1092 
motion of the vortex elements is the translational current (according to 
equation (10)) there will be formed in front of the body an infinitely 
thin vortex layer (of finite total intensity) which extends itself 
backward in a cylindrical sheet, parallel to the direction of the 
current, which sheet surrounds the body along the parallel circle 
of largest diameter. This is sketched in fig. 12, where the vortex 
sheet has been indicated by a thick line. Outside the cylinder the 
motion is grrotational, inside it generally not. Along the cylindrical 
surface the w-component of the velocity changes abruptly. 
For the stationary motion the following solution is found *) (the 
formulae refer to the absolute flow; the system of coordinates w, y, z 
moves with the body, the a-axis is in the direction of motion): 
Let p be a potential function, then we have outside the considered 
cylindrical space: 
Vie © oa” oc awe fem) 
and inside it 
USM Oe Va er en ee) ae a) 
where v*(y,z) indicates the value of yyw at the point at the back 
of the body witb the y- and z-coordinates: y,z. Here (a, y, 2) 
is defined by the following conditions (that follow from the equation 
of continuity): 
gp EN etek LA 
further at the front of the body: 
0 
(52) ES U aster ko ieee Clay 
On 0 : 
and at the back: 
dv, dv: ò ò 
T= ty lle ick ane A 
Oy dz : 
At the back of the body we have 
Vl. «(parallel to the c-axis) … erna fae) 
Here the fluid sticks to the body. At the front on the contrary only 
C. W. OSEEN, Beiträge zur Hydrodynamik I, Ann. de Phys. 46, p. 231, 1915. 
In the following papers (p. 623 and 1130) OsEeEN treats the properties of the 
solution of the non-simplified equations. These are written in the form: 
Ov 1 
Oak FT ptger)-uAv=A 
Ot 2 
Then the vector A=e(v>Xw) is treated as “external force". In the paper of 
p. 231 A has not been considered. 
1) C. W. OseenN, Ann. d. Phys., lc. p. 249. 
