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accuracy altitude angle applied approximation arithmetical mean ascension and declination assumed azimuth Bessel catalogue celestial sphere centre chronometer circle circumpolar stars clamp clock co-ordinates collimation computation constant convenient correction culmination derived determined difference earth east ecliptic employed ephemeris equal equations of condition example expressed follows formula geocentric given gives Greenwich horizon hour-angle i2mo instant interpolation July latitude limb logarithms longitude mean error mean solar measured meridian method micrometer middle thread moon moon's right ascension morocco multiplied Nautical Almanac normal equations number of observations obtained parallax plane pole precession prime vertical probable error proper motion reading reduced refraction result semidiameter sextant sidereal star's Substituting subtract Suppose telescope tion transit instrument unknown quantities values vernier weight write zenith distance zenith telescope