408 



MAGNETIC CONDITION OF THE GLOBE. 



Let us consider the parallels corresponding to two infinitely near 

 equipotential surfaces V l and V 2 (Fig. 92) ; let ds be the arc of the 



Fig. 92. 



meridian comprised between them, and dn the perpendicular distance 

 of the two surfaces at the same point. If F be the magnetic force 

 and I the inclination, we have evidently 



dn ds cos I 



from which is deduced 



(i) 



3V 



The horizontal component, perpendicular at every point to the 

 magnetic parallel, is therefore inversely as the distance of two con- 

 secutive parallels ; but the total force and the horizontal component 

 are not necessarily constant along a magnetic parallel, as is the case 

 on Biot's theory. 



435. MAGNETIC EQUATOR. The sum of the magnetic masses 

 being null for the whole system, and also separately for each of the 

 magnetised bodies, there is a level surface for which V = ; this 

 surface cuts the terrestrial globe along its neutral line if it is the 

 only magnetic body, or in the vicinity if the other magnetic bodies 

 are sufficiently distant. 



The magnetic parallel where the potential is zero is called the 

 magnetic equator; along this equator the force is not constant, nor 

 is it necessarily horizontal. On Biot's theory the equator was a line 

 of which the inclination was null. 



