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

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750.]
METHOD OF RECOIL.
349

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

, (19)

then the first elongation

(say). (19)

The velocity instantaneously communicated to the magnet at starting is

. (20)

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

. (21)

The next negative elongation will be

. (22)

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

. (23)

Now let an instantaneous current, whose total quantity is , be transmitted through the coil at the instant when the magnet is at the zero point. It will change the velocity into , where

. (24)

If is greater than , 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,

. (25)

The magnet is then allowed to come to its positive elongation

, (26)

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

; (27)

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

. (28)

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