EFFECT OF THE SHIP'S HEELING, 185 



and therefore the new term introduced into JET.2 - f-^ 



will be 



6lm . sin b . cos b . cos a 

 sin h. H. cos 2A .2, - 3 - 



= sin h . HN. cos 2A. 

 The new term introduced into yz is 



and therefore the new term introduced into V. 





 will be 



-L -rr A v l m (cos 2 . sirfa sin 2 6) 

 sin h . V. cos A . 2, - - a - ' 



r 3 



= sin h . VR . cos A. 



Combining this with the preceding, the whole additional 

 force towards the magnetic east is 



. - sin h {HN. cos 2 A + VR . cos A}. 



Uniting the terms derived from subpermanent magnet- 

 ism and from induction, we have the following forces 

 introduced by the ship's heeling : 

 Towards the north, 



sin h x {K. sin A + EN. sin ZA+VR. sin A}. 

 Towards the east, 



- sin h x {K. cos A + EN. cos ZA+VR. cos A}. 



The latter is the only force which disturbs the 

 direction of the compass-needle. 



