244 
PROFESSOR M. J. M. HILL ON’ A SPHERICAL VORTEX. 
Calling’ this potential U, and expressing the velocity components in Clebsch’s 
fbi’in, viz., 
T — 4- X 
^ ar’ 
where 
Then 
dy \ dfL 
w = ^ 4- \ ^5 
oz oz 
/ 0 3 3 \ \ 
3 , 3 \ _ 
aj'"- ®’ 
X = 3Z^ [W - tt2}/(4a2). (XLXair.), 
= d 
dr 
15Z 
J(L + rV - 2rt2 
(LXX.), 
X = U - |(^ + If (I^XXXIX.), 
where L is to be replaced by 4o’“X/(3Z) after the integrations with regard to r have 
l)een performed. 
Note added May 2nd. 
The time taken by the particles on the surface 
r2 (R3 _ ftS) ^ _ ,/r 
to revolve once completel}^ round is 
- d*) - 2 si,r> y(l«* - d*)]-''-df, 
or putting 
X = 2 (irC - -f , 
it is 
4c . . - 
4(2-X)«['(1 -Xsiir <4- 
