84 
PROFESSOR W. M. HICKS OX VORTEX MOT I OX. 
Hence 
[1 — (/+ UY") = constant. 
The constant is nearly j — f ~ a say ; then 
or the curve is the ellipse 
- + i/"? = - “. 
t-O 0 
_^ 1 
Hence the angular pitch = ^ ~ ^ ~~ ^ ‘ 
r 
Now 
r J 1 x- d} \ ^ 2 J 1^) 
/ =-4—= 
[ a 
— j — - 2 ~ — 
a- [ ay- X- J L \ V 
X^ 
The angular pitch of the stream^lines is therefore 
2 / 
77 
V- 
J {y) 
V > = 
y' 
IT 
P 
where 
tP — — 
F — 2 
J iy) 
Hy)-'F4y~ 
7 
Now y is determined by J (y) — y sin y + 27/' = 0, therefor( 
— i 
F — 2 
sin y — 2y 
J {X) 
x^ 
sin y — ^y 
J (A.) y- 
x^ 
— 1_ ^ _L 1_ - 
^ y- ^ sni y 
y 
V- 
- 3 
Note for Xi aggregates = i — — 
When the value of \ is fairly large we substitute for y from equation (36) 
y = miT + 2, 
