148 



PARTICULAR CASES OF EQUILIBRIUM. 



Near the pole A, on the outside, the force is 



it is equal to < for //, = 2, and becomes 3 </> when ft is very great. 



This force, therefore, is then thrice its primitive value; this is the 

 case with conductors. 



In the present case the external lines of force are no longer per- 

 pendicular to the surface. It could be easily shown that the tangen- 

 tial components are equal, and that the ratio of the angles 6 and <o 

 (Fig. 43) of the perpendicular to the lines of force on the outside and 

 inside satisfies the law of refraction. 



tan o> 



For the equator, where co = , this equation also gives 6 = 



The lines of force which touch the sphere on the equator are then 

 tangents to the surface. 



Fig. 44. 



164. CONCENTRIC SPHERICAL LAYERS IN A UNIFORM FIELD. 

 It is easy to generalise the preceding problem, and to apply it to a 

 series of concentric spherical layers. In a uniform field of strength 



4> let there be a system of concentric spheres S 15 S 2 , S 3 (Fig. 44) 



having the radii a lt a 2t a z . . . , and the specific inductive capacities 



