The pressure of water waves upon a fixed obstacle 413 
These expressions may be evaluated in terms of two integrals which may 
be shown to have the following values: 
Dp 2 
i HP (u) edu = pe? {H?)(p) + iH? (p)} +— (11) 
p >) 
} AP (u)edu = pe’{ HP? (p) —iH#?(p)} — = (12) 
vO 
We shall write (11) as L(p)+ 2/7, and (12) as M(p)—2/7. We also put 
p, = 2kl;  p,—K(l+a); p,=K(l—a); p, = 2ka. (13) 
We select five points at which to make the calculations, the bow, stern, 
shoulders and amidships; and, in the notation indicated, we have 
el) = ihetettl 1 — Ja} Ln) — Eps) ~ Eps ml 
ie tetova] 1 — Sol Lp) L (py) — M(ps) 4 tl 
€(0) = ihe'™[1 — 4o{ L(4p,) — L(bpy)— M(kp,)+Mpo}], (14) 
(9) 
¢(—a)= iheiet oof — ha) L(p3) + IM (p.)— M(p,)+ ll 5 
in 2 
¢(—l) = al - 3a{ M(ps) + M(p,)— M(ps) — a : 
We apply these results to Model No. 1144 of the National Physical 
Laboratory. This was a model of the given form used by Wigley (1931) 
in comparing calculated anc observed wave profiles along the sides of the 
model when advancing through still water. For the present purpose we 
suppose the model held at rest while regular plane waves of amplitude h 
and wave-length 277/« are moving past it. The dimensions of the model were 
f= ites C7 = 2GOite3 1 = O-0S ith, (15) 
We calculate only one case, namely, when the wave-length is equal to the 
total length of the model. Thus, in the notation of (13) we have 
ji, = O28 Dy = GEOR Py = 2PZSS Ya = lle, (16) 
We have also ~ = 0-129. Using tables of Bessel functions, € may be calcu- 
lated from (14). We are not concerned with the phase of the total oscillation 
at each point, but only with its amplitude. We find the ratio of the amplitude 
474 
