WAVE RESISTANCE OF A CYLINDER 333 
take the fluid motion to be that due to a certain distribution of sources 
and sinks over its surface and of amount o per unit area at each point. We 
assume this distribution in the present problem in order to obtain the wave 
motion to the first approximation. Thus in (26) we replace m by oc(t), 
where c is the velocity at time ¢; if (h,k, —f) is a point on the surface of 
the body we also put x—h for x, y—k for y, and 
ow’ = (€—h—s,)cos 6+ (y—k)sin 0, 
and the required velocity potential is obtained by integrating over the 
surface of the body. 
We shall not carry the general problem further meantime, but consider 
the case of a slender ship form. Here the usual! approximation is to take 
o = —(éy/eh)/27, where the surface of the form is given as an equation 
for y in terms of h and f; further, the source distribution is taken to be in 
the longitudinal section of the form by the plane y = 0. We obtain, in 
this case, 
trots tt 
yest Z{z Soa | and ar fa [ext costein(g itr) 
(27) 
with w’ = (&—h—s,)cos6+ysin#@. This result is equivalent to that 
obtained by Sretensky by a different method. 
The pressure at any point is given by p @¢/ét, neglecting the square of the 
fluid velocity; and the resistance is found from 
pea | [vo _f") oY aN df’, (28) 
taken over the longitudinal vertical section. Hence, from (27) and (28), 
we find 
=* | I3 oF a'df’ x 
x ff [le arene ies rn bahay + 
t 7 
gp CO) sm9 a0 oy 
+2] &Y an'af [| fanar | eemar i As 
0 —T. 
x | eI Neos(kw’ )cos{g!x?(t—7)}« dk, (29) 
0 
with ow’ = (h’—h+s,—s,)cos 0. 
543 
