Wave Resistance 468 
Using these results in (27), we obtain 
R = BEM e+ [ Ko (0) + (1 + 35) Ki () + pete Ko (VFB 
iD) 
x, ¢ (a8) 
Haran ter ee svFrR), co 
with « = gf/c?, B = gk/c?. 
Values have been calculated from this, using tables of Bessel functions, 
and graphs are shown in fig. 1. 
The ordinates are values of Rf?/zgeb°, while the abscissae are those of 
c/\/(gf). The curves are for different values of the ratio k/f; the curve 
0:8 
0-6 
0-4 Viigo = 
0-6 07 08 0-9 1-0 V4 1:2 1:3 
e/V (gf) 
Fic. 1. 
Rf? /rgeb 
for k/f = 0c is the graph of Ro, the resistance in an infinite stream, and 
the other curves show the increase of resistance with increasing nearness 
of the wall. 
8—It may be remarked that the present method of calculating the 
forces gives not only the wave resistance, which is the resultant force in 
the line of motion, but can also be used to give the resultant force in any 
direction; for instance, in (3) it is only necessary to replace u by the 
component velocity in the required direction. 
For the problem treated in § 7, the force on A in the direction towards 
the wall is given by 
= Od, | bg 
Y 4roM (= Ate ma): (1) 
416 
