184 ON MAGNETISM. 



The new term introduced into x* is 

 sin L 2r 2 {sin6. cos&. cosa. sin A. cos^l sin&. cos5. si 

 and therefore the new term introduced into H. 2 

 will be 



, _ T , ^ 6?m . sin b. cos b . cos a 



81Iia.il. 31X1 24. 2 - * - 



The new term introduced into xz is 

 s 2 .sin a. cos a. 



and therefore the new term introduced into F. 2 - i 



r 



will be 



. _ T _ . A _ cos 2 6 . sin 2 a) 



sm ^ . F. sin ^4 . z, - - 5 - '- 



Call the summed fraction R: (it will be seen that 

 R = M + PQ): then the term in question becomes 



Combining this with the preceding, the whole additional 

 term towards the magnetic north 



= sin h {HN . sin 2 A + VR . sin A}. 

 The new term introduced into xy is 



sin h . r" { sin b . cos 5 . cos a (cos 2 ^! sinM) 

 + 2 sin b . cos b . sin a . sin -4 . cos A], 



