14 Mr Basset, On the Potentials of the surfaces formed by [Oct. 25, 
13. Now when 2 is a small quantity, JZ,=1, J, = 5 approxi- 
mately; also 
K i cos bd@ | 
oe P, (a? + ¢°)?’ 
ae * xcos ddd 
Oa oe 
0 @+¢)? 
se) 
alo (1+ 62’ 
ie | 
when «=0. Also, 
eK, =a2k!+2K,’, 
mi raf SE gf oneae, 
0 @+ gy lo @teH 
neo [: cos 26d@ 3 cos 26 dé 
eK,’=-| ——,+3] m~-; 
o(1+e) Jo 1 +6) 
=) 
when «=0. Therefore 2°K,=0 whenz=0; . 
2 
5 Ky 2K =1, 2=0; 
C=1. 
Hctics a ac iret pose Eee (26). 
14. We shall now apply the preceding analysis to determine 
the potential of the induced charge, when a cardioid of revolution 
is placed in a field of force whose potential is 
V,+Ae+ Bp sin 0. 
If V, V,, V, be the respective portions of the resulting 
potential, we have shown that 
ve ( ‘ Fey en tes) ap od dh, 
where 7 =1 is the equation of the surface of the conductor. Hence 
at the surface 
[Foy Tag) dr=— 2" 
Jo 
