EFFECT OF THE SHIP'S HEELING. 183 



F be the subpermanent force acting on the red end of 

 the needle towards the fore part of the ship : 8 that 

 force parallel to the ship's deck which acts towards 

 the starboard side : K that towards the ship's keel. 

 When the ship heels through the angle Ji, the forward 

 force is not thereby disturbed, but the horizontal force 

 towards the starboard side becomes S cos h K sin h. 

 But the transversal magnet which has been correcting 

 the compass when the ship was on even beam, and 

 whose power therefore was S in the plane parallel 

 to the deck, now exerts the horizontal power Scosh. 

 Therefore the new force of subpermanent magnetism in 

 the horizontal plane, towards the starboard side, pro- 

 duced by the ship's heeling is 



K sin h, 

 which produces 



+ sin h. K . sin A towards the north, 

 and sin h.K.cos A towards the east. 

 For the forces produced by induction, let x, y, 2, be 

 measured horizontally towards the north, horizontally 

 towards the east, and vertically, as in Article 68. 

 Consider cos h as = 1. Then, using the notation of 

 Article 68, 



o; = r.cos 6.cosa.cos-4 r cos 5. sin a. sin A 



+ sin h . r . sin b . sin A ; 

 y = r.cos 6. cos a. sin A +r.cos b. sin a. cos A 



sin h.r.sin b.cosA ; 

 z = r.sin 5 + sin /&.?'. cos Z>. sin a. 



