PROFESSOR W. M. HICKS ON VOKTEX l^IOTION. 
51 
9. The form of the stream lines for a monad aggregate have been delineated by 
Hill. The general form of the stream lines for a poly-ad is obvious, and there is no 
special reason for drawing them accurately at present. It will be well, however, 
to determine the position of the equatorial axes, for the particular case of homo¬ 
geneous poly-ads, that is in which 
The condition at an equatorial axis is that 
^ ^ = 0 when 0 = 
ivrp ar Z 
in which xfj denotes the stream-function referred to the boundary at rest. A]q:)lying 
this to the p-th layer in an w-ad 
t = 2,7 { A„,' + h - i Kr - ^ + i } sii.'ft 
The equation for the equatorial axis is therefore 
or 
r’ (a'^, - a^_i) - ^ {a^ - a;_,) r' - (a; - «;_,) ~ 0. 
This may be written 
, 1 — 1 . A’? , — 1 . 
0. 
a'Ai — 1 ' 
1 
1 1 ^ 3 5 
4 s _ 1 
1 
Now 
therefore 
and 
For a monad 
K-i {^-1 - 1) = I Vi - 0. 
K-i - 1 
-1 = 4 
3 
— i (4 + 1) - 4 = 0. 
6 = 0 r~ = 
for a dyad 
Beyond dyads 
Then 
a 
v/2 
hi =1 or' — 4 a® = 0 r= 1T 720a,. 
r = nearly = (1 -f 
+ {5 - i(f6,_,+ 1)] 
Now hp_i is nearly 4 
=i+(I - 2/,_,) f=5= 
= 0. 
H 2 
o 
