Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/115

74.] the probable error of an experiment with the torsion-balance is considerable. As an argument that the attraction is really, and not merely as a rough approximation, inversely as the square of the distance, Experiment VII (p. 34) is far more conclusive than any measurements of electrical forces can be.

In that experiment a conductor $$B$$, charged in any manner, was enclosed in a hollow conducting vessel $$C$$, which completely surrounded it. $$C$$ was also electrified in any manner.

$$B$$ was then placed in electric communication with $$C$$, and was then again insulated and removed from $$C$$ without touching it, and examined by means of an electroscope. In this way it was shewn that a conductor, if made to touch the inside of a conducting vessel which completely encloses it, becomes completely discharged, so that no trace of electrification can be discovered by the most delicate electrometer, however strongly the conductor or the vessel has been previously electrified.

The methods of detecting the electrification of a body are so delicate that a millionth part of the original electrification of $$B$$ could be observed if it existed. No experiments involving the direct measurement of forces can be brought to such a degree of accuracy.

It follows from this experiment that a non-electrified body in the inside of a hollow conductor is at the same potential as the hollow conductor, in whatever way that conductor is charged. For if it were not at the same potential, then, if it were put in electric connexion with the vessel, either by touching it or by means of a wire, electricity would pass from the one body to the other, and the conductor, when removed from the vessel, would be found to be electrified positively or negatively, which, as we have already stated, is not the case.

Hence the whole space inside a hollow conductor is at the same potential as the conductor if no electrified body is placed within it. If the law of the inverse square is true, this will be the case what ever be the form of the hollow conductor. Our object at present, however, is to ascertain from this fact the form of the law of attraction.

For this purpose let us suppose the hollow conductor to be a thin spherical shell. Since everything is symmetrical about its centre, the shell will be uniformly electrified at every point, and we have to enquire what must be the law of attraction of a uniform spherical shell, so as to fulfil the condition that the potential at every point within it shall be the same.