88 
MR. F. W. DYSON ON THE POTENTIAL OP AN ANCHOR RING. 
0 
Then, by making C the centre of gravity of the cross-section, we obtain the 
equation -f- /So/Sg + . . . = 0 ; so that vanishes compared with ySg. 
We shall show that ySg is of order cry /Sg of order cr^, &c., where cr denotes ajc, and 
is taken fairly small. 
To the first order of the small quantities /Sg, /3^, the potential of the ring is the 
potential of the solid ring r = a, together with the potential of a distribution on the 
ring of surface density a cos 2y + /^g cos 3y + cos 4y), it will be most con¬ 
venient to find the potential in this way, and take account of the terms arising from 
separately. 
§ 21,— To find the Potential of a Surface Distribution 0/3^ cos 2y on the Ring at 
a Point on the Axis. 
Let 
Z OCQ = y : z OOP = a : z PCQ = f. 
OC = c : CQ = a : CP = Pt. 
Then 
I cos 2(f) cos 2a 
- - cos 
(T 
(f) cos a — y cos 3(f) cos 3a 
