MARINER'S COMPASS. 673 



In order to calculate the effect of the horizontal component H, 

 we shall replace it by its two projections 



X = H cos(, Y= -H'sinf. 



The magnetisation produced by the former gives an action the 

 horizontal component of which, F 2 , is in the plane of symmetry. 

 If we put 



F 2 = aH cosf, 



and let H 2 be the resultant of the forces H and F 2 , the deviation <5 2 

 due to the horizontal component will be defined by equations 



sin ( sin 8 2 sin(f-8 2 ) 

 xi2 r 2 H 



which give sensibly 



a 

 (it) sinS 2 = - sin2f. 



2 



This deflection is null when the head is directed towards one 

 of the four cardinal magnetic points, and its signs are different in 

 two adjacent quadrants ; this is a quadrantal deviation. 



The projection Y = - H sin f gives, in like manner, a horizontal 

 action 



F' 2 = -<?H sinf. 



The corresponding deflection S' 2 is sensibly determined by the 

 equation 



(12) sin8' 2 = sin 2f ; 



this is still a quadrantal deviation. 



1234. When the disturbing actions are weak, it may be assumed 

 that the deflections produced by each of them simply add themselves, 

 and the total deflection may be represented by an expression of the 

 form 



(13) sin6 = (A) + B sinf+C cosf+D sin2+(E cos2). 



The two terms in brackets are usually very small, since they simply 

 arise from want of symmetry in the distribution of masses of iron 

 or steel, or the disymmetric position of the compass on board. 

 VOL. ii. x x 



