PROFESSOR M. J. M. HILL ON A SPHERICAL VORTEX. 
243 
B, On the Surface of the Sphere. 
Velocity parallel to axis of r = Z sin 6 cos B 
Velocity parallel to axis of ^ = Z (1 — sin^ 6) 
V I TT 9 o n I 9i4~ n 
— -P A = I z- cos- e + + — 
P -’4 P 
C. IrrotationaJ Motion outside the Sphere. 
Velocity parallel to axis of r — 3a®Zr (z — Z)/{2V\i‘) 
Velocity parallel to axis oi‘z = a^ZfS (z — Zdf — 
V 
+ V = 
\Z^ 
5-4 
\3 
I! ' 
+ 3 cos^ ^ 14 \ -rj 
[ \ Ii 
R 
P 
Current Function xp z= — cdZr^j{2'Pv^) 
Surfaces containing' the same narticles of fluid 
O X 
Zr^(R^ — a^)/(2Pt^) = const. 
Velocity potential = — a^Z {z — Z)/(2Tl®) 
(XXXV.). 
(XXXVI.). 
(XLIV.). 
. (XXXIL). 
. (XXXITL). 
. .(XLTIL). 
(XXXVIIL). 
. . (XLL). 
. (XXXI.). 
Supplementary Remarks. 
The velocity potential outside the sphere is the same as that which would be 
produced by the distribution throughout the S])bere of matter of density 
- l5Z{z - Z)/(87rfC).(LI.). 
The potential of this distribution inside the sphere is 
Z{z - Z) ( 3 R 2 _ 5cC)/(4a2) . 
2 I 2 
(LIT). 
