38 ELEMENTARY LESSONS ON [CHAP. i. 



(c) Two Spheres in contact. If two spheres in 

 contact with each other are insulated and charged, it is 

 found that the density is greatest at the parts farthest 

 from the point of contact, and least in the crevice 

 between them. If the spheres are of unequal sizes 

 the density is greater on the smaller sphere, which has 

 the surface more curved. On an egg-shaped or pear- 

 shaped conductor the density is greatest at the small 

 end. On a cone the density is greatest at the apex ; 

 and if the cone terminate in a sharp point the density 

 there is very much greater than at any other point. At 

 a point, indeed, the density of the collected electricity 

 may be so great as to electrify the neighbouring particles 

 of air, which then are repelled, thus producing a con- 

 tinual loss of charge. For this reason points and sharp 

 edges are always avoided on electrical apparatus, except 

 where it is specially desired to set up a discharge. 



(d) Flat Disc. The density of a charge upon a 

 flat disc is greater, as we should expect, at the edges 

 than on the flat surfaces ; but over the flat surfaces the 

 distribution is fairly uniform. 



These various facts are ascertained by applying a 

 small proof-plane successively at various points of the 

 electrified bodies and examining the amount taken up by 

 the proof-plane by means of an electroscope or electro- 

 meter. Coulomb, who investigated mathematically as 

 well as experimentally many of the important cases of 

 distribution, employed the torsion balance to verify his 

 calculations. He investigated thus the case of the 

 ellipsoid of revolution, and found the densities of the 

 charges at the extremities of the axis to be proportional 

 to the lengths of those axes. He also showed that the 

 density of the charge at any other point of the surface of 

 the ellipsoid was proportional to the length of the per- 

 pendicular drawn from the centre to the tangent at that 

 point. Riess also investigated several interesting cases 

 of distribution. He found the density at the middle of 



