(174) 
only on g. Now the question is: is it possible to choose those con- 
stants in such a way that the potential of a spherical shell with a 
radius R becomes constant for points inside the shell? 
Wir = [ g(r) dr =| (Aeon + Ber + Cr) dr = 
A B Lt 
Sg EE 
q q 2 
B 1 
Ent yarn © RRD = OUR PP 
a habe ae DRH P+ 
> 
a 
i 1 
ge Bt) — SET PL rg ONE eae 
en rs 
q q 
The expression must now depend on r. It is easy to see that we 
have only to take A= fef and B= — fe? , to get (f= con- 
stant): 
A MS an: See i f st 
Vel aeg er er ee Er 
2 Rr | 7 q gie, ar ‘ 
= ioe 
in which we have also fulfilled the second condition. 
The potential function becomes therefore: 
emt ; er” 
p(r) = f a? — — fell + C. 
r r 
Considered superficially we now get in contradiction with the 
theorem of LaPLAcE, which states that the law of NEwTon is the 
only law which fulfils the condition, that the spherical shell exer- 
cises no force on a point inside it. In reality this theorem includes 
more. The function of forces must namely keep this property without 
change of the constant, whatever the radius of a spherical shell may 
be. However in the case discussed by us the radius of the shell is 
given and in the potential we have therefore introduced constants 
depending on the radius of the shell. 
As solution of equation (4) we found two integrals. If we had 
substituted function (6a) in equation a and if, in the same way 
as before, we had sought the conditions which the different coef- 
ficients must fulfil, we should have found that C=0 and further 
sing R 
F(R) > 
gk 
