1106 
From this equation we see that 8g is defined by the function A(§), 
viz. by the form of the body; in this equation A does not occur. 
4 2 
For the circular cylinder we have: V,? = 4 — sep A=— zi and 
a 
8 (a—s)VB+ 2a 
WZ Ss 
: 3V ak a? 
This expression is zero for Bs =a; i.e. 120° from the most forward 
point of the circle. This is rather far backward; the experiments 
and the calculations according to PRANDTIL’s theory give for this distance 
somewhat less than 90°. This difference is caused by the calculation 
of the convection, which keeps here a finite velocity up to the 
surface so that gs is slept along too far by the flow. 
According to (/) the order of magnitude of the thickness of the 
boundary layer is of the order of «= of the order of Vk8 = of 
va a 
the order of [4 sao the order of ——. 
U VR 
V. Values of w and v for 8 > 6, 
When we suppose, that (J) and (V’) may be used up till B=&,, 
the distribution of w for 8 > 8, is found by the diffusion into each 
other of the two distributions that exist in 8= —, for positive and 
negative values of a respectively (which are equal and opposite). 
This gives: 
Bs ZN See 
A — a? — 
w= — ee ss exp ees Ay Ce eN (V/T) 
V xk (B—E) 4k(8—S) 4k(8—B,)(8—S) 
A 
The distribution of the velocity is then found from: 
1 Go 
Ve f ede. lr aante IEEE) 
0 
where V,U is the velocity of the irrotational motion in the direction 
of the a-axis (i.e. along the line a= 0). 
With the aid of these formulae the distribution of the vorticity and 
the flow in the boundary layer have been calculated by graphical 
integration. In order to obtain everywhere abstract numbers, we 
have put: 
B= Ba ; §=Xa ; a=2CV ka; 
Then (J) and (V/J) take the form 
1 1 
ws ze f aX. (XB,0 = Tet C) 
where p and f are numerical quantities. 
