MR. F. W. DYSOJn^ on THE POTENTIAL OF AN ANCHOR RING. 
55 
•) I 
[cos 3x + (2 cos 2x - i cos 4x) s + [H 
Jo^ = [cos 4x + m cos 3x - i cos 5x ) 5 + . . . } 
JG^ = ,Tpfi[ccs5x+ • • •!• 
These five sets of formnlre will be referred to as (A), (B), (C), (D), (E). 
Section 11 .—The Potential of an Anchor Itimj at an External Point. 
§ 4. The potential of an anchor ring at a point on its axis may be easily found in 
several ways. One simple method is to divide the ring into elements by spheres, 
having the given point as centre. 
JP 
Let QAR be a circle which by revolution round OP generates an anchor ring. 
Let C be its centre, and let 00 be perpendicular to OP. 
With centre P describe circles, dividing the circle QAR into elements ; let QR and 
Q'R' be two of these circles. 
By revolution of the figure round OP we obtain an anchor ring divided into 
elements. 
Iiet 
AC = a. 00 = c. 
Z PCQ = rjj 
PO = R. PQ p. 
z OOP = a. 
