λ = H1 (Mean DF at compass position towards magnetic North) Ship’s multiplier λ = H1 (Mean DF at compass position towards magnetic North) H( DF ashore towards magnetic North) λ 2 = H2 (Mean DF at compass position towards magnetic North after DF improved with Kelvni’s spheres) λ (before DF improved with Kelvin’s balls example about 0.8) less than 1 λ2 (after DF improved with Kelvin’s balls example about 0.85) less than 1

Vertical Force Instrument (VFI)

Angle of Dip

μ = Z 1 = d1 μ 2 = Z 2 = d2 Z d Z d Z L L m m d w Z w x d = Z x m x L + Z x m x L w x d = 2mL x Z W, m, L are constant values Therefore Z α d μ = Z 1 = d1 Z d μ 2 = Z 2 = d2 Z d

λ 2 = numerically equal = μ2 (called ship’s multiplier) μ = Z 1 (Mean vertical force at compass position, resulting from Z, R force, and induction on soft iron by Z) Z force ashore μ2 = Z 2 (Mean vertical force at compass position when HE magnets and Kelvin’s spheres in place) λ 2 = numerically equal = μ2 (called ship’s multiplier)

Vertical force instrument- An extremely accurate instrument which measures the magnetic dip generated by the lines of force of the Earth's magnetic field. This dip circle is made of a brass cylinder with two glass flat end-windows, containing a centrally mounted magnetic needle free to rotate about its supporting axis in a vertical plane. The angle of dip is 0° at the equator and 90° at the poles. At the magnetic north and south poles, the needle dips vertically and the angle of dip is 90°. This precision instrument needs to be kept immobile and sometimes even enclosed in a box so that the needle will not be disturbed by electrostatic forces or breeze. One of its most important uses in travel was to tell the difference between the geographic North Pole and the North Magnetic Pole. The inside of the dip circle is marked Made in France. The instrument comes in a beautiful wood box with purpel felt lining.

Hf & Zf RATIO’s  = 28 = 0.8 35 SHORE SHIP Hf = 28 Hf = 35 Zf Zf

2 = 30 = 0.85 Hf & Zf RATIO’s SHORE SHIP 2 = Ship’s multiplier 35 2 = 30 = 0.85 35 SHORE SHIP Hf = 30 Hf = 35 Zf Zf 2 = Ship’s multiplier

Level and heading N – S (magnetic) V.F.I. Level and heading N – S (magnetic) Keep the instrument ashore from disturbing fields in N- S direction 1 meter above the ground. Red end will dip down in NHS in direction of the earth field

V.F.I. Level the needle by sliding the weight on high side until needle becomes horizontal , couple due to Z is now nullified. Note the reading d cm on scale Ex- 10 cm 2 (ship’s multiplier) if known from records Multiply shore reading by 2 and set the weight to this position on the needle ( 10 cm x 0.85 = 8.5 cm) d

Take the instrument to the vessel Kelvins spheres and Flinders bar should be in place before using the instrument Head the vessel E/W (mag). Remove compass bowl and replace with the VFI in N/S plane. Needle will dip again due to influence of vertical magnetic forces at compass position.

Vertical force instrument -principle