1103 
not occur’), so that the question arises: when does this reversion 
of the flow begin, is it connected with a definite value of R? 
Further, how far does the region of the counter currents extend; 
is it at first a thin layer which becomes thicker with increasing R 
and which afterwards diminishes again? That the length is finite, 
is proved by the consideration that the differences in velocity are 
finally quite dissolved by the friction, so that in the axis the current 
must reassume the original direction. 
A second question is the following: in the image of the absolute 
flow the stream lines are not closed according to Stokes and OsEEN - 
Lams, but they are for the ordinary irrotational motion (the limiting 
current of §§ 7 and 8). Where is the passage from one case to 
the other? 
The figures 19— 24 are meant as a possible interpolation between 
the considered limiting cases (they have been sketched for the two- 
dimensional case). Of course they can by no means claim the name 
of approximation ’). | 
Such flows are observed at the beginning of the motion. After- 
wards they change into a more or less irregular motion. It is 
not known for which value of A the lability of the laminar one 
begins *). 
$ 10. Application of the method of $ 7 to the calculation of 
the diffusion and the convection of the vorticity in the trrotational motion. 
I. Notation. U=velocity of the indisturbed parallel current; v, V= 
velocity of the irrotational motion, v U==velocity of the fluid in the 
In the following cases: flow of Strokes round a sphere; of Osren 
round a sphere and round a cylinder; and of Burgess round a sphere (see the 
quotations of § 5) we see from the formulae given by the authors that in the 
image of relative flow the velocity v on the axis behind the body has the same 
value as that of the original current U. 
2) The distribution of the vorticity given in the figures has not been derived by 
calculation from the distribution of the velocities; they were only sketched on 
view. Fig. 22 gives the beginning contraction of the vortices to a vortex sheet. 
In Fig. 24 the length of the domain of the counter currents has been left 
undetermined. 
Theoretical and experimental investigations on the flow produced by a sphere 
for medium values of R in a space bounded by solid walls have been made by 
W. E. Wiutams, Phil. Mag. (6) 29, p. 526, 1915. In the paper several photo's 
and drawings are represented. 
8) The “coagulation’’ of the vorticity cannot increase or decrease its quantity. 
Therefore even in the real, turbulent flow the “wake” must remain of finite length. 
The figures 22—-24 may be said to represent the “mean state" of the fluctuating 
current. 
