PROFESSOR W. M. HICKS OK VORTEX MOTION. 
85 
where 
Therefore 
h-l (h-l){h + 2){h + b) 
z — —-1--, 
« D« 
a = mTT, h = 2 [ — )™a“ . 
— — - -4- 1 
^ 2 (« + 2)2 -t- 2 
(- 1)" 
Sin z 
(a + c) ^_yn, 
— o 
— L _^ + J-_ - _ 
2 ^ 2«2 z- 
a + z h 
- 3 
= i_—4-1 
— 2 „ -2 ^ 2 
1_1- 4 _ 1 . 
2 „2 I 2 . 
■2{h-l)(^ , 5 4 2 & + 5 
6a2 
1 -''' icF) V - V “ 
— 1 _ -T 4. 1_ 
— 2 „2 ^ 2 •> ('ft _ 
(&- 1 ) 
1 + 0 ^(h + 25 + 5 — h — 1 “ — 65 — r — 
— 1_— 4- i _ 
- 2 -V 2 ^ _ 1 
2 + ^^ - o 
_ 1 
1 
./2 + i 
1 - 
- (5 + 2) + 
(5 - 1) (5 + 5) 
(5 - 1) (5 + 5) 
1 - 
¥ + 65 - 1 
r = 
1 ^ 2 - - 1 ) + 5 ) «' 5 + 2 - ~ 
and the pitch is 
7 T 
V 
/. 
5 + 2 - 
(5-l)(5 + 5)- 
1 - 
5'’ + 65-1 
2^2 
=^V{ 
6 + 2 + 
(5 + 2)'' - 95 
2a“ 
} 
Now 
where 
and 
h = 2{-Y(-^ JX, 
XI”' = niT — 
X = - X 
3 \ , / 3 
2177 
nir 
