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Measurements of cosmic ray secondary to primary ratios and the spectrum of high Z primaries up to hundreds of GeV per nucleon (Esposito etal., 1990, ApJ, 351, and references therein) show that the spectrum of primary cosmic rays softens with increasing energy. The results can be organized neatly through use of a simple model of cosmic ray propagation wherein all primary cosmic rays have the same hard source spectrum, roughly a spectral index of -2.1 to -2.3, which is modified by rigidity dependent escape from the galaxy to the softer observed high energy spectrum. If supernova are the dominant source of galactic cosmic rays then nucleon-nucleon interactions of the accelerated particles with interstellar material swept up by the expanding remnant would emit high energy gamma radiation. These gamma rays probe the cosmic ray spectrum at the source and would carry the signature of a hard source spectrum. Observations with the Energetic Gamma Ray Experiment Telescope (EGRET) ! on the Compton Observatory show mo re than 30 unidentified sources of E $>$ 100 MeV gamma rays concentrated along the galactic plane (Fichtel et al., 1994, ApJS, in press). A statistical survey of the positions of 9 radio bright galactic supernova remnants (F $>$ 100 Jy) with 27 unidentified EGRET sources in the first and fourth quadrants, $|$b$|$ $< 5\deg$, suggests a strong correlation for three sources. The position of the supernova remnants are 39, 39 and 27 arcmin from the best respective EGRET source position, and each overlaps the 68\% confidence contour of the EGRET source when the angular size of the remnant is considered. The probability of a positional correlation of three radio bright supernova remnants occurring accidentally is less than 0.2\%.
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