676 CONSTANTS OF MAGNETISATION. 



where A, B, C, D, and E are coefficients, the meaning of which 

 follows from the course of the calculation. 



Removing the denominator and replacing the angle f-8 by (', 

 we have finally 



(16) sinS = A cosS + B sinf ' + C cosf + D sin( 2 f + 5) + E cos(2' + 8). 



It will be seen that, by definition, if we refer to the original 

 equations, the coefficients A and E are very small. Disregarding 

 8 in the terms of correction, we find again the expression (14). 



We may also replace cos 6 in equation (16) by unity, which gives 



. A + B sinf' + C cosf' + D sin2f' + E cos2f 

 i - D cos 2<^ + E sin 2f 



the term E sin2f in the denominator being negligable. 



Without insisting on the methods used for determining the 

 values of the coefficients, we may add that this mode of correction 

 gives excellent results when the deflection does not exceed 20; but 

 it becomes very difficult to apply when the deviations are consider- 

 able, as is often the case for ships which contain large masses of 

 iron and steel. 



1237. The action of the ship on the compass is really equivalent 

 to that of a magnet, which would produce the components P, Q, R, 

 and of a mass of soft iron placed near the compass in a determinate 

 direction and at a convenient distance, provided that the action of 

 the compass itself on this mass of soft iron produces no induced 

 magnetisation capable of producing a distinct perturbation by its 

 reaction on the compass. 



It is therefore possible to compensate exactly the action of the 

 vessel, by placing in a fixed position near the compass a magnet 

 the components of whose field are - P, - Q, and - R, and a mass of 

 soft iron which counterbalances the magnetisation of the mass of soft 

 iron by the earth ; the deflection will be neutralised. It is, however, 

 difficult to arrange the compensation in this manner by methodical 

 trials, and in practice it is better to use several magnets by which 

 the various terms of the deflection are separately neutralised. 



This mode of correction is due particularly to Sir George Airy.* 

 It may first of all be observed that the vertical components and the 



* G. AIRY. Phil. Trans. 1856. 



