64 STATIC ELECTRICITY 



remote sides of the two balls, so that the distance is rcalh 



than 8i. 



Let us now take into account the true distance I mm 

 centre, i.e. the chords instead of the arcs, and aK> tl,< true x 

 of the arm at which the force on the ball acts. L- 

 AOB = a, the angle between a and b. Ixit be the t< 

 M the couple due to it. Let F be the force on b due to a. 

 let ON be perpendicular to AB. 



Then F.<)N = M 



F.ON 



and 6 = - 



But 



ON-OA< 



and assuming the invn>e Mjuare law, 



P ' 





1 



in. \ 



Then to verify the law we ought to find that 



6* 



Cl.s '' 



Or that tan | sin | is constant. The values of this product for 

 the experiments we have <li^tu^-(d .m the following: 



a 



36 

 18 



36 

 144 



".75 J 



0Un|- 



S-()l."> 

 3-568 



:3 1 



The numbers in the third column are fairly near together. 



The torsion balance may be used also for the case in which the 

 charges on a and b are opposite in sign, though the experin 

 is not so easy when the repulsion is replaced by attraction. 

 within a certain distance equilibrium is unstable, a small di^- 



