674 CONSTANTS OF MAGNETISATION. 



We may, lastly, to the same degree of approximation, replace, in 

 the second member, the real azimuth of the head, which is unknown, 

 by the apparent azimuth '; the deflection is then expressed by the 

 formula 



(14) sin 8 = A + B sin f ' + C cos f ' + D sin 2(' + E cos 2f ', 



the coefficients of which will have to be determined experimentally. 

 The first term A is the mean value of the deviation; the two 

 following represent a semicircular deviation, and the two latter a 

 quadrantal deviation. 



1235. There is still to be considered the action produced by 

 the obliquity of the vessel, or the heeling error. Let / be the in- 

 clination of the ship on the starboard, or towards the right. The 

 components of the terrestrial action should be replaced by 



Yf = Y cos / + Z sin /, 

 Z- = Zcos/-Ysin/, 



and the component X does not vary. In this case each of the 

 coefficients A, C, and D contains a term sensibly proportional to 

 the inclination. 



1236. In order to make the calculation more completely, we 

 may observe that, when the ship is on an even keel, and assuming 

 the superposition of the different magnetisations, the components 

 X', Y', and Z' of the resultant field may be represented by the 

 expressions 



X' = X + P+ aX +(Y)+ cZ, 



(15) Y' = Y + Q + (</X)+ .Y 

 Z'=Z+R+ 



in which the parameters a, b, t, d . . . . refer to the induced mag- 

 netisation of the earth. We have put in brackets the terms which 

 are very small, for they destroy themselves in the conditions of 

 symmetry of the ship and of the compass. 



If H' is the horizontal component of the resultant field, I the 

 magnetic inclination, we have 



X=Hcos, Y = -Hsinf, Z = HtanI. 



X' = H'cosC', Y'= -H'sinf. 



