A series of 150 Å/mm spectrograms of bright K-systems, observed with the Cassegrain spectrograph of the 82-inch McDonald reflector, shows an effect that may prove to be useful in the derivation of spectroscopic parallaxes for extragalactic nebulae. A well-marked relationship was found between the width of the spectral lines and the apparent brightness of certain members of the Virgo cluster of galaxies. The giant elliptical galaxies NGC 4486 (M 87) and NGC 4649 (M 60)M 31 and M 81. For progressively fainter Virgo cluster ellipticals the spectral lines tend to become narrower, as if there were a line width-absolute magnitude effect for the brighter members. This effect may also be present in the giant Sb spirals, for NGC 4594 also has spectral lines considerably broader than those in M 31 and M 81. When the distance modulus of the Virgo cluster becomes known with some precision, the high-luminosity members of this rich cloud of galaxies may serve to calibrate a line width-absolute magnitude relationship. This may then be used for the estimation of spectroscopic parallaxes of more distant galaxies, provided their spectra can be obtained with a dispersion high enough to show the true line width.