294 Prof. Anderson, On Apparent Electrification, etc. [Apr. 26, 



Hence, JBT, -y— 1 + K 2 -— - + ^ir<r x = 0, 



dn^ dn 2 



and -^— ^ + -y-= — 47rcr = 0. 



awj dn 2 



To remove the apparent electrification is, then, equivalent to 

 finding the actual surface density <r x of a distribution of electricity 

 on the bounding surface of two media of specific inductive 

 capacities K-^ and K 2 which would produce an apparent surface 

 density — <r , there being no other electricit}' in the field. This 

 problem admits, in many cases, of an easy solution. 



As an example, consider the case of a charge e at the centre 



of a sphere whose radius is a and specific inductive capacity K x , 



the medium outside the sphere being of specific inductive capacity 



K 2 . 



e e ( 1 1 \ 

 Inside the sphere the potential is -^ — ^~\w~~&')> an( ^ 



K x r a \K 2 KJ 



e 

 outside it is -™— . The surface density, a, of the apparent 



electrification is, consequently, -r — - (-=- — -==■ 



To find the real electrification which will remove all apparent 

 electrification, we must find the distribution a x on the sphere which, 

 of itself, would produce an apparent distribution of surface density 



— - — - hr-17 • This is easily shewn to be — -. — - ( 1 — -^ ] , 

 4*7ra 2 \K 2 KJ J 4ura 2 \ KJ 



and is, therefore, not equal to — a unless when K 2 =l. When 



this surface distribution is placed on the sphere, the potential 



both inside and outside is ^- , and the force is consequently the 



same on both sides of the surface, as it ought to be when there is 

 no apparent electrification. 



Suppose, on the other hand, we bring the surface to zero 

 potential by means of a flame. The potential at all points outside 



will be zero, and the potential inside ■==- ( j . The surface 



density of the actual electrification of the surface is, therefore, 



— 7 — - , which is not — a and not opposite to a unless when 

 Ki> K 2 . Besides, there is still an apparent electrification of 



Q 



surface density — - — r^-. 

 J 47ra 2 iT 1 



