Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/106

 CHAPTER II.

ELEMENTARY MATHEMATICAL THEORY OF STATICAL ELECTRICITY.

Definition of Electricity as a Mathematical Quantity.

63.] We have seen that the actions of electrified bodies are such that the electrification of one body may be equal to that of another, or to the sum of the electrifications of two bodies, and that when two bodies are equally and oppositely electrified they have no electrical effect on external bodies when placed together within a closed insulated conducting vessel. We may express all these results in a concise and consistent manner by describing an electrified body as charged with a certain quantity of electricity, which we may denote by $$e$$. When the electrification is positive, that is, according to the usual convention, vitreous, $$e$$ will be a positive quantity. When the electrification is negative or resinous, $$e$$ will be negative, and the quantity $$e$$ may be interpreted either as a negative quantity of vitreous electricity or as a positive quantity of resinous electricity.

The effect of adding together two equal and opposite charges of electricity, $$+e$$ and $$-e$$, is to produce a state of no electrification expressed by zero. We may therefore regard a body not electrified as virtually charged with equal and opposite charges of indefinite magnitude, and an electrified body as virtually charged with unequal quantities of positive and negative electricity, the algebraic sum of these charges constituting the observed electrification. It is manifest, however, that this way of regarding an electrified body is entirely artificial, and may be compared to the conception of the velocity of a body as compounded of two or more different velocities, no one of which is the actual velocity of the body. When we speak therefore of a body being charged with a quantity $$e$$ of electricity we mean simply that the body is electrified, and that the electrification is vitreous or resinous according as $$e$$ is positive or negative.