COULOMB'S BALANCE. 171 



is in its place, the two knobs are kept in contact by the slight torsion 

 which results from the displacement of the movable one. If the 

 system is electrified, the two balls divide the charge of electricity ; 

 they repel each other, and by a suitable torsion A of the micrometer 

 they are brought back to an angular distance a, such that the torsion 

 is A + a, and the moment of the couple which tends to bring the 

 needle to its position of equilibrium is C(A + a) (700). 



If / is the distance from the axis to the centre of the movable 

 ball, and f the repulsion between the two balls, the moment of this 



force in respect of the axis is equal to fl cos - . The equation of 

 equilibrium is therefore 



(i) //cos^ = C(A + a), 



which gives 



C A + a 



f ~7~~a' 

 cos - 



2 



In the most general case, in which the two balls are at different 

 distances / and /' from the axis, if d be the distance of the centres 

 of the balls, h the perpendicular let fall from the axis on the 

 direction of d, we have 



hd=ll' sin a. 



The moment of the force/ being /A, the equation of equilibrium 

 becomes 



The distance, moreover, is ^iven by the equation 



We must thus consider the force f to be determined as a function 

 of the dimensions of the apparatus, of the observed angles, and of 

 the coefficient of torsion, which will be measured by the ordinary 

 methods (707). 



/( 801. MEASUREMENTS OF MASSES OR OF POTENTIALS. Let m 

 and m' be the charges of the two balls, expressed in electrostatic 

 units. If the electricity were distributed uniformly on each of them, 



