MR. F. W. DrSON" ON THE POTENTIAL OF AN ANCHOR RING. 
1085 
^ = 
ST 
^2' 
?>a~ 1 cl 
c& fl cl 
-1- 
^ 2 ^ 8 cclc^ U\c clc 
i 4 T+ 
3072 \c clcj ' 81920 Vc clc 
1 cl 
Mfr ,a^l3.^(cP 
2 4 \cM 
dz’^ 
cd 1 dl 
fp 
I /I d\^ 
— ST 
24 ^ clc dd^ 
^ 4: G do 12% \c dc 
I , . 1 dl 
Ma2 ^ /^4 
4!\ 8 
2 
5^\f^ 
16 / VA'* 
+ --i--'r,(4‘ + ^)(^.-6|4. + ~)cI 
( 66 ). 
Using the fact that ^ ~ ^ + ^^3 = 0 , and neglecting terms of order higher 
c dc dz'’ 
than (- ) since f- ] I is of order — at the surface of the ring, we find that 
\ p / ^ c dc] ® 
crc'^ 
24^ _ \. _,^cd\d , /I d\2 
■/ — if“r “T 
Ma^ccr 
Therefore 
where 
and 
8 c clc ' 64 V c c^c 
cr 
3072 V c Ac 
1 A A 
+ 
81920 \c dc 
1 A 
a®c® 
f3«3 1 cl {%d + bcd)cdjl clV cdc^ n dV 
1 4 c Ac 16 \c dc) 8 \c dc) 256 
_ J5ah /I Ay cdc^ /I A V , <^dc^ /I A' 
^ [ 8 \c Ac/ 6 \c clc) 32 \'c Ac 
1 A 
c Ac 
1 
/3, , 5 / 83 ^ 
+ <24+ 48 
f - ~ 
c dc 
^ MaA , r -r , 1 AI , , J1 A\3 
'? = — |a„I + «,ac- ^ + «#VI + . , . 
an — 1 + 
_ 3(7 3(7 ^ 
— 8 + T 
% = + A (i + ) — ^3 
16 
8 
— R Z ^ 
<^3— 3.210"’“ g g 
_ g-i - _ ^ a 5;Sy 
” 5.211 256 ^3 32 24 48 
cr 
« 
c 
(67). 
( 68 ), 
. (69). 
§ 35. Let the point sr', 2 ', cj)' be on the surface of the ring, so that 
st' = c — II cos -)(, 
z' = Ji sin X‘ 
