A 850 micron map of the interacting spiral galaxy M51 shows well-defined spiral arms, closely resembling the structures seen in CO and HI emission. However, most of the 850 micron emission originates in an underlying exponential disk, a component that has not been observed before in a face-on galaxy at these wavelengths. The scale-length of this disk is 5.45 kpc, which is somewhat larger than the scale-length of the stellar disk, but somewhat smaller than that of atomic hydrogen. Its profile can not be explained solely by a radial disk temperature gradient but requires the underlying dust to have an exponential distribution as well. This reinforces the view that the submm emission from spiral galaxy disks traces total hydrogen column density, i.e.the sum of H2 and HI. A canonical gas-to-dust ratio of 100+/-26 is obtained for kappa(850)=1.2 g**-1 cm**2, where kappa(850) is the dust opacity at 850 micron.
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