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Observations with the EGRET telescope on the Compton Observatory reveal the extensive, high-energy gamma ray emission which results from cosmic ray interactions with the photons and matter in the plane of the Galaxy. The study of this diffuse emission from the Galaxy, which is the most prominent feature of the high-energy gamma-ray sky, is expected to yield information about the production and distribution of cosmic rays in the Galaxy. In this paper we present spectra of the diffuse emission from the Galactic plane for energies in the range 30--30,000 MeV, averaged over $10^\circ\times 4^\circ$ bins $(\Delta l\times \Delta b)$, with strong point sources removed. These spectra are compared with those predicted by the model of the diffuse gamma ray emission by Bertsch et al.\ (1993), which has been extended and enhanced as part of this work, to verify the model and to assess the variation of the cosmic ray electron and proton densities across the Galaxy.