  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 $x\lesssim 0.02$. 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\%.
