On some Electrical Experiments and Inductions. 193 



the surface is greater, the ratio being the inverse square of the 

 radii. 



Suppose 100 radial lines like a b to be drawn equidistant, and 

 let c represent an extremely thin disk of metal perpendicular to 

 one of the radii. We know that on the inner side of c negative 

 electricity appears, and on the outer positive. These are shown 

 by the arrow-heads, or rather what are more correctly to be taken 

 as V marks. Thus c towards b presents a positive entrant or 

 male aspect, and c towards a presents a negative recipient or 

 female aspect. Upon each of the 100 radial lines we may ima- 

 gine an infinite number of such disks without any disturbance of 

 the electricity between the concentric spherical surfaces ; and if 

 each is marked like c with the symbol of the electricity that is 

 developed on each side, we shall have each of the 100 lines re- 

 presented thus >»[>[» , which exhibits the nature of the static 

 polarizing power that exists in the space between a and b. The 

 intensity of this force depends on the distance between the lines, 

 diminishing as the distance increases. To obtain a clear idea of 

 this, we may suppose another disk d similar to c and close to it. 

 We may also imagine these disks to be extended all round so as 

 to become spherical surfaces C, D concentric with A. The electric 

 equilibrium will not be disturbed. We have next to suppose the 

 electricity or electric lines between A and C to be discharged, also 

 those between D and B. We shall then have remaining the electri- 

 city between C and D. Let the radius of A be considered as unity, 

 and that of C be denoted by r ; we may then represent cd by dr. 

 Let D be supposed immoveable, and C moveable and expansible. 

 The force that attracts C to D is uniform through the element of 

 space dr, and is proportional directly to the spherical surface C, 

 that is to r 2 , the spherical surface of A being unity, and inversely 



as the square of the density of electricity upon C, that is to -%, 



the density upon A being considered unity. Hence the static force 



r 2 1 

 of C towards D is thus -^ = — [supposing the static force of A, 



when as originally charged towards an exterior concentric sphe- 

 rical surface at distance dr (the electricity being supposed engaged 

 between the two as in the case of C and D), to be unity], and the 



space through which this static force ~2 acts being dr, the differen- 

 tial of the work performed by the surface C in expanding to D by 



dr 

 the influence of the electric force is -%, the integral of which is 



1 . This gives us the value of the work performed by the 



spherical surface A expanding to infinity under the influence of the 



