518 T. H. Havelock. 
Fig. 1. 
point (0, 0, —f), we take the velocity potential from a previous paper in the 
form* 
¢ = cr al i Ke" @ +N + to cos § dO de 
28 | ace da 
=/ | KF (0, «) e-*F- 2) + *? cos 0 dO di. 
4T J—3r/0 
with 
F (0 ro) es A Bay 58S? Se UB BR 
K — ky sec? 8 + iu sec 0’ 
o=azxcos f+ ysin 0. (7) 
The real part of the expression is to be taken, and further the limiting value 
as u> 0. The surface elevation is obtained from 
0 _ od 
Oz Oz 
After some reduction, ¢ is obtained in the form 
2M f kK oM | am 5 ie { Cina 
SL 6d0 SEEN Ts Sara 
: c (a? + y? + f?)%? “ WO sh oi \, | — ky sec? @ + ip sec 0 
ene | se 
Se er cdicn, 4(8) 
K — Ky Sec? 0 — iu sec 8] 
Transforming the integral with respect to « in (8), and taking the limiting 
value, we obtain 
i 2) . 
kK, sec? 8 cos m msin mf — 
2 | Ko Sect 0 cos mf + m sin mf , z= mdm, for o > 0; (9) 
0 m* + K,2 sect 0 
* © Roy. Soc. Proc.,’ A, vol. 118, p. 28 (1928). 
291 
