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Analytic expressions are derived for the enhancement and quenching of a fluorescing molecule outside and in the interior of a metallic spherical nanoshell. The competing effects of enhancement and quenching are a strong function of the radial location of a molecule exterior to the shell. For a fluorescing molecule inside the shell, the enhancement and quenching are a weaker function of radius and a stronger function of the shell thickness. The enhancement and quenching also have a strong wavelength dependence arising from plasmon resonances excited within the particle. For an external molecule, a shell produces a larger peak enhancement than a solid homogeneous sphere of the same diameter. Calculations are presented to illustrate these effects in a silver shell.