152] Examples 135 



must have the same direction and stand in a constant ratio to one another. 

 In this case we must have 



K 12 = K 2 i = = 0, 



In the more general equations (77), there are not nine, but only six, 

 independent constants, for, as we shall afterwards prove ( 176), we must 

 have 



K^ K ZI) K 23 = I S2 , K sl = K n 



REFERENCES. 



On Inductive Capacity : 



FARADAY. Experimental Researches. 1252 1306. 

 On Molecular Polarisation : 



FARADAY. I.e. 16671748. 

 On Experimental Determinations of K : 



WINKELMANN. Bandbuch der Physik (2te Auflage), 4, (1), pp. 92150. 



EXAMPLES. 



1. A spherical condenser, radii a, b, has air in the space between the spheres. The 

 inner sphere receives a coat of paint of uniform thickness t and of a material of which 

 the inductive capacity is K. Find the change produced in the capacity of the condenser. 



2. A conductor has a charge e, and F l5 F 2 are the potentials of two equipotential 

 surfaces completely surrounding it ( Vi > F 2 ). The space between these two surfaces is 

 now filled with a dielectric of inductive capacity K. Shew that the change in the 

 energy of the system is 



3. The surfaces of an air-condenser are concentric spheres. If half the space between 

 the spheres be filled with solid dielectric of specific inductive capacity K, the dividing 

 surface between the solid and the air being a plane through the centre of the spheres, 

 shew that the capacity will be the same as though the whole dielectric were of uniform 

 specific inductive capacity 



4. The radii of the inner and outer shells of two equal spherical condensers, remote 

 from each other and immersed in an infinite dielectric of inductive capacity K, are 

 respectively a and 6, and the inductive capacities of the dielectric inside the condensers 

 are K l9 K 2 . Both surfaces of the first condenser are insulated and charged, the second 

 being uncharged. The inner surface of the second condenser is now connected to earth, 

 and the outer surface is connected to the outer surface of the first condenser by a wire 

 of negligible capacity. Shew that the loss of energy is 



where Q is the quantity of electricity which flows along the wire 



