MARINER'S COMPASS. 675 



Putting again 



P=/H, -Q = ?H, R = ;-Z; 



H' = //'H, ZWZ. 



Substituting these values in the preceding expressions, we obtain 



Ji cos f ' = (/ + c tan I) + (i + #) cos f $ sin f , 

 -/?' sinf' = (^+/tan I) - (i + *) sin +d cos f, 



s' = (r + i +k) +g cot I cos f /* cot I sin f. 



These equations give the components of the resultant field as 

 a function of the terrestrial field of the permanent magnetism, of 

 the parameters, and of the ship's head. 



In order to get the deviation itself, the two first equations are 

 added after having multiplied them respectively by sin f and cos f , 

 the second is then subtracted from the first after having multiplied 

 them respectively by cos f and sin f, so that the former member 

 contains the sine and cosine of the angle -' = S. We thus find, 

 after a few simple reductions, 



d-b 

 ti sin S = -- + (/ + c tan I) sin f + (q +f tan I) cos 



2 



a-e . b+d 



H -- sin 2<; H -- cos 2f, 



2 2 



h' cos 8=1+ - + (/ + <: tan I) cos f- (?+/ tan I) sin 



fl--^ . ^ + ^/ . 



H --- cos 34 -- sin 2C. 



2 



Dividing these two equations by the quantity 



a + e 



and then the first by the second, we get 



sin 8 A + B sin f+C cos+D sin 2^+E cos 



cosS i + B cos-C sin+ D cos 2(-E sin 2f '' 



X X2 



