1100 
layer as independent of y, v, and wv, are connected by the equa- 
tion of continuity. 
0 
For the vorticity w = — = we therefore have: 
Y 
Ow Ow Ow =) 25 
DE =S Oy? En v, 55 + Vv, Oy - 5 e 4 = ( ) 
c. From the solutions of the equations (which for the greater 
part must be obtained by numerical approximation) we find that in 
the case of a retarded flow outside the boundary layer, there is a 
point in this layer where the direction of the flow is reversed, so 
that counter currents are formed and the currént coming from the 
frontside leaves the surface. The place of this point is independent 
from L. 
The dimensions of the boundary Jayer in the direction of y are 
1 
given by the form of the body and are proportional to Dn times 
the dimensions of the body. 
Thus we find by both these methods (of $ 7 and $ 8) that for 
high values of A a vortex sheet leaves the surface of the body at 
both sides (eventually round the body) and emerges into the fluid 
as has been indicated by Osten. For increasing values of R howe- 
ver this sheet evidently does not only become thinner so that it 
approaches to a surface of discontinuity, but it fits more closely 
round the body so that the irrotational motion outside gradually 
extends over a greater space and finally becomes the ordinary 
irrotational flow *). 
§ 9. Remark on the motion for mean values of R. 
The calculation according to the methods of $ 6—8 teaches that 
for high values of A there is formed behind the body a forward 
current opposite to the original direction of the current, which is 
in agreement with the experimental results *). For R—0O this does 
1) The considered bodies must not have sharp edges (as was demanded in § 1). 
Therefore the above remark does not say anything against HELMHOLTz’s disconti- 
nuous flow along a plate with sharp edges. 
2) In the image of the absolute flow the velocity immediately behind the body 
is greater than U (the fluid “overtakes” the body), the stream-lines must therefore 
be packed more closely together than in the original parallel flow. As to the 
distribution of the vorticity: at the back of the body we havea layer of ‘‘opposite” 
vortex motion (see above § 3, II). 
