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In the magnetic meridian the vertical and horizontal components of the magnetic field are ; Bv = Bsinδ and Bh = Bcosδ.The projection of the horizontal component Bh onto the geographic meridian is Bg = Bhcosθ.
The plane perpendicular to the geographic meridian makes angle 180∘−(90∘+θ) = 90∘−θ with the magnetic meridian. The projection of Bh onto this plane is Bp = Bhcos(90∘−θ) = Bhsinθ.
The apparent angles of dip in the geographic meridian and the plane perpendicular to it are given by
tanδ1=Bv/Bg ;
tanδ2=Bh/Bp ;
Therefore :
tanδ1 / tanδ2 = Bp / Bg = (Bhsinθ) / (Bhcosθ) = tanθ
θ = tan−1 (tanδ1 / tanδ2)
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