Page:Scientific Memoirs, Vol. 2 (1841).djvu/238

considering the earth as an actual magnet, we should prefer to ascribe terrestrial magnetism simply to constant galvanic currents in the earth. But if we consider the earth as an actual magnet, we are obliged to ascribe to each of its portions, of the size of the eighth of a cubic metre, on an average, at least^[1] as great a force of magnetism as that contained in one of the above-mentioned bars. Such a result will be an unexpected one to philosophers.

32.

The manner of the actual distribution of the magnetic fluids in the earth necessarily remains undetermined. In fact, according to a general theorem which has been already mentioned in the 2nd article of the Intensitas, and will be treated of in greater detail at a future opportunity, we may substitute for any supposed distribution of the magnetic fluids in the interior of a body occupying space, a distribution on the surface of the same space, which shall leave the effect on every point of external space precisely the same. It may be easily concluded from hence, that one and the same action on all external space may be deduced from an infinite number of different distributions of the magnetic fluids in the interior.

We are enabled to assign on the other hand that fictitious distribution on the surface of the earth, which shall be perfectly equivalent to the actual distribution in the interior, as regards the external resultant of the forces; and the spherical form of the earth allows us to do so in a very simple manner.

We may express the density of the magnetic fluid in each point of the earth's surface, i. e. the quantum of the fliud which corresponds to the unit of surface, by the formula

${\frac {1}{4\pi }}\left({\frac {V}{R}}-2Z\right),$

or by $-{\frac {1}{4\pi }}(3P'+5P''+7P'',\,{}+9P^{\mathrm {IV} },\,\mathrm {\&c.} )$

The result of this formula will be hereafter exhibited by a graphical representation. We shall only notice here that it is negative in the northern and positive in the southern parts of the earth, but in such manner that the dividing line cuts the

1. In as far as we are not prepared to assume the magnetic axes of all the magnetized particles of the earth to be everywhere parallel to each other,—the more imperfect this parallelism, the greater must be the average force of magnetism in the parts to produce the same total magnetic moment.