Page:On Faraday's Lines of Force.pdf/4

158 methods of Faraday, the connexion of the very different orders of phenomena which he has discovered may be clearly placed before the mathematical mind. I shall therefore avoid as much as I can the introduction of anything which does not serve as a direct illustration of Faraday’s methods, or of the mathematical deductions which may be made from them. In treating the simpler parts of the subject I shall use Faraday’s mathematical methods as well as his ideas. When the complexity of the subject requires it, I shall use analytical notation, still conﬁning myself to the development of ideas originated by the same philosopher.

I have in the ﬁrst place to explain and illustrate the idea of “lines of force."

When a body is electriﬁed in any manner, a small body charged with positive electricity, and placed in any given position, will experience a force urging it in a certain direction. If the small body be now negatively electriﬁed, it will be urged by an equal force in a direction exactly opposite.

The same relations held between a magnetic body and the north or south poles of a small magnet. If the north pole is urged in one direction, the south pole is urged in the opposite direction.

In this way we might ﬁnd a line passing through any point of space, such that it represents the direction of the force acting on a positively electriﬁed particle, or on an elementary north pole, and the reverse direction of the force on a negatively electriﬁed particle or an elementary south pole. Since at every point of space such a direction may be found, if we commence at any point and draw a line so that, as we go along it, its direction at any point shall always coincide with that of the resultant force at that point, this curve will indicate the direction of that force for every point through which it passes, and might be called on that account a line of force. We might in the same way draw other lines of force, till we had ﬁlled all space with curves indicating by their direction that of the force at any assigned point.

We should thus obtain a geometrical model of the physical phenomena, which would tell us the direction of the force, but we should still require some method of indicating the intensity of the force at any point. If we consider these curves not as mere lines, but as ﬁne tubes of variable section carrying an incompressible ﬂuid, then, since the velocity of the ﬂuid is inversely as the section of the tube, we may make the velocity vary according to any given law, by regulating the section of the tube, and in this way we might represent the