744 
PROFESSOR W. M. HICKS ON THE THEORY OF VORTEX RIXGS, 
or substituting for A, 
"i+i 1 -©} 
+ T 
yU, a 
9 
v/2\ K 
whence 
£ 2 
£.= _P15ESh J lo „W, _Ai\l /_ / 9 _M\ 
* 2 Ah+Z l g V 2 \ V/J Vi+AV V/‘ 
Case (1) when there is no added circulation 
— 18 
7. 7.2 7.2 & 7, 1 4 7,2 4 
A/g /I'O ““A'j /tj /to 
Case (2) when the added circulation is very large 
(30) 
h -{ kg ^ +i ( l ”V 
Value of e x .—Substituting for A x in equation A (1) 
-4A 0 (L 1 -ij+je 1 +5^* 1 i >=0 
7r 1 ( fiyd Tcf fa \ T , ix x a ( Ay fa 
4 - - o f ~/2 j Ll + 4 tV 2 + A, 2 -/,! 2 7^/2 
= ^ ) l0g ^ } • • • ( 31 ) 
Value of U v —Substituting in C (1), the surface velocity is given by 
-fffo +3*i»)=4A 0 ( ! +W)+-f i-, 2 +¥~j V 
V= - J7{ iA « (1 - W )+ 2 f V+¥ ^ O} 
_ ^’1 1 f J'tfL/'i 7. 2\_i 4 ; Aa. 4 , 2 / 1 i13 7, 2\ 4A«> j 2 Aq 4 , 4 1 
-2aW2\TrA l kl ^2 A ' x ^ 1+ 4 ^ ' ^2 ^ 13 ,/2 ^ J 
7*i 
Airctk- 
(1 -V) 
• (32) 
This is the velocity along the surface of the core, not just outside it. 
