Correction

Figures & data

Table 3. Worked examples of reducing measured zenith angles to geodetic zenith angles (Eq. 9)(9) $z=Z+\left(\xi \mathit{.}cos\left(\alpha \right)\mathit{+}\eta \mathit{.}sin\left(\alpha \right)\right)$(9) and error propagation (Eq. 10) using the deflection errors from Appendix A. The [unrealistic] cases of zero observational error are included to assist in gauging the relative contributions of the deflection errors.

Measured zenith angle ($Z$)	Uncertainty $\sigma (Z)$	Geodetic azimuth of line ($\alpha$)	Uncertainty $\sigma (\alpha )$	Geodetic zenith angle ($z$)	Uncertainty $\sigma (z)$
45° 00’ 00”	±2”	00° 00’ 00”	±1”	45° 00’ 02.44”	±3.48”
85° 00’ 00”	±2”	45° 00’ 00”	±1”	84° 59’ 56.10”	±3.59”
89° 00’ 00”	±2”	90° 00’ 00”	±1”	88° 59’ 52.04”	±3.70”
45° 00’ 00”	±0”	00° 00’ 00”	±0”	45° 00’ 02.44”	±2.85”
85° 00’ 00”	±0”	45° 00’ 00”	±0”	84° 59’ 56.10”	±2.98”
89° 00’ 00”	±0”	90° 00’ 00”	±0”	88° 59’ 52.04”	±3.11”

Table 4. Worked examples of reducing measured directions to the ellipsoid (Eq. 11) and error propagation (Eq. 12) using the deflection errors from Appendix A. The [unrealistic] cases of zero observational error are included to assist in gauging the relative contributions of the deflection errors.

Measured horizontal direction ($D$)	Uncertainty $\sigma (D)$	Geodetic zenith angle ($z$)	Uncertainty $\sigma (z)$	Geodetic azimuth of line ($\alpha$)	Uncertainty $\sigma (\alpha )$	Reduced horizontal direction ($d$)	Uncertainty $\sigma (d)$
45° 00’ 00.00”	±1”	45° 00’ 02.44”	±3.48”	45°	±1”	44° 59’ 52.65”	±3.15”
45° 00’ 00.00”	±1”	84° 59’ 56.10”	±3.59”	45°	±1”	44° 59’ 59.36”	±1.03„
45° 00’ 00.00”	±1”	88° 59’ 52.04”	±3.70”	45°	±1”	44° 59’ 59.87”	±1.00”
45° 00’ 00.00”	±0”	45° 00’ 02.44”	±0”	45°	±0”	44° 59’ 52.65”	±2.98”
45° 00’ 00.00”	±0”	84° 59’ 56.10”	±0”	45°	±0”	44° 59’ 59.36”	±0.26”
45° 00’ 00.00”	±0”	88° 59’ 52.04”	±0”	45°	±0”	44° 59’ 59.87”	±0.05”

The online version of this article has been corrected.