779 
ff dre (Pp) Pu 
dn = EE: Gr | 
fre Tjele) 
which differs from #, and F, by an amount of the order «. 
Ill. Let us now suppose that during an element of time dt the 
forces f do not act. Then the motion takes place under the in- 
fluence of the frictional and the pressure forces; diffusion and con- 
vection of vortices take place, ete. The pressure and the frictional 
forces being all finite, the velocity v will only change by an amount 
of the order dt; 6, is displaced over a distance V dt and is not 
deformed. Along oi and o, v, however, will no longer have the 
value V. The impulse of the motion of the fluid will keep its value 
unaltered. 
In order to obtain the motion that would have existed when the 
forces f had worked, the following motions have to be superposed : 
a. Outside o, the distribution of the vortices is right, as in this 
region no forces are active; here we must therefore superpose 
an irrotational motion, the potential of which is defined by 
òg* 
On 
b. Inside 6; no vortices appear as along this surface Aw’ = 0. 
Therefore we must superpose here too an irrotational motion, so that 
everywhere v becomes equal to V; it is perfectly defined by the 
boundary condition for the normal component °). 
c. Between o; and o, a vortex layer must be generated connecting 
these two motions. The total intensity of this layer is given by: 
fetan=ax tue ET OER EB) 
== Vr ta. (AlONS OJ Ee ike (22) 
The structure of the layer must be thus that the impulse is equal 
to the time integral of the resultant of the forces /: 
da aff { de dy det Wa paden „erk HRA 
1) Strictly speaking the vorticity both outside ou and inside c; has been influenced 
by. the change of the distribution in the transition layer; this amount is of the 
1 
order: exp. = a} which has been neglected here. 
td t 
2) The intensity of the vorticity generated in the transition layer is determined by 
rot f; to this both f„ and f; will contribute. As ft has a maximum in the layer 
(along oi and ou ft =O or finite; in the middle of the layer f is of the order 
