MR. F. W. DrSON ON THE POTENTIAL OF AN ANCHOR RING. 
79 
Thus we have, in addition to the equations above, for the determinations of 
A^, Ag, &c., 
ICC 
A] 4 " Agcr'^ + + &c. = — 
Solving the equations 
4A + 1 
A. = »V 1- 
KC 
A + 1 „ 4A3 + 17X + G 
cr-" — 
64 
A, = - wcH 1 + o-A + — o-«) 
Aq = — wc^cr^ 
12a — 1 , /ce /3A + 2 . 12A" + A + 1 
A^ = - wc^ + 
A5= + 
128 277 V 16 
KC 9A + 10 
+ 
256 
cr~ 
277 384 
KC 81A + 56 
^ 18432 
Substituting these values we obtain 
A 7 
B 
c r 4 a2 + 8A + 1 „ 2a3 + 9a2 + 6A 
277 1^ 16 64 
_ 4Jl 
:t 2 + 
- (X 
= (T~ 
2A + 3 . 4A2 + 5A - 2 
+ 
64 
The kinetic energy is given by the equation 
• ad 
X 
-R = a 
= - Trp 
TTp 
yjj' d\fr 
Jq [^(a) 
2tt 
A/c + VC- (B — cr cn.s Y + A co.s 2y) 
A, ^ A. 
r:i*-+ 
c — a cos X 
ivc^ fB-1 
lyjr 
adx 
' d 
a ax 
1 fZi|r\ 
~ ^ rfR/ 
irpacio . clyjr , 
“ 2^j„ (l-<^«0'^x)5rdx 
VpAK^ d- Trpc^ ^B — ^- ~jKW 
+ 7T~plVC I Ai ^ 1 — O-^ + 
3A + 5 
64 
cr 
- A 
20a + 17 
^ 32 
+ I AqO-^ 
= Trp \ Ak^ + 
4A2 + 5A - 2 
64 
+ 1 + 
4A + 1 
16 
CT' 
J 
