AM 69-15 

THE SPIRAL AFTEREFFECT. II. 

SOME INFLUENCES OF VISUAL ANGLE AND RETINAL 

SPEED ON THE DURATION AND INTENSITY OF 

ILLUSORY :NIOTION 

Approved by 

~~ J. RoBERT DILLE, M.D. 

CHIEF, CIVIL AEROMEDICAL 

INSTITUTE 

Mary Jane Williams, M.S. 

William E. Collins, Ph.D. 

August 1969 

Released by 

~MD P. v. SIEGEL, M.D. 

FEDERAL Am SuRGEON 

Department of Transportation 

FEDERAL AVIATION ADMINISTRATION 

Office of Aviation Medicine 
THE SPIRAL AFTEREFFECT. II. 

SOME INFLUENCES OF VISUAL ANGLE AND RETINAL SPEED ON THE 

DURATION AND INTENSITY OF ILLUSORY MOTION* 

I. Introduction. 

Visual illusions have been a persistent problem 

in aviation research. Many o£ these illusions are 

produced by misleading cues. Movement aftereffect, however, represents a different type o£ 

visual illusion-that which occurs following the 

cessation o£ real motion. Included amonO' these 

is the spiral aftereffect-the apparent r:versed 

motion o£ a spiral after it ceases spinning. The 

influence o£ visual angle upon the duration o£ 

movement aftereffects has been typically approached in past studies by varying stimulus size 

at a constant distance. Infrequently, distance 

variation \vith the same size stimulus has been 

employed,9 10 13 and in one investigation 1 both . ' s1ze and distance were alternately varied to produce the same visual angles. Most o£ the studies 

used no more than two or three visual angles 

and the conclusions reached by the various investigators are in conflict. 

Thus, Freud4 found a positive linear relationship £or spiral aftereffect (SAE) duration scores 

using visual angles o£ 2°, 4°, and 8°, but McKenzie and Hartman14 obtained no significant 

differences among scores with angle variations o£ 

2° 8', 4° 14', and 6° 22'. Holland12 13 duplicated 

the latter result with angles o£ 4° and 6°, However, Pickersgill and J eeves/5 using visual angles 

within the same range, found a nonlinear eff~ct: 

a significant increase £rom 2° 52' to 5° 44' but a ' decrease at 11° 26'. Similarly, Fozard, Fuchs, 

Palmer, and Smith3 found, with three visual 

angles, that duration scores were highest at either 

2° 23' or 4° 46', but decreased notably at 9° 23'. 

G~anit9 10 used a wide range o£ visual angles, 

varymg the distance o£ his stimulus-a waterfall drum-from the observer. He found a 

marked peak in duration scores between 2° to 

4° o£ visual angle. He noted that as visual angle 

decreased, so must the retinal speed-the speed 

1 

o£ the stimulus pattern at the eye, as distinct 

£rom the physical speed o£ the stimulus. As the 

drum's distance £rom the retina increased, the 

retinal image it formed would diminish, and since 

the drum maintained a constant speed a O'iven • ' 1::> 

pomt o£ the stimulus pattern \vould move through 

a smaller distance per unit time across the retina. 

The retinal speed, "which actually establishes the 

speed sensation," would be less. 

Scott and Noland,17 re-emphasizing the importance o£ retinal speed, presented a formula £or 

calculating the "speed o£ eliciting motion" 

(SEM), which subsumes visual angle as a £actor 

and is expressed in minutes o£ arc per second 

( minarcsjsec.). They calculated the SEM £or 

three previous studies, those o£ Scott 16 o£ . ' Gramt,9 10 and o£ Freud,4 and found that the 

aftereffect in each study increased £rom 30 to 132 

minarcsjsec. and then declined. They concluded 

that aftereffect duration could be predicted on 

the basis o£ SEM alone, though other variables 

might also influence it. 

Collins and Schroeder1 varied visual angle by 

both size and distance manipulation, using nine 

visual angles ranging £rom 1° 12' to 18° 56'. 

They confirmed the peak in duration scores £rom 

2° to 4° reported by Granit. They also calculated 

SEM £or their data and £or the data o£ Fozard 

et az.s They found that £or their own data SAE 

durations increased £rom 30-60 minarcs;s:c. declining thereafter. But £or the data o£ Fo~ard et al. 3 , peaking occurred at considerably higher 

*A major portion of the material presented here was 

submitted by the first-named author to the Psychology 

Department, University of Oklahoma, in partial fulfillment of the requirements for the degree of Master of 

Science. Assistance rendered by David J. Schroeder 

and Ruth Ann Mertens during pilot studies, and helpful 

comments by Dr. Walter C. Gogel during preparation 

of the manuscript, are gratefully acknowledged. 
SEM values depending upon the comanipulation 

of other variables, although visual angle appeared 

to be a dominant factor. 

Though computed after the fact from studies 

designed to test the influence of other variables, 

SEM has never been systematically manipulated 

in reported experiments. The present study was 

designed to evaluate its influence and, using 

variations of both size and distance across a wide 

range of visual angles, to obtain information concerning the influence of visual angle upon the 

duration and perceived intensity of the spiral 

aftereffect. 

II. Method. 

Subjects. Subjects ·were 10 paid male volunteers, 20-29 years of age, who met the visual 

requirements for "mechanics and skilled tradesmen" on the Bausch and Lomb Ortho-rater: uncorrected distant acuity of at least 20/30, near 

acuity at least 20/25, normal muscle balance, and 

normal depth perception. Actual perception of 

the illusion was required in preliminary trials 

which also served as demonstration and practice. 

Apparatus. The subject observed the spirals 

in a 48-foot visual alley, at one end of which 

was the enclosed, illuminated observer's box. The 

subject sat with his head positioned in a chin 

rest and sighted the spiral through a binocular 

eyepiece. The sides and far end of the alley 

were draped in white; the floor was tiled in a 

light-dark gray checkerboard pattern. Fluorescent lighting recessed in the ceiling was uniform 

along the length of the alley. 

Six spirals of 4-, 8-, 10-, 12-, 14-, and 16-inch 

diameters were used. Each was a photographic 

reproduction of a three-throw arithmetic spiral 

with the white background area equal to that of 

the black spiral coil. These were rotated so as to 

produce an expanding aftereffect. 

Attached to the drive shaft of the variablespeed motor was a Plexiglas disc v.'ith 12 magnets 

mounted at its circumference which, as the motor 

revolved, induced current in a solenoid. This, in 

series with a diode rectifier, sent a direct current 

to a voltmeter. A calibration curve, derived by 

use of an electronic digital counter, related the 

readings of the voltmeter to motor speed so that 

a given motor speed could be obtained by adjusting the resistor speed control until the voltage 

corresponding to that speed registered on the 

voltmeter. 

2 

The motor-voltmeter apparatus was set on a 

wheeled cart, on one side of which was mounted 

a flat-gray plyboard screen. (17 X 18 inches) 

which faced the observer and served as a viewing background. Spirals were attached to the 

drive shaft of the motor which projected through 

a hole in the screen. 

Conditions. There were five conditions: (1) 

With angle constant (A), the six spirals were 

used at distances varied to produce a constant 

visual angle ( 4 °) , and both retinal speed (50 

minarcsjsec.) and motor speed (75 r.p.m.) were 

constant; (2) ·with size constant, an 8-inch spiral 

was employed at distances ranging from 2.37 ft. 

to 38.18 ft., giving visual angle variations from 

1° to 16°; (3) with retinal speed varied from 20 

to 200 minarcsjsec. (S1 ), or held constant, at 20 

or at 50 minarcsjsec. (S2 ). (Limitation of motor 

speed capacity precluded the use of one constant 

retinal speed from 1° to 16°. The lower value 

was used at 1° and 2° ; both values were used 

at 4° as a check upon continuity of function.); 

( 4) with distance constant, the six spirals were 

viewed at a distance of 4.77 ft. giving a visual 

angle from 4° to 16°; (5) with retinal speed 

either varied from 50 to 200 minarcsjsec. (Dt) 

or held constant at 50 minarcsjsec. (D2 ). These 

conditions were presented to the subjects in counterbalanced order, one condition per day for 5 

consecutive days. The various size-distance-speed 

combinations within each condition (see Table 1) 

·were almost completely counterbalanced among 

subjects. 

Pre- and.Post-Trials. To test for possible fatigue or habituation effects either within a day's 

session or over the 5 days, a standard stimulus 

(an 8-inch spiral at 9.55 ft. rotating at 75 r.p.m.) 

was presented in two pre-trials and two posttrials for each session. Both duration and intensity measures were obtained. The intensity 

of the aftereffect in the first pre-trial was arbitrarily called "100%" and served as the standard against which all intensity judgments were 

made during that session. 

Procedure. Each trial was immediately preceded by a 15-second period with the subject's 

head positioned at the eyepiece, but with his eyes 

closed. This procedure was necessary in order 

for the motor to reach and stabilize at the desired speed at very low r.p.m. At a signal from 
TABLE 1.-The Stimulus Conditions Used in the Various Sessions 

Size Constant Sessions: 

Spiral size Distance Visual angle SEM* at motor speed of Motor speed for 

(Inches) (Feet) (Degrees) 120 r.p.m. (minarcs/sec.) 20 minarcs/sec. (r.p.m.) 

8 38.18 1 20 120 

g 19.29 2 40 60 

8 9.55 4 80 30 

SEM at motor speed of Motor speed for 

75 r.p.m. (minarcs/sec.) 50 minarcs/sec. (r.p.m.) 

g 9.55 4 50 75 

g 4.77 g 100 37.5 

g 2.37 16 200 1g,g 

Distance Constant Sessions: 

Spiral size Distance Visual angle Motor speed for SEM at motor speed of 

(Inches) (Feet) (Degrees) 50 minarcs/sec. (r.p.m.) 7!'i r.p.m. (minarcs/sec.) 

4 4.77 4 75 50 

g 4.77 8 37.5 100 

10 4.77 10 31.3 125 

12 4.77 12 25 150 

14 4.77 14 21.5 175 

16 4.77 16 1g,g 200 

Angle Constant Session: 

Spiral size Distance Visual angle 

(Inches) (Feet) (Degrees) Motor speerl (r.p.m.) SEM (minarcs/sec.) 

4 4.77 4 75 50 

8 9.55 4 75 50 

10 11.93 4 75 50 

12 14.32 4 75 50 

14 16.70 4 75 50 

16 19.09 4 75 50 

SEM refers to the. speed of eliciting motion of the stimulus. 

TABLE 2.-Means and standard deviations for the duration (in seconds) of the spiral aftereffect. Each mean is based on an average of three judgments for each of 10 subjects. 

Distance constant (4.77 ft.) 

Condition 

40 go 100 12° 140 16° 

Dl_ -- - ------- - --- M _____________ 14.62 14.26 14.73 13.05 12.77 13.58 SD ____________ D2 10.61 10.63 12.02 10.96 11.32 11.90 _______________ M _____________ 14.43 13.30 14.36 13.67 12.39 14.15 SD ____________ 6.72 6.07 6.96 7.04 6.34 g,48 

Size constant (8 inch spiral) 

(Spiral speed: 120 r.p.m.) (Spiral speed: 75 r.p.m.) 

Condition 

10 20 40 40 go 16° 

gt ________________ M _____________ 16.51 16.91 16.11 15.65 13.8g 9.go SD ____________ 6.51 7.39 7.23 7,0g 9.09 g,62 

(20 minarcs/sec.) (50 minarcs/sec.) 

82---------------- M _____________ 19.47 

SD _______ -- _ -- 9.95 

Condition 

4 in. 

A ________________ M _____________ 16.42 SD ____________ 10.97 

the experimenter, the subject viewed the rotating 

spiral for 15 seconds and then maintained fixation while marking the duration of the illusion 

by pressure on a microswitch which was connected 

14.80 13.33 17.42 12.44 9.52 

g,66 7.85 11.65 8.71 9.g6 

Angle constant (4°) 

gin. 10 in. 12 in. 14 in. 16 in. 

16.41 17.71 1g.02 19.25 19.34 

9.35 9.45 9.6g 9,g1 11.93 

to a time clock. When the duration score was 

recorded from the clock, the subject rated the 

intensity of the illusion on the basis of the day's 

100% standard. 

3 
TABLE 3.-Means and standard deviations for the rated intensity (in percent) of the spiral aftereffect.. Each mean is 

based on three ratings for each of 10 subjects unless otherwise indicated. 

Distance constant (4.77 ft.) 

Condition 

40 go w• 12° 140 16° 

D1 _______________ M ____________ _ 61.00 63.20 59.50 51.4 4g,3o 52.60 

D SD ___________ _ 27.54 27.45 32.93 30.90 32.13 31.39 2 _______________ M ____________ _ 67.70 64.50 53. 10 49.20 51. go 6o,go SD ___________ _ 22.20 22.70 30.26 33.77 29.01 31.59 

Size constant (g-inch spiral) 

Condition (Spiral speed: 120 r.p.m.) (Spiral speed: 75 r.p.m.) 

St ________________ M ____________ _ SD ___________ _ 

10 

132.70* 

130.65* 

20 

103.70* 

43.1g* 

40 

gl, 30 

19.93 

40 

77.20 

29.17 

go 

59, go 2o,gg 

16• 

26.90 

23.75 

(20 minacrcs/sec.) (50 minarcsjsec.) 

S2 ________________ M _____________ 109.40 SD ____________ 54.20 

Condition 

4 in. 

A ________________ M _____________ 69.20 SD ____________ 25.13 

*For N=9 (see text and Figure 2), these values are: 

M ____________ _ SD ___________ _ 

III. Results. 

10 

91. g9 

21.60 

Average of the three duration scores and of the 

three intensity ratings for each subject at each 

trial setting were obtained. These means were 

then averaged to provide a group mean for each 

setting. These, presented in Tables 2 and 3 and 

plotted in Figures 1 and 2, show, for both duration and intensity measures, different functions 

with size variation and distance variation, and a 

sharp divergence from the expected horizontal, 

straight-line function with visual angle and retinal speed held constant. 

Visual Angle 

Visual Angle Constant. 

A: With a systematic increase of size and distance to maintain a 4° visual angle, and with 

r.p.m. and SEM constant, the aftereffect might 

be expected to be essentially the same in duration and intensity at each setting of the A session. 

Instead, duration scores (Figure 1a) increased 

significantly ( t = 3.257; p < .01) from the smallest 

(closest) to the largest (farthest) spiral. Intensity ratings (Figure 2a) showed a similar increase, but the rise just failed to reach significance at the .05 level ( t = 2.194; t of 2.262 re79.20 53.70 76.00 50.50 29.30 

34.21 2g,59 16.69 27.76 26.54 

Angle Constant (4°) 

gin. 10 in. 12 in. 14 in. 16 in. 

g5,30 

16.9g 

73.60 71. 10 73.50 7g.oo 

16.33 17.17 21. g3 17.45 

20 

91.11 

17.73 

4 

qui red for significance at .05 level) . Therefore, 

though visual angle was constant, the aftereffect 

increased in duration (and in intensity) as size 

and distance increased. 

Di8tance Con'5tant. 

D 1 and D 2 : \Vhen visual angle was varied by 

manipulating spiral size at a constant distance, 

no significant effect upon duration scores (Figure 

1 b) or intensity ratings (Figure 2b) was found 

in either the D 1 or D2 sessions. There may be a 

slight tendency for duration and intensity to 

increase with smaller visual angles, a possibility 

receiving some slight confirmation (not statistically significant) from data obtained with an 

additional, smaller (2°) angle presented to the 

last six of the 10 subjects tested. 

Size Constant. 

S1 : ·with r.p.m. constant at 120, duration scores 

increased from 1° to 2°, and then declined to the 

4° angle (Figure 1c). The decline continued 

from 4° to 16°, a significant difference (t=4.199; 

p<.01) with r.p.m. at 75. As with duration 

scores, intensity ratings declined significantly 

(t=5.618, p<.001) from 4° to 16°, but did not 

differ significantly from the 1° to the 4° angles. 
20 

19 

18 

17 

en 16 

Q 

z 

0 2 3 4 5 6 7 8 9 10 I I 12 13 14 15 16 

(.) 

w SPIRAL DIAMETER IN INCHES 

en 

z 15 (b) 

.,_ 14 e~./~c a 

(.) 

w 13 Distance Constant (4.77') c ·~/ LL. D1: •-• 75 RPM 

LL. 12 o2:o-o 50 Minarcs /Sec w 

0::: 

w 2 3 4 5 6 7 8 9 10 If 12 13 14 15 16 

.,_ 

VISUAL ANGLE IN DEGREES LL. 

<{ 

_J 20 (c) <{ 0 

·a::: 19 \ 

a... \ 

en 18 \ 

\ 0 

LL. 

17 .......... ..... , ........... 

0 16 ....... \ . 

z 15 \ 

0 o, 

14 ' .,_ ' • <{ ' 0 

0::: 13 

::> 0 

Q 12 

I I Spiral Size Constant (8" Diameter) 

{ ·-· 75~ RPM 

10 S I e- -• 120 RPM • { o--o 20 Minarcs I Sec 0 

9 s2 o-o 50 Minarcs I Sec 

2 3 4 5 6 7 8 9 10 I I 12 13 14 15 16 

VISUAL ANGLE IN DEGREES 

FIGURE 1. Durations of the SAE obtained from 10 subjects for the five experimental conditions. Note the peaking 

effect at the 2° visual angle in chart (c). 

5 
90 

80 

70 

60 Visual Angle Constant ( 4 °): 50 Minarcsl Sec; 75 RPM Motor Speed 

Iz 

w 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 

(.) 

SPIRAL DIAMETER IN INCHES 

a:: 

w (b) a.. 70 D 

z 60 • ~~- D 

50 Distance Constant (4.77') 0~~::-:::::::~::::::=- I- D1:•-• 75 RPM (.) 40 

w D2: D-D 50 MinarcsiSec 

Ll.... 

Ll.... 

w 2 3 4 5 6 7 8 9 10 II 12 13 1.4 15 16 

a:: VISUAL ANGLE IN DEGREES w 

ILl.... 140 <( (c) X 

_J 130 

<( 120 a:: 

a.. II 0 0 

en \ 

100 \ X 

Ll.... \ 

0 90 ·-, ....... ...... 

>- 80 

Ien 70 \,''a~ z 60 w ' . ' I- 0 

50 0 

z 

40 Spiral Size Constant (8" Diameter) 

30 { ·-· 75 RPM 

sl •--• 120 RPM 

20 { o--o 20 Minarcs I Sec s2 o-o 50 Min arcs I Sec 

2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 

VISUAL ANGLE IN DEGREES 

FIGURE 2. Perceived intensity of the SAE obtained for the five experimental conditions. All data points are based 

on 10 subjects with the exception of the 1 o and 2° visual angles in the S1 session of chart (c) ; these points are 

based on an N of 9. The subject excluded from these plots gave unusually high ratings to stimuli at these two 

angles; the two "X's" indicate the position of those points if the deviant subject is included in the means 

(i.e., for N=lO). 

6 
Instead of a rise to a peak, intensity ratings 

showed a flattening from 1° to 2° and a drop to 

4°. Extreme ratings of one subject, which markedly inflated the group mean intensity at the 1° 

and 2° angles were eliminated from the 120-

r.p.m.-constant portion of this session (see Figure 

2c). 

tained by varying it widely, at least above 50 

minarcs/sec. In 8 1, retinal speed increased from 

50 minarcsjsec. at 4° to 200 minarcsjsec. at 16°, 

but at no angle do these scores or ratings differ 

significantly £rom those obtained with retinal 

speed constant at 50 minarcsjsec. in 82 • Indeed, 

at the largest angle the data points £or sl and 82 

(obtained at 200 and at 50 minarcsjsec. respectively) almost coincide on the figure, both for 

duration and £or intensity (see Figures 1c and 

2c). Similarly, with Distance Constant, a constant SEM (D2 ) produced virtually the same 

£unction as that obtained where, with r.p.m. constant (D1 ) it increased fourfold (Figures 1b and 

2b). 

S2: With SEM constant, duration scores did 

not peak at 2° as they did in the sl session, declining instead from 1° through 4 ° ( t = 3.4 7 4; 

p<.01) with 20 minarcsjsec. constant, and from 

4° to 16° (t=5.251; p<.001) with 50 minarcsj 

sec. constant (Figure lc). Intensity ratings 

(Figure 2c) also showed a significant decrease 

£rom the 1° to the 4° angle (t=2.933; p<.02), 

and £rom the 4° to the 16° angle (t=5.264; 

p<.001). Thus, with SEM constant, SAE 

duration and intensity decreased steadily as a 

£unction of increasing visual angle (and o£ decreasing r.p.m.). 

Retinal Speed 

In general, holding retinal speed constant did 

not produce an effect different £rom that obPre- and Post-Trials. 

Pre- and post-trial group means and standard 

deviations are presented in Table 4. With duration scores, there is no progressive decline either 

within sessions or over sessions. With intensity 

ratings, however, vdthin session declines were 

significant for the first three of the five sessions. 

TABLE 4.-Means and standard deviations for the duration (in seconds) and rated intensity (in percent) for the standard 

spiral stimulus given to each subject in Pre- and Post-experimental trials at each session. Each value is basetl on two trials for each of 10 subjects unless otherwise indicated. The standard stimulus was an 8-inch spiral, rotating 

at 75 r.p.m., 9.55 feet from the subject. 

Duration Intensity 

Day 

Pre Post t Pre Post t 

1*--------------- M _____________ 14.06 14.81 0.664 92.50 67.50 3.656*** SD ____________ 2.93 4.00 8.78 18.03 1 ________________ M _____________ 15.49 94.75 SD ____________ 5.49 8.03 2 ________________ M _____________ 15.80 15.75 0.887 96.25 67.75 3.067** SD ____________ 6.11 7.55 8.10 26.79 3 ________________ M _____________ 14.33 16.45 1. 469 98.00 72.25 3.567*** SD ____________ 7.54 10.73 3.29 23.55 4 ________________ M _____________ 16.51 16.93 0.301 97.00 84.75 1.622 SD ____________ 12.47 12. 12 4.68 21.52 5 ________________ M _____________ 14.21 14.02 0.134 97.50 73.20 2.051 SD ____________ 10.28 11.81 4.08 35.79 

*Data for this day are based on 7 subjects. (No Post data were obtained for three subjects.) 

**Significant beyond the .02 level. 

***Significant beyond the .01 level. 

IV. Discussion. 

The SAE seems to vary in intensity as it does 

in duration in response to the experimental 

manipulations o£ this study, the plots o£ the two 

measures across visual angle or spiral size being 

generally parallel £or each session (compare 

Figures 1 and 2). Wohlgemuth18 reported similar results when judgments of duration and 

"vividness" both were studied-the latter not 

7 

being quantified but merely expressed in terms 

o£ a given after-effect being "more" or "less" 

intense than a preceding one. 

An exception to the similarity between the two 

measures is the statistically significant decline in 

intra-session intensity ratings o£ the "standard" 

stimulus £rom pre- to post-test £or 3 of the 5 

days, a decline not found with duration scores. 

Though SAE "strength" apparently decreased 
within some sessions, the decrement was not sufficient to alter the duration scores, as measured 

by the pre- and post-tests. Adequate spacing of 

trials apparently prevented habituation as well 

as fatigue effects from manifesting themselves 

in SAE duration scores. 

Results of the five sessions seriously prejudice 

an assumption of either visual angle or retinal 

speed as the predominant influence on SAE 

measures. Manipulating visual angles produced 

results that differed according to the manner of 

variation (i.e., change of stimulus size or change 

of distance). At a given angle, wide differences 

in retinal speed produced no differential effect 

on SAE measures except possibly at low values. 

Further, where both visual angle and retinal 

speed were constant (A condition) , there was a 

significant increase in aftereffect duration (Figure 1a) and a general increase in intensity ratings (Figure 2a) as stimulus size and distance 

were concomitantly increased. Other determinants must be operating. 

Granit9 found results identical to those of our 

A condition in an extension of his aftereffect 

experiment which yielded the peak in duration 

scores between 2° to 4°. He placed a reduction 

screen in front of the waterfall drum with a 

square window in it through which to observe the 

moving stripes. With varied window sizes of 

12-, 9-, and 6-cm. square, he obtained a family of 

curves, each peaking between 2° and 4°, but 

ranged on the ordinate score according to window 

size, the larger windows producing consistently 

longer durations. At any given distance, then, 

there was a positive linear relationship for size 

and duration (a discrepancy from the peaking 

he obtained in each of the family curves). However, one may also adduce from these curves that 

at any visual angle, durations increased with 

size-distance increase, exactly the result of the A 

condition of the present study. ( Costello2 also 

reported the duration produced by a larger, more 

distant spiral as longer than that of a smaller, 

closer spiral sub tending the same visual angle.) 

To explain his discrepant results, Granit9 mentioned that size constancy might be operating 

differently in the two test conditions. In the 

present study there were ample cues to distance 

in the texture density of the checkered floor and 

in the perspective lines formed by the ceiling and 

sides of the visual alley. On the basis of size 

constancy principles, it may be assumed that the 

8 

subjects would have been aware of the changes 

in spiral size in the D 1 and D2 sessions, of the 

constant size of the spiral (and changing distances) in the sl and 82 sessions, and of the 

changes in both spiral size and distance in the A 

sessions. The results of this study may, therefore, be reinterpreted in terms of perceptual 

variables. In particular, the duration of the 

SAE appears to increase with increases in perceived size (S') per unit of retinal size (visual 

angle 8). This S 'I 8 ratio, a variable of longstanding interest in the visual perception work 

of Gogel,5 6 8 is probably equivalent, in the present experiment (and under the usual form of 

the "size distance in variance hypothesis"), to 

perceived distance (Gogel's D'). If it is assumed that perfect size constancy occurred for 

the subjects in this experiment then, in the A 

session, with 8 constant ( 4°) and S' increasing 

as spiral size was increased, S' /8 would also 

increase; thus, SAE durations were longer for 

larger values of S' j8. In the D sessions, S' /8 

would have been a constant (unity, i.e. 1) for 

each stimulus as spiral size and visual angle were 

concomitantly increased at a single distance; no 

significant change in duration scores would be 

predicted, then, from the smallest to the largest 

visual angle, and none occurred. In the S sessions, still assuming perfect size constancy, S' 

would have been constant with (8-inch spiral) 

while 8 increased as the spirals were placed closer 

to the subjects. Thus, S' /8 would have increased 

from the largest to the smallest angles in the S 

sessions and, as in the D sessions, SAE durations 

increased with increases inS' j(). 

That an ilfusion might vary with certain perceived rather than physical characteristics of the 

stimulus receives support from the report of 

Gogel and Mershon5 that the perceived whiteness 

contrast of two discs is influenced not only by a 

real displacement in depth between them but also 

by apparent or perceived displacement. What 

Gogel and Mershon7 term "a relationship between 

perceptual events" may apply to the results of 

this study; i.e., the characteristics of aftermovement may be determined by the phenomenal, 

as well as by the retinal or physical dimensions 

of the stimulus. Additionally, Hildt and Van 

Liere11 have reported longer SAE durations for 

"depth-cued" as opposed to "non-depth-cued" 

test figures. 
The above paradigm, though hypothetical, 

neatly fits the result for all conditions except for 

the slight peak in duration scores in sl not found 

in S2• This peaking (or flattening) effect at 

small visual angles is apparently a reliable phenomenon for an "r.p.m. constant" condition; it 

can be found in the data of Granit,9 10 Pickersgill 

and Jeeves,I5 Fozard et al.,3 and Collins and 

Schroeder.1 Granit9 10 explained the peak as 

reflecting an increase in the aftereffect with increased visual angle and retinal speed to the 

point (2° to 4°) where the rod receptors begin 

to predominate. The increasing rod density at 

larger visual angles was thought to inhibit cone 

function in a progressive fashion, thereby causing 

the steady decline in aftereffect measures as angle 

size was increased beyond 4°. 

However, alternate explanations can be proposed which involve either a breakdown of size 

constancy at the greater distances or the possible 

influence of retinal speed at low values, i.e., below 

approximately 50 minarcsjsec. Increases in SEM 

from 50 to as much as 200 minarcs/sec. clearly 

produced no significant differential effect on SAE 

duration or intensity measures at various angles, 

either with distance constant or with size constant. Yet at the 4° angle in the S2 session, 

where a direct comparison can be made of data 

for the same visual angle on the same experimental day, there is a difference in duration 

scores obtained with stimuli of 20 minarcsjsec. 

from those obtained with 50 minarcsjsec. that is 

considerable, though it does not reach significance at the .05 level. 

If retinal speed change is an effective variable 

only at low rates (below, say, 40 to 50 minarcs/ 

sec.), then the peaking phenomenon in sl may be 

due to a rise in SEM from 20 to 40 minarcsjsec. 

(from the 1° to the 2° visual angle), with the 

increase to 80 minarcsjsec. at 4° failing to overcome the natural trend of decreasing scores with 

increasing retinal size. The maintenance of a 

constant retinal speed within this "effective 

range" would then explain the failure of the 

peaking effect to appear in the S2 session. 

An interesting possibility is that the "speed 

effect" noted above may be actually one of perceived speed. That is, subjects may perceive 

increases in speed only below a fairly low critical 

value. This possibility is consistent with the 

suggested influence of perceived size and per9 

ceived distance upon the duration and intensity 

of the aftereffect. 

Although the above explanations account for 

the present results, and several aspects of these 

data agree with comparable information in the 

studies of Granit9 10 and of Collins and Schroeder/ there are also points of disagreement among 

the studies. Thus all of the just-noted studies 

show peaking or flattening effects and declining 

SAE durations with increased angle size in size 

constant (r.p.m. constant) plots of the data. The 

results of the angle constant condition of the 

present study agree with what may be adduced 

from the data of Granit,9 10 but are inconsistent 

with those to be adduced from the data of Collins 

and Schroeder1 (where, for two angles, a 16-inch 

spiral gave slightly shorter durations than an 

8-inch spiral) . The results of the distance constant condition approximate the findings of Collins and Schroeder1 (some slight decline at angles 

larger than 10°) rather than those of Granit.9 10 

We have at present no clear explanation for these 

differences. 

V. Summary. 

The influence of visual angle and retinal speed 

upon the duration and intensity of the spiral 

aftereffect (SAE) was evaluated under five conditions : (a) Angle constant (A) -retinal speed 

and visual angle were held constant across a 

variety of spiral-size and viewing-distance combinations; (b) size constant-spiral size was held 

constant at a variety of distances and of visual 

angles, with retinal speed either varying ( S1 ) 

or held constant ( S2 ) ; (c) distance constantseveral spiral sizes (visual angles) were employed at a constant distance with retinal speed 

either varying (D1 ) or held constant (D2 ). 

Duration and intensity measures were affected 

in a parallel fashion. The SAE scores increased 

significantly in A with increases in spiral size 

and distance, and decreased significantly-with 

the exception of a rise in duration scores from 

1° to 2° in S1 -as angle size increased (and distance decreased) in the S conditions. But no 

significant effect was found at nearly the same 

visual angles in the D conditions. Perceptual 

rather than physical variables seem to account 

for the results. If it is assumed that perfect size 

constancy occurred during the experiment, then, 

in the A and the S sessions, SAE durations were 
longer :for larger values o:f perceived size per 

unit o:f retinal size. Since the latter ratio would 

have been identical :for all stimuli in the D sessions, no significant effect would be predicted 

across the various angles, and none occurred. 

Retinal speed variation produced no apparent 

effect, except possibly at low values. The :fact 

10 

that perceived (rather than physical) characteristics o:f the stimulus situation may have the 

most significant effects on the duration o:f illusory 

motion has considerable pertinence to the evaluation o:f effective :factors in the production o:f a 

variety o:f other visual illusions which can occur 

in aviation environments. 
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11 

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