MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
69 
When 
cr = 1 
X = 
2-3820 
-- = 4-3820 - 
•0286 -h -0003 
cr = 2 
X = 
1-6889 
= 3-6889 - 
a 
-0798 + -0022 
cr — S 
X = 
1-2834 
— = 3-2834 - 
!? 
-1229 + -0073 
cr = 4 
X = 
-9957 
= 2-9957 - 
<1 
-1691 + -0152 
cr = 5 
X = 
-7726 
— = 2-7726 - 
5 
•1818 + -0260 
The numbers are given which arise from each term, as they serve to indicate 
roughly the convergency of the series. 
They give 
q = -7216c 
for (T = 1, 
q = -87000 
for cr = 2, 
q = -99170 
CO 
11 
b 
q — I'lOOc 
for cr = 4, 
q = r200c 
for cr = 5, 
which agree with some figures given by Mr. Hicks in the ‘ Phil. Trans./ 1881. Aug., 
1892.] 
Section IV .—Motion of an Anchor Ring in an Infinite Fluid. 
§ 10. All cases of motion of an anchor ring in a fluid may be found by 
compounding 
(i.) Linear motion parallel to the axis of the ring. 
(ii.) Linear motion jDerjDendicular to the axis of the ring. 
(iii.) Rotation round a diameter of the central circle. 
(iv.) Cyclic motion through the ring. 
Let $ be the velocity potential in cases (i.), (ii.), or (iii.), and be Stokes’ stream¬ 
line function in cases (i.) or (iv.). 
Then (a) <I> and 'F are single-valued functions; 
ih) They and their differential coefficients are finite and continuous at all 
points of the fluid, and vanish at infinity ; 
(c) <1) satisfies the equation = 0, and satisfies the equation 
cm _ 1 ^ 
dz“ us dm 
