Stimulated by a scholium in Newton's Principia we find some beautiful results in classical mechanics which can be interpreted in terms of the orbits in the field of a mass endowed with a gravomagnetic monopole. All the orbits lie on cones! When the cones are slit open and flattened the orbits are exactly the ellipses and hyperbolae that one would have obtained without the gravomagnetic monopole.The beauty and simplicity of these results has led us to explore the similar problems in Atomic Physics when the nuclei have an added Dirac magnetic monopole. These problems have been explored by others and we sketch the derivations and give details of the predicted spectrum of monopolar hydrogen.Finally we return to gravomagnetic monopoles in general relativity. We explain why NUT space has a non-spherical metric although NUT space itself is the spherical space-time of a mass with a gravomagnetic monopole. We demonstrate that all geodesics in NUT space lie on cones and use this result to study the gravitational lensing by bodies with gravomagnetic monopoles.We remark that just as electromagnetism would have to be extended beyond Maxwell's equations to allow for magnetic monopoles and their currents so general relativity would have to be extended to allow torsion for 1 general distributions of gravomagnetic monopoles and their currents. Of course if monopoles were never discovered then it would be a triumph for both Maxwellian Electromagnetism and General Relativity as they stand! 2

Using the 1ϩ3 formulation of stationary spacetimes we show, in the context of gravitoelectromagnetism, that the plane of the polarization of light rays passing close to a black hole undergoes a rotation. We show that this rotation has the same integral form as the usual Faraday effect; i.e., it is proportional to the integral of the component of the gravitomagnetic field along the propagation path. We apply this integral formula to calculate the Faraday rotation induced by the Kerr and NUT spaces using the quasi-Maxwell form of the vacuum Einstein equations.

By decomposing the Riemann curvature into electric and magnetic parts, a duality transformation, which involves interchange of active and passive electric parts, has recently been proposed. It was shown that the Schwarzschild solution is dual to the one that describes the Schwarzschild particle with cloud of string dust or a global monopole. Following the same procedure we obtain the solution dual to the NUT spacetime.

Using the fact that the null geodesics in NUT space lie on spatial cones, we consider the gravomagnetic lens effect on light rays passing a NUT deflector.We show that this effect changes the observed shape, size and orientation of a source. Compared to the Schwarzschild lens, there is an extra shear (a differential twist around the lens axis) due to the gravomagnetic field which shears the shape of the source. Gravomagnetic monopoles can thus be recognized by the spirality that they produce in the lensing pattern.All the results obtained in this case (magnification factor, orientation of images, multiplicity of images, etc. ) depend on Q, the strength of the gravomagnetic monopole represented by NUT metric. One recovers the results of the usual Schwarzschild lens effect by putting this factor equal to zero.