Surveying
When a star is between the pole and the horizon, the relationship between latitude (λ), zenith distance (z) and declination δ, is

θ = z + δ
θ = δ - z
θ = (z + δ) - 180°
θ = 180° - (z + δ)

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Surveying
The length of a chain is measured from

outside of one handle to inside of other handle
centre of one handle to centre of other handle
inside of one handle to inside of other handle
outside of one handle to outside of other handle

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