248 ELECTROSTATICS. [PT. II. CH. VI. 



129. Mathematical Conclusions. Law of Force. We 



have used the words electrification, electricity, and charge to 

 denote a measurable quantity, which possesses the property of 

 conservation, that is of remaining unchanged in amount. For if 

 electricity disappears, it is by the disappearance of two equal 

 quantities of opposite sign, whose algebraic sum was zero. We 

 need define these terms no further than by their properties, and 

 for the present, the single property of exerting force is sufficient. 

 We may speak of electrification occupying definite portions of 

 space, for the field of force is such that lines of force issue from 

 positive electrifications and run into negative electrifications. 

 Electrifications being always examined by examining their fields 

 of force, we may consider the field of force as specifying the 

 electrification. Certain writers have gone farther, and insisted 

 that electricity does not exist, but that lines of force and electrical 

 energy are the only real entities. Such a question is purely 

 metaphysical, and of no importance to the physicist. It is 

 obviously of no importance whether we define electricity as that 

 which exists where lines of force converge, or say that the 

 electricity exerts force upon other electrifications. If we wish to 

 use the term "electrical fluid" or "matter" we may do so, provided 

 we use "fluid" or "matter" simply as convenient terms, without 

 attributing to electricity any of the properties of ordinary fluids or 

 of matter. It has, so far as we know, no inertia, the fundamental 

 property of matter, nor is it incompressible. We may then define 

 a charge of electricity as a "something," "fluid," or "matter," which 

 possesses the unique property of repelling or attracting other 

 charges of electricity, according to the signs of the two charges. 

 By definition the force is proportional to the charge, and it is 

 natural to suppose that the force between two electrified elements 

 will be in the line joining them, and proportional to some function 

 of the distance. Experiment VIII shows that the force depends 

 on something beside the distance, but if we suppose all space to be 

 filled with the same dielectric medium, such as air, the assumption 

 is justified by experiment. This supposition will accordingly be 

 made for the present. We shall also suppose all conductors to be 

 made of a single material. 



We shall now deduce the law of the force from the result of 

 Experiment VII, that there is no force within a hollow conductor. 

 Let the conductor be in the form of a sphere. On account of 



