154 Transactions of the Royal Society of South Africa. 
and we get for the equations for (p and \p 
j /l , J:_ ^_3_cot_0 02) 
For the components of velocity Vp and vq we have 
_ ^ _ _ JL 1 ^ 
S<p 1 
vq = 
pS9 p3 gijj3 g • dp 
(13) 
Section 5. 
Uniform Stream . 
For a uniform stream of velocity, Vo parallel to the ?j-axis we have 
where <po is the velocity potential of such a motion. 
On integrating we get 
(Po = — VoZ = — VoP COS ^ - - - (14) 
where the arbitrary constant is taken as zero. 
From equations 0 we further have 
o = + -L. 
r ' (tz ' 
where xl^o is the stream-function for this motion. 
Integrating, we get 
4^. - -^l" - pi sinM - - (15) 
The lines rpo = const, are in this case lines parallel to the ;s-axis, and 
hence we have the case of a circular cylinder. 
From equations 8 the stress-components are given by : 
r9 0 
ez— — VoV. 
Yvom equation 10 the displacement ue is given by 
Vurz 
Ue = — , 
where the constant c is taken such that over the plane z = o the displace- 
ment is zero. 
