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in this case they are not identical with the paths of the particles 
of the fluid. 
By relative flow will be meant the image of the flow as seen by 
an observer that regards the body as being at rest. This is therefore 
the real stationary state’). As will be known both states may be 
derived from each other by increasing or decreasing by U all 
velocities parallel to the axis of motion. 
In the diagrams of the distribution of the vortices the density of 
the vorticity is indicated by vertical hatching. In some sketches the 
“opposite” vorticity (see $ 3) is indicated by broken horizontal hatching. 
§ 2. Introduction. 
The state of flow is governed by the propagation or the dispersion 
of the vorticity. This is caused by two phenomena: diffusion and 
convection. The equation for the vortex motion which may be 
deduced from the equations of Eurer: 
Ov 1 
QT) SS A at e . . . 
di ° ve +r4Ov—(v.y)v . : (2) 
by differentiation is: 
raw MEIN COMPU) von ene CE) 
The first term at the right hand, with the coefficiént of friction », 
gives the diffusion of the vorticity. As will be known the velocity of 
diffusion has no definite value: it depends on the concentration gradient 
of the diffusing matter or state. There is no diffusion front or a 
propagation of waves. 
Besides this term we see at the right hand side the convection 
terms: — (Vv. 7) w + (W. 7) v, which express: 
1° that the vorticity is carried along by the current; 
2° that the vortex vectors turn with the fluid particles and are 
deformated together with these. 
In one case the last term fails: viz. in the plane or two dimen- 
sional motion’). In this case the operation (W. 7) (the differentiation 
in the direction of w) is zero. The first term is of more importance 
1) Some investigators as f.i. |. AHLBORN speak of lines of force and of current 
to indicate what has been called here absolute and relative flow. 
’) In the original paper the three-dimensional motion was mentioned here too; 
this is not correct, as has been remarked to me by Prof. Pranoprt. 
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