New results for the double spin asymmetry $A_1^{rm p}$ and the proton longitudinal spin structure function $g_1^{rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{rm p}(x)$ by about a factor of two in the region $xlesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $Delta Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{rm p}$. The uncertainty of $Delta Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{rm A}/g_{rm V}| = 1.22 pm 0.05~({rm stat.}) pm 0.10~({rm syst.})$, which validates the sum rule to an accuracy of about 9%.
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