PROFESSOR W. M. tTICKS ON VORTEX MOTION. 
99 
Therefore 
- f('-^ + v + 
dr p 
T- + Zf' 
— Ziv I = 
1 r/('^)/'('^) 
/ 27r?’ f/r 
Lm' 
+ rF'(^) 
LW)]= 
473--r'" 
\j±v)Y , iss^r 
“1" 9 
Stt’/ 
Ztt 
and 
_ 2 f p . V + Ti-"" - ZiA = f- 
dz \ 
'I'm' dz 
'Itti' 
H- tF'(t//) 
d l/W. , if)' 
SttV 27r 
z?,; 
Therefore 
— + V 4- ^ ^ = arbitrary function of f. 
o 2 OTT?’" 'Jtt 
Therefore 
— 4- V + -| \r 4- o-' 4" — ■2)“] + V7 ^ ~ arbitrary function of t 
This arbitrary function of t is in this paper always a constant. 
The last equation, together with the following, are the important equations 
K = xjj ttZv^, 
T = 
1 die 
'lirr dz 
1 dyjr 
’Itt)' dz 
1 die 1 dMr 
U'= -pr q = r - r Z, 
Zirr dr iTTr dr 
|-| = ^/W/'W + >'r'W. 
- 7 S + S'= “/W/'W - 2-=^'«• 
Whenever the conditions for the continuity of the t and tu components of the 
velocity have been satisfied at a separating surface whose equation is \fj = const., 
then if the irrotational motion outside the surface have cr = 0, we must have cr = 0 
when ifi is equal to the parameter of separating surface, if there is to be no slip there. 
Therefore /'(^) = 0, when if/ is equal to the parameter of separating surface. 
This is the case in the Third Section of the Paper.] 
o 2 
