10 Mr Basset, On the Potentials of the surfaces formed by [Oct. 25, 
In (12) put sinh ¢ =z, then 
Fa —— en Vitz dz 
oy +2 
=i [ io cos AO. dOdz 
a ea ae 
_ [> cos rnd. dO 
Wie Ako G 
= { cos (A7 sinh y) dy. 
0 
10. The same result may also be arrived at by employing 
Neumann’s transformation of Laplace’s equation. For if we put 
_ fery 
ce Cc ? 
then a we 008 5, naa/Esin8, 
and the curves & and 7 are a family of confocal parabolas. Also 
Ge» foX\e Il 
2 el SeELD i 
ar a - (je) Acr’ 
hence Neumann's transformation can be employed and Laplace’s 
equation becomes, 
Ete eS i Cac 
EdE\ dE] " qdn\" dy] \E° a) de® 
Putting as usual V = Usin (m0 +), it follows that U can be 
expressed in a series of products of the form XY, where X is a 
function of & only, which satisfies the equation, 
Gran xe DG m 
de + € dé P i 
and Y is a function of 7 only, which satisfies the equation, 
GRE IL GNY m 
Le ye ge ere. 18). 
dn? * dx? “fi n° iu) 
If the equation of the surface of the conductor is y=1, the 
