(1) tan θ = tan z. cos A,
where θ is the subsidiary angle which must be determined for the purpose of computation, z is the true zenith distance, and A is the distance from the North point.
(2) cos Δ = cos z . cos (c - θ)[134] cos θ,
where Δ is the N.P.D. of the celestial object, and c is the colatitude (90° - lat.) of the place of observation.
In the example taken this gives us—
(1) tan θ = tan 88° 21′ . cos 66° 38′
θ = 85° 50′ 45″
(2) cos Δ = cos 88° 21′. cos (39° 52′ - 85° 50′ 45″) cos 85° 50′ 45″
Δ = 73° 57′ 50″
Declination, δ, = (90° - Δ) = 16° 2′ 10″ N.