46 



Prof. Thomson on the Mathematical Theory of 



announced by Mr. Harris. He has, however, found that it is 

 expressed with tolerable accuracy by the formula 



c(c-2ay 



where c is the distance between the centres of the spheres, a the 

 radius of each, k a constant, which will depend on a and on the 

 charge of the battery with which A is in communication. 

 Though however this formula may give results which do not 

 differ very much from observation within a limited range of 

 distances, it cannot, according to any theory, be considered as 

 expressing the physical law of the phsenomenon. For, according 



to it, when the balls are very distant, F ultimately varies as -g. 



Now it is clear that the law of force must ultimately become 

 the inverse cube of the distance, since the quantity of electricity 

 induced upon B will be ultimately in the inverse ratio of the 

 distance, and the attraction between the balls as the product of 

 the quantities of electricity directly, and as the square of the 

 distance inversely, and hence the formula given by Mr. Harris 

 cannot express the law of force when the balls are very distant. 

 In the experiments by which his formula is tested, the force of 

 attraction is measured by means of an ordinary balance and 

 weights : the only comparison of results which he publishes is 

 transcribed in the following table. 



From this table we see that the formula is verified in three 

 cases to the extent of accuracy of the experiments. Comparisons 

 extended to a much wider range of distances would be required 

 to establish it, and it would be necessary to take precautions to 

 prevent the experimental results from being influenced by dis- 

 turbing causes. In the experiments made by Mr. Harris we 

 find that no precautions have been taken to avoid the disturbing 

 influence of extraneous conductors, which, according to the 

 descriptions and drawings he gives of his instruments, seem 

 to exist very abundantly in the neighbourhood of the bodies 

 operated upon, being partly metal in connexion with the insu- 

 lated system with which the body A communicates, and partly 

 uninsulated metal, in the fixed parts of the electrometer, and in 

 the moveable parts by which B is supported. The general effect 



