188 ON MAGNETISM. 



by a multiple of sin h x cos A enables us to correct it 

 by application of a magnet. In Article 51, Figure 41, 

 putting h for <, that is to say placing a magnet in the 

 ship which shall be vertical when the ship is on even 

 beam and which will have the inclination h when the 

 ship has the heel h, we found that its horizontal force 

 on the red end of the needle is 



When the ship's head is north, or A = 0, this force acts 

 transversely to the needle, and is wholly available (and 

 so, with changed sign, when the ship's head is south). 

 But in any other position of the ship's head, the force 

 acts obliquely on the needle, and must have the factor 

 cos A. The efficient force is therefore 



ca . , A 



sin A . cos A. 



a 2x 

 (c a ) 



This follows the same law as the force which we wish to 

 neutralize : and therefore, by proper choice of the poles 

 of the magnet, and by sliding it up and down parallel 

 to the ship's masts, a position may be found in which it 

 will entirely correct the heeling-error. 



Unfortunately, the terms included in the bracket 

 both depend on geographical position, and the correction 

 which is valid in one part of the earth will not be valid 

 in other parts. The correction of the heeling-error 

 deserves, more than any other point, the attention of 

 practical magnetists. 



