Surveying
If ‘δ’ is the declination of the Polaris and ‘λ’ is the latitude of the place, the azimuth of the Polaris, is

cos δ/cos λ
tan (90° + δ)/tan (90° + λ)
sin (90° - δ)/sin (90° - λ)
cos (90° - δ)/cos (90° - λ)

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Surveying
The error due to eccentricity of inner and outer axes can be eliminated by

double sighting
taking both face observations and taking the mean of the two
reading both verniers and taking the mean of the two
taking mean of several readings distributed over different portions of the graduated circle

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