Determinants of Apparent Visual Size with Distance Variant Author(s): Alfred H. Holway and Edwin G. Boring Source: The American Journal of Psychology, Vol. 54, No. 1 (Jan., 1941), pp. 21-37 Published by: University of Illinois Press Stable URL: http://www.jstor.org/stable/1417790 Accessed: 06/01/2009 03:49 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=illinois. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].

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DETERMINANTS OF APPARENT VISUAL SIZE WITH DISTANCE VARIANT By ALFRED H. HOLWAY and EDWIN G. BORING,Harvard University

The size of the retinal image is a peripheraldeterminantof visual size. Presumably,if all other determinantswere constant,perceivedsize would vary directly with the visual angle, which might even be used then as a measureof apparentsize. It has been known for a long time, howeversince Fechnerl and Hering,2 at any rate-that the visual angle does not provide a consistentmeasureof perceivedsize when the distancefrom O to the stimulus-objectis varied.Martius'experiment3in 1889 demonstrated that the apparentsize of objects may change scarcelyat all when distance changes,and nowadaysit is customaryto use the term 'size constancy'as a reminderthat, when perceivedsize is constant,the visual angle sometimes is not.4 Ordinarily,of course, size is not constantin spite of distance.Even the philosophersof the eighteenthcenturyremarkedthat two parallel rows of trees appearto convergeas one views the vista between the rows, and they attributedthe convergenceto the law of the visual angle and the underestimationof the greaterdistances.5To get things startedtowarda solution of this problem, Hillebrand6and othersworked out the form of the curve that the walls of a short,narrowalleyshouldhavein orderto appearequally separatedat every distance;7these studies were factual in emphasis.Recently,Thoulessshas conceivedof the organismas regressingin perception from a proximal perceptualdatum (the retinal image) toward a more remote one (the real object), so that actualperceptioncan be regardedas * Acceptedfor publicationApril 26, 1940.

'G. T. Fechner, Elemente der Psychophysik, 1860, II, 311-313. 2E. Hering, Beitriige zur Physiologie, I, 1861, 13-16. 3G. Martius, Ueber die scheinbare Grisse der Gegenstande und ihre Beziehung zur Grosse der Netzhautbilder, Philos. Stud., 5, 1889, 601-617. 4Cf. K. Koffka, Principles of Gestalt Psychology, 1935, 87-97, 235-240. ' Cf. J. Priestley, The History and Present State of Discoveries Relating to Vision, Light and Colours, 1772, 700-704; see also W. Porterfield, A Treatise on the Eye, 1759, 6 F.II, 381-384. Theorie der scheinbaren Grbsse bei binocularen Sehen, Denkschr. Hillebrand, d. kais. Akad. d. Wiss. zu Wein, math.-nat. KI., 72, 1902, 255-307. 7 E.g., W. Blumenfeld, Untersuchungen iiber die scheinbare Gr6sse in Sehraume, Zsch. f. Psychol., 65, 1913, 241-404, who also gives an excellent history of this problem, 243-274. 8R. H. Thouless, Phenomenal regression to the real object, Brit. J. Psychol., 21, 1931, 339-359; 22, 1931, 1-30. 21

22

HOLWAY AND BORING

a compromise between the proximal datum and objective constancy. Brunswik9has stressedthis compromisein his concept of an intermediate perceptualobject, the Zwischengegenstand,and his associate Holaday10 has shown the propertiesof the Zwischengegenstandto depend upon a varietyof perceptualdata. Size constancyis thus an hyperbole,exceptas the descriptionof a limiting case. It is not a general rule. Only at times does the organismsucceed in seeing an object with no change of size at all when distance is altered. On the other hand, these remarksapply with equal force to the law of the visual angle, the relation which prompted Fechner and Hering to make their originalobservationson the relationof size to distance.This law, too, is a specialcase. Let us scrutinizethesecases. Accommodatedobjectswhich subtendequal visual angles are equal in apparent size. That is the law of the visual angle. If the angle Os, subtendedby a standard stimulus, is equal to the angle O0, subtendedby a comparisonstimulus, then tan Oc = tan 0s ........................[A] and Sc = (Dc/Do)S. .......................[B] where Sc is the linear size of the comparison object; S., the linear size of the standard; D,, the distance from O to Sc; and D,, the distance from O to the

standardS.. The size of the comparisonstimulus (= apparentsize of the standard) is equal to the size of the standard stimulus multiplied by the ratio of their respective distances. The law of size constancy, on the other hand, states simply SC= S. ............................[C] where Sc and S. have the same meaning as in Equation [B]. Equation [C] expresses exactly the idea communicated to many investigators by the term size constancy. The size of the comparison stimulus is equal to the size of the standard, irrespective of their distances from 0.1' Fig. 1 shows these two relations in'the way in which they are presented later in the present paper. The standard and comparison stimuli are circular in outline, uniformly and equally illuminated as O sees them. The diameter of the standard stimulus subtends a constant visual angle (0. = 1?). Sc is the size, in inches, of the comparison stimulus. Dc is constant at 10 ft. D, is varied from 10 to 120 ft. The broken line drawn parallel to the axis of abscissas is the locus of all data which obey the law of the visual angle. The oblique line is the locus of values conforming to the law of size constancy. If size constancy were a general rule, then the apparent size of the standard 9E. Brunswik, Die Zuganglichkeit von Gegenstinden fir die Wahrnehmung und deren quantitative Bestimmung, Arch. f. d. ges. Psychol., 88, 1933, 377-418. 0 B. E. Holaday, Die Grissenkonstanz der Sehdinge bei Variation der inneren und ausseren Wahrnehmungsbedingungen, Arch. f. d. ges. Psychol., 88, 1933, 419486. 1 For the more general mathematical implications of the principles of size constancy, see E. G. Boring, Size constancy and Emmert's law, this JOURNAL,53, 1940, 293-295.

23

DETERMINANTS OF APPARENT VISUAL SIZE

stimulus (i.e. the measuredsize of the comparisonstimulus after the subjective equation is made) should be related to D, by a function that is linear in form (slope = tan 1?). If, on the other hand, the law of the visual angle were of general validity, then Sc should be constant,i.e. independentof distance. What actually happens is to be found for specific conditions.Systematicallydetermined relationsof this sort are wantedand wanting.12 It must be kept in the mind that the

30

FIG.1

c

c ,-

"

O0

I

LAW OF THE VISUALANGLE I

,

40

D

,m

80

t

m

120

FIG. 1. LAWS OF VISUAL ANGLE AND OF SIZE CONSTANCY FOR OBJECTS OF ONE DEGREE

Sc is the diameterin inches of the comparisonstimulusas equatedin perceivedsize to the diameterof a standardstimulus (angle subtended= 1?). The comparison stimulusis at a constantdistance (10 ft.) from 0. The abscissavalues are the distances in feet from O to the standardstimulus.The oblique brokenline designates the locus of all data obeyingthe law of size constancy.The brokenline parallelto the axis of abscissasis the locus of all pointsobeyingthe law of the visual angle. arrangementof the experimentis not in the usual form for testing size constancy, since the visual angle subtendedby the standardstimulus is kept constantat 1?, so that the physicalsize of the standardstimulusmust be increasedproportionally to the distance.It is for this reasonthat size constancyis representedin the graphs by a straightline through the origin with slope equal to tan 1?, and the law of the visual angle is a horizontalline with slope equal to zero.

The present paper is a study of such functions, obtained under conditions in which distanceis a commonvariant,as variouseffectsof binocular regard,of accommodation,and of the visual frame of referenceare successively eliminated. Functions relating the size of an adjusted stimulus 12Koffka,

op. cit., 1935, 91, complained of the lack of complete data for this

functionalrelation:"Althoughthe firstexperimentsof this kind were madein 1889 by Gotz Martius,we have to the presentday no completeknowledgeof the quantitative relations,the range of distancesover which the investigationshave been carried out beingratherlimited."

24

HOLWAY AND BORING

to the distancefrom O to a standardstimulussubtendinga constantvisual angle (0, = 1?) were studied under four different sets of conditions: (1) binocular regard, (2) monocular regard, (3) monocular regard throughan artificialpupil, and (4) monocularregardthrough an artificial pupil and a long black reductiontunnel stretchingfrom O to the standard stimulus,eliminatingmost of the visual frameof reference.The consequent data provide quantitativefunctions for a greater range of distancesthan has heretoforebeen availablefor such a varietyof conditions. PROCEDURE The general plan of the experiment is sketched in Fig. 2. O sat in a chair at the intersection of two long darkened corridors where he had an unobstructed view

L

-D

5^1;?D

i

D

>o R -I

FIG. 2. PLAN VIEW OF THE CORRIDORS

Sc indicates the position of the comparison stimulus located at a constant distance (D =- 10 ft.) from 0. S. at a distance D, from O, indicates one of the positions occupied by the standard stimulus. The standard stimulus always subtended a visual angle of 1 . Distance from O to the standard was varied from 10 to 120 ft. Pc and P. indicate the positions of the projectors. of a standard and a comparison stimulus. The comparison stimulus S,, a uniformly illuminated circular light-image, was centered on a large white screen (8 x 8 ft.) by an ordinary projector. The screen stood at a constant distance (10 ft.) from O throughout the experiment. The image on this screen could be continuously varied in size by means of an iris diaphragm conjugate with the screen. The standard stimulus Ss was provided in a similar manner by another projector. The distance from the O to Se, however, was not constant but was systematically varied by placing the screen at various fixed distances, ranging from 10 to 120 ft. The light images for these stimuli were formed by means of circular apertures cut in thin brass plates conjugate with the standard screen. At all distances, S. subtended a constant angle (1?) at the eye of O. The intensity of the light (flux per unit area) from S. was constant and equal to that from SG.The intensities of the light from S8 and Sc at the eye of 0 were thus identical for all measurements. E regulated the size of the comparison stimulus by varying the opening of the adjustable diaphragm conjugate with Sc until 0 signified that the standard and comparison stimuli were perceived as equal in size. 0 first fixated the standard stimulus (1 ), then the comparison, looking back and forth until satisfied with the equation.

DETERMINANTS OF APPARENT VISUAL SIZE

25

E measured the diameter of Sc with a meter stick. No restriction was imposed upon O in regard to the length of time taken for the judgments. All experiments were performed after midnight. Except for a few high lights, the corridors were dark. The brightest high lights were formed by light reflected from the waxed surface of the dark green tile on the floor of the corridor. Thus constellations of light images, not simply the primary images of the 'stimulus,' were located on the Os' retinas. Five Os were employed: A. C. S. Holway, L. M. Hurvich, M. J. Zigler, A. H. Holway, and E. G. Boring. E.G.B. and M.J.Z. served as Os for the first complete sets of measurements. For them, 20 measurements for size were made at every TABLE I AS A FUNCTION APPARENTSIZEOFSTANDARDSTIMULUS OBSERVATION: BINOCULAR OFITSDISTANCE

D8= distance(ft.) fromO to standardstimulus. At all distances, standardstimulussubtended a constant visual angleof one degree. Sc= av. size (in.) of N settings of comparisonstimulus, locatedat a distance of Io ft. from0 and equated in perceivedsize to standardstimulus.Intensity of light fromthe stimuli was constant at eye of O. m.v.= meanvariation. 0 sat erect, facing the stimuli successively with direct binocularregard. A.H.H. L.M.H. E.G.B. A.C.S. M.J.Z. (N= io) (N= 20) (N= 5) (N= r) (N= 20) De Sc m.v. Sc m.v. Sc m.v. Sc m.v. Sc m.v. 0o

2.2

0.21

2.2

0.1

2.2

20 30 40

0. 9

4.6

0.44

4.8

0.40

4.7

0.32

9.5

0.48

9.4

o.8i

50 60

II.S

0.7I

70

80

90 00oo 120

I5.8 8.7 20.6

I3.5

0.42

I3.2 I5.9

o.60 0.39

17.1

o.55

0.70 1.13 1.07

25.5

0.66

2.2

o.

4

7.0

0.44

12.0

o.51

I5.5

0.62

2.4

o.i8

4.5

0.45

8.9

0.35

I3.7

0.48

16.4

0.75

17.6 0.37

I9.8

0.36

24.0 24.5

I9.9 25.3 28.4

0.93 1.75

I5.0

0.7I

0.93 I.02

23.0 25.2

0.93 i.i6

1.o8

distance; 10 were made by increasing the size of S, until O reported that the visual impression produced by it was equal in extent to that produced by S,; 10 more were made by decreasing the size of Sc. The two procedures gave practically identical results, and for each distance the 20 measurements were averaged to obtain the desired measure of central tendency. A smaller number of results was secured from the other Os. BINOCULAR OBSERVATION

The measurementsfor the binocularobservationsare shown in Table I. These data were obtained with binocularregardby altering the diameter of the comparisonstimulus Sc, until it appeared equal to the standard stimulus (1?) in respect of perceivedsize, as the distancefrom O to the standardstimuluswas varied from 10 to 120 ft. The measurementsfor each O are also exhibited in Figs. 3-7. The coordinatesare expressedin linear units. The ordinatesgive the size of the

-

-

26

-

HOLWAY AND BORING

comparisonstimulus (in.), the abscissasthe distance (ft.) from 0 to the standardstimulus.Fig. 8 is the compositeof the binoculardata for all Os. The size of the comparison stimulus Sc in all instances increases with the distance of S, from 0. In other words, the apparent size (= Sc) of a standard stimulus varies