SHIP CONSTANTS AND DEVIATION-COEFFICIENTS. 



FUNDAMENTAL EQUATIONS. 



Let the Earth's magnetic force, acting on a magnetic needle at a given position on 

 board ship, be resolved into three rectangular components, two of which are horizontal 

 and one is vertical, viz: X, in the direction of the fore-and-aft line towards the ship's head; 

 Y, towards the starboard side; and Z, towards the keel; A' and Y are the two horizontal 

 components, and Z is the vertical component. Furthermore, let X', Y' , and Z' represent 

 the same components resulting from the combined action of the Earth's magnetic field 

 and that of the ship. Then the well-known, fundamental equations in the mathematical 

 theory of ship deviations, first given by Poisson in 1824, are 



Z' = X + aX-t-6F-fcZ + P (1) 



Y' = Y + dX + eY^fZ + Q (2) 



Z' = Z + gX + hY^kZ + R (3) 



The parameters o, h, c, d, e, f, g, h, k depend on the amount, arrangement, and induc- 

 tive capacity of the soft iron of the ship. P,Q, R are parameters depending on the amount, 

 arrangement, and permanent or subpermanent magnetism of the hard iron of the ship. 



The above formulse assume that the ship's magnetic field results partly from the 

 permanent magnetism of hard iron and steel and partly from the transient, induced magnet- 

 ism of soft iron, the latter supposed to be directly proportional to the intensity of the 

 inducing force. It is, furthermore, assumed that the length of the magnetic needle is 

 infinitesimally small in comparison with the distance to the nearest iron aboard the ship. 

 These assumptions may be regarded as amply fulfilled on the Galilee, in view of the small- 

 ness of the parameters for this vessel. If the vessel is not on even keel, corrective terms 

 enter, which for the Galilee under the usual observing conditions could be regarded as 

 negUgible. 



Deviation Formula. 



Let the so-called deviation-coefficients for the magnetic elements, declination (D), 

 inclination (I), horizontal intensity (H), and vertical intensity (Z), be 



ForD.- A^,B„C„D„E, 



Fori: A,,B,,Ct,D,,E, 



ForH: A„ B„ C, D„ E, 



For Z: A,,B., C. 



Then the deviation formulae for D, I, H, and Z, after various transformations and ap- 

 proximations, may be written as follows:^ 



D' - D = 5D = Ai + Bi sin t + d cos f -h 2)^ sin 2f -f- E^ cos 2f (4) 



r -I =5/ = ^, -I- fi. cos f -t- C, sin f + Acos2f + j&, sm 2f (5) 



i/'-/f = 5// = A, + 5, cosf-l-C, sin f -!- Dft cos 2f + i?^ sin 2f (6) 



Z' -Z =5Z =^ + B, cosf-l-C, sinr (7) 



'The reader may be referred to the following treatises, for example: Admiralty Manual for the Deviations of the Com 

 pass, London, 1912, pp. 96-99; F. Bidlingmaier, Magnetische Beobachtungen an Bord, pp. 469-478 of Neumayer's Anleitung 

 zu wissenschaftlichen Beobachtungen auf Reisen, Hannover, 1905; E. Mascart, Traitede Magn^tisme Terrestre, pp. 402-436, 

 Paris, 1900. 



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