287-291] 



Confocal Coordinates 



245 



289. Lord Kelvin* quotes some interesting experiments by Coulomb on the density 

 at different points on a circular plate of radius 5 inches. The results are given in the 

 following table : 



Much more remarkable is Cavendish's experimental determination of the capacity of a 



circular disc. Cavendish found this to be times that of a sphere of equal radius, 



1 "57 



while theory shews the true value of the denominator to be or 1*5708 ! 



290. By inverting the distribution of electricity on a circular disc, taking 

 the origin of inversion to be a point in the plane, of the disc, Kelvin f has 

 obtained the distribution of electricity on a disc influenced by a point charge 

 in its plane, a problem previously solved by another method by Green. The 

 general Green's function for a circular disc has been obtained by HobsonJ. 



Spherical Bowl. 



291. Lord Kelvin has also, by inversion, obtained the solution for a 

 spherical bowl of any angle freely electrified. Let the bowl be a piece of a 

 sphere of diameter /. Let the distance from the 

 middle point of the bowl to any point of the bowl 

 be r, and let the greatest value of r, i.e. the dis- 

 tance from a point on the edge to the middle point 

 of the bowl, be a. Then Kelvin finds for the elec- 

 tric densities inside and outside the bowl : 



F 



27T 2 / 



FIG. 80. 



Some numerical results calculated from these formulae are of interest. The six values 

 in the following tables refer to the middle point and the five points dividing the arc from 

 the middle point to the edge into six equal parts. 



* Papers on Elect, and Mag. p. 179. 

 t Papers on Elect, and Mag. p. 183. 

 Trans. Caml. Phil. Soc. xvm. p. 277. 



