Wave Resistance. 586 
4. We have now to consider the remaining terms in (4), namely, the last 
three terms under the integral sign. 
T T 
A complete valuation of these over the whole range of velocity would be 
troublesome ; but fortunately the range of most interest, and one in which 
there is more chance of agreement between theory and observation, corresponds 
to fairly large values of p, roughly between 10 and 40. We can obtain an 
asymptotic expansion which is suitable for this range. We shall write 
a = gd/c* = Bp, (15) 
where 3 is the ratio of draught to length. 
Then, with the understanding that real parts of complex expressions have 
to be taken, we have 
{ra — GEE P {(cos* O= cs cos° é) cos (p sec 4) 
\ * 4 
—_— — 4 i d 
a sin (psec #} $ 
a [ ( shes en PP sce?) cos? (sec d + 2h el seep dd 
Pp 
OMe fs: = pales) 2 i me + t\? 
oN ra - a 
t Z Es 
( i Pp a 2p 
= (n/2p)* &” {Q (0) — 2e~*7Q (28) + e *7Q (48)}, (16) 
234 
