80 
PROFESSOR W. M. HTCKS ON VORTEX MOTION. 
Since ‘i\ ], also ViVo = c, 
Hence the roots are 
._ N“c +1 
= ~ OO 
28 ' o —r.2' 
V'c ?-i +1 
and 
and the clenoininator becomes 
CLo — 1 o 
28 ' To—Ti 
\-c r, + l 
28 ' 
Whence 
V = 0 
N- ,, 
^8 - 
(x- - xf) {xz - rr) (1 “ ~ 
X dx. 
X p 
4\ 
1 -V 
in this put 
So that 
(y-.'/d {v±-y) 
_ y^+y i _ Vi-yx 
y o o 
28 28 
dy, where y = x~. 
cos 6 . 
y -yi = —w (1 “ cosd) y-i-y- 
V-I-Vi 
(1 + cos 6 ). 
Then 
n = ^ — y de, 
o?—xz 
and 
= \/ 1 “ v/i E {h, (f)), where siir ^ = 71^'i • 
XT, 37 
7 2 _ ^2 .Fl _ ^2 ^ 
- 1-y^ - 
X~C 7\ + 77 + 2 
_ ’’2 - ’’l — ^ n-77 
ri — — 
X^c +1 
28 7-2-77 
1 — 4c 
3X-C 
28 
X“c 
l-ic+Xi-io-^ {3 - Xl - 40 
(37), 
