90 ON MAGNETISM. 



There is only one case of these equations which 

 offers any interest. If (f> 2 =(f> 1 + 9Q () ) then cos <f> 2 = sin ^ ; 

 and the sum of the squares of the two equations becomes 



(cotan. d$* + (cotan. d^) z = (cotan. True Dip) 2 , 

 from which the angle <, has disappeared. 



Thus it appears that the True Dip can be obtained 

 from observation of the apparent dips in two planes, 

 with no condition as to the position of these planes 

 except that their azimuths differ by 90. This condition 

 can always be secured by means of the azimuthal circle 

 on which the dip-apparatus is mounted. 



41. Determination of the Total Terrestrial Magnetic 

 Force at any locality : lines upon the Earth's surface 

 passing through points of equal dip, and lines passing 

 through points of equal Total Force : historical changes. 



By the investigations extending from Articles 26 to 

 34, the terrestrial horizontal magnetic force is measured. 

 And by those from Articles 38 to 40, the dip is measured. 

 It is plain that the Total Force = Horizontal Force x se- 

 cant of True Dip : and thus the total terrestrial hori- 

 zontal magnetic force is ascertained, without risk of in- 

 accuracy, except at points where the dip is nearly ver- 

 tical (that is, at points near the magnetic poles). 



We confine our attention to this method, because it 

 is the only one which does not rely on the constancy of 

 a needle's magnetism, and because it is very accurate 

 except close to the magnetic poles, where the value of 

 the total force can be inferred from those around it by 

 the laws of continuity. Determinations have been made, 



