Surveying
If θ and δ be the latitude of a place and declination of a star respectively, the upper culmination of the star will be north of zenith if its zenith distance, is

θ + δ
δ - θ
θ - δ
(θ + δ)/2

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Surveying
If the lower clamp screw is tightened and upper clamp screw is loosened, the theodolite may be rotated

on its inner spindle with a relative motion between the vernier and the graduated scale of lower plate
on its outer spindle without a relative motion between the vernier and gra-duated scale of lower plate
on its outer spindle with a relative motion between the vernier and graduated scale of lower plate
on its inner spindle without a relative motion between the vernier and the graduated scale of lower plate

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