We report a series of nine experiments which show that a single roll-tilted line in darkness induces changes of the orientation perceived as vertical (VPV) that are similar in magnitude and direction to those measured by Witkin and Asch (1948a) [Studies in space orientation. I. Perception of the upright with displaced visual fields. Journal of Experimental Psychology, 38, 762-782] with the classical square 4-sided frame, and we describe the configuration-independent mass-action rules by which the influences of the individual lines influences are combined. Clockwise (cw) and counterclockwise (ccw) orientations of a line produce cw and ccw displacements of the VPV setting, respectively, with effect magnitude increasing approximately linearly with line orientation (e.g., a 66.25 degrees - long line at 25 degrees horizontal eccentricity that varies in roll-tilt through +/-13.2 degrees around vertical generates a systematic variation in VPV over +/-7 degrees). The slope of the VPV-vs-roll-tilt function increases with line length along a negatively accelerated exponential function (length constant = 17.1 degrees). The influences of two bilaterally symmetric lines combine linearly and algebraically and the combined influence is linearly related to the sum of the VPVs for the 1-line components with a slope equal to 0.91 for short lines and 0.66 for long lines; thus, VPV for short lines manifests nearly complete additive summation, but for long lines, the 2-line VPV is nearer to the average of the VPV values for the two components measured separately. The effectiveness of the conjunction of two line segments within a visual scene does not depend on their separate orientations, only on their sum. Individual lines from pitched-only planes or from combinations of such planes generate identical influences to those generated from lines in frontoparallel planes with the same image orientations at the eye of the observer (their "retinal orientations"). Retinal orientation is the key to the induction of VPV change independently of the line's plane of origin.