MR. R. W. DYSON ON THE POTENTIAL OF AH ANCHOR RING. 
1103 
^- ' 2 ) + |(>»S 7 ^ i) + £ 
and if m be the strength of each ring, 
vi f 1 ('■. Scj , '\ 1 /' 8 c.t , \ 1 dl 1 dl ] 
i li 7 . (‘‘’S t; - b " ^ 77 - b + ^ ^ ^ * j • 
Let us write = z. 
Then 
2 ^ _ 1 ^ 
dCj Co 
_ f’" (Cj- — C]C 2 COS (f) + Z^) cos (/) d(j) (Cj- — qc .2 cos 0 + Z^) 6’^ cos (j) d(f) 
Jo Cl {Ci — 2C1C3 cos </) + Cg'^ + «")* j0 (Ci^ — 26\C3 cos + c^- + 
_— Cj- p (c2 — CjCj cos ^ + c- + 2;“) cos 
cos </) + Cg^ + 2")? 
_ C3- — Cj- p (Cj' — CjCj cos I 
C^Cg J 0 ”* ^^1^3 
_Cg- — Cj' p cos ^ _j_ / a 3\ r ~ 
Cj^Cg ] 0 (Cj* — cos </) + Cg- + 2 ^^ ' Jo (b“ ~ ^qCg cos 0 + Cg^ + 2-) 5 
_ r_^ 
J 0 (^ 1 ” ” ^^1^3 
cos (f> + c. 
(cg - — cd) d4> _ 
cos 0 + Cg^ + 7s!-)^' 
Therefore 
-=: ^ - b+(-^z - «.-) £ ^ (123). 
Now the rings are at their greatest distance apart when z^ = 2.3 or when z vanishes. 
Now, equation ( 123 ) shows that this takes place when = c^. 
When Cl = Cg let the value of each be k, and let and % each = a. Also let 
«!, 0,1 : K3, be the values of c^, : Cg, a^, when z^ — z^, i.e., when the rings are in 
the same plane. 
Then these quantities are connected by the equations 
0^1 = a /c, 
+ K-l = 2/<~, 
Mlog?a-b + f(log®'' 
Cg .J ' K_ /c^/cg cos 
2 '^/ Jox/{/Ci" — 2/Ci/Cg 
/' 8/c 7 \ , K“ cos (bdS 
- X ( Og’ 7 ~ 4 j + +23 - 2/c2cOS^} 
/Cj/Cg cos <f> d(f) 
cos 0 + « 2 "} 
and 
