The electrophoretic mobilities of rigid rodlike tobacco mosaic virus (TMV) particles solvated in water and in 80% glycerol/20% water solutions with a wide range of electrical double-layer thicknesses have been measured by Deggelmann et al. (Deggelmann, M., Graf, C., Hagenbuchle, M., Hoss, U., Johner, C., Kramer, H., Martin, C., and Weber, R., J. Phys. Chem. 98, 364-368 (1994)) and the present authors, respectively. The measured mobilities have a dependence on the electrical double-layer thickness much weaker than that predicted by theories for the mobility of cylinders of infinite length. To interpret the experiments, we develop an approximate theory for the mobility of finite aspect ratio particles with arbitrary ratios of the double-layer thickness to the rod length and diameter. This uniformly valid approximation interpolates between previous theories for infinite rod length and for infinitesimal rod thickness. A comparison of the uniformly valid theory with the experimentally measured mobilities indicates that TMV has a negative charge of 1000e in water and 400e in the glycerol solution.