1095 
The value of v* proves to be <0, so that tbe velocity in the 
wake is >1. In the image of the relative flow a forward current 
is therefore formed. The stream line for yO follows the z-axis 
for x >1, the circle until about 6 = + 90°, then it leaves this and 
approaches asymptotically to the lines y = + 1,18. 
As further dv*/dy < 0 for y > 0 the direction of rotation of the 
vorticity is here opposite to that in the boundary layer y= +1 U). 
§ 7. Application of a method of calculation of Bousstnesg. 
The limiting flow of OserN we discussed above is very different 
from the flow which usually takes place in a fluid with infinite- 
simal friction. The most typical particularity in the case of OsrEN 
is the discontinuity of v at a cylindrical surface that surrounds the 
body. The form of the surface of discontinuity is determined by the 
way in which the convection of the vortex motion has been calculated: 
the vorticity moves in the direction of the x-axis with the translational 
current (/ only, so that it extends from the thickest part of the 
body backward in an infinitesimally thin layer (fig. 12). When however 
we attend to the elementary description of the initial development 
motion of the (§ 3)*) we should expect fora great velocity and a small v 
that the thin vortex layer at the surface of the body is slept back- 
ward by the current along that surface viz. towards the point where 
1) The degree of inaccuracy of this solution may be estimated by calculating the 
value of the stream function ),,, for y=1 and 6 = 90°; it has the value 0,933 
instead of 1,000. Further the values of v, are for 6 = 90°, 120°, 150° and 180° 
resp.: 0,126, 0,074, 0,034 and O, instead of all being O. In order to avoid diffi- 
culties the fears have been a little shaped. 
An approximation to NV = 10, gave for A, till Ajo resp.: 
+ 0,366; + 0,419; + 0,240; + 0,024; — 0,059; — 0,019; 
+ 0,028; + 0,020; — 0,011; — 0,021; — 0,010. 
From this follows: 
Wats for ral; @ =90° : 0,977 
v, for 6=90° (therefore y= 1) : 0,018. 
In this case we have: 
vA, == 1514905 22 A, = 2,30. 
The general character of the motion therefore does not change by this closer 
approximation. 
2) Also in the limiting case of Osren the original flow, when it starts from 
the state of rest, is the ordinary irrotational motion. According to Ann. d. Phys., 
Le. p. 246/247 the flow outside the space described by the body is everywhere 
irrotational; the potential ¢ is determined by: Ao =O U cos (nx) at 
one 
>On 
