1886.] the revolution of Limagons and Cardioids about their axes. 7 
Therefore at the surface, 
oe _ =" 3B, 0, (YP) — Pay) 7° (5 P,. () 
Cc 1 . 
ies (ase I) Ie ay 8 
7 Wy tele = 1h 
es win 1) P OO fin acto Mnihe 
1 /1 = 2 (7? — 2 — wy) 
a ae ree 2 eke oS ABM cl 5 
= — 647rac (y*— 1)?. (uty) : 
Let ail ikea 
(w+) 
dv py —2r? + 3 
dy Jyf—1 (uty) 
Hence 
(of Ut (1 =p!) (y' 2 — uy) 
(u +7)" 
~~ ee wang ee 
3 (a+ Pl (y?- ) 
= (f= 1} 50 ava Yo 2 2 (7 1 1 : 
— 7 r (-)* An +1) 150" + 2? — 1)? On P,! (4) 
(2n + 1) 
Meneame (YF 1 2, yey 
13." () +» (+1) QM. 
8. When the solid is moving parallel to its axis with velocity 
V in an infinite liquid, the current function vr can be determined 
from the fact, that it is equal to Up cosec @ when U is the potential 
of the induced charge, when the solid is placed in a field of electric 
force whose potential is — 4Vpsin @. 
To prove this, we observe that yf satisfies the equation 
dp dp dy _ 
Wee tap? p da (10, a). 
* See Quarterly Journal, Vol. x1x. p, 361, where T, and #, are written respec- 
tively for P,| and Q,,). 
