148 ON MAGNETISM. 



head : so that A + a is the azimuth of that particle from 

 the north. Let b be the angular depression of the 

 particle. Then if r be the distance of the particle from 

 the compass ; x, y, z, the ordinates towards the north, 

 towards the east, and vertically downwards ; we have 



x = r . cos b . cos (A + a) , 



y = r . cos b . sin (A + a), 



z = T . sin b. 



Let / represent the local intensity of terrestrial 

 magnetism ; B the local dip, estimated positive for the 

 northern hemisphere ; m a constant for any particle 

 under consideration, representing its susceptibility of 

 inductive magnetization ; 21 the length of the small 

 magnet into which it is changed. Then the ordinates 

 of the blue end of the small magnet are 



x I cos B, y, z l sin B. 



Its distance, or the square root of the sum of the squares 

 of these quantities, omitting P, I s , &c, is 



r (x cos B 4- z sin B). 



The resolved part of its attraction on the red end of 

 the compass -needle in the direction of a? is 



( I }~ 5 



I'm (x I cos B) \r - (x cos B + z sin B ) Y 



x ( 1 , cos B ~jX cos B + z sin B 



I ^3 j 1 ~ *~^ \-ol~ p 



Similarly, the attraction in the direction of y is 



