For pt.II see ibid., vol.12, no.7, p.106 (1979). The author considers a line-element which, in linearised gravity, is associated with the gravitational field of an arbitrary accelerating, rotating, axially symmetric source. If the body rotates about its symmetry axis and moves along its symmetry axis when viewed in the background flat space-time and if its linearised field (Riemann tensor) is free of wire singularities then the body must move with uniform acceleration and rotation and its mass must be constant.