  We study two experimental ways to measure the heavy-quark content of the
proton: using the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and/or the azimuthal
$\cos(2\phi)$ asymmetry in deep inelastic lepton-nucleon scattering. Our
approach is based on the following observations. First, unlike the production
cross sections, the ratio $R(x,Q^2)=F_L/F_T$ and the azimuthal $\cos(2\phi)$
asymmetry in heavy-quark leptoproduction are sufficiently stable, both
parametricallly and perturbatively, in a wide region of variables $x$ and $Q^2$
within the fixed-flavor-number scheme of QCD. Second, both these quantities,
$R(x,Q^2)=F_L/F_T$ and $\cos(2\phi)$ asymmetry, are sensitive to resummation of
the mass logarithms of the type $\alpha_{s}\ln\left(Q^{2}/m^{2}\right)$ within
the variable-flavor-number schemes. These two facts together imply that the
heavy-quark densities in the nucleon can, in principle, be determined from
high-$Q^2$ data on the Callan-Gross ratio and/or the azimuthal asymmetry in
heavy-quark leptoproduction. In particular, the charm content of the proton can
be measured in future studies at the proposed Large Hadron-Electron (LHeC) and
Electron-Ion (EIC) Colliders.
