The empirical relationship between the luminosity of a spiral/irregular galaxy and its rotational velocity, known as the luminosity-line-width or Tully-Fisher relation (Tully and Fisher 1977), has become one of the most widely used extragalactic distance indicators. Despite the fact that a similar technique was applied to estimate the distance of M31 by Öpik (1922), Hubble (1936b) failed to recognize it as a useful way to measure extragalactic distances. The method languished until Roberts (1962) discussed a variant. Later, Balkowski et al. (1974) noted the more direct correlation between luminosity and HI 21-cm line-width. Tully and Fisher (1977) were the first strong advocates of its use as a distance indicator. Consequently, they are now associated with the ``Tully-Fisher relation'' (hereafter TF relation) and its application to the extragalactic distance scale problem.
Spiral and irregular galaxies are common in both the field and in all but the richest clusters. Consequently, the TF relation is an extremely valuable technique for extensive mapping of local large scale structure, the Hubble flow, and any associated peculiar velocities. In addition, since the local population is dominated by spirals and irregulars, the TF relations can, at least in principle, be calibrated directly by Cepheids. The TF relations provide an opportunity to go from local calibrating galaxies to the ``smooth'' Hubble flow in a single step. As an example of the influence of the TF relations, Sandage and Tammann (1976) reassessed their previous work on the distance scale in light of the TF relation and also discussed many of the general uncertainties. A comparison of the distance to the Virgo Cluster determined by Tully and Fisher (1977) with the value obtained by Sandage and Tammann (1976) is presented by Fisher and Tully (1977) and illustrates how differences in samples, extinction, and particularly line-width corrections can lead to quite different results. For reference, Tully and Fisher (1977) obtained a distance for the Virgo Cluster of 30.6 ± 0.2 mag, while Sandage and Tammann (1976) obtained 31.4 ± 0.2. The revision of the Hyades modulus to 3.23 mag (e.g., Hodge and Wallerstein 1966; Hanson 1975) shifts these two estimates to 30.8 and 31.6 mag.
The necessary data consist of apparent magnitudes, usually corrected for Galactic and internal extinction, and some measure of rotation velocities, corrected for projection effects, for a sample of galaxies. Usually, the rotational velocity is obtained via the doppler broadening of the HI 21-cm line, although Fabry-Perot imaging and long slit rotation curves (both obtained via H) are useful as well.