4 Mr Basset, On the Potentials of the surfaces formed by [Oct. 25, 
the form =BP.,”(z) sin (m@+ 8), where m must be always less 
than n. 
é dn\* =) i 
4. Putting (2) se C de =J 
we easily obtain by means of (3), 
E26 
Tre 
r° (vy? —1)2 
where p is the length of the perpendicular from the origin on to 
the tangent plane to the surface. Also 
_ 16c*(1 + pv) 
(w+) 
_16¢ J1— a me 
(m+ )° 
The expansion of 7 in terms of harmonics is given in Ferrers’ 
Spherical Harmonics, Ch. v., viz. 
? 
T—Ac>, (=) (en -e WO. PE, (i) ee (4). 
To obtain the expansion of r and rp, we have 
kD wl oie v 
162 (w+ v)® € (w+v) 
=3) (n+) Pwo) Ga» Sl 
=—$>) ©’ Gr +1) 2@1) 0, P, @).-...e (5). 
2 2 = dQ, dP, 
=3J1—p? J - 132 (-)* (Qn +1) Gy du 
= 555 (=)) (On + 1) Q 2G IPE te: ee (6). 
5. We can now obtain the potential of the induced charge, 
when the surface is placed in a field of electric force, whose 
