How does the pendulum precess when it is taken around a general path C? For transport along the equator, the pendulum will not precess. [...] Now if C is made up of geodesic segments, the precession will all come from the angles where the segments of the geodesics meet; the total precession is equal to the net deficit angle which in turn equals the solid angle enclosed by C modulo 2 π. Finally, we can approximate any loop by a sequence of geodesic segments, so the most general result (on or off the surface of the sphere) is that the net precession is equal to the enclosed solid angle.