SECTION V. 



THE THEORY OF TERRESTRIAL MAGNETISM, GIVING THE EXPRESSIONS 

 OF THE MAGNETIC FORCES ON THE EARTH'S SURFACE, THE EARTH 

 BEING REGARDED AS A SPHERE. 



1. LET V represent the magnetic potential, and let X, Y, Z be the 

 magnetic forces in three directions at right angles to one another, X being 

 the force towards the north perpendicular to the Earth's radius, Y the force 

 perpendicular to the meridian towards the west, and Z the force towards the 

 Earth's centre. 



X being the longitude and the colatitude, and r the distance from 

 the Earth's centre, 



cosO p. and ~ = sin 6= (I /r)'*; 



v dV (\- 



hence X. = -- ^ = ' 



rdO r 



y= dV 



r sin 6d\ r d\ ' 



__ dV 



~^ ; 



if east longitudes be considered positive. We may distinguish the two 

 systems of values of V corresponding to magnetic forces whose origin is 

 situated inside and outside the Earth's surface respectively by affecting 

 them with the suffix n when the corresponding value of V involves a 



positive power of - , and with the negative suffix, n, when the value of 



V involves a negative power of - . 



A. n. 51 



