( 166 ) 
rd R 
pp(p)dp=2RrF(R) g(r) +2RrF(R) . . . (a) 
rk 
If we differentiate this identity twice with respect to r and also 
twice with respect to &, and put f ror) dr= yw (r), we get: 
W'(r + RB) — y" (nr — R) = 4 RE (R) g(r) +2 Br F(R) gp" () 
and 
wy" (r+ R)— wy" —R)=4r pO) F(R) +2 Arp) F'(B) + 
4+ 47]"(R)+2RrF"(R). 
The left side members of these equations are the same, so also 
2RE(R) g(r) + Rr F(R)p' (7) = 2 rg (r) F(R) + 
+ Rr g(r) F" (2) + 27 F'(R) + Kr F" (BR) 
or 
2¢'(r) tre") 2F(R)HRF(B) 1 2F(R)+4RF'(B) 
rp (r) Zij RF (£) p (r) RF (R) 
R and r not being dependent on each other, we get separately 
2E'(2) + RE'(R) _ 
Een 5, PE ee =C), in which C; is an absolute constant 
RE(R) 
2F'(R RE"(R 
as ; Clk gt Dn HAC also absolutely constant 
RF (R) 
9 " 
Sere Moke a 0 
rp (r) p 5 
The solution of equation 3 will furnish the general form for the 
required potential function. 
If we write r=2 and p(r)=y, the last equation becomes 
Py 2 dy 
Fae: eS of een (7 a“ Cy e . . . « . 4 
dx? a dr Eee (4) 
or 
d? d 
pe Ao eee a le 
dx? dz 
or 
a hed 
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