98 
PROFESSOR W. M. HICKS OK VORTEX iMOTION. 
Hence we can take 
Therefore 
K — 770“ Z = l}/. 
1 (lyjr 
iir/' 
(/z 
1 y 
7.+^- 
lirv dr 
We have now 
d j p T- + 7ij-\ (It , I'dr dvj\ cr 
A- { j + ^ + j = -cu + - T 
7 / o , s: 
d / p , , T' + IV- 
Now 
dz \ p 
dr 
+ V + 
d }v 
V f (It dvj\ 
(It ^ \(Iz dr / 
dw 
_ _ iy ^ ^ /(It _ 
It. " ~ ~dz ~ ~ dr ~ dr 
(ho (ho 
dt ~ ^ ^~dz' 
Therefore 
i ^(7 + ^^ + 
= <irj W-r 
1 (I\}r /(It dw\ 1 
27rr dr \ dz dr 
[/(■A)]” 
4.vH(«P> 
''/>- + V + 
„ \ /(ir dw 
1 d-ijr /(It dw\ 
277/’ (/? c/r / 
Hence 
/(It dw\ 
~ 
(I ; (lyp j 
dz~dr\ 
[/(W 
dz Ldr 
\ r ) 
277?’’^ _ 
1 
cZ 
(If 
/(It (ho\~ 
/77-^l 
dr 
-dz 
^ r /_ 
Therefore 
/(It dw\ |— /(It (hv\ 
d^ d j dz dr | d^^ | d | dz dr 
dr dz 
dz \_(Ir 
+ 
Trr 
= 0 . 
Therefore 
dyjr (I 
7lr dT 
1 /(It dw 
jlz dr 
d-ijr d 1 /(It (ho\ / {\lr) f'{yp') 
dz d r 
r \d -, 
z dr ) 
277/’' 
Therefore 
1 /d.T dw\ /(f) f (^) , -C^W , X 
Y' 1 dyfr d'-yp- 
dr 
dr dz- 
- 277r^F(^//)-/(V/)/(^//). 
