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We present a precise measurement of the proton longitudinal double-spinasymmetry $A_1^{\rm p}$ and the proton spin-dependent structure function$g_1^{\rm p}$ at photon virtualities $0.006~({\rm GeV}/c)^2<Q^2 < 1~({\rmGeV}/c)^2$ in the Bjorken $x$ range of $4 \times 10^{-5} < x < 4 \times10^{-2}$. The results are based on data collected by the COMPASS Collaborationat CERN using muon beam energies of $160~{\rm GeV}$ and $200~{\rm GeV}$. Thestatistical precision is more than tenfold better than that of the previousmeasurement in this region. In the whole range of $x$, the measured values of$A_1^{\rm p}$ and $g_1^{\rm p}$ are found to be positive. It is for the firsttime that spin effects are found at such low values of $x$.

Longitudinal double-spin asymmetry $A_1^{\rm p}$ and spin-dependent structure function $g_1^{\rm p}$ of the proton at small values of $x$ and $Q^2$