Demonstration of the parallel transport method. Sources lying at the points A and B both have their vectors v_a (red) and v_b (blue) point to the South Pole and thus have position angles ξ_a = ξ_b = 180°. However, they are not aligned. In order to compare them v_a should be parallel-transported to location B following the great circle passing through A and B (dashed line). The resulting vector is (green). t_a and t_b are the vectors tangent to the sphere and parallel to the plane of the great circle at locations A and B, respectively. The angle (v_a, t_a) is equal to the angle (, t_b) in order to ensure that v_a is parallel to . e_θ and e_ϕ are the unit vectors pointing northward and eastward. The two sources have different reference systems.