1886.] the revolution of Limagons and Cardioids about their axes. 5 
potential is V,+ Ax+ Bpsin @; for denoting the portions of the 
resulting potential due to each of these three terms bye V6 Ven Vix; 
we obtain 
ie selena ( "(n nie aa Pay (eee. (7), 
a See —)* (2n+1)n (n+) Fey P, () P(H)--(8) 
pee ORY 5. (—)" (2n +1) oe hy POP, (u) ...(9). 
6. The attraction of the solid can most readily be found from 
the fact, that the component parallel to any axis (say x) is the 
potential of a surface distribution of matter of density ol, where / 
is the x-direction cosine of the normal, and o the volume- -density 
of the solid which is supposed to be uniform throughout its mass. 
Hence if X, X’ be the values of the z-components at an external 
and an internal point respectively, the surface conditions are 
X — X’=0, 
AG OG 
aia a = Amol eislevelts) alate aisle latetalatetsyevalatcrate (10), 
where dn is an element of the normal drawn outwards. 
dv 
Now a rT 
Lae 
2 Ae.’ 
COD) aX _ Acp CMG aXe ) 
dn dn Pr as Gy 
= - 2A,P, (y) @, %) P, ). 
Then if the accents denote differentiation (10) becomes 
- a =o — 2A, {Q, (1) P, (y) — Pa) @, MEP, 
C y 
= ras 2 Es <a A IP ( J) 
, (y 1) nu () 
