The magnetic resonance method of determinng nuclear magnetic moments in molecular beams, recently described by Rabi and his collaborators, has been extended to allow the determination of the neutron moment. In place of deflection by inhomogeneous magnetic fields, magnetic scattering is used to produce and analyze the polarized beam of neutrons. Partial depolarization of the neutron beam is observed when the Larmor precessional frequency of the neutrons in a strong field is in resonance with a weak oscillating magnetic field normal to the strong field. A knowledge of the frequency and field when the resonance is observed, plus the assumption that the neutron spin is 1/2 , yields the moment directly. The theory of the experiment is developed in some detail, and a description of the apparatus is given. A new method of evaluating magnetic moments in all experiments using the resonance method is described. It is shown that the magnetic moment of any nucleus may be determined directly in absolute nuclear magnetons merely by a measurement of the ratio of two magnetic fields. These two fields are (a), that at which resonance occurs in a Rabi type experiment for a certain frequency, and (b) that at which protons are accelerated in a cyclotron operated on the nth harmonic of that frequency. The magnetic moment is then (for J=12, μ=HbnHa. n is an integer and HbHa may be determined by null methods with arbitrary precision. The final result of a long series of experiments during which 200 million neutrons were counted is that the magnetic moment of the neutron, μn=1.935+0.02 absolute nuclear magnetons. A brief discussion of the significance of this result is presented.