1087 
Laminary motion for different values of R. 
§ 4. The flow round a sphere according to Stokus. The method 
indicated by Stokes for the solution of the hydrodynamical equations 
neglects the convection terms. It gives therefore the flow at the 
end A0 of the series; the velocity U must be very small, so 
that the influence of the friction dominates. Equation (4) is reduced 
to the simple equation for the diffusion: 
Ow 
The most known solution of this equation is that for the stationary 
motion of a sphere’). The vortex motion diffuses from the surface 
symmetrically forward and backward; its intensity is given by: 
sin Ó 
3 
Jl ZES Ua aT . . . . . . . : (8) 
2 r 
(a is the radius of the sphere; r and @ are polar coordinates with 
the centre of the sphere as pole and the direction of motion as axis). 
This distribution is represented in fig. 5. 
The stream function for the absolute flow is: 
3 2 
Mani al» =) int 6 EI A es (8) 
By means of this the figures 6 and 7 for absolute and relative 
flow have been drawn. These figures too are symmetrical at both 
sides. 
§ 5. The motion according to OsreN. 
OskEN has remarked that the considerations leading to the neglection 
of the convection terms hold in the immediate neighbourhood of 
the sphere; at great distances from it the velocity of diffusion dimi- 
nishes to zero, while the convection current always keeps the same 
velocity U: hence the convection will predominate here. 
tographic photo’s are found in: E. F. Retr, Technical Report Advisory Committee 
for Aeronautics, London 1912—13, p. 133 (Rep. N°. 76); and in L. BAIRsTOW, 
Applied Aerodynamics, London 1920, p. 345, fig. 167 (photo by J. L. NAYLER, see 
Techn. Rep. etc. Rep. N°. 382 of May 1917). 
The vortex layer behaves as a so-called „filament-line”, (see L. Bairstow, 
lic. p. 348). 
1) See fi. H. LamB, Hydrodynamics, Cambridge 1916, p. 587. LAMB also gives 
a fine diagram of the absolute flow. 
