If elliptical galaxies are triaxial systems, it is possible to derive the distribution f (b / a, c / a) of the intrinsic axial ratios from that of the projected ones, only if an assumption is made on the length of the middle axis (Benacchio and Galletta 1980; Binney and de Vaucouleurs 1981). Considering the sample of major and minor axis dust lane ellipticals it should be possible to put constraints on f. In fact, since the permitted planes for the dust are those defined by the major and minor axes each with the intermediate axis, the apparent major axis coincides with the true major axis for the minor axis dust lane ellipticals, and the apparent minor axis coincides with the true minor axis for major axis dust lane ellipticals. In this way the apparent distribution is a function of f and of only one projection angle, which is the angle between the intermediate axis of the galaxy and the line of sight.
The distribution of the intrinsic axial ratios of dust lane ellipticals can be constrained further by considering the relative number of minor to major axis dust lane ellipticals. The number of ellipticals with the dust lane along the minor axis listed in Table I is 30, while major axis ones are 9, so that the latter galaxies represent 22% of the total. On the other hand this percentage in the compilation of Ebneter (1986) is 57%, owing to the inclusion among major axis dust lane ellipticals of a large number of galaxies possessing a luminous disk. It should be noted that the survey of Hawarden et al. (1981), which has the advantage of being statistically meaningful since it is based on a survey on the Sky Survey plates, lists 6 major axis dust lane ellipticals (excluding doubtful cases) as against 12 minor axis ones. The fact that in our listing, minor axis dust lane ellipticals outnumber major axis ones leads us to belive that there is an intrinsic paucity of the second ones with respect to the first. As has been mentioned already, the potential of a triaxial galaxy which acquires gas (and dust) from outside will force the gas to orbit in the planes defined either by the minor and intermediate axes, or by the major and intermediate axes. The settling toward one of the two planes depends on the orientation of the initial rotation axis of the gas. The shape of the galaxy defines the fraction of the orientation sphere for which the gas will settle onto one of the two planes (Steiman-Cameron 1984). It is therefore clear that the total fraction of objects with dust rings or disks perpendicular to the major axis that we observe as minor axis dust lane ellipticals, is a function of the distribution of the intrinsic flattening, which is again constrained by an observational quantity. In other words the result on the relative number of minor to major axis dust lane ellipticals would indicate a tendency toward prolateness than toward oblateness for our sample of galaxies. A statistical analysis along these lines is in progress by Bertola, Galletta, Vietri and Zeilinger.