TERRESTRIAL MAGNETISM. 195 



which it is less. The direction of the horizontal magnetic force 

 in each point of this line is obviously peqDendicular to it^ and 

 towards the side where the greater values of Fare found. If ds 

 be an infinitely small line in this direction, and V^ -i- dV^ the 



dV°. 

 value of Fat the other extremity of this Une, then —z— is the in- 

 tensity of the horizontal magnetic force at this place. As here 

 also the series of points corresponding to the value of V= F° 

 + d F° 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 Fare between V^ and V° -i- d F°, and where 

 the horizontal intensity is in an inverse ratio to the breadth of 

 the zone ; so by making F 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 diAaded into an 

 infinite number of infinitely narrow zones, the direction of the 

 horizontal magnetic force being everywhere perpendicular to the 

 di\'iding lines, and its intensity being in an inverse ratio to the 

 breadth of the zone at the jDlace in question. The two extreme 

 values of F coiTespond in this point of view to two points, in- 

 closed by the zones, at wliich 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 considei'ed 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 distribu- 

 tion 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 cer- 

 tainly 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- 



