Page:Scientific Memoirs, Vol. 2 (1841).djvu/85

Rh "Let $$N\;S$$ be a fixed magnet in a horizontal position; it is required to find its influence on a second needle, $$n\; s$$, suspended to a thread; the relative position of the two needles being shown in the annexed figure:

The action of the first needle upon the second will consist in imparting to it a tendency to turn in the direction indicated by the arrows, the letters $$N$$, $$n$$ designating the North poles, and $$S$$, $$s$$ the South poles. The moment of rotation is expressed by a number, exactly in the same way that the action of terrestrial magnetism on a needle vibrating freely has been indicated above. The magnitude of the moment of rotation depends, however, on the distance, and on the magnetic force in both needles. Thus for example (supposing the distances to be sufficiently great), at equal distances it would be augmented six-fold, by doubling the magnetism of one of the needles and trebling that of the other.

"The effect depends on the distance in such manner, that, at twice the distance the effect will be th, and at three times the distance th of the effect produced at the simple distance; bearing in mind, however, that this law is correct only for very great distances, and cannot be extended to small ones. As all distances, when referred to a selected unit, can be expressed by numbers, this law maybe expressed thus: 'the moment of rotation, multiplied by the cube of the distance, is constant for very great distances.' This product may be termed with propriety the moment of rotation reduced to the unit of distance; remembering that, according to the remark above made, the actual moment of rotation at the unit of distance, when the distance is small, may differ considerably from the reduced moment. This, however, does not prevent us from employing the reduced moment of rotation as a measure of the magnetism of the needles, and from considering as unity, the magnetism of that needle, which imparts to another needle, (of equal magnetism, and in a given position) a reduced moment of rotation equal to the effect of the unit of weight on the arm of a lever whose length is the unit of distance."