194 Mr. J. J. Waterston on some Electrical 



electricity with which it is charged. This value is expressed by 

 unity, which means the static force at A acting through the 

 radius of A. 



53. Compare the charge on A with a charge of equal density 

 on another sphere Z with twice the radius of A. The quantity 

 of electricity on Z must be four times that on A to have equal 

 density with it ; and the density being equal, but the surface of 

 Z four times that of A, the static force on Z is four times the 

 static force on A ; and as the integral is that force acting through 

 the radius of the respective spheres, it comes to pass that the 

 integral of the charge on Z is eight times the integral of the 

 charge on A ; and the quantity of electricity on a square inch of 

 the surface of Z, although equal to the quantity on a square 

 inch of A, has twice its mechanical equivalent. 



This may seem somewhat of a paradox ; but a little considera- 

 tion as to the rate of divergence of the electric lines will make it 

 clear. Thus let c d (fig. 26) represent the space occupied by an 

 electric line or root on the surface of the sphere A, and ef the 

 same on the surface of Z, b being their common centre. Now, 

 the density being the same, cd=ef=oi, and cf> is the static force 

 common to both. These lines on proceeding outwards diverge, 

 so that if cd or a becomes up in B distance out from the surface 

 of A, efov a becomes up in 28 distance out from surface of Z. 

 The statice force of both being (£, we have <fi8 the first dynamic 

 increment of a line issuing from surface of A, and 2<f>8 the first 

 dynamic increment of a line issuing from the surface of Z. All 

 the successive increments have the same ratio, therefore the inte- 

 grals have also this ratio. 



54. Thus we see by clear induction from the elementary laws 

 established by the experiments of Cavendish and Harris, that an 

 electrically excited surface contains only the roots of lines of 

 force, in which lines the mechanical power of the electricity 

 resides. Work is, as it were, stored up in these lines, and the 

 static intensity at a point in one of them depends on the close- 

 ness of the neighbouring lines at that point only. The closer 

 they are packed the more intense the longitudinal force, and the 

 more intense the lateral force of repulsion. Indeed these forces, 

 as they increase and diminish together, seem to be identical, or 

 a mode of reaction. The repulsive tension exists in the plane 

 m n (fig. 27) transverse to the electric line Ip I in which the con- 

 tractile tension is manifested. 



When two bodies charged with the same electricity are brought 

 closer together, the lines become more closely packed. Mecha- 

 nical power, or work, requires to be expended in order to force the 

 bodies closer together, i. e. to force the electric lines closer 

 together. The lateral repulsion of the lines has to be overcome, 



