We present a new measurement of the spin-dependent structure function g(1)(d) of the deuteron from deep inelastic scattering of 190 GeV polarized muons on polarized deuterons. The results are combined with our previous measurements of g(1)(d). A perturbative QCD evolution in next-to-leading order is used to compute g(1)(d)(x) at a constant Q(2). At Q(2) = 10GeV(2), we obtain a first moment r(1)(d) = integral(0)(1)g(1)(d)x=0.041 +/- 0.008, a flavour-singlet axial charge of the nucleon a(0)=0.30 +/- 0.08, and an axial charge of the strange quark a(s)=-0.09 +/- 0.03. Using our earlier determination of Gamma(1)(p), we obtain Gamma(1)(p) - Gamma(1)(n)=0.183 +/- 0.035 at Q(2) = 10GeV(2). This result is in agreement with the Bjorken sum rule which predicts Gamma(1)(p) - Gamma(1)(n)=0.186 +/- 0.002 at the same Q(2). (C) 1997 Published by Elsevier Science B.V.