Wave Resistance of an Ellipsoid. 482 
From (12) of the previous paper, the wave resistance is given by 
ar 2 
R = lérpic,! | P2 sec? 040, (11) 
0 
P — lan al LET EEE ant {Jl Roped — y Pere 
rQ—a) (eae ae l)\ “ae@—e BA 
X cos (Kgx sec 0) dx dy, (12) 
the integral for P being taken over the ellipse (9), and xy = g/u?*. 
Comparing with (6) and (7), we obtain for the integral in the expression for 
P the value 
{2n3 (a? — c2) (b? — c2)}V2 Jai [ko sec 0 {a2 — co? — (b? — c?) sec? oy") (13) 
Ko” sec 9/26 {a2 — c? — (b® — c®) sec? 6}3/4 
when cos 0 > »/{(b? — c?)/(a? — c®)}, and a similar expression when cos 0 
is less than this value. Collecting these expressions, and for comparison with 
previous results, putting tan 0 = ¢, we obtain finally 
(2 ae aX)? (a? pat b2)3/2 ent 
327?gea7b*c* 
day lice Is/p {eq? (a? — 6) (1 + #) (1 — o1?t?) JEEP —2xoft qt 
@ (1 Eas oc?) 3/2 
° [ye ficg? (a = (5) ae ?) (at? — 1)} HEIR en 2eoSt dt 
+ ibe SS an dt, (14) 
where a” = (b? — c?)/(a? — 6°). 
This expression is for an ellipsoid moving horizontally in the direction of the 
longest axis, and having the least axis horizontal and the mean axis vertical ; 
or, we may say, with the beam less than the draught. 
4. We consider now the case when the beam is greater than the draught ; 
that is, keeping the axes Ox, Oy, Oz as before, we have a>c> 6b. The 
elliptic focal conic is now in the horizontal plane and is given by 
x 2 
amma Uararemepe as) y = 0. (15) 
The doublet system is distributed over the area bounded by (15), the axes being 
parallel to Oz and the moment per unit area being given by 
abou a z 
MG Oe ee oe . (16) 
