aperture 
1) See „Zeitschrift fiir physikalische Chemie”, XIIL, 4, Seite 720, 1894. 
