MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
53 
'Iz 
sin 2x + (I sin x + a sin 3x) s + (| sin 2x + 3-0 sin 4x) 
/m + 13 . 
+ 
\ t)4 
sill X "1“ ‘n2V sill 3x + yl s sin 5x) + 
dz 
dz 
dz 
3 ! 
^ (sin 3x + (-f sin 2x + sin 4x) 
+ iii sin X + M sin 3x + 3^ sin ox) s* + 
3: 
- (sill 4x + {} sin 3x + isiii ox) s + . . . 
4! 
(s»^ 5x+ 
Ji = 
(C) 
- I/ + —cos X s + cos Sx ) s 
, f33l + I lot- 23 'i ,, 
+ r X —£93— cos ix 1 s* 
/540/ + 27 240/ - 23 
V 20T8 768 
105/ - 176 
3072 
Jo = 
,4 ] ^os X + ^ + i cos 2x) 6- + 
cos 2x H-yyAl cns 4x ) 5* + 
4/ + 21 
•2 X + 5a cos 3x 
+ 
/12/ + 6 12/+19 
128 
/ + 
\ 256 
64 
cos 2x + tIs cos 4x 
, /18/ + 1 35/+ 32 , , 3 . .14., 
+ (“+AA cos X-cos 3x + +tt8 cos ox) H- 
J,= 
cos 2 x + (y cos X + y cos 3x) s 
/52/ — 21 \ 
+ ( 5^ + i COS 2x + -/a cos 4x j s'- 
+ f cos X + taV cos 3x + tIs cos 5x^ + 
J.i = 
‘H 
, 41.5 (cos 3x + (I cos 2x + i cos 4x) .5 
+ (lb cos X + 3 2 cos 3x + 3 ^ cos 5x) + 
Jo = ^4 (cos 4x + (ftcos 3x + t cos 5x )5 + . . .] 
4! 
Je = ^ci>5 (cos5x+ . . .}■ 
