  The inclusive double-spin asymmetry, A_1^p, has been measured at COMPASS in
deepinelastic polarised muon scattering off a large polarised NH3 target. The
data, collected in the year 2007, cover the range Q2 > 1 (GeV/c)^2, 0.004 < x <
0.7 and improve the statistical precision of g_1^p(x) by a factor of two in the
region x < 0.02. The new proton asymmetries are combined with those previously
published for the deuteron to extract the non-singlet spin-dependent structure
function g_1^NS(x,Q2). The isovector quark density, Delta_q_3(x,Q2), is
evaluated from a NLO QCD fit of g_1^NS. The first moment of Delta_q3 is in good
agreement with the value predicted by the Bjorken sum rule and corresponds to a
ratio of the axial and vector coupling constants g_A/g_V =
1.28+-0.07(stat)+-0.10(syst).
