485 T. H. Havelock. 
wave resistance in one or two definite cases. In a former paper* the com- 
parison was made for a submerged prolate spheroid, and from the formule 
given then numerical calculations were made later by Wigley} in connection 
with an experimental investigation. We may make now a similar comparison 
for a flat ellipsoid moving in the direction of the greatest axis, that is, for the 
case a > b > c worked out in § 3 above ; it has, moreover, been found possible 
to put all the expressions into the same analytical form, and we can see from 
inspection the difference between them. 
Michell’s formula for wave resistance is 
4out f 2 mdm 
a p2 ee 22 
| 2 ( aly Q ) (m?ut /g? pool 1) ( ) 
where - 
adn) = | | z GAP ONE Teal (23) 
The integration in (23) is taken over the vertical longitudinal section of the 
model, that is, in the present notation, over the section by tae zy-plane; 
and 0z/dx is derived from the equation to the surface. Applying this to the 
model specified by (8), with Ox at a depth f below the surface, and putting the 
expressions into the form used in § 3, we obtain after some reduction 
cm/2 
R = 4 “lgpKg?u? | INO GEO cares (Nhs); (24) 
0 
ha 2 2\1/2 
N= \| ( = = — z) ered °° GOs (gx sec 0) dx dy, (25) 
a 
the integration in (25) being extended over the area of the ellipse 
a/a? + y?/b? = 1. 
Carrying out the integrations in (25), we obtain finally 
4a3 ee. R =| | Isak o ? (a7—b*) (1+?) )(1=B622?) acai en72 * oft? 7 
32779ea7b7c? 0 IBA Pe 
Pag cree leer ae as 
vp (e771) 3? (26) 
where B=) Na*—b?. 
* «Proc. Roy. Soc.,’ A, vol. 103, p. 574 (1923). 
+ W. C.S. Wigley, ‘Trans. Inst. Nav. Arch.,’ vol. 68, p. 131 (1926). 
