781 
the potential g** by the methods of classical hydrodynamics *). This 
part of the impulse is received back by an equal decrease of velo- 
city of the body *). 
Now III and [V may be combined: the discussion of III remains 
valid for a non uniform motion, when only we replace in (22) and 
(23) V by V + dV, the velocity of the body at the end of the 
element of time dt. 
§ 6. Summary. 
When a body in a fluid is brought into motion a vortex layer 
is generated at its surface. This layer diffuses into the fluid by the 
friction and is carried on by the current, is ‘“washed away”. At 
the surface new vorticity is generated, which diffuses again etc. 
The generation of each vortex layer demands a certain impulse and 
the sum of the impulses that must be produced per second, forms 
the resistance W experienced by the body. At a definite moment 
the total impulse of all vortices together is equal to the time inte- 
gral of W: 
t 
fwa =I@M=e2 CA —of2V; 
the impulse may be calculated from the products: 
| (circulation) . (surface) 
of the separate vortex lines. 
1) Example: For a sphere (radius =a) we have for òV =1 the potential 
p** =1 37-2 cos §. From this follows for the tangential velocity of the fluid 
along the surface: — 4sin 4, while the tangential velocity of the sphere itself is: 
+ sin 6, so that the intensity of the vortex layer is: 
—sin Ó. 
2 
The impulse of this layer is: 
. 3 
Ge CG; A; = | a dé. Be G- xa? sin? 0 = 2x va’. 
0 
An : 
Subtracting from this the amount OAs pa? for the impulse of the fluid sub- 
stituted for the sphere we find the well known value: 
An dt © 
3 ua je mr 
(LAMB, le. p. 116). 
2) For a non uniform motion this ““acceleration resistance’ may sometimes be 
separated from the total resistance; see G. Cook, An experimental determination 
of the inertia of a sphere, moving in a fluid, Phil. Mag. 89, p. 350, 1920. 
