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II WDI'.i 11 IK 1 il PHYSIOLOGY 



M I ROI'HYSIOLOGY III 



various phenomenal types of movement [see Boring 



pp. 596-597, for an inclusive list]. 

 The report was followed during tin- next two 

 decades l>\ more than 100 other studies of apparent 

 motion. Manx ol these were concerned with further 

 quantification of the interval / and the distance >. 

 [The earlier studies are summarized in Koflka's 

 chapter (283) on motion perception in Bethe's 

 Handbuch; for later reviews, sec Neff (359) and 

 Graham (166).] Results were at times discordant 

 as in details, and it became clear, soon after Werthei- 

 mer's report, that his values for / (e.g. 60 msec, for 

 optimal movement) did not necessarily hold in other 

 experimental settings. Nevertheless most of the later 

 studies have confirmed the basic sequence (from per- 

 ceived succession via optimal motion to simultaneity) 

 and the crucial role of the interval / in determining 

 these Stages. The complex interdependence of /, s 

 and the intensity of stimuli (t) is usually specified in 

 the form of Korte's "laws' (289) of apparent motion 

 which can be stated briefly in the following set of 

 formulas [see Boring (53) and Graham (166)]: 



[f i = const., / ,,t ~ s; s ov , ~- /. 

 [f t = const., Jo,,! ~ *; topi ~ s. 

 Us = const., /o,„ ~ 1//; * op t ~ i/«. 



Thus, for a given intensity i, the time interval / 

 between the stimuli has to be increased (decreased) 

 as the distance s is increased (decreased), in order to 

 maintain optimal motion. For a given time interval 

 /, the same direct relations hold between i and ,r; 

 as one is changed, the other has to be changed in the 

 same direction to keep the perception of motion in- 

 variant. Finally, if the distance 1 is held constant, 

 t and / vary reciprocally; for instance, an increase 

 in intensity h.is to be counterbalanced by decreasing 

 the interval, and conversely. 



There are difficulties with these expressions which 

 make 11 unwise to call them 'laws'; the upper and 

 lower limiis ol their validity need to be defined. 

 I line are some contradictory experimental results 

 even in the midrangc ol values (3(101, ,md there is an 

 Unfortunate ambiguity in the parameter / which is 

 me. ml to designate luminous energy as well as area 

 oi the targets (166). However, ii is possible, in prin- 

 ciple, to give these expressions the precision obtained 

 in parametric studies of other sensor) dimensions 

 and in obtain an isokinetic surface which defines con- 

 ditions of optimal motion perception (in direel anal- 

 ogs 10 isochromatic and isophonic contours, de- 

 picted in figs 1 .mil 2). Such an isokinetic surface 

 would lie in .1 tridimensional space, in which r, / 



nc. 30. Effects of recent exposure history and of stimulus 

 configuration on the path of apparent movement. /, // Alter 

 repeated exposure of lines a and b, at intervals leading to 

 apparent motion from a to b, observers continue to report 

 motion from a to b over the paths indicated by curved arrou > 

 ///: The two V-shaped patterns u and b, if alternately exposed in 

 the positions shown, lead to apparent motion through the 

 third dimension, in and Out of the projection surface, thus 

 maintaining the shape of the V. [Adapted from Wertheimer 

 (536), Koffka (283) and von Schiller 1308).] 



and i are coordinates specifying conditions of optimal 

 movement. Outside of the surface, and to one side 

 of it, would be the conditions for simultaneity; to 

 the Other side, those for succession. 



Undoubtedly, other factors in addition to s, t 

 and i can enter into the determination of apparent 

 motion effects, such as earlier exposures I see fig, 30), 

 or special colors or shapes of the targets (fig. 30). 

 Ambiguous patterns can be designed which permit 

 alternative motions to be perceived (508). Some of 

 these patterns have been used in tests of cerebral 

 dominance by Jasper (239) and ('alter (86) How- 

 ever, the most important aspect of apparent motion 

 is the observer's inability to discriminate optimal 

 apparent motion from real motion of a single target 

 over the same path (mo, to6, 360), and the remark- 

 able inierchangealiilitv ol spatial and temporal 

 determinants expressed in the formulas given above. 

 Another and simpler wav ol demonstrating this inter- 

 changeability is to project three spots ol light, A, 

 B and C, in a dark room so that they form a horizontal 

 line with the middle dot, B, equidistant from A 111 

 the left and C to the right II A and B are made to 

 alternate slowly (but within the range of apparent 

 motion), and B and C more rapidlv (though -till 

 within that range 1, then the distance from A to B 



