68 Prof, Thomson <m the Mathematical Theory of 



the dielectric is solid, it would require, to produce a given 

 potential in the interior of A, k times the charge which would 

 be necessary to produce the same potential when the dielectric 

 is gaseous, and therefore the body A in a given state, defined by 

 the potential in its interior, produces on the interior surface of 

 B, by induction, through the solid dielectric, a quantity of elec- 

 tricity k times as great as through a gaseous dielectric. On this 

 account Faraday calls the property of a dielectric measured by 

 k, its " specific inductive capacity/' 



In Farada/s experiments an apparatus (which is in fact a 

 Leyden phial, in which any solid or fluid may be substituted for 

 the glass dielectric of an ordinary Leyden phial) is used, corre- 

 sponding to the case we have been considering, in which A is a 

 conducting sphere (2*33 inches in diameter), and B a concentric 

 spherical shell surrounding it (the distance between the surfaces 

 of A and B being -62 of an inch). In the shell B there is an 

 aperture into which a shell-lac stem is fixed ; a wire, attached to 

 A, passes through the centre of this stem to the outside of the 

 shell, and supports a ball of metal, M, which is thus insulated 

 and connected with A. It may be shown that in such an appa- 

 ratus the state of the ball A and of the shell B will approxi- 

 mately be not affected by the aperture in the latter, or by the 

 wire supporting M, and that the distribution of electricity on M 

 will be approximately the same as if the wire supporting it and 

 the conductors A and B were removed. Hence the sole relation 

 between A and M will be that the potentials in their interiors are 

 the same ; and therefore the latter, which is accessible, may be 

 taken as an index of the state of the former. 



To determine the specific inductive capacity of any dielectric, 

 Faraday uses two apparatus of the kind just described, precisely 

 equal and similar, in one of which the space between A and B is 

 filled with air, and in the other with the dielectric to be exa- 

 mined. One of these apparatus is charged, and the intensity 

 measured : the balls M, M' in the two are then made to touch 

 and separated again, and the remaining intensity on the first 

 (which is equal to the intensity imparted to the second) is 

 measured. If this be found to differ from half the original 

 intensity, it will follow that the specific inductive capacity of the 

 substance examined differs from that of air, which is unity, and 

 its value may be determined by means of a simple expression 

 from the experimental data. To investigate this, let us fii-st 

 suppose each apparatus to be charged, and let it be required to 

 find the intensity on the balls after they are made to touch, and 

 then removed from mutual influence ; and let the dielectrics be 

 any two substances, whose inductive capacities are k, k'. Let 

 p, p' be the intensities before, and a the common intensity after 



