1105 
face. A is determined by the boundary condition for v. When the 
boundary layer is sufficiently thin (as has heen assumed), we have 
at all its points, except for the nearest neighbourhood of 8, and 9,: 
rime RN Ee vat te Wi GEE) 
where n is the normal to the surface, while V,U denotes the velo- 
city of the potential current at the foot of the normal, which is a 
function of 8. Then the velocity in the boundary layer is: 
n a 
B 
1 1 a 
~— ee ee a S kil: OUA SAAN 
v= wdn = wda = a Pai saleete : : 
0 0 A 
At the surface (2 = 0),-v 0; when « increases indefinitely, we 
come outside the boundary layer and we may put v= JV,, so that, 
(IIL) 
PB 
Vir de Aen es Nps a Ee 
At 
whence A is given by: 
ae a 4 
a aaa Od 
IV. Formulae (V), (1) and (111) roughly describe the flow in the 
boundary layer (the velocity in the direction perpendicular to the 
surface must be determined with the aid of the equation of conti- 
nuity). From (///) we can immediately derive the occurring of the 
reversed flow. The values of A at points near 8 namely are here 
multiplied by a greater factor than at points situated more towards 
the front, which is especially obvious for small values of «. At the 
points 8, and 8, V,=0O; between these V, has a maximum at a 
point Bn, so that according to (V) A is positive for 8 < Bp, negative 
for 8 > Bm. For 8B >PB, in (111) these negative values of A will 
count more than the positive ones; from a certain value of 8 they 
will predominate, so that the sign of V is inverted. 
When « approaches zero, we have: 
B 
ve 4 Soe d Li 
if VakV, VBS 
A 
so that the point 8s where the current leaves the surface is given by 
Ps 
A 
faro ROE 
Vas 8 
