170 Transactions of the Royal Society of South Africa. 
The velocity along the ^-axis is given by 
-ir -L 'tr 
r—o 
Writing now, 
where h^ = ^ and i^oing over to the limit for r o, we find 
.2- + (a + r^' ^ 
+ J- 
At 2 = 0, (iJ.) = 0, and further, it is a maximum at ^ = ± ^ ' '^^^i'® 
4.1, 1 • w ^ X "^"^c 
the velocity is efiuai to + = . 
a . 54 
Let us again superpose upon this motion a uniform stream parallel to 
the X-axis, the velocity of the stream being v^. The resultant velocity- 
potential will l)e given by 
1>6 = 1^0 + ^'g' 
where the values of cp,, and ^'g are given by equations 14 and 22. 
If we choose 7 ^-"^ ^ , then the stream-lines for such a motion 
a5i 
will approximately be as shown in Plate XVI, fig. 1. From this, then, we 
o1)tain a l»ody such as shown in Fig. 2, in which the stress-components will 
be given l)y 
Jv \ V 
The displacement iie is given by 
■ „,= 7j-M. + .) + i^.(^)-i{(.-.^)K-2Ei;. 
where the plane ^ = — is taken as the plane of zero displacement, h being 
great compared to a. The moment of the terminal couples is ^^^-^ , where 
r^ the radius of the T)ody at > = ± ex. 
The equation of the l)oundary lines of the body in a meridian plane 
will l)e given l)y 
V 
^ 0, - = constant, 
where is given 1)y ecjuation 23. 
