354 Note i : on the theory of the electric jiuid 



conductors. Suppose that there is a deficiency of five units of electricity for 

 each square centimetre of the surface on both sides of a sheet of gold leaf whose 

 thickness is the hundred thousandth part of a centimetre. We have no reason 

 to believe the gold leaf to be entirely deprived of electricity, but even if it were, 

 we must admit that every cubic centimetre of gold requires more than a million 

 units of electricity to saturate it. 



But we have by no means reached the limit of our experimental evidence. 

 For Cavendish shows in Art. 49 that if in any portion of a bent canal the re- 

 pulsion of overcharged bodies is so great as to drive all the fluid out of that 

 portion, then the canal will no longer allow the fluid to run freely from one end 

 to the other, any more than a siphon will equalize the pressure of water in two 

 vessels, when the water does not rise to the bend of the siphon. 



Hence if we could make the canal narrow 'enough, and the electric repulsion 

 of bodies near the bend of the canal strong enough, we might have two con- 

 ductors connected by a conducting canal but not reduced to the same potential, 

 and this might be tested by afterwards connecting them by means of a con- 

 ductor which does not pass close to any overcharged body, for this conductor 

 will immediately reduce the two bodies to the same potential. 



Such an experiment, if successful, would determine at once which kind of 

 electricity ought to be reckoned positive, for, as Cavendish remarks in Art. 50, 

 the presence of an undercharged body near the bend of the canal would not 

 prevent the flow of electricity. 



But even if the electric fluid were not all driven out of the canal, but only 

 out of a stratum near the surface, the effective conducting channel would thereby 

 be narrowed, and the resistance of the canal to an electric current increased. 



Now we may construct the canal of a strip of the thinnest gold leaf, and we 

 may measure its electric resistance to within one part in ten thousand, so that 

 if the presence of an overcharged body near the gold leaf were to drive the 

 electric fluid out of a stratum of it amounting to the ten thousandth part of 

 its thickness, the alteration might be detected. Hence we must admit either 

 that the one-fluid theory is wrong, or that every cubic centimetre of gold con- 

 tains more than ten thousand million units of electricity. 



The statement which Cavendish gives of the action between portions of 

 the electric fluid and between the electric fluid and ordinary matter is nearly, 

 but not quite, as general as it can be made. 



Since the mode in which the force varies with the distance is the same in 

 all cases, we may suppose the distance unity. Two equal portions of the electric 

 fluid which at this distance repel, each other with a force unity are defined to 

 be each one unit of electricity. 



Let the attraction between a unit of the electric fluid and a gramme of 

 matter be a. Since we may suppose this force different for different kinds of 

 matter, we shall distinguish the attraction due to different kinds of matter by 

 different suffixes, as a 1 and 2 . Let the repulsion between two grammes of 

 matter entirely deprived of electricity be r n , these two portions of matter 

 being of the kinds corresponding to the suffixes i and 2. 



