  We present measurements of $\nu_{\mu}$ charged-current cross section ratios
on carbon, iron, and lead relative to a scintillator (CH) using the
fine-grained MINERvA detector exposed to the NuMI neutrino beam at Fermilab.
The measurements utilize events of energies $2<E_{\nu}<20~GeV$, with $\left<
E_{\nu}\right>=8~GeV$, which have a reconstructed $\mu^{-}$ scattering angle
less than $17^\circ$ to extract ratios of inclusive total cross sections as a
function of neutrino energy $E_{\nu}$ and flux-integrated differential cross
sections with respect to the Bjorken scaling variable $x$. These results
provide the first high-statistics direct measurements of nuclear effects in
neutrino scattering using different targets in the same neutrino beam. Measured
cross section ratios exhibit a relative depletion at low $x$ and enhancement at
large $x$. Both become more pronounced as the nucleon number of the target
nucleus increases. The data are not reproduced by GENIE, a conventional
neutrino-nucleus scattering simulation, or by the alternative models for the
nuclear dependence of inelastic scattering that are considered.
