1 66 PARTICULAR CASES OF EQUILIBRIUM. 



of one of the spheres, and the charges are equal, the approximate 

 formulae give the potentials as a function of the masses, the value 

 of the force as a function of the masses, and the force as a 

 function of potentials with a degree of approximation which is 



, and for the various forces respectively. As the relative 



300 16 17 j 



errors amount to , when <r=3'8, it will be seen that they will 



diminish very rapidly for greater distances. 



We may therefore, as a particular case, regard Coulomb's method 

 for determining the action of two electrified masses as perfectly 

 exact; and Coulomb's method will give with the approximate for- 

 mulae very exact results for the measurement of potentials, if we 

 take care that the distance of the surfaces of the spheres sensibly 

 exceeds the diameter of one of them. In determining potentials by 

 means of the balance, we ought always to take special precautions 

 for eliminating or for calculating the influence of the sides of the 

 cage. 



178. MOTION OF SMALL BODIES IN THE ELECTRICAL FIELD. 

 We have seen that (162) a dielectric sphere of radius #, placed in a 

 uniform field where the force is <, becomes electrified so that the 

 internal action of the equivalent layer is 



This coefficient h is equal to - for the dielectrics whose 



4 



specific inductive capacity is 2, and it is equal to unity for con- 

 ductors. 



From this we deduce (159) 



= u (f> = 



47T 



The coefficient K is equal to for conductors, and has a 



47T 



smaller value for dielectrics, since the factor h is always less than 

 unity. 



