1089 
To take this into consideration Osren has kept the constant trans- 
lational current U in the equation; equation (4) has not been sim- 
plified to (7) but to: 
—= — UW) , a 
vOw me, BEE (10) 
In the nearest neighbourhood of the body this does not give an 
amelioration, on the contrary rather a little change for the worse, but 
the inaccuracy remains of the same order of magnitude as in Stokes’ 
Ua 
solution viz. of the order —, or of the order of R. 
Vv 
For the stationary motion of a sphere OsreN finds in the imme- 
diate neighbourhood of the sphere the same solution as Stokes and 
therefore the same value of the resistance. This was also found by 
Lams in another way. At a great distance however all has been 
“drawn backward”. The distribution of the vorticity is defined by: 
3 1 + U7r/2v U (r—a) 
w= — Va? 
2 r? 2v 
„sin O, exp 
RE 0 
2aU 
v 
and represented in fig. 8 (the figures have been drawn for R= 
= 0,4). The asymmetry between front and back side is evident. 
Because of the exponential factor at the end of (41) w is very small 
outside a parabolical space f.i. bounded by: 
| 20v 
ie 
(where at the outside the exponential function is smaller than 
0,000045). Here the motion becomes therefore nearly irrotational. 
The stream function is given by: 
NE 
3 ge Ua 
bil Et ear 1 — exp Eer * sin? 6 (12) 
2 : 2v 4r 
See fig. 9 and for the relative flow fig. 10. Fig. 11 gives on 
a smaller scale (i.e. for higher values of r) the distribution of the 
vorticity and the absolute flow; it shows that outside the para- 
bolically bounded space the motion approaches a radial current 
1) C. W. Osren, Arkiv f. Mat. Astron. och Fysik. Bd. 6, N°. 29 (1910). 
H. Lamp, Phil. Mag. (6) 21, p. 112, 1911 and Hydrodynamics, p. 594 seqq. 
LAMB gives a discussion of the character of the motion (from which these 
remarks have been taken) and also gives a solution for the corresponding two- 
dimensional problem. (In this last case Stokes’ method does not give a solution), 
