We present a new measurement of the virtual photon proton asymmetry Ap1 from deep inelastic scattering of polarized muons on polarized protons in the kinematic range 0.0008 <x <0.7 and 0.2 <Q2 <100 GeV2. With this, the statistical uncertainty of our measurement has improved by a factor of 2 compared to our previous measurements. The spin-dependent structure function gp1 is determined for the data with Q2 > 1 GeV2. A perturbative QCD evolution in next-to-leading order is used to determine gp1(x) at a constant Q2. At Q2 = 10 GeV2 we find, in the measured range, ∫0.70.003 gp1(x)d x = 0.139 ± 0.006(stat) ± 0.008(syst) ± 0.006 (evol). The value of the first moment Γp1 = ∫10gp1(x)dx of gp1 depends on the approach used to describe the behaviour of gp1 at low x. We find that the Ellis-Jaffe sum rule is violated. With our published result for Γd1 we confirm the Bjorken sum rule with an accuracy of ≈ 15% at the one standard deviation level. © 1997 Elsevier Science B.V.