MAGNETICAL INSTRUCTIONS. 13 



The complete investigation of the mathematical formulae for the correction of the Declination 

 Inclination, and Force, by Archibald Smith, Esq., F.R.S., will be found in the Philosophical Transac- 

 tions for the years 1843, 1844, and 1846, inNos. V., VI., and VIII. of the memoirs entitled " Contribu- 

 tions to Terrestrial Magnetism." * The practical application of these formula; to the corrections of the 

 deviations of the Standard compass is divested of all technical difficulty, and rendered easy by the 

 forms and tables given in the "Admiralty Manual of Compass Deviation" for calculating the 

 coefficients, A, B, C, D, E. 



The coefficients being known, the deviation (S) on any point of the compass may be computed 

 by the following equation (p. 112, 3d edition) — 



S = A + B sin £" + C cos £' + D sin 2f + E cos 2f 



£" denoting the azimuth of the ship's head by Standard compass ; or the expression for sin S may be 

 put under the following form (p. 114) — 



sin 8 = A + J& + C 2 sin (f ' + a) + D sin 2 f + E cos 2 f 



C 

 B' 



Q 



in which a is the angle whose tangent is ™ and is nearly the easterly azimuth of the line of no 



deviation. 



For the correction of the Inclination and Force, B and D are required, also the additional co- 

 efficients, c, d, A'.t 



Of these coefficients D, E (and also A') may be expected to remain constant, or to have the 

 same values in whatever part of the globe the ship may be, whilst no material alteration is made in 

 the distribution of her iron. They may, therefore, be regarded as determined, once for all, by the 

 deviations observed when the ship is first swung, though they may possibly be obtained more exactly 

 by taking the mean of the values obtained on all occasions when that process is repeated. The co- 

 efficient A in the deviation formula; may also be considered as constant, but as instrumental errors 

 form a part of this coefficient, and varying values may result, these values when large may be con- 

 sidered as wholly due to that source. 



B and C are variable coefficients, and depend on the Dip, and also on the proportion of the iron 

 which changes its magnetic state cotemporaneously with changes in the geographical position of the 

 ship, to the permanently magnetic iron ; — or to iron of an intermediate quality, and of which the 

 magnetism is neither permanent on the one hand, nor, on the other, are its changes cotempo- 

 raneous with changes of the Dip, but are consequent on such changes, and require a greater or less 

 interval to conform to them. It is on account of the uncertainty of the law according to which these 

 two coefficients B and C vary in different ships, that when a ship has changed considerably her geo- 

 graphical position it is desirable to repeat the process by winch the values of these important 

 coefficients may be redetermined. 



Little difficulty need be experienced on this point, as by the aid of steam, or indeed under sail, 



* The reader of the " Contributions " will observe that in them, following M. Poisson, the positive values of £ and 

 £' are reckoned from North to West, the negative from North to East, contrary to the usage of the " Admiralty Manual 

 of Compass Deviation." This however does not affect any of the formulae contained in these instructions. 



t In the notation of the " Admiralty Manual of Compass Deviation " — 



c =-2- d=m? A'=l+a= A(l+D). 



\+a l+a 



