Summary table covering all ship’s magnetic compass coefficients—including $\lambda$ (lambda) and $\mu$ (mu)—detailing their names, deviation types, causes, formulas, course and latitude effects, and methods of correction.

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Magnetic Compass Coefficients & Parameters Table

Coefficient / Parameter	Type of Deviation	How Caused	How Found / Formula	Effect of Course	Effect of Latitude	How Corrected / Adjusted
Coefficient A	Constant deviation (same magnitude & sign on all headings).	Asymmetrical placement of compass off centerline, lubber line misalignment, observation errors, or transient effects during rapid swinging (Gaussin/Retentive error).	$A = \frac{\delta_N + \delta_{NE} + \delta_E + \delta_{SE} + \delta_S + \delta_{SW} + \delta_W + \delta_{NW}}{8}$ (Mean of deviations on 8 main headings).	Unaffected by change of course (constant on all headings).	Independent of magnetic latitude.	Physical/mechanical alignment of compass bowl/lubber line, or allowed for mathematically.
Coefficient B	Semicircular deviation (maximum on E/W, nil on N/S).	Fore-and-aft magnetic forces: Permanent magnetism ($P_B$) from hard iron in hull, and Induced magnetism ($i_B$) in vertical soft iron ($c$-rod) induced by $Z$.	$B = \frac{\delta_E - \delta_W}{2}$ (Calculated from deviations on East and West headings).	Varies directly as $\sin(\text{compass course})$: $\delta_B = B \sin \theta$.	$P_B \propto \frac{1}{H}$; $i_B \propto \frac{Z}{H} = \tan(\text{dip})$. Total $B$ changes with magnetic latitude.	$P_B$ corrected by Fore-and-Aft permanent magnets in binnacle. $i_B$ corrected by a vertical soft iron Flinders Bar placed fore or aft .
Coefficient C	Semicircular deviation (maximum on N/S, nil on E/W).	Athwartship magnetic forces: Permanent magnetism ($P_C$) from hard iron in hull, and Induced magnetism ($i_C$) in vertical soft iron ($f$-rod) induced by $Z$.	$C = \frac{\delta_N - \delta_S}{2}$ (Calculated from deviations on North and South headings).	Varies directly as $\cos(\text{compass course})$: $\delta_C = C \cos \theta$.	$P_C \propto \frac{1}{H}$; $i_C \propto \frac{Z}{H} = \tan(\text{dip})$. Total $C$ changes with magnetic latitude.	$P_C$ corrected by Athwartship permanent magnets in binnacle. $i_C$ corrected by slewing Flinders Bar or athwartship Flinders bar .
Coefficient D	Quadrantal deviation (maximum on NE, SE, SW, NW; nil on N, E, S, W).	Induced magnetism in symmetrical horizontal soft iron: continuous athwartship beams ($-e$ rod, $+D$) and continuous F&A girders ($-a$ rod, $-D$) induced by $H$.	$D = \frac{\delta_{NE} - \delta_{SE} + \delta_{SW} - \delta_{NW}}{4}$.	Varies directly as $\sin(2 \times \text{compass course})$: $\delta_D = D \sin 2\theta$.	Independent of magnetic latitude (disturbing force and directive force $H$ change in exact same proportion).	Soft Iron Spheres (divided athwartship soft iron) placed on brackets on either side of binnacle.
Coefficient E	Quadrantal deviation (maximum on N, E, S, W; nil on NE, SE, SW, NW).	Induced magnetism in unsymmetrical horizontal soft iron situated diagonally ($45^\circ$) to F&A line ($b$ and $d$ rods of same name).	$E = \frac{\delta_N - \delta_E + \delta_S - \delta_W}{4}$.	Varies directly as $\cos(2 \times \text{compass course})$: $\delta_E = E \cos 2\theta$.	Independent of magnetic latitude.	Soft Iron Spheres placed diagonally at $45^\circ$, or by slewing $D$-correcting spheres through angle $M$ where $\tan 2M = \frac{E}{D}$.
Heeling Error (HE)	Semicircular deviation when ship heels (maximum on N/S, nil on E/W).	Vertical forces (permanent vertical force $R$, induced vertical $k$-rod, and athwartship $e$-rod) acting at an oblique angle when ship heels.	Difference in deviation between heeled and upright conditions, or assessed using Vertical Force Instrument (VFI) .	Varies directly as $\cos(\text{compass course})$ and angle of heel $i$.	Varies with latitude as $\frac{Z}{H} = \tan(\text{dip})$ for induced parts and $\frac{1}{H}$ for permanent part $R$ (reappears with change of latitude) .	Vertical permanent magnets placed in Heeling Error Bucket below compass bowl inside binnacle .
Lambda ($\lambda$)	Directive Force Ratio (Not a deviation; mean horizontal directive force ratio) .	Attenuation of Earth’s $H$ by continuous steel structure ($\lambda_1$), restored/increased by divided soft iron spheres ($\lambda_2$) .	$\lambda_1 = \frac{\text{Mean } H \text{ at compass}}{\text{Mean } H \text{ ashore}}$ (before spheres); $\lambda_2 = \frac{\text{Mean } H \text{ at compass}}{\text{Mean } H \text{ ashore}}$ (after spheres) .	Mean ratio over all $360^\circ$ courses (constant ratio for a given configuration) .	Virtually independent of latitude as force at compass and ashore vary proportionally with $H$ .	Soft Iron Spheres increase $\lambda_1$ to $\lambda_2$ ($\approx 0.85 - 0.90$). $\lambda_2$ (“Ship’s Multiplier”) is used to set VFI for HE correction ($n_1 = n \times \lambda_2$) .
Mu ($\mu$)	Vertical Force Ratio (Not a deviation; mean vertical force ratio) .	Screening and vertical magnetization of ship’s hull and structure under Earth’s vertical field $Z$ .	$\mu_1 = \frac{\text{Mean } Z \text{ at compass}}{\text{Mean } Z \text{ ashore}} = \frac{\text{VFI scale reading on board}}{\text{VFI scale reading ashore}}$ (before HE correction) .	Mean ratio over all $360^\circ$ courses (constant ratio for a given configuration) .	Varies directly with Earth’s vertical force $Z$ across latitudes .	Adjusted using vertical HE corrector magnets until $\mu_2 = \lambda_2$ at a well-corrected compass .

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