X907.] AND MOUNTAIN FORMATION. 403 



and P^ = o. Hence we may put for points at the earth's surface, 

 where r = a, and P^ = o. 



_ V= a{P' 4- P"^- P"'+ • . •), (9) 



where P', P" , P'", depend only on ^i and A. 



The magnetic potential for the earth calculated in this way repre- 

 sents observations with the desired accuracy. Since Gauss showed 

 that any distribution of magnetism within the earth, as respects the 

 effects in outer space, may be completely represented by an appro- 

 priate surface distribution, it follows that the existing distribution 

 of the earth's magnetism is most probably confined to the crust of 

 the globe. In fact this is the only part of our planet sufficiently 

 cooled to maintain magnetic properties once established in its ele- 

 ments. The field of force thus arising about the earth might, how- 

 ever, be slightly modified by electric and other effects depending on 

 the sun and moon, and the diurnal movement of the illuminated 

 hemispheres of our globe. These effects as determined by observa- 

 tion are much too large to be ascribed to direct actions of the sun 

 and moon, and are believed to be indirect effects depending largely 

 on charges operating in the upper regions of our atmosphere. 



This upper atmosphere is always exposed to the radiation of the 

 heavenly bodies, and no doubt accumulates a potential powerful 

 enough to influence the field near the earth's surface. Discharge 

 of this potential is witnessed in the aurora borealis, which is accom- 

 panied by conspicuous disturbances of the earth's magnetism. 

 Gauss showed that the location of the constant part of the earth's 

 magnetism must necessarily be in the body of the globe, and not in 

 the atmosphere or outer space. 



In his " Algemeine Theorie des Erdmagnetismus," 1838, Gauss 

 treated of a sphere magnetised in any manner. If X, Y, Z, be the 

 components of the earth's resultant magnetic force at any point on 

 the surface, in the directions of geographical north, west and the 

 zenith of observer, the horizontal intensity H, declination 8, and 

 inclination t, are fully defined by the equations : 



Y Z 



H=VX^+Y\ tan 3 = -^, tan.= -==^^. (10) 



