94 
PROFESSOR W. M. HICKS ON VORTEX MOTION. 
where Uq is the velocity of translation of a Hill’s aggregate of the same volume and 
circulation. 
The stream pitch of these aggregates at the axis takes a very simple form, viz., 
TT 
The first K root is = 4-4935 = 257° 27' 30." 
The equatorial axis has a radius = *6106a. 
U = -eiSOUo, M = •0826wrp, 
E = 10-724Eo, V = -SOlG/r. 
Angular pitch of stream lines at surface = 257° 27' 30". 
,, ,, ,, axis = 297° 4'. 
The forms for the stream sheets xfj are shown in fig. 4, Plate 2. It is to be noticed 
that there is a considerable difference between the angular pitches outside and on the 
axis, whereas in the Xl^^ aggregate they were 
very nearly the same. 
The second Xj parameter is = 7-7253 = 
: 450° - 7° 22' 27". 
The equatorial axes are given by 
^ = XiX = 2-7437 
and 6-1168, 
01 , 
r ='3552a and 
-7918a. 
Radius of internal nucleus = -5816a. 
u = - 3 - 094 U 0 
/rj//i,2 = ~ 1-2500 
M = — -2403m/r 
Ml = ‘0826T/i]fjii 
E= 26-803Eo 
Mo = -lOOSin.ojao 
fxj = 4-9740/r 
vi = 1-2707/xi 
fji,2 = — 3-9740ja 
j'2 = l-5135p,2 
Total angular pitch of outside 
= 442° 37' 33". 
,, ,, on inside nucleus = 257° 27' 30". 
,, ,, j, outer shell = 185° 10'. 
Angular pitch at inner axis = 297° 4'. 
,, ,, outer ,, = 261° 39'. 
In all the Xj aggregates the expression for the angular pitch at an axis is 
