1 Introduction

Bars have been recognized in galaxies since the time of Curtis (1918) and Hubble (1926), but only recently have methods been developed that quantify the impact of these features on galaxy structure. Bar strength is important in galaxy morphological studies because phenomena such as gas inflow, angular momentum transfer, noncircular motions, lack of abundance gradients, nuclear activity, starbursts, and the shapes and morphologies of rings and spirals, may all be tied in various ways to the effectiveness with which a bar potential influences the motions of stars and gas in a galactic disk (e.g., Sellwood & Wilkinson 1993; Buta & Combes 1996; Knapen 1999).

In the past, bar strength was judged visually from galaxy images on blue-sensitive photographic plates. Hubble (1926) divided galaxies into barred (SBa, SBb, ...) and normal (Sa, Sb, ...) spirals along a famous "tuning fork''. This view was revised by de Vaucouleurs (1959), whose classification volume recognized apparent bar strength (SA, SAB, SB) as a continuous property of galaxies called the "family''. De Vaucouleurs' main contribution here was to recognize the existence of galaxies having a bar intermediate in apparent strength between nonbarred and barred spirals. This is the essence of category SAB.

However, neither the Hubble nor the de Vaucouleurs bar classifications can be expected to be accurate measures of bar strength because apparent bar strength is impacted by wavelength, the effects of extinction and star formation, inclination and bar orientation relative to the line of sight, and also on observer interpretations. It is well known that bars are more prominent in near-infrared images than in blue-light images (e.g., Block & Wainscoat 1991; Knapen et al. 2000; Eskridge et al. 2000). Clearly, the near-infrared is the best wavelength regime for judging bar strength.

In the near-infrared, one probes the older, star dominated disk. This led Block & Puerari (1999) to propose a simple classification scheme for spirals in the near-IR involving the dominant Fourier m-mode and the pitch angle of the spiral arms. Old disks may be grouped into three principal archetypes: the tightly wound $\alpha$ class, an intermediate $\beta$class (with pitch angles of $\sim$25$^{\circ}$); and the $\gamma$class, in which the pitch angles in the near-infrared are $\sim$40$^{\circ}$. Flat or falling rotation curves give rise to the tightly wound $\alpha$ class; rising rotation curves are associated with the open $\gamma$ class. Hence, these dust penetrated classes are inextricably related to the rate of shear in the stellar disk (Block et al. 1999).

In this paper, we further describe the newest quantitative parameter in our near-infrared classification scheme: the gravitational torque of a bar embedded in its disk, based on the theoretical definition of Combes & Sanders (1981). This parameter, called $Q_{\rm b}$, has recently been developed by Buta & Block (2001). Our goal here is to build on this study and to evaluate the visual bar classifications of Hubble and de Vaucouleurs by comparing them with $Q_{\rm b}$.