THE FORCE ON A SMALL CHARGED BODY 63 



lixed at the top of the tube through which the suspending wire 

 passes. The position of the torsion rod is read by means of a scale 

 running round the side of the glass case containing it. A ball a is 

 at the end of a thin vertical shellac- 

 rod which can be passed through a 

 hole in the top of the case and fixed 

 so that the ball is in the horizontal 

 plane containing the torsion rod and 

 at the same distance from the centre 

 a^ the ball b. The method of using 

 the balance will be understood from 

 the following account of one of 

 Coulomb's experiments. 



Both a and 6 being without 

 charge, the torsion head was turned 

 no that b was just touching a when 

 the wire was free from twist. A 

 charge was then imparted to a ; it 

 was at once shared with />, which \\a^ 

 then repelled through 36, so that the 

 torsion on the wire was 36. The 

 torsion head was then moved round 

 till the angle between <i and h \\.-IN 

 18, this requiring a motion at the 

 head of 126. The torsion of tin 



e was not, however, increased to 



126 + 36, as thelouer end had turned 



in the same direction a> the upper 



igh 1S ? . The total torsion was 



fore only 126 + 18 = 144. 



Tlu- head \UIN then turned round until the angle between a and /; 

 was 8J; the additional turn of the torsion head was 441, giving 

 a total torsion of 441 4- 126 + 8 = 575. 



Assuming as a first approximation that up to 36 the repulsive 

 force acts always at the same arm and that the distance between 

 a and b is proportional to the angle between them, then, if the 

 first observation is correct at a distance 36, 

 the force is proportional to the torsion due 



to 36. 



According to the invi-r-e -<juare law, the 

 tor-ion at 18 should be 36 X 4 = 144, 



Fio. 60. 



and at 8* it should be 36 X = 645. 



The last result gives a torsion very 

 considerably in excess of that actually 

 observed, viz. 575 J. At such a small 

 distance as 8J the charges affect each 

 other and, Ix-ing like in sign, collect on the 



