This study investigates the development and testing of an approximation method for the Mine Surveyor to calculate meridian convergence. This study, a detailed review of experimental techniques, follows a statistical experimental approach to establish how accurate an alternative method performs against traditional methods of meridian convergence calculation used by the Mine Surveyor. The spatial study is defined by the geographical range of the existing Schreiber Geodetic Tables, ranging from 70 km south of Ndola (Zambia) to 10 km north of De Aar (South Africa). The sample size is established under the constraint of an infinite population. Linear regression in collaboration with the hold-out validation technique is adopted to statistically refine the alternative method of calculation. The computational outcomes of the refined alternative method in comparison to the unrefined method are predominantly closer to the traditional outcomes. Computational outcomes specific to the hold-out validation set demonstrate a maximum sub-{1^{\prime\prime }} variance of {0.650^{\prime\prime }}. A sub-variance of {0.650^{\prime\prime }} satisfies the South African Mine Survey limits of error. The subsequent clustering of variances at specific variance intervals are similar to comparative studies conducted by T. Soler and R.J. Fury with respect to meridian convergence.