672 CONSTANTS OF MAGNETISATION. 



1232. Let us consider three rectangular co-ordinates, one x 

 along the ship's head, y from larboard to starboard that is, towards 

 the right and z downwards towards the keel. This latter axis 

 is vertical, and the two former are horizontal when the ship is on 

 an even keel. 



The permanent magnetism, and the induced magnetisation which 

 it gives rise to in masses of soft iron, produce on the compass a 

 force which is constant in magnitude and direction in reference 

 to the ship; let P, Q, and R be the projections on the three axes. 

 When the distribution of the magnets and of the soft iron is sym- 

 metrical, the value of Q is very small, and the horizontal component 

 F 1 = /s/P 2 + Q 2 is sensibly parallel to the plane of symmetry if the 

 compass itself is situated in this plane. But the component Q has 

 appreciable values whenever the head of the vessel on the building 

 slips was not in the magnetic meridian ; the force F x makes then 

 with the head an angle a which is called the starboard angle. 



If this were the only action, then if H is the horizontal com- 

 ponent of the earth, H x the resultant of the forces H and Fj, and 

 3j the deviation or the angle of the resultant H x with the magnetic 

 meridian, 



sin(f+a) sinSj s 



The deviation S l is null when the head is in the azimuth - a or 

 TT - a, and it changes sign on passing from one side to the other of 

 this direction; this is a semicircular deviation. If the ratio of the 

 forces F T and H is very small, we may write approximately 



F P O 



(10) sin8 1 = ^sin(f+a) = sinf+^cosf. 



The deviation is sensibly in the inverse ratio of H ; the sign is 

 the same all the world over, and the same value in all points of a 

 magnetic parallel. 



1233. For the terrestrial field, we may first of all observe that 

 the vertical component Z produces a magnetisation independent of 

 the direction of the ship, and that its action on the compass gives 

 a component situate in the plane of symmetry. The corresponding 

 deflection is then semicircular also ; it becomes zero at the equator, 

 and changes sign on passing from one hemisphere to the other. 



