15, 16] The Fundamental Conceptions of Electrostatics 13 



square of the distance. And when the charges on the two balls are varied 

 it is found that the force varies as the product of the two charges, so long as 

 their distance apart remains the same. As the result of a series of experi- 

 ments conducted in this way Coulomb was able to enunciate the law : 



The force between two small charged bodies is proportional to the product 

 of their charges, and is inversely proportional to the square of their distance 

 apart, the force being one of repulsion or attraction according as the two 

 charges are of the same or of opposite kinds. 



16. In mathematical language we may say that there is a force of repul- 

 sion of amount 



a) 



where e, e are the charges, r their distance apart, and c is a positive 

 constant. 



If e, e are of opposite signs the product ee' is negative, and a negative 

 repulsion must be interpreted as an attraction. 



Although this law was first published by Coulomb, it subsequently 

 appeared that it had been discovered at an earlier date by Cavendish. 

 whose experiments were much more refined than those of Coulomb. Caven- 

 dish was able to satisfy himself that the law was certainly intermediate 

 between the inverse 2 + ^ and 2 J^th power of the distance. Unfor- 

 tunately his researches remained unknown until his manuscripts were 

 published in 1879 by Clerk Maxwell. 



The experiments of Coulomb and Cavendish, it need hardly be said, 

 were very rough compared with those which are rendered possible by modern 

 refinements of theory and practice, so that these experiments are no longer 

 the justification for using the law expressed by formula (1) as the basis of 

 the Mathematical Theory of Electricity. More delicate experiments with the 

 apparatus used by Cavendish, which will be explained later, have, however, 

 been found to give a complete confirmation of Coulomb's Law, so long as 

 the charged bodies may both be regarded as infinitely small compared with 

 their distance apart. Any deviation from the law of Coulomb must accord- 

 ingly be attributed to the finite sizes of the bodies which carry the charges. 

 As it is only in the case of infinitely small bodies that the symbol r of 

 formula (1) has had any meaning assigned to it, we may regard the law (1) 

 as absolutely true, at any rate so long as r is large enough to be a measurable 

 quantity. 



