Apparent dip

• If the dip circle is not kept in magnetic meridian, the angle made by the needle with horizontal is called the apparent dip for that plane. If the dip circle is at an angle ϕ to the meridian then B_H' = B_H cosϕ
• B_V' = B_V (no charge in vertical component)
• If θ₁ is the apparent dip and θ is the true dip
• we have ......(1)
• Now if the dip circle is rotated through an angle of 90° from this position it will now make an angle (90° – ϕ) with the meridian.
• Now B_H'' = B_H cos(90 – ϕ) = B_H sinϕ
• Now the apparent dip is θ₂ then
• .......(2)
• From (1) and (2) cot²θ₁ + cot²θ₂ = cot²θ

Note :

• If the earth is considered as a short magnet with its centre coinciding with the centre of the earth, then the angle of dip Θ at a place where the magnetic latitude λ is given by
• Tanθ = 2 Tanλ
• (or) θ = Tan^–1(2 Tanλ)

Derivation :

• For M sinλ, Point 'P' is an axial point
• Hence
• For M cosλ, point P is an equatorial point
• Hence
• But B₁, B₂ represent B_V, B_H at point 'P'
• ∴ Dip at point P,
• ∴ Tanθ = 2 Tanλ