Page:Scientific Memoirs, Vol. 2 (1841).djvu/241

artificial magnets and in a locality sufficiently distant from iron, never showed the slightest deviation, (which we should rather expect,) the equality of the two fluids might with the highest degree of probability be inferred for the whole earth; though without wholly excluding the possibility of some inequality.

The only difference which the existence of such an inequality would occasion in our theory would be, that $P^{0}$ (Art. 17) would no longer be $=0$. The consequence of this would be, that for all external space it would be necessary to add to the expression for $Z$ the member ${\frac {R^{2}P^{0}}{r^{2}}}$; so that on the surface of the earth the (constant) member $P^{0}$ must be added, but $X$ and $Y$ would be in no respect affected. When there shall exist in future times a much more extensive collection of accurate observations than we at present possess, it may be examined whether a vanishing value of $P^{0}$ is or is not required for their accurate representation. With our present data such an undertaking would be wholly useless.

36.

Another part of our theory on which there may exist a doubt is, the supposition that the agents of the terrestrial magnetic force are situated exclusively in the interior of the earth. If we seek for their immediate causes, partly or wholly, without the earth, and confine ourselves to known scientific grounds, we can only think of galvanic currents. But the atmosphere is no conductor of such currents, neither is vacant space; thus, in seeking in the upper regions for a vehicle of galvanic currents we go beyond our knowledge. ·But our ignorance gives us no right absolutely to deny the possibility of such currents; we are forbidden to do so by the enigmatical phenomena of the Aurora Borealis, in which there is every appearance that electricity in motion performs a principal part. It will therefore still be interesting to examine what form magnetic action arising from such currents would assume on the surface of the earth.

37.

Let us, then, assume the existence of constant galvanic currents in a concave sphere, $S$, surrounding the earth, and call $S'$ all the space included by $S$, and $S''$ all the space external to $S$. Whatever may be configuration of the galvanic currents, we can always substitute for them a fictitious distribution of the