Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution

When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static two-body solution can be given an invariant formulation in terms of a force 4-vector. The norm of this force is calculated for Bach's two-body solution, which is known to be in one-to-one correspondence with Schwarzschild's original solution when one of the two masses l, l' is made to vanish. In the limit when, say, l' tends to 0, the norm of the force divided by l' and calculated at the position of the vanishing mass is found to coincide with the norm of the acceleration of a test body kept at rest in Schwarzschild's field. Both norms thus happen to grow without limit when the test body (respectively, the vanishing mass l') is kept at rest in a position that becomes closer and closer to Schwarzschild's 2-surface.