MR. W. M. HICKS ON TOROIDAL FUNCTIONS. 
G43 
This expression for the capacity in an infinite series is more convergent than 
When the section of the ring is not very large compared with the radius of its 
circular axis, 
<1= 2 ct( p’+ ) very nearly* 
or 
where 
(40a) 
2 
v/h 2 - 
R+ v/R 2 - 
Measured in terms of the capacity of a sphere whose radius is equal to a tangent 
from the centre to the tore, the capacity is 
0 3EE'—7r 
2 EE 
When 11=3 r the omission of the term depending on p - introduces an error of about 
‘27 per cent. 
Jc 2 may be expressed in terms of the angle subtended at the centre by the tore, viz.: 
if this angle be 2 a, 
7 , 2 cos« <,« 
Ar=— -=cos a sec 
1 + cos a Z 
7 / a 
k — tan - 
When 
F=sin 3° (about r= 1 - L 0 “ll) q= ‘733 X capacity of above sphere 
F=sin 6 ° (about r— 3 R) q=z-898 X . . . 
18. We may find the potential also for the electricity induced on a tore, put to 
earth, by a charged circular wire with the same axis as the tore. For the potential 
of the wire (u, v) for points within ( u ') is (3Gb) 
4*1 = v / C—T {SP'nQ,! cos n(v—v') — \ P' 0 Q 0 } 
whilst that for points outside the tore (u tJ ) due to the charge induced on it is 
v/C— cos n{y—cL,) 
* The expression given in the 1 Proceedings’ is incorrect. 
4 o 2 
