Abstract: Angular measurements data were obtained using a manual glass scale Theodolite. Morning, afternoon and evening observations were made for the 3 months of November, December and January. Reductions and rigorous adjustments were made to obtain the best estimates for the observation analysis. Temperature and pressure measurements were also, taken alongside the angles so as to find the optimum period for best observations free of atmospheric refraction. The coefficient of lateral refraction determined for Bauchi was 0.0567, while the monthly means of the observations were subjected to standard statistical tests. From the result of these tests it is concluded that: the arithmetic mean of angular measurement was 87°17' 49.28''. The best period for angular measurements in Bauchi is between 12:00 noon to 4:00 pm. The best month in the year for angular measurements is January. All daytime horizontal angles measured within the period must be subtracted by 1.5''.