PERCEPTION 



1643 



age error of setting the pins while moving the head 

 and eyes is much smaller than with fixed gaze; motion 

 parallax seems to aid in detecting depth. For this 

 reason, von Tschermak-Seysenegg (512) called his 

 device a 'parallactoscope,' by analogy with the stereo- 

 scope. In a further development of these techniques, 

 Graham et al. (167) designed an apparatus permitting 

 the observer to judge separation in depth of two pins 

 moving at identical rates (but at variable distance 

 along the line of regard) before the observer's sta- 

 tionary eye. The situation involves, in essence, appre- 

 hension of differential velocities under rigorously 

 controlled conditions. Graham et al. (167) obtained 

 the remarkably low threshold (for velocity difference) 

 of 30 sec. of arc per second of time. Finally, an in- 

 genious variation of parallactoscopy is represented by 

 the shadow-caster arrangements employed by Gibson 

 et al. (150), in which the shadows of two random dot 

 patterns are superimposed on the same screen (thus 

 controlling accommodation) and moved at inde- 

 pendently varying rates. The efTect for most obser- 

 vers is one of separation of the two arrays in depth, 

 indicating the close connection between motion and 

 depth perception which Gibson (154) has stressed. 



The device also lends itself to further studies ol 

 the ways in which differences in velocity are seen- — 

 a matter investigated under simpler stimulus condi- 

 tions by Ekman & Dahlback (1 1 1 J who elaborated a 

 subjective scale of velocity. Using the psychophysical 

 method of fractionation, they obtained a function 

 relating subjective to objective velocity according to a 

 power law, as Stevens (451) would have predicted. 

 The exponent // in this particular instance turned 

 out to be 1.77, indicating thai perceived velocity in- 

 creases nearly as the square of the objective velocity 

 of a moving target. 



By far the most thorough studies of perceived 

 'real' motion are those of Brown (66-68). In his 

 experiments, the moving objects were small black 

 squares pasted 20 cm. apart on endless white bands, 

 spun at variable speeds behind a variable opening 

 (the widest opening being 2x15 cm.). A stationary 

 fixation point was provided in the center of the 

 opening. This simple device permitted the study of 

 real motion as a function of objective rates of move- 

 ment, size of moving objects, size of opening traversed, 

 distance of the device from the observer, illumination 

 and presence or absence of perceptible structure in 

 the surround. By placing two devices side by side, and 

 varying one or several factors in one of them, the 

 observer could be asked to set the other in such a way 

 as to keep certain perceptual effects invariant. 



Outstanding among Brown's results are the follow- 

 ing: different thresholds for different perceived stages 

 of movement; the crucial role of the surround; the 

 equally crucial role of size of moving object and open- 

 ing; the so-called transposition of perceived velocities 

 with changing size; and the relative -constancy' 

 of perceived velocity with varying distance from the 

 observer's eyes. 



phenomenal stages. Table i gives the thresholds 

 obtained by Brown for the four major stages in per- 

 ception of real motion. We have already mentioned 

 the first threshold for minimal rate (2 to 3 min. of 

 arc per sec. of time); below this speed, motion can be 

 inferred from changes in position of the object (as 

 for the hour hand of a watch) but cannot be per- 

 ceived. At speeds above this threshold range, motion 

 is seen It is al this stage that the seen movement is 

 indistinguishable from optimal apparent motion 

 produced Stroboscopically over the same distance. 

 As speed of the moving belt is increased, a second 

 stage 1^ reached that of apparent reversal in the 

 direction of movement; the moving square appears 

 paradoxicallv at the far end of the opening and seems 

 to jump back toward the point where it enters. With 

 still higher speed, a third stage comes in where the 



observer reports seeing two or several squares for 

 every single square that traverses tin- opening. With 

 (slight) further increases in speed, the observer re- 

 ports fusion; instead of seeing one or several black 

 squares, he sees a gray sneak covering their track. 

 Table 1 indicates 10 what extent threshold values 

 tend to overlap, nevertheless, the sequence as such 

 can be demonstrated with striking regularity. Para- 

 phrasing Brown (68), we can say that a future physio- 

 logic theory of perceived movement must explain 

 both "real and apparent movement, phenomenal 

 velocity, increase in the number of moving objects, 

 the thresholds for fusion, and the impression of dura- 

 tion produced by watching objects in motion.' 

 This means that a really satisfactory theory of any 



table i. Thresholds of Four Stages in Perceived 



Real Motion* 



1 i Minima] rate 



2) Apparent reversal 



;{i Apparent multiplication 



4) Fusion 



* Data from Brown (68). 



2-6 min. of arc per sec. 



3-9 deg. of arc per sec. 



7-15 deg. of arc per sec. 



1 2-3J deg. of arc per sec. 



