12 Mr Basset, On the Potentials of the surfaces formed by [Oct. 25, 
T 
as [ n Sinandndd 
G n° + cos’ d 
* sin end 
Or 0 (n 24.1) 
a4 a. sin ydy | 
TJo (a? +47)?” 
LF 2 (—)"2"T' (m + 4) jie sin ydy 
= j eae 
oa) e 
err ot + | ses 
(146) 
The value of K,, may be deduced in a ata manner from 
(15). 
Since the functions P,"(v) and Q,”(v), where v> 1, ultimately 
reduce to the functions J,, and K,, respectively; and the ae 
P(e), where p< 1 ultimately "reduces to the function J,,; 
follows that the potential at all points outside the ae 
7 =1 is of the form, 
F=Ssnieec) i Fa) 
0 
and at an internal point 
V’ = sin (md + @,,) I F(X) 1, (0) re Ag) dn, 
where F is a function whose value depends upon the nature of the 
problem considered. 
KO Tal) 
ng oe 
If we invert these results with respect to the focus, it follows 
that the potential at all points outside the surface bounded by the 
revolution of the cardioid 7 =1 is 
Lay OD), 
V="Ssin (mp + «,,) | F (x) 
r lhe 
and at an internal point, 
V =" Ssin (mp +24) [ ie 0) Aan) an 8) an...(22), 
where in this case, 
