Precise measurement of the transverse asymmetry A_T' in ^3\vecHe(\vece,e') as a function of the squared momentum transfer Q^2 in the region of the quasi-elastic peak provides a uniquely valuable means of extracting the neutron magnetic form factor G^n_M and will impose constraints on recent calculations of the ^3He quasi-elastic asymmetry. Unlike the transverse-longitudinal asymmetry A_TL', the transverse asymmetry is not sensitive to details of the ^3He ground state wave function. The relative model-independence of the quasi-elastic A_T' measurement, in combination with the reduced systematic uncertainty in the combined beam-target polarization afforded by our simultaneous measurement of the elastic ^3He transverse asymmetry, will permit us to extract the neutron magnetic form factor to an accuracy of 2%. An experiment to measure the inclusive quasi-elastic transverse asymmetry A_T' in ^3\vecHe(\vece,e') at low Q^2, E95-001, is being conducted at Jefferson Lab at the beginning of 1999.

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