Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/381

Suppose that we set the magnet swinging by means of a transient current whose value is $Q_{0}$. If, for brevity, we write

then the first elongation

The velocity instantaneously communicated to the magnet at starting is

When it returns through the point of equilibrium in a negative direction its velocity will be

The next negative elongation will be

When the magnet returns to the point of equilibrium, its velocity will be

Now let an instantaneous current, whose total quantity is $-Q$, be transmitted through the coil at the instant when the magnet is at the zero point. It will change the velocity $v_{2}$ into $v_{2}-v$, where

If $Q$ is greater than $Q_{0}e^{-2\lambda }$, the new velocity will be negative and equal to

The motion of the magnet will thus be reversed, and the next elongation will be negative,

The magnet is then allowed to come to its positive elongation

and when it again reaches the point of equilibrium a positive current whose quantity is $Q$ is transmitted. This throws the magnet back in the positive direction to the positive elongation

or, calling this the first elongation of a second series of four,

Proceeding in this way, by observing two elongations + and −, then sending a positive current and observing two elongations