Wave Resistance of a Spherord. PTT 
In particular, we obtain the simplest system by taking the confocal which 
reduces in the limit to the elliptic focal conic 
2 2 
Res 03 ae 
a2 — 2 62 — ¢ 
1, (6) 
with a> b> c. In this case the volume distribution of doublets reduces 
to a surface distribution over the plane area bounded externally by (6). The 
moment per unit area is found by putting 42 = — c? + $ and taking limiting 
values as § +0, taking into account the factor (5) and the limiting thickness 
of the confocal at each point. We may refer to the distribution found in this 
way as the image system for an ellipsoid in a uniform stream. 
If the motion is parallel to Oz, the doublets are parallel to Ox and are 
distributed over (6) with a moment per unit area given by 
abcu (1 Mage CEy hl 2 - (1) 
= (2 on a9) (a2 =F e2)i2 (62 8 c2)1/2 a2 — c2 62 — ¢2 Z 
There are similar expressions for motion parallel to Oy, Oz with Bo, Yo 
respectively in place of ap. 
3. We shall specify now the particular results for spheroids, using the known 
values of %, Bo, Yo. We take Ox to be the axis of symmetry, with c= 6b; 
and consider first motion parallel to the axis of symmetry. 
For a prolate spheroid, the focal conic reduces to the line joining the foci 
of the generating ellipse. The image system reduces to a line distribution 
along Oz, from « = — ae to x = ae, of moment per unit length 
Au (ae? — 2°), (7) 
where 
AW} = 4e/(1 — 2) — 2 log {(1 + &)/(1 — 2} (8) 
with e? = 1 — 62/a?. 
For an oblate spheroid under the same conditions, the system is a surface 
distribution of doublets parallel to Ox, over the circle 
r= 0; yf = bee (9) 
where e’? = 1 — a?/b?; and the moment per unit area is 
Bu (b2e’2 — ye — zy, (10) 
with 
B7!=27(sin7! e'—e’ N1i—e'?). (11) 
For motion at right angles to the axis of symmetry, we take Oy as the direction 
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