( 252 ) 
If we subtract fi q?u? dr from the two members of this equation, 
we get: 
d d d 
[vu gu) uúdr =|: (— cos a + en cosy) ds — 
w dx dy dz 
IEEE +0 
HG Amt dn 
DrricHLet ') in his proof of a corresponding theorem concerning 
1 
the potential function —, has surrounded the spaces that present a 
i ts 
singularity by closely surrounding surfaces, and he construed a 
cube, the centre of which coincides with the origin of the coordinate 
system, while it compasses all the spaces that present a singularity. 
By doing so we may make use of the above equation for the space 
contained between the sides of the cube and the surfaces construed 
round the places which offer a singularity. The first term of the 
right-hand member consists of the sum of a number of surface 
integrals, which are reduced to zero for the surfaces of the cube, 
when the edges of the cube increase infinitely, while the surface 
integrals taken over the surfaces which enclose the places offering 
a singularity, furnish two values of opposite sign, so that the result 
for every surface is zero. Then Y2u = q?u. The volume integral of 
the left-hand member is therefore also zero. 
So: 
(GE) Cayenne 
from which follows: 
In these considerations the more general function : 
Acer + Bar 
ip 
p(r)= 
must be excluded as potential function. 
1) Vorlesungen über die im umgekehrten Verhältniss des Quadrats der Entfernung 
witkenden Kräfte von P. G. Lesnunn-Diricuuer. blz. 32. 
