The misalignment which is seen in the Poggendorff illusion can be studied with better control by using a configuration which has only two line segments. Two experiments were conducted in which subjects judged collinearity of a test segment, this judgment being subjected to a biasing influence from a second (induction) segment. Exp. 1 held the test segment at one of three orientations relative to the observer (30-degrees, 45-degrees, and 60-degrees) and systematically varied the orientation of the induction segment in 15-degrees increments through the range of possible positions. The orientation of the page relative to the observer was varied as well. Exp. 2 varied the test segment through a greater range of angles and sampled more levels of induction segment orientation. Analysis indicated that projection errors follow orderly rules similar in kind to but different in magnitude from those observed for the Tilt Illusion, most notably, (a) misprojection is greatest when the orientation of the interfering line is similar to that of the line segment being projected and (b) the strength of this influence decreases as the relative angle becomes orthogonal. Also, the orientation of the segment being projected relative to the observer serves to modulate the strength of the basic induction effect. These perceptual interactions are discussed in relation to neural models for orientation selectivity.