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We have measured the ratio g& /F& over the range 0.029 ( x ( 0.8 and 1.3 ( Q~( 10 (GeV/c) using deep-inelastic scattering of polarized electrons from polarized ammonia. An evaluation of the integral fo g~(x, Q2) dx at fixed Q2 = 3 (GeV/c)2 yields 0.127~0.004(stat)~0.010(syst), in agreement with previous experiments, but well below the Ellis-Jaffe sum rule prediction of 0.160~0.006. In the quark-parton model, this implies Aq = 0.27~0.10.PACS numbers: 13.60. Hb, 11. 55.Hx, 13.88.+e, 14.20.Dh Measurements of the longitudinal and transverse spindependent structure functions gi(x, Q ) and gq(x, Q ) for deep-inelastic lepton-nucleon scattering have become an increasingly important tool in unraveling the complex structures of the proton and neutron.Of particular interest are the integrals I t (Q ) = f"g (x,tQ )dx the proton and I i (Q ) = ftI gi (x, Q ) dx for the neutron.

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