172 
Transactions of the Royal Society of South Afrit 
The components of velocity will be given by 
= -^(-»-)*>|B,K + B,E 
where 
^ " 4>ar ' 
+ 2ar • ^ + W j 
p _ (1 + A;'2) ^2 _|_ ^2 _^ ,.2 
^1 = tTo . — 10 
k^ 4>ar 
= K 1+A;'2 _ ^2. ^2 + ^^2_ 
C2 = 5 
(25) 
(26) 
G-omg over to the limit for r=o as in the case of the ring-source, we 
find for the ^--component of velocity along the ^-axis, 
\ a o 4^2 _ ^2 
[z'+ a^ 
For z = 0, (vj = 
For o^\z\ (v,) >o (.>o). 
0 ^ I ^ I £ oc (?;.) Z 0. 
The maximum values are at 0 = o when {vz.)r=o ~ 
z ± --y-^ , where (i;J^=, = ^ . — -. 
-J a"" i i 
From this we see that the stream-lines will approximately be as shown 
in the figure below : 
a2 
and at 
