Page:Scientific Memoirs, Vol. 2 (1841).djvu/207

which it is less. The direction of the horizontal magnetic force in each point of this line is obviously perpendicular to it, and towards the side where the greater values of $V$ are found. If $d\,s$ be an infinitely small line in this direction, and $V^{0}+d\,V^{0}$ the value of $V$ at the other extremity of this line, then ${\frac {d\,V^{0}}{d\,s}}$ is the intensity of the horizontal magnetic force at this place. As here also the series of points corresponding to the value of $V=V^{0}+d\,V^{0}$ forms a second line situated infinitely near to the first, and thus marks out on the surface of the earth a zone, within which the values of $V$ are between $V^{0}$ and $V^{0}+d\,V^{0}$, and where the horizontal intensity is in an inverse ratio to the breadth of the zone; so by making $V$ vary by infinitely small but equal steps from the lowest value on the surface of the earth to the highest, the whole surface of the globe becomes divided into an infinite number of infinitely narrow zones, the direction of the horizontal magnetic force being everywhere perpendicular to the dividing lines, and its intensity being in an inverse ratio to the breadth of the zone at the place in question. The two extreme values of $V$ correspond in this point of view to two points, inclosed by the zones, at which the horizontal force is $=0$, and where therefore the whole magnetic force can only be vertical: these points are termed the magnetic poles of the earth. The lines dividing the zones are no other than the intersections of the surfaces considered in Article VII. with the surface of the earth, whilst it is only at the poles that they are in contact with it.

12.

The form of the system of lines described in the above article is strictly but the simplest type, which might be subject to many exceptions were we to take into account every possible distribution of magnetism in the earth. We shall not, however, exhaust this subject here, but shall only add a few elucidatory remarks as to the cases of exception. The magnetic condition of the earth, no doubt is such, that the form of the system of lines on its surface corresponds to the description. At least there are certainly no exceptions on the great scale, though probably there may occur local ones. Some philosophers have considered the earth as having two north and two south magnetic poles, but it does not appear that an essential condition was previously ful-