  Measurements of the associated production of a W boson and a charm (c) quark
in proton-proton collisions at a centre-of-mass energy of 8 TeV are reported.
The analysis uses a data sample corresponding to a total integrated luminosity
of 19.7 fb$^{-1}$ collected by the CMS detector at the LHC. The W bosons are
identified through their leptonic decays to an electron or a muon, and a
neutrino. Charm quark jets are selected using distinctive signatures of charm
hadron decays. The product of the cross section and branching fraction
$\sigma$(pp $\to$ W + c + X) $\mathcal{B}$(W $\to$ $\ell\nu$), where $\ell$ = e
or $\mu$, and the cross section ratio $\sigma$(pp $\to$ W$^+$ + c + X) /
$\sigma$(pp $\to$ W$^-$ + $\mathrm{\bar{c}}$ + X) are measured inclusively and
differentially as functions of the pseudorapidity and of the transverse
momentum of the lepton from the W boson decay. The results are compared with
theoretical predictions. The impact of these measurements on the determination
of the strange quark distribution is assessed.
