( 165 ) 
dw, of which M is the vertex, then this cone will cut from the 
shell a volume BR? dR ew. If g is the density, the mass of the element 
in A is: &dRdwe. If g(r) represents the form of the potential 
function, the potential energy of a unity of mass in P in conse- 
quence of the element in A is: R?dRdog plp), p representing the 
distance between A and P. 
If we turn the figure round MP as axis, the element in A describes 
an annular space, so that fro= 22 sinO@d0; O representing /AMP. 
In consequence of the annular space the potential energy in P is: 
oe REAR alae 6 oth) = —2nk*dRdcoOog(p) . 
Now p?= RF? Jr? — 2 Rrcos 0, in which r= MP, so 
2pdp=—2RrdcosO. 
The expression for the potential energy becomes therefore: 
Un R°dR 
1 tj j 
mid dp p (p) 
or because 47 R? dg represents the mass of the shell: 
1 M 7 
Oppel P(P)D - 
The integration over the whole of the shell gives: 
Batok 
1 =f ; 
3 Rr pp(p)dp. 
r—R 
If F(A) represents the before mentioned coefficient and F(R) a 
function of & which is also to be determined, we may write: 
rd R 
tE -M 
a pp) PPP) PH=FR Mor) + F(E)M, 
scaly: 
If we leave an absolute constant out of account, this equation 
furnishes the potential function, belonging to a force acting in the 
required manner. 
Let us put: 
