450 Influence of Masses of Iron 



cos «, and cos a acting in the directions of the axes a , ajm6 a,^ 



are equivalent to a force represented by unity, and acting in the 

 direction we have assumed for that of the dip. Whence we con- 

 clude that the distribution of the fluid assigned to any point t by 

 the theorem, is such as would produce a force equal and oppo- 

 site to that of the terrestrial magnetism ; and consequently such as 

 will fulfil the conditions to which we have arrived in page 447. 



Having thus deduced the laws which regulate the accumula- 

 tion of the magnetic fluids in masses of iron of all forms ; it will 

 now be merely an affair of analysis to determine the deviations 

 which their attractions are capable of producing upon compasses 

 whose situations are known with respect to the given body. 



When the given body is of an irregular form, the deviations 

 produced can only be obtained by knowing the attractions for 

 three other directions of the dip : but if the mass be either sphe- 

 rical or spheroidal, the effect may be calculated by a direct pro- 

 cess. Thus; let A G D S (fig. 9) be the given sphere ; where O is 

 the centre; N S the direction of the dip ; and O' the centre of the 

 second sphere (page 447-8) ; let also C be the place of the com- 

 pass, and join CO, CO'; the first of which cuts the sphere in 

 some point P ; join N P, A P ; and produce the latter to meet 

 the horizontal circle G H P in H, through which point draw OC' 

 meeting the vertical C C in C/ : then the necessary construction 

 will be finished by drawing in the vertical plane the axe OA, and 

 the rectangular axes O G, OD in the plane of the horizon, OG 

 being also parallel to the magnetic meridian. 



From what has been proved in page 447-8, it will then follow 

 that the attraction of the sphere to the compass at C will be the 

 result of a positive and a negative force, that vary respectively as 



— : and — ^. Or resolving the last into the rectangular forces 



Ca, aO% and assuming CO = d, N0P = 4;, and 00'= e; 

 the attraction in the direction C O will vary as 



1 d+ e cos * 



^^ j tP-\-e-+2ed cos (py^ 



And in the direction O a, as 



c. sin ^ 



But since e is infinitely small, these expressions will reduce to 

 the two following respectively, 



2c. cos (f 



c. si)i (p 



(2) 



It 



