SECTION VI. 



THE THEORY OF TERRESTRIAL MAGNETISM, GIVING THE EXPRESSIONS 

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

 ACCOUNT THE SPHEROIDAL FIGURE OF THE EARTH. 



1. LET us now take into account the spheroidal figure of the Earth. 

 Let r, 6', \ be the polar coordinates of a point on the spheroidal surface 

 referred to the Earth's centre as origin and axis of figure as initial line ; 

 let 6 be the geographical colatitude (the angle which the normal makes 

 with the axis) and let p. = cos 6 and // = cos 6'. 



The angle of the vertical \l> 6' 0. 



The values of the sines and cosines of these angles for values of 

 differing by 1 from to 90 have been computed, the eccentricity e of 

 the elliptic section in the plane of the meridian being derived from Bessel's 

 dimensions of the Earth as given in Encke's tables in the Berliner Jahrbuch, 

 1852. 



The expressions for the magnetic potential and for the magnetic forces 

 X, Y, and Z, in terms -of the Gaussian magnetic constants g, h will be of 

 the same form as those given above for the sphere (see p. 403). 



Let X be the total force towards the north perpendicular to the 

 Earth's radius, Y the total force perpendicular to the geographical meridian 

 towards the west, Z the force towards the Earth's centre, then 



_ 1 dV dV 



rdff' rsm0'd\' f ~^r 



(east longitudes being considered positive). 



