Page:Scientific Memoirs, Vol. 2 (1841).djvu/83

Rh needle produces a force or moment of rotation when the needle is not in the magnetic meridian: this moment of rotation is greater, the more the needle deviates from the magnetic meridian; and is greatest when the needle is at right angles to that meridian. This maximum of effect is always to be understood when the moment of rotation simply is spoken of; it may be represented by a given weight acting on a lever of given length, and consequently by a number, if the weights and lengths are expressed in numbers, according to arbitrary units. Now this moment of rotation and the time of vibration are very simply connected, by means of an intermediate quantity, dependent on the figure and weight of the needle, called its moment of inertia, and which may be calculated according to known rules. If the needle is not a perfectly regular body, or if it carries any appendage when in vibration, other means are required for the determination of its moment of inertia, the description of which would lead us too far; suffice it to say, that it is always possible. The moment of inertia then being known, the moment of rotation produced by the earth's magnetism on the magnetism of the needle, may be concluded from the observed time of the vibration of the needle."

If we designate by the letter $$C$$, the moment of inertia, after it has been multiplied by $$\pi^2$$, i. e., 9·8696… and divided by twice the height of the fall of a heavy body in the unit of time, we may conclude from $$C$$, and from the observed time of vibration $$t$$, the greatest moment of rotation caused by the earth; it is

"It is possible to determine the moment of rotation by direct experiment, without observing the time of vibration. An apparatus, expressly adapted to this purpose, has been recently placed in the Göttingen Astronomical Observatory, and is susceptible of great accuracy; but for the present purpose it is unnecessary to dwell on this point.

"The moment of rotation, produced by the earth's magnetism on a given needle, offers a new way of measuring the force of the earth's magnetism, or, to speak more accurately, a new form of the previous mode of measurement, over which it has this advantage, that one portion of the individuality of the