( 248 ) 
II. If w represents the potential in a point z,y,z of an agens 
which fills several spaces continuously and is spread over several 
A sin (qr 
surfaces, the potential function being gi (r) mer SAE we get 
a: 
for the potential the differential equation : 
Vwy4=—¢y4—4aeAsna.... « (4) 
some points and surfaces being excepted; g represents the density 
in that point. 
It is easy to find equation: 
Aer + Bear A+tB (A+ B)g@r (B— A)q?r? 
— —q(B—A 
r r 1{ Kn mn 2 uw 3 
Let us put: 
Ae-v + Ber A+B 
“id r 
Ae 
By applying the operation VY? to the two members of the last 
AAB 
fe 
equation but one, taking into account that V* = 0, we find: 
Agar gaa hoe) edel (A+ B)q?r 
Vv” E Vu) op FB Aat + 
) 
) 
4 Ae—¥ + Ber 
Si ree es 
ar 
Ve HV RSH Pen aks eee 
The proof of the first theorem is based on this consideration. The 
potential w in a point z,y,2 of an agens with a cubic density @ 
and a surface density ¢, becomes if the potential function is (7): 
w= leprae += jogp(r)ds 
if » represents the distance from point 2,y, to the elements of 
space or of surface for which the density is represented by @ or o. 
We have: 
AtB 
g(r) = — +» (equation 5) 
