applied to Statical Electricity. 23 



on each surface ; then the capacity 



°=¥^y • (138 > 



Within the dielectric we have the variation of M* perpendicular 

 to the surface 



- 



Beyond either surface this variation is zero. 



Hence by (115) applied at the surface, the electricity on unit 

 of area is 



\Er \fr 



±m-' < 139 > 



aud we deduce the whole capacity of the apparatus, 



C = 4» < 140 > 



so that the quantity of electricity required to bring the one sur- 

 face to a given tension varies directly as the surface, inversely as 

 the thickness, and inversely as the square of E. 



Now the coefficient of induction of dielectrics is deduced from 

 the capacity of induction-apparatus formed of them ; so that if 

 D is that coefficient, D varies inversely as E 2 , and is unity for 

 air. Hence 



D =vJ? < 141 > 



where V and Y 1 are the velocities of light in air and in the 



V 



medium. Now if i is the index of refraction, =f- =«, and 



D=Jj (142) 



r* 



so that the inductive power of a dielectric varies directly as the 

 square of the index of refraction, and inversely as the magnetic 

 inductive power. 



In dense media, however, the optical, electric, and magnetic 

 phenomena may be modified in different degrees by the particles 

 of gross matter ; and their mode of arrangement may influence 

 these phenomena differently in different directions. The axes 

 of optical, electric, and magnetic properties will probably coin- 

 cide ; but on account of the unknown and probably complicated 

 nature of the reactions of the heavy particles on the aitherial 

 medium, it may be impossible to discover any general numerical 

 relations between the optical, electric, and magnetic ratios of these 

 axes. 



It seems probable, however, that the value of E, for any given 



