MAGNETIC EFFECT OF SYMMETRICAL IRON. 151 



Also yz = r 2 . sin b . cos b . sin ( A + a) 

 = r 2 . sin b . cos 6 . (sin -4 > cos a -f- cos ^4 . sin a) : 



7 



which gives for the sum of ~ , 



. , ^ Qlm . sin . cos b . cos a 

 sin -4 . 2, - 3 - . 

 / 



Finally, s 2 = r 2 . sin 2 b, 



, ,, , . 



and the term g produces the sum 



r 3 

 Now assume the following notation ; 



2lm v 31m . cos 2 b ^ 21m /., 3 



^ 2lm (^ 3 B 

 , or 2 -p- f 1 - g cos 8 



6?wi . sin 5 . cos b . cos a 

 - 3 - 



3lm . cos 2 b . cos 2a ,. 



. sin 2 b ^ , , . ., 

 -^-- p or S - (l-3sm 2 = . 



These four quantities Jf, JV, P, ft do not depend on the 

 terrestrial force or on the position of the ship, but are 

 truly constants of the ship, depending only on its con- 

 struction and its susceptibility of magnetism. Then the 

 disturbing forces are, 



