Page:Philosophical magazine 21 series 4.djvu/315

applied to Electric Currents. 291 We have thus determined three quantities, F, G, H, from which we can find P, Q, and R, by considering these latter quantities as the rates at which the former ones vary. In the paper already referred to, I have given reasons for considering the quantities F, G, H as the resolved parts of that which Faraday has conjectured to exist, and has called the electrotonic state. In that paper I have stated the mathematical relations between this electrotonic state and the lines of magnetic force as expressed in equations (55), and also between the electrotonic state and electromotive force as expressed in equations (58). We must now endeavour to interpret them from a mechanical point of view in connexion with our hypothesis.

We shall in the first place examine the process by which the lines of force are produced by an electric current.

Let AB, Pl. V. fig. 2, represent a current of electricity in the direction from A to B. Let the large spaces above and below AB represent the vortices, and let the small circles separating the vortices represent the layers of particles placed between them, which in our hypothesis represent electricity.

Now let an electric current from left to right commence in AB. The row of vortices $$gh$$ above AB will be set in motion in the opposite direction to that of a watch. (We shall call this direction +, and that of a watch -.) We shall suppose the row of vortices $$kl$$ still at rest, then the layer of particles between these rows will be acted on by the row $$g h$$ on their lower sides, and will be at rest above. If they are free to move, they will rotate in the negative direction, and will at the same time move from right to left, or in the opposite direction from the current, and so form an induced electric current.

If this current is checked by the electrical resistance of the medium, the rotating particles will act upon the row of vortices $$kl$$, and make them revolve in the positive direction till they arrive at such a velocity that the motion of the particles is reduced to that of rotation, and the induced current disappears. If, now, the primary current $$A B$$ be stopped, the vortices in the row $$gh$$ will be checked, while those of the row $$kl$$ still continue in rapid motion. The momentum of the vortices beyond the layer of particles $$pq$$ will tend to move them from left to right, that is, in the direction of the primary current; but if this motion is resisted by the medium, the motion of the vortices beyond $$pq$$ will be gradually destroyed.

It appears therefore that the phenomena of induced currents are part of the process of communicating the rotatory velocity of the vortices from one part of the field to another.

[To be continued.]