THE FORCE OiN A SMALL CHARGED BODY 65 



placement making a greater change in the attraction than in the 

 torsion. 



Coulomb also tested the inverse square law by a method which 

 possesses interest since it corresponds to the vibrating-needle 

 method which he employed in his magnetic experiments. An 

 insulating shellac needle was suspended horizontally by a cocoon 

 fibre, a small charged disc being fixed at one end of it. It was 

 placed in the field of an insulated globe charged in the opposite 

 way, and the time of oscillation was observed to vary directly as 

 the distance from the centre of the globe, the result which we 

 should expect, assuming the inverse square law. 



Coulomb showed in the following manner that the force on a 

 given charged body is proportional to the charge acting. Sup- 

 posing a and 6 in the torsion balance to be exactly equal spheres, 

 on contact they will be equally charged and the torsion rod will be 

 repelled through a certain angle. If a is now withdrawn and its 

 charge shared with a third equal sphere, only half the charge 

 remains on it. Replacing it in the balance, it is found that 

 only half the torsion is needed to keep the ball b at its original 



ince from a. Hence it follows that if two small bodies a 

 distance d apart contain charges Q and Q' the force on either is 

 proportional to QQ'/^ 1 ' 



Two other researches of historical intm ->t made by Coulomb 

 may be here referred to that on the distribution of electrification 

 on conductors of various forms by means of the proof plane which 

 he invented for the purpose, and that on the rate of loss of 

 charge and on the best methods of insulation. He showed that 

 with a givi-n conductor insulated in a given way the rate of loss 

 was proportional to the total charge, though the rate varied on 

 different days, being, in accordance with common experience, more 

 considerable on damp than on dry days. Coulomb ascribed the 

 loss partly to the air and partly to the supports, supposing that 

 the air was a conductor when containing much water-vapour. We 

 know that his supposition as to water- vapour was a mistake 

 for it, like air, is an excellent insulator. It is true that if air is 

 nearly saturated with water-vapour the rate of loss of charge is 

 icntly great, but this is almost certainly due to the condensa- 

 tion of a thin layer of water on the surface of the supports, which 

 latter may be hygroscopic and may so condense the vapour into 

 water before normal saturation is reached. We now know that 

 neither dry air nor water-vapour is a perfect insulator, for there 

 is a loss of charge due to the presence of electrified "ions" in 

 the air, and the electrified surface draws to itself the ions with 

 opposite charges. But this loss is exceedingly slow under ordinary 

 condition-. 



inverse square law may be illustrated by the following 

 expeiim Two metre rules are fixed horizontally, one over the 



other (Fig. 58). A conducting sphere A is mounted on a pillar, 



