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We report an analysis of the interstellar $\gamma$-ray emission in the thirdGalactic quadrant measured by the {Fermi} Large Area Telescope. The windowencompassing the Galactic plane from longitude $210\arcdeg$ to $250\arcdeg$ haskinematically well-defined segments of the Local and the Perseus arms, suitableto study the cosmic-ray densities across the outer Galaxy. We measure no largegradient with Galactocentric distance of the $\gamma$-ray emissivities perinterstellar H atom over the regions sampled in this study. The gradientdepends, however, on the optical depth correction applied to derive the \HI\column densities. No significant variations are found in the interstellarspectra in the outer Galaxy, indicating similar shapes of the cosmic-rayspectrum up to the Perseus arm for particles with GeV to tens of GeV energies.The emissivity as a function of Galactocentric radius does not show a largeenhancement in the spiral arms with respect to the interarm region. Themeasured emissivity gradient is flatter than expectations based on a cosmic-raypropagation model using the radial distribution of supernova remnants anduniform diffusion properties. In this context, observations require a largerhalo size and/or a flatter CR source distribution than usually assumed. Themolecular mass calibrating ratio, $X_{\rm CO} = N({\rm H_{2}})/W_{\rm CO}$, isfound to be $(2.08 \pm 0.11) \times 10^{20} {\rm cm^{-2} (K km s^{-1})^{-1}}$in the Local-arm clouds and is not significantly sensitive to the choice of\HI\ spin temperature. No significant variations are found for clouds in theinterarm region.

Constraints on the Cosmic-Ray Density Gradient beyond the Solar Circle from Fermi gamma-ray Observations of the Third Galactic Quadrant