Page:Scientific Memoirs, Vol. 2 (1841).djvu/89

Rh The ratio which the force of the bar on the needle (at the given distance $$R$$) bears to that of the earth's magnetism is expressed by the quotient and according to equation (III.)

But according to equation (II.) and, makes known to us the maximum moment of rotation which the bar with the magnetism $$M$$ would exert on a similar bar at the distance $$R$$; for this maximum, according to the fundamental laws of magnetism, must be $$\frac$$; and the above equation, gives $$\frac = \frac. \mathrm{tang}\, v$$.

This result, multiplied by the cube of the distance $$R$$, gives double the moment of rotation; and the square root of the half gives the force of the bar in absolute measure; or

If, finally, we divide by the moment of rotation exerted by the earth on the needle, calculated according to equation (I.) we obtain and this number expresses the absolute measure of the earth^s magnetism.

"This appears the most easily understood exposition which can be given, without the use of mathematical signs, of the possibility of expressing the force of the earth's magnetism by a number which shall be perfectly independent of the individuality of the magnetic bars employed. In the actual application some points will appear in a somewhat different form, without, however, affecting in the least the nature of the method; and it will, besides, be necessary to take into consideration several collateral circumstances."