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The geometry of perceived space (phenomenal geometry) is specified in terms of three basic factors: the perception of direction, the perception ofdistance or depth, and the perception of the observer's own position or motion. The apparent spatial locations of stimulus points resulting from these three factors thereupon determine the derived perceptions of size, orientation, shape, and motion. Phenomenal geometry is expected to apply to both veridical and illusory perceptions. It is applied here to explain a number of representative illusions, including the illusory rotation of an inverted mask (Gregory, 1970), a trapezoidal window (Ames, 1952), and any single or multiple point stimuli in which errors in one or more of the three basic factors are present. It is concluded from phenomenal geometry that the size-distance and motion-distance invariance hypotheses are special cases of the head motion paradigm, and that proposed explanations in terms of compensation, expectation, or logical processes often are unnecessary for predicting responses to single or multiple stimuli involving head or stimulus motion. Two hypotheses are identified in applying phenomenal geometry. It is assumed that the perceptual localization of stimulus points determines the same derived perceptions, regardless of the source of perceptual information supporting the localizations. This assumption of cue equivalence or cue substitution provides considerable parsimony to the geometry. Also, it is assumed that the perceptions specified by the geometry are internally consistent. Departures from this internal consistency, such as those which occur in the size-distance paradox, are considered to often reflect the intrusion of nonperceptual (cognitive) processes into the responses. Some theoretical implications of this analysis of phenomenal geometry are discussed.

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Two methods of measuring perceived distance as a function of familiar size were compared in five experiments. The method which uses the perception of motion concomitant with a motion of the head. unlike the method of verbal report. is considered to provide a measure of perceived distance that is unaffected by factors of cognitive distance. The results of the experiments indicate that although the perceived egocentric distance of an object can vary somewhat as a function of the cue of familiar size, the larger variation often found with verbal reports of distance is based upon cognitive. not perceptual, information. The cognitive information is interpreted as resulting from the perception of the object as off-sized and the observer's assumption that the perceived size of an object will vary inversely with its physical distance.

Abstract-Using the head motion procedure, the apparent distance of a point of light in an otherwise dark visual field was measured under conditions in which oculomotor cues (accommodation, convergence) and absolute motion parallax were varied together and separately. It was concluded that absolute motion parallax is almost as effective a cue to distance as are oculomotor cues from monocular observation, but is not as effective as oculomotor cues from binocular observation. Evidence was also presented that the null adjustment method, used in conjunction with the head motion procedure, provides an unbiased measure of apparent distance.

This study is concerned with two questions regarding the illusory motion of objects that occurs concomitantly with motion of the head. One is whether this illusory concomitant motion, unlike the perception of real motion, is paradoxical in the sense that, although the object appears to move, it does not appear to go anywhere. The second question is whether illusory concomitant motion can be explained by errors in convergence produced by a tendency for the convergence of the eyes to displace in the direction of the resting state of convergence. Both questions receive a negative answer. In Experiment 1, it is shown that the illusory motion perceptually can add to or subtract from apparent motion resulting from real motion. In Experiment 2, it is shown that, for a binocularly viewed object at a near distance, the error in convergence (fixation disparity) is far too small to be an explanation for the illusory object motion associated with a moving head. The results of both experiments support an interpretation of illusory concomitant motion in terms of errors in the apparent distance of the stimulus object and the veridical perception of its direction.241

Adjacency is an important variable in the perception of object characteristics. The significance of this factor is expressed in the adjacency principle (Gogel, 1965b) which states that the effectiveness of cues between objects in determining perceived object characteristics is inversely related to the relative separation of the objects. The adjacency principle has been demonstrated to apply to the perception of depth from binocular disparity or size cues (Gogel, 1963(Gogel, , 1965b(Gogel, , 1967 but it also can be applied to other perceived characteristics such as the perceived whiteness of objects. For objects in the same Ironto-parallel plane, the magnitude of the whiteness contrast between a test and induction object is inversely related to the separation between the objects (Freeman, 1967). However, adjacency can occur in depth as well as in a fronto-parallel plane, and it has been demonstrated that the former as welI as the latter type of adjacency can be important in determining perceived characteristics (Gogel, 1963). The purpose of the present study is to explore the possibility that depth adjacency is a significant factor in the determination of simultaneous whiteness contrast.If a large black disc is presented under strong iIlumination in an otherwise totalIy dark visual field, the disc wiII appear to be white or whitish-grey. If a smalI white disc with a luminance much greater than that of the large disc is placed on the large disc, the large disc will decrease sharply in perceived whiteness. This decrease in perceived whiteness is known as the Gelb effect. Stewart (1959) has shown that, contrary to what had been previously assumed, the Gelb effect can be explained as a contrast phenomenon since it follows the general laws of contrast. The size and location of the small disc on the large disc predictably modifies the apparent whiteness of the large disc. In the present study the Gelb effect was measured with different apparent separations in depth between the large and small disc. It is expected, if depth adjacency is an important factor in whiteness contrast, that increasing the apparent depth separation between the two discs wiII decrease the darkening effect that the small disc has upon the perceived whiteness of the larger disc.A change in Ironto-parallel separation involves a change in relative retinal position. A change in only radial depth, however, produces little change in the relative positions of objects on the retina even though binocular observation is used. It follows that, if a change in radial depth position alone is found to be significant in this study, factors other than relative retinal location must be involved in simultaneous whiteness contrast, i.e., the contrast phenomenon is not determined solely at the retinal level of organization. Furthermore, if it can be demonstrated that the significance of the depth dimension for the induction effect is independent of the particular depth cues used in registering the depth dimension, it is likely that the important factor in the adjacen...