PROBLEMS IN DEPTH PERCEPTION: 

Perceived Size and Distance of Familiar Objects 

Released by 

Walter C. Gogel 

Henry W. Mertens 

Approved by 

AM 66-.22 

~~ ~AM> J. RoBERT DILLE, M.D. 

CHIEF, CIVIL AEROMEDICAL 

INSTITUTE 

June 1966 

P. v. SIEGEL, M.D. 

FEDERAL Am SURGEON 

FEDERAL AVIATION AGENCY 

Office of Aviation Medicine 
Qualified requestors may obtain Aviation Medical Reports from Defense Documentation 

Center. The general public "may purchase from Clearinghouse for Federal Scientific 

and Technical Information, U.S. Dept. of Commerce, Springfield, Va. 22151 
PROBLEMS IN DEPTH PERCEPTION: 

Perceived Size and Distance of Familiar Objects 

I. Introduction. 

Familiar size is usually regarded as an important empirical cue determining the apparent 

distances of objects. The learning process that 

is assumed to occur in the development of this 

distance cue depends upon the relation between 

the retinal size of an object and its physical distance from the observer ( 0). A simple explanation of the process involved in this cue system 

is as follows. In a situation in which many cues 

are present to determine the perceived distance of 

the familiar object, 0 might be expected to learn 

to associate the retinal size of the familiar object 

with its perceived distance. As the result of 

many such associations involving the same familiar object at different distances, presumably 0 

would perceive the familiar object as being at a 

particular distance from himself solely as a consequence of the presence of a particular retinal 

size. Clearly, such a learning process would be 

expected to result in a proportionality between 

the physical distance D and the perceived distanceD' of the object from 0; i.e., 

D'=O D, (1) 

where 0, the constant of proportionality, is unity 

if the resulting perception of distance is veridicaL 

Although this simple account of the learning 

process involved in familiar size as a cue to distance may seem convincing, it raises several questions. It is by no means certain that the observer 

can "see" the size of his retinal image.1 •

2 By this 

it is meant that it is not certain whether the 

number of millimeters or the number of retinal 

receptor units subtended by the retinal image 

(its absolute size) can be a datum of perception. 

If the absolute size of the retinal image is not 

responded to by 0 at some level of neural organization, it would seem reasonable that the absolute 

retinal size of the familiar object cannot become 

associated with a perceived distance. 

1 

A second difficulty that enters this description 

of familiar size as a distance cue is the specification of retinal size. Should retinal size be defined as a linear extent on the retina or as an area 

on the retina? Neither definition is easy to apply 

to the retinal size resulting from an irregularly 

shaped object such as a tree. A learning problem 

parallels this problem of specifying the stimulus. 

Which aspect of retinal size (linear extent or 

area or some other dimension) is associated 

through past experience with perceived distance? 

These different aspects of retinal size are complexly related to object shape and can be different functions of the physical distance of the 

object from. 0. I£ it is assumed, for example, 

that linear extents on the retina are associated 

with apparent distance, which of the many possible linear extents is involved? Perhaps the 

learning occurs only with respect to the retinal 

extent of some salient feature of the object. I£, 

on the other hand, the learning includes all linear 

extents on the retina, it might be hypothesized 

that irregular objects (objects whose definition 

requires the specification of many linear extents) 

would be more difficult to associate with distance 

than would regular objects. 

A second explanation of the familiar-size cue 

to distance involves the relation between perceived size and perceived distance. The sizedistance invariance hypothe8is asserts that for a 

given visual angle (} (retinal size), the ratio of 

perceived size to perceived distance is a constant.8 

This can be expressed4 as 

S' /0 =K D' (2) 

The term S' is the perceived (or apparent) size 

of the object, (} is the visual angle or retinal size 

of the object expressed in radians, D' and D have 

the definitions given previously, and K is an observer constant. I£ familiar objects have perceived sizes because they are familiar, it follows 
that the familiar-size cue to distance is an instance of the size-distance invariance hypothesis.5 

The learning process involved in this second explanation must be more complicated than that 

in the first explanation since perceived size as 

well as retinal size must be associated with the 

familiar object and in turn associated with perceived distance. 

The second explanation of familiar size as a 

cue to distance probably is superior to the first 

in that familiar or assumed size does affect perceived size,1l and it is clear that perceived size 

and perceived distance are related in some manner/ The problems involved in the first type of 

explanation are, however, also present in the 

second. Both explanations require that the absolute size of the retinal image of the familiar 

object is a stimulus event that is available for 

the learning process, both require a definition of 

retinal size that is relevant to objects of irregular as well as regular shape, and both are vague 

as to which aspect of retinal extent is related by 

past experience to perceived distance. A possible 

solution to. the problem of specfying the significant variable involved in the size cue is found by 

considering S' j() in Equation (2) as a single 

term. It has been asserted that relative values 

of S' /B constitute the size cue to the perceived 

depth between objects (a perception of relative 

depth) where S' is the perceived size associated 

with the frontally oriented object whose retinal 

size is B.7 The term S' jB is the perceived size 

per unit of retinal size. It is suggested that objects (and all parts of objects) that appear at 

the same frontoparallel plane have equal values. 

of S' j(). For ~xample, for a tree all parts of 

which appear in the same frontoparallel phine, 

the perceived width of the trunk per unit of 

visual angle (retinal size) of the trunk width 

will be the S' j() value for all other portions of 

the tree. Also, it is suggested that objects or 

parts of objects that appear at greater or lesser 

distances have greater or lesser values of S' jB, 

respectively. If Equation (2) were correct, it 

would be possible to apply S' /B to the perception 

of the distance of a familiar object from 0 (a 

perception of absolute distance) as well as to 

perceived relative depth. From this point of 

view, instead of learning to associate a particular 

distance with each particular retinal size of each 

particular familiar object, an 0 merely would 

2 

learn to associate a scale of S' jB with a scale of 

D'. Assuming that such learning had occurred, 

any effective determiner of the size of any portion 

of a frontoparallel object would result in the 

object having a specific S' /B and, therefore, according to Equation (2), would also result in a 

perception D' that the object is at a specific 

distance. 

It is possible that familiar size is an inadequate cue to the perceived distance of objects 

from 0 while remaining an adequate cue to the 

perceived distance between objects. It has been 

stated that relative values of S' /B can provide 

cues to perceived relative distance independently 

of perceptions of absolute distance. 2

•

7 This is 

equivalent to asserting that the perceived relative 

depth between two objects as a function of the 

familiar-size cue is not a result of 0 perceiving 

the distance of each of these objects from himself 

and subtracting the lesser from the greater perceived distance. The purpose of the present 

study is to investigate both the adequacy of familiar size as a cue to perceived distance, and 

the relation between perceived absolute and perceived relative depth from this cue system. 

The relation between familiar size and perceived absolute distance usually has been investi· 

gated by using comparison fields against which 

the perceived distance of the experimental object 

is judged. It has been pointed out that this 

method permits the direct comparison of S' j() 

values between the experimental object and parts 

of the comparison field and, therefore, does not 

necessarily measure the perceived absolute distance that the familiar object would have if the 

comparison field were not present.7 If comparison fields are defined as any visual field or object that occurs either simultaneously with or in 

the temporal vicinity of the experimental object, 

the importance of this objection is increased. 

From this point of view, comparison fields are 

not limited to measurement fields deliberately 

introduced by the experimenter (E), but are 

visual fields of any sort encountered by 0 prior 

to or during the experiment. It follows, for example, that one presentation of a familiar object 

becomes a comparison field for subsequent presentations of the same or different objects to the 

same 0. This example suggests that if the relation between familiar size and perceived absolute 

(rather than perceived relative) distance is to 

be measured, the familiar object should be the 
only visual stimulus present and successive presentations of the familiar object to the same 0 

should be avoided. Only a few studies have met 

these requirements. In a study by Gogel, Hartman, and Harker,8 three retinal sizes of a sevenof-spades playing card were presented, in an 

otherwise dark visual field, to four groups of 20 

O's with three of the four groups receiving different retinal sizes in the first presentations. 

The perceived distances of the playing cards were 

measured by verbal reports and by throwing 

darts. It was concluded from the average results 

from the first presentations that different perceptions of absolute distances did not occur as a consequence of the different retinal sizes. Perceived 

relative distance, however, occurred between 

successive presentations of the different retinal 

sizes to the same 0. These results suggest that 

the perception of relative depth from familiar 

size cannot always be explained as a difference 

between two perceptions of absolute distance. 

Baird9 presented different angular sizes of a 

rectangular strip of light to three different 

groups of 10 O's in an otherwise dark visual field. 

The O's verbally estimated the distance to the 

rectangular strip after being informed that the 

length of the strip was 12 inches. The average 

response of each group was approximately that 

which would be expected from the particular 

retinal size and the assumed size of 12 inches. 

Considerable intersubject variability occurred, 

however, and significant median differences were 

present only between the largest and each of the 

other two retinal sizes. While it is questionable 

whether the information that the strip was 12 

inches long resulted in the perception of a 12-

inch length, it seems from this study that, at least 

for the largest retinal size used, some variable associated with retinal size had a behavioral if not 

a perceptual consequence. Epstein10 presented 

photographs of one of three coins (a dime, 

quarter, or half-dollar) separately to each of 

three groups 15 O's and used objects in a comparison field to measure the perceived absolute 

distance and perceived size of the coins, which 

were always at 135 em from 0 and subtended 

identical visual angles. The average results were 

approximately those which would be expected 

if familiar size were a fairly veridical cue of 

perceived absolute distance. In order to determine whether these results were an artifact of the 

use of comparison fields, Epstein11 repeated the 

3 

experiment, with different O's, using nonvisual 

measures of perceived size and distance. To give 

the O's experience in the use of the nonvisual 

measures, a training session was introduced prior 

to the experimental session. In. the training session, the size and distance of copper disks having 

approximately the diameter of a dime, quarter, 

or half-dollar were judged under full-cue conditions using correction procedures. All three 

disks were located at each of the three distances 

that the coins would have to be in order to produce approximately the constant angular size 

used later in the experimental session. The results obtained in the experimental session were 

similar to those obtained in the earlier experiment. Epstein concluded that the relation between perceived size and perceived distance 

:found in the earlier study is not a methodological 

artifact of the use of comparison fields. I:f comparison fields can be defined to include visual 

fields presented in the training session shortly 

before presenting the experimental objects, however, it is likely that the methodological problem 

involved in the use of comparison fields was 

equally present in both studies. 

II. Apparatus. 

In the present study, the role of familiar size 

in the perception of distance was investigated 

with measurements made of the perceived size 

(S') as well as the perceived distance (D') from 

0. A ten-of-clubs playing card was the familiar 

object of the study. The playing card was presented under both static and dynamic conditions. 

In the static conditions, the retinal size of the 

card stimulus remained constant for any single 

presentation. In the dynamic conditions, 0 

could vary the retinal size of the playing card 

while viewing it. 

A. Statio and Dynamic Situations. The apparatus for producing the card stimuli for both 

the static and dynamic presentations is illustrated 

in Figure 1. The 0 monocularly viewed an image 

of a playing card (/) on a screen (W) through 

mirrors M1 and M2 with the remainder of the 

visual field totally dark. The screen was 400 em 

from 0 as measured along the optical path from 

the viewing position. The image on the screen 

was produced by mounting a positive transparency T of the playing card on an otherwise 

opaque baffle placed in front of a point source 

of light ( P). The light was produced by means 
L 

- R 

--- 1 ~· --- - . VISUAL ALLEY 

w 

I p 

-oTFIGURE 1. A top-view schematic drawing of the apparatus and visual alley. 

of a 300-watt Sylvania concentrated-arc lamp 

with a source diameter of 0.11 inch. In order to 

reduce image distortion resulting from the finite 

size of the source, a negative lens (L) with a 

focal length of 11 mm was placed a short distance in front of P. Light from the point source 

P passed through the transparency T to produce 

an image I of a playing card on the rear projection screen W. The image on this screen 

(Polacoat Lenscreen) was visible to 0 as a white 

playing card with black numbers and black clubs, 

with the playing card (R) apparently suspended 

directly in front of himself at a distance D' and 

having a perceived width S'. The visual angle 

( ()) of the width of the card was inversely related 

to the distance DT of the transparency from the 

point source.12 The transparency and baffie were 

mounted on a small cart that could be moved 

toward or away from Pat a constant speed along 

a track provided by an optical bench. The cart 

was moved by means of a constant-speed motor 

controlled by E or 0, as required. Calibration 

related the position of the cart along the track 

to the visual angle (J of the image of the card on 

the screen, or to the distanceD from 0 at which 

a normal-sized playing card would have to be 

placed to subtend the visual angle 8. Throughout this study, the visual angle () of the image of 

the playing card on the screen will be referred to 

as the visual angle of the playing card. 

The viewing position of 0 contained an adjustable chair and an adjustable head and chin 

rest together with a pair of eyepieces. The view4 

ing was monocular (right eye only) with the 

left eyepiece occuluded. To the left of the viewing position was a light adaptation surface ( L 

in Figure 1) with a brightness of 15 ft-L. This 

surface was shaped to fit around the nose of 0 

so as to present a homogeneous visual field. The 

visual field was homogeneous in order to avoid 

producing a comparison field with which 0 could 

compare the subsequently presented stimuli.7 

Microswitches were mounted on both the adaptation apparatus and the viewing position for the 

playing card in order to insure that no stimulus 

was visible except when O's head was properly 

positioned in the apparatus. 

A kinesthetic standard, invisible to O, was 

provided to assist 0 in judging the perceived 

distance ( D') of the playing card. For this 

purpose, two round stationary rods that 0 could 

grasp, one in each hand, were located (one to the 

right and the other to the left of the viewing 

position) at approximately the level of O's chest. 

On top of each rod was a small peg. The distance between pegs was 3 feet. Also, two square 

posts approximately 6 inches high and % inch 

wide were located near the viewing position at 

about the height of O's waist. These posts were 

used in the measurement of the perceived width 

(S') of the playing card. The left post was 

stationary, while the right post could be moved 

to the right or the left by 0 until the distance 

between the posts was equal to the perceived 

width. The viewing position, the two rods and 

posts, and the light-adaptation apparatus were 
all contained in a compartment covered with 

black cloth to completely exclude any extraneous 

light :from reaching O's eye. At the viewing position, the eyepiece in :front o:f O's right eye contained an aperture 1.3 em in diameter. No portion o:f this eyepiece or aperture was visible to 

0 while viewing the playing card. 

Two sets o:f static situations were used. The 

angular size o:f the width o:f the cards was 7.3°, 

3.9°, and 1.9° in the set presented first and 5.9°, 

2.3°, and 1.4° in the set presented second. These 

angular sizes correspond to normal playing cards 

located 1.48, 2.79, and 5.71 and at 1.80, 4.72, and 

7.68 :feet :from O, respectively. Two sets o:f 

dynamic situations were also used with the same 

O's. At the position o:f the right round rod, a 

small plastic ring was located. When 0 pressed 

the plastic ring, a microswitch was activated that, 

by controlling the motor in the dynamic adjustments, changed the position o:f the cart on the 

track in either direction and, hence, controlled the 

visual angle and the perceived distance o:f the 

playing card. To prevent 0 :from basing his 

distance judgments on the length o:f time he 

pressed the ring in the dynamic situations, six 

different starting positions (visual angles o:f · the 

card) were used. These were 7.3°, 6.3°, 4.7°, 3.1°, 

1.5°, and 0.8°. It is readily demonstrated that 

the constant track speed in the point-source apparatus produced a rate o:f change o:f visual angle 

proportional to that produced by a playing card 

also moving with a constant speed.12 In the 

present study, the dynamic stimulus always was 

equivalent to a normal playing card moving directly toward or away :from 0 at a constant speed 

o:f 7.7 em/sec. 

For both the static and dynamic situations, 

care was taken that no object was ever visible 

except the playing card. The luminance of the 

playing card as viewed :from the O's position 

always was 0.14 :ft-L. 

B. Comparison Field. A well-structured visual 

field (visual alley o:f Figure 1) was used with 

half the O's during the second static situation. 

Since the well-structured field provided S' jO 

values that 0 could compare with the playing 

card, it is called a "comparison field" even though 

0 was never instructed to make comparisons between the playing card and this field. The comparison field was monocularly visible to 0 (right 

eye only) through the partially transmitting, 

partially reflecting mirror M1 (Figure 1) only 

5 

when the lights above the alley were turned on, 

and an occluder at the front of the alley was 

raised. The floor of the alley, which was 4 feet 

wide and extended 48.7 :feet :from 0, contained 

an assortment o:f :familiar objects (but no playing 

cards) and was covered with light- and dark-grey 

rectangles ( 18 inches long by 9 inches wide). 

The walls and back o:f the alley were formed by 

white curtains. In order :for the portion o:f the 

alley close to 0 to be visible, a ramp was constructed to slope upward :from the alley floor 

beginning at a distance o:f 5.7 feet and extending 

to the position o:f M1 (0.7 :feet :from 0). White 

objects to be used with the distance judgments 

were identified by letters or numbers and were 

placed along the alley floor at 3, 7, 12, and 22 

:feet :from 0. ·when size judgments were required 

in the comparison field, blue re<:.tangles whose 

widths subtended a constant visual angle o:f !:2° 

were successively placed at each o:f these same 

distances. 

C. 0 alibration Situation. The methods of using 

verbal reports to indicate perceived distance and 

the hand-adjustment apparatus to indicate perceived size were evaluated oy using a :full-cue 

visual field called the calibration situation. For 

this purpose, the curtains at the :far end o:f the 

alley were pushed aside, and a viewing position 

consisting o:f a chin rest was positioned directly 

above this end of the alley. Numbered rectangles, to be used with the verbal reports, were 

located at 2, 5, 8, 14, 20, and 26 feet along the 

alley :from the viewing position. Blue rectangles, 

1, 2, 4, 8, and 15 inches wide, to be used with a 

hand-adjustment apparatus, similar to that described previously, were presented one at a time 

at a constant distance o:f 3.5 :feet. The perceived 

width o:f a normal-sized playing card (king of 

hearts) also presented at 3.5 feet from 0 was 

measured at the end o:f the calibration series. 

The calibration situation represents the situation 

with the most complete size and distance cues 

and is the only portion of the experiment in 

which binocular observation was used. 

III. Observers. 

The O's of this study were 60 men between·the 

ages of 18 and 40 who had at least a high-school 

education, who were naive with respect to the 

purpose of the study, and who had an uncorrected visual acuity of at least 20/20 in each eye 

as measured with the Bausch and Lomb Orthorator at both the near and far points. 
IV. Procedure. 

A. First Set of Statio Situations. In both the 

·first and second sets of static situations, every 

0 was successively presented with each of three 

angular (retinal) sizes of the playing card. Each 

of the six possible orders of successive presentations of the three image sizes was used with a 

different group of 10 O's with the result that each 

angular size was presented first equally often. 

Thus, 20 of the O's were first presented with the 

largest, 20 of the O's with the middle, and 20 of 

'the O's with the smallest of the three retinal 

sizes .used in each set of static situations. 

Before the experimental conditions were presented, the observation booth was lighted, and 0 

was instructed in the use of the round rods and 

square posts and was given practice in moving his 

head between the viewing position and the light 

adaptation apparatus. 0 was informed that the 

distance between the two pegs, one on the top of 

each rod, was 3 feet. In an attempt to isolate 

0 from previous stimulation that could act as 

a comparison field, the light in the observation 

booth was turned off and 0 remained in total 

darkness for 10 minutes. After this period, 0 

positioned his head in the light-adaptation device, which was activated for 30 seconds. Following the light adaptation, 0 positioned his 

head in the viewing position and observed the 

playing card suspended in front of himself in 

an otherwise black field of view. While grasping the round rods with one thumb on each peg, 

0 verbally estimated the distance that the playing 

card seemed to be from himself in feet or in 

inches or in a combination of both. The two 

square posts were used by 0 to indicate perceived width (S'). For this purpose, 0 grasped 

the square posts, one in each hand and moved 

the right post laterally until the distance between the inner surfaces of the posts seemed to 

be the same as the width (left to right extent) 

that he saw in the playing card. Since the posts 

were not visible, the adjustment was made 

kinesthetically. One adjustment started with the 

square posts far apart and the other with the 

square posts together. Throughout tnis experiment, the average of these two adjustments is a 

width score. At no time either during or between any of these judgments were the square 

posts or the round rods or any other portion of 

the apparatus other than the playing card visible 

to 0. Following the distance and size judgments 

6 

made with respect to the first presentation of the 

playing card, a shutter was closed, occluding 

O's view of the card; a different visual size of the 

playing card was produced; the shutter was 

opened, and another distance report was obtained. 

This procedure was repeated with the third visual 

angle of the playing card. In the first set of 

static situations, the only width score (S') that 

was obtained followed the first presentation, 

whereas D' was obtained for all three static 

presentations. The 0 was light-adapted immediately prior to the first presentation only. 

Thirty to 60 seconds usually occurred between 

presentations throughout the experiment. 

B. First Set of Dynamic Situations. Upon completing the judgments involving the first set of 

static situations, 0 was light-adapted and presented with the first set of dynamic situations. 

Before permitting 0 to view the card, E adjusted 

the playing card to the required starting position for the particular dynamic presentation and 

threw the switch that allowed 0 to adjust the 

playing card in apparent depth. While grasping 

the round rods and viewing the playing card 

(monocularly), 0 adjusted the visual angle of 

the image on the screen until the card appeared 

to be at a distance from himself that was equal 

to the specified multiple of one, two, or three 

times the distance between the pegs on the two 

rods. Each of the 60 O's was given each multiple 

twice in random order with the restriction that 

the order of conditions throughout the first set of 

static and dynamic situations. was duplicated 

with half the O's. The resulting six dist!!-nce 

adiustments were randomlv paired with the six 

starting sizes with the restriction that a particular starting size was paired with a particular 

task (multiple) equally often. The starting sizes 

were equivalent to a real playing card 1.48, 1.71, 

2.30, 3.51, 7.15, and 13.16 feet from 0. Since the 

O's were aware that the distance between the 

round rods was 3 feet, veridical depth adiustments 

of the cards would have been adjustments equivalent to 3,. 6, 9 feet. Two size (width) adiustments were completed only after 0 had finished 

the six dynamic distance adjustments. 

C. Second Set of Static Situations. The procedure for the second set of static situations was 

identical to that for the first set except that a 

different set of three image sizes was used, the 

two size judgments did not occur until the completion of all the distance judgments, and half 
o£ the O's in the second set viewed the comparison alley £or 30 seconds prior to each static 

presentation. The orders o£ presenting the three 

card sizes to the group o£ O's viewing the comparison field were duplicated £or the O's who 

saw only the images o£ the playing card. 

D. Second Set of Dynamic Situations. The 

procedure £or the second set o£ dynamic situations was identical to that o£ the first except that 

the same O's who had previously viewed the comparison alley in the second set o£ static situations 

made size and distance judgments with respect 

to objects in the comparison alley prior to being 

presented with the second set o£ dynamic situations. With hal£ o£ the O's, the size judgments 

in the comparison alley were made before the 

distance judgments. With the remaining O's this 

order was reversed. 

E. Comparison Field and Calibration Situation. 

The sizes and distances to be judged in the comparison field (with 30 O's) were presented in 

random orders with size judgments preceding 

and following the distance judgments equally 

often. The calibration situation was always 

presented last £or all 60 O's. The sizes and distances to be judged in the calibration situation 

were presented in random orders (except £or the 

normal-sized king o£ hearts, which was always 

presented last). As in the case o£ the static and 

dynamic situations, distance judgments in the 

comparison field and calibration situation were 

made verbally, and size judgments were :t;nade 

kinesthetically. 

After finishing the experiment, each 0 was 

questioned as to the manner in which he made 

his size and distance judgments in the experiment. 

V. Results. 

As indicated by the question period that £ollowed the O's completion o£ the experiment, six 

O's made angular size rather than apparent size 

adjustments during the first nart or during most 

o£ the experiment. It was as though these six 

O's imagined a frontal plane either at the distance o£ their hands or at some other distance 

and judged the width o£ the playing card as angularly projected on that plane. Two other O's, 

despite the instructions, adjusted the movable rod 

of the hand-adjustment apparatus with respect to 

the right edge of the card without regard to the 

resulting separation between the rods. Since 

"phenomenal" judgments were required in order 

to test Equation (2), the results from these eight 

0 's were omitted from the data, and eight other 

O's were used in their place. 

A. Results From the First and Second Set of 

Static Situations. The results from the first set 

of static situations are given in Table 1. The. 

() values are the visual angles subtended by the 

1mages of the playing card on the screen. The 

D values are the distances in centimeters at which 

a normal-sized playing card (5.7 em wide) would 

have to be placed to subtend the visual angle 0. 

The D' values are the average perceived distances 

o£ the playing card obtained £rom the verbal 

reports converted to centimeters, with each 

average based on 20 verbal reports. The values 

o£ D j8 were found by dividing D by 5.7 em., the 

width of a normal-sized playing card.. Each 

D' !S' value in Table 1 is the average of 20 values 

of D' jS', one from each 0, with each S' the 

mean of the two size adjustments made by a particular 0. The standard deviations ( u) o£ D' 

and D' 1 8' indicate the variability between O's 

in these types of scores. The average value of 

8' was 8.6 em £or the first set o£ static situations, 

with a standard deviation of 8.4 em. One 0 in 

the first static situation was unable to separate 

TABLE 1. Average results and standard deviations ( u) in centimeters from the first set 

of static situations. S' and D' are the perceived width and the perceived distance 

associated with a playing card of physical width S, located ·at a simulated distance 

D, in centimeters, and subtending a visual angle (). 

First Second Third 

presentation presentation presentation 

() 7.3° 3.9° 1.9° 7.3° 3.90 1.9° 7.3° 3.90 1.9° 

D 45 85 174 45 85 174 45 85 174 

Mean D' 125 116 116 32 84 263 45 108 194 

u of D' 227 125 65 17 72 261 64 106 144 

DIS 7.8 14.8 30.4 7.8 14.8 30.4 7.8 14.8 30.4 

Mean D'/S' 8.2 16.6 17.6 5.4 11.0 30.6 5.9 13.6 25.9 

u of D'/S' 5.4 9.3 11.3 3.8 8.5 21.0 4.2 11.3 10.8 

7 
the posts sufficiently far to indicate the·perceived 

width of the card. This 0 adjusted the posts to 

one-half the perceived width, and consequently 

the adjustments from this 0 were doubled to determine his value of S'. 

Of particular interest in Table 1 are the means 

resulting from the first presentations of the three 

different retinal sizes ( ()) with each size first 

presented to a different group of 20 Os. These 

are the only data of the study that, by meeting 

the requirements discussed previously, are designed to provide valid measures of perceived 

absolute distance D' for use in testing Equations 

(1) and (2). It will be seen from Table 1 that, 

contrary to Equation (1), the average values of 

D' in the first presentation are not only disproportionate to D, but fail to increase with increases in D. It seems, however, that a few O's 

saw the playing card in the first presentation as 

both distant and large. Two of these O's had been 

first presented with the large value of () and two 

O's with each of the smaller values of 0. When 

these four deviant values of D' were removed, the 

resulting D' values were 54, 90, and 107 em for 

D values of 45, 85, and 174 em, respectively. The 

standard deviations computed from the distributions of D' with these deviated values removed 

were reduced from the values shown in Table 

1 for the first presentation to 40, 48, and 55 em, 

respectively. The average values of D' jS' in 

Table 1 associated with the largest and intermediate values of (} are similar to the expected 

values of D' jS' and, therefore, support Equation 

(2), but the average D' jS' resulting from the 

smallest () does not. Throughout this study, half 

the degrees of freedom ( df) were used whenever 

the distributions were heterogeneous in variance and involved equal numbers ( N) or O's. 

In the case of heterogeneity and unequal N's, 

the value of t required for significance was calculated13 and compared with the experimentally 

obtained value. Using the t test, the 8.2 value 

of D' IS' obtained from the largest retinal size 

was significantly different beyond the 0.01 level 

from both the 16.6 and 17.6 values obtained 

from the two smaller sizes (t=3.35, df=19, and 

3.48, df=19, respectively) at the 0.05 level. A 

comparison of the values of D' and D' jS' in 

Table 1 indicates the merit of measuring S' as 

well as D' in testing whether familiar size is a 

determiner of perceived absolute distance. It 

seems, considering the D' jS' values from the first 

8 

presentation, that the combination of the perceived size and the visual angle of the playing card was a determiner of perceived absolute 

distance for the two larger values of () (D up to 

about 3 feet) but not for the smallest value of 

() (D approximately 6 feet). 

The results from the second and third presentations in Table 1 are generally more i~ agreement both Equations (1) and (2) than are the 

results from the first presentation. . The effect 

of successive presentations is to make the D' and 

D'jS' scores more likeD and DjS. If D'=D 

and D'jS'=DjS, it would be concluded that 0 

pereceived that a normal-sized card was located at the distances (D) given in Table 1. 

Such perceptions might be termed veridical distance perceptions. It seems, from the averages 

of Table 1, that to whatever extent perceptual 

veridicality was approximated on the first presentations, it occurred only with the two largest 

imag~ sizes, and preceptual veridicality with respect to the smallest image size was approached 

only as a result of successive presentations. . It 

should be noted that intersubject variability 

tends to be large, so that perceptual veridicality, 

when it occurs in Table 1, should be regarded 

as an average rather than as an individual 

achievement. 

As shown in Table 1, the average D' jS' obtained from the smallest image size of the playing card increased from the 17.6 value obtained 

in the first presentation to 30.6 in the second 

presentation and 25.9 in the third presentation. 

Each of these increases was significant beyond 

the 0.025 level (t=2.43, df=19, and 2.37, df=38, 

respectively). These changes can be explained in 

terms of relational judgments occurring over 

time. For the purpose of this explanation, it is 

convenient to regard D'/S' as a perceived 

distance corrected for individual differences in 

perceived size. Furthermore, it is useful to consider two factors as determining this perceived 

distance (per S') for any image size. The first 

factor is the tendency for 0 to perceive the card 

as being located at a particular distance from 

himself regardless of the perceived distance of 

this card with respect to the prior presentations 

of the card in the experiment. This might be 

called the absolute localization effect. The second factor is the tendency to perceive the card 

at a particular distance as determined by the 

distance cues between the card and previous 
presentations of the card. This might be termed 

the relative localization effect. Both the absolute and relative localization effects can be 

present to determine a particular perceived position of the card. Clearly, as discussed above, 

in the case of the second or third presentation 

of the smallest image size, the relative localization effect determined the perceived position of 

the card. The prior presentation of the two 

largest image sizes (which in general were most 

correctly perceived with respect to distance) increased the veridicality of the perceived distance 

associated with subsequent presentations of the 

smallest image size. Conversely, however, the 

erroneously perceived distance associated with 

the first presentation of the smallest image size 

might have reduced the veridicality of the perceived distances associated with subsequent presentations of the larger image sizes. Indeed, it is 

found that the D' jS' resulting from the intermediate image size (0=3.9°) is 16.6 when this 

size was presented first and 7.9 when it was 

immediately preceded by the presentation of the 

smallest image size. This difference is significant 

beyond the 0.01 level with a one-tailed test ( experimentally obtained t=3.34, calculated t, 01 =2.64, 

N=10 and 20). Similarly, the average D' jS' 

from the largest image size (7.3°) was 8.2 when 

it was presented first and 4.5 when it was preceded by the presentation of the smallest image 

size. Using ~ one-tailed test, this difference is 

significant beyond the 0.05level (t=2.20, d/=28). 

It seems that the relative localization effects resulting from relative size cues occurring between 

successive presentations are important in deter-' 

mining perceived position even though (as is the· 

case with the larger image sizes) the subsequent presentations would ordinarily be localized 

somewhat by familiar. size as a cue to absolute 

distance. It follows that O's will tend to use 

relative size cues between successive presentations to determine perceived distance even in circumstances where absolute localization effects 

would otherwise occur. 

The results from the second static situation 

both for the condition in which the monocularly 

viewed alley (comparison field) containing many 

objects did or did not precede each presentation of the card are given in Table 2. Each of 

the means and standard deviations in Table 2 is 

based upon 10 scores, one from each 0. The 

notation of Table 2 is the same as that of Table 1. 

According to Table 2, no obvious effect upon 

the subsequently perceived distances of the playing card seems to have occurred as a consequence 

of the interpolation of the comparison field. It 

will be noted that the standard deviations of D' 

and D' jS' in Table 2 show little tendency to decrease with increasing numbers of presentations. 

Large and continuing observer differences are . 

characteristic of Table 2 as of Table 1. 

B. Re8ult8 From the First and Second Sets of 

Dynamic Situations. The task of 0 in the 

dynamic situations was to adjust th~ playing card 

until it appeared at 3, 6, or 9 feet from himself. 

The range of possible adjustments of visual angle 

provided by the apparatus was from 0.8° to 

7.3°. It was found in the dynamic situations 

TABLE 2. Average results and standard deviations (u) in centimeters from the second 

set of static situations. S' and D' are the perceived width and perceived distance associated with a playing card of physical width S, located at a simulated distance D, 

in centimeters, and subtending a visual angle o. 

First Second Third 

presentation presentation presentation 

0 5.9° 2.3° 1.40 5.9° 2.3° 1.40 5.9° 2.3° 1.40 

D 55 144 234 55 144 234 Cl5 144 234 

DIS 9.6 25.3 40.9 9.6 25.3 40.9 9.6 25.3 40.9 

No comparison field 

D' 56 155 200 63 116 247 49 140 265 

u of D' 24.9 105.2 80.8 40.4 48.3 97.1 43.7 45.2 65.9 

D'/S' 10.3 18.5 31.1 10.9 19.5 29.2 3.5 25.8 55.4 

u of D'/S' 4.5 14.8 18.5 5.8 15.2 9.7 1.6 8.1 28.8 

Comparison field 

D' 58 201 183 46 137 326 75 122 197 

u of D' 25.7 254.2 66.0 23.2 49.2 320.4 50.5 40.6 . 40.9 

D'/S' 14.1 20.4 30.7 8.8 28.0 43.0 96. 26.3 43.4 

u of D'/S' 9.8 8.7 9.0 5.3 14.3 26.6 6.1 17.8 25.7 

9 
that for five O's the visual angle of the playing 

card could not be made sufficiently large so that 

the card appeared to 0 to be at 3 feet. For 

four other O's, the visual angle could not be 

made sufficiently small so that the card appeared to 0 to be at 9 feet. In order to permit comparisons between the different dynamic 

conditions, none of the data from these O's was 

used in the analysis of the results from either 

the first or second set of dynamic situations. The 

remaining 51 O's were divided into two groups, 

depending upon whether later in the experiment 

the O's were or were not presented with a com400 

300 

-ci 

c 

... 

' E 

~ 200 

Q) 

(I) ' 

roo 

0 

0 roo 200 300 

D' (em.) 

a. No Comparison Field Group 

parison field. The reason for this division will 

become clear when the results from the second 

set of dynamic situations are considered. Results from the 27 O's who later were presented 

with the comparison field and from the 24 O's 

who were never presented with the comparison 

field are shown in Figures 2a and 2b, respectively. The values of 8 used in Figure 2 are 

the visual angles, expressed in radians, of the 

image of the playing card adjusted by 0 in 

order to produce the perceived distance of 3, 

6, or 9 feet (91, 183, or 274 em, respectively) 

given on the abscissa. A value of S' is the 

400 

300 

200 

roo 

0 ,_--------.-------~--------, 

0 roo 200 300 

D' (em.) 

b. Comparison Field Group 

FIGURE 2. The relation between perceived size S' (per unit of retinal size 8) and perecived distanceD', for two 

groups of O's in the first set of dynamic situations. 

mean of the two width judgments that followed 

the completion of the distance judgments in 

the first set of dynamic conditions. The values 

of 8' /8 used on the ordinate are the means of 

distributions of 8' /8 with 8' expressed in centimeters. It became evident in the analysis of 

the data that starting size was an important 

variable in determining the final adjustments in 

the dynamic situations. This was tested statistically by computing for each 0 the difference 

between the results from the first dynamic situ10 

ation when using a smaller rather than a larger 

starting size for each of the three distance tasks. 

The resulting mean difference in 8' I 8 (averaged 

over the three distance tasks and all 51 O's) was 

216 cmjrad with the smaller of the pair of starting sizes producing the greater value. This 

difference was significant beyond the 0.01 level 

of confidence (t=7.72, df=50). Therefore, the 

data from the different starting sizes are presented separately in Figure 2. The number of 

O's involved in each data point in Figure 2 
varied from 5 to 10. The numbers associated 

with each of the curves of Figure 2 represent 

the visual angle of the starting size of the playing card expressed in degrees. According to the 

size-distance hypothesis of Equation (2), all 

the data curves of Figure 2 should be the same 

curve passing through the origin with a constant 

slope (K). In general, the curves of Figure 2 

if extended would approximately pass through 

the origin. In agreement with the above analysis, 

however, the smaller starting sizes ( 0.8° and 

1.5°) tended to require larger values of S' j() in 

order to achieve the same D' than were required 

when the larger starting sizes (3.1 ° to 7.3°) 

were used. No clear differences seem to be present between the curves resulting from the larger 

starting sizes. The differences between the data 

curves from the largest and smallest group of 

starting sizes may be explained in a manner 

similar in principle to that used in explaining 

the changes in the results occurring between successive presentations in the first set of static situ300 

~ 

-o 200 c 

... 

' E 

3 

<D 

...... 

-CJ) 100 

0 

0 100 200 300 

o' (em.) 

a. First Static 

ations. For this purpose, the adjustment of the 

angular size of the card by 0 may be considered 

as consisting of a series of distance judgments 

made with respect to a rapid succession of presentations, with each judgment in the series made 

relative to the illlmediately preceding presentation. It is possible that interaction effects resulting from such a series of judgments may accumulate in one direction or the other as a function 

of the starting size. Since, according to Figure 

2, the S' j() value necessary to achieve a particular D' was usually greater for smaller rather 

than larger starting sizes, it can be concluded 

in general that, for a given S' /0, the image 

appeared to be closer when it was preceded by 

the smaller rather than the larger starting sizes. 

That this seems consistent with the direction of 

the results obtained in the static situations is 

shown in Figure 3,in which the data from the 

static situations are presented in the same form 

as the results from the dynamic situations shown 

in Figure 2. Each data curve in Figure 3 gives 

300 

200 

100 

0 

0 100 200 300 

o' (em.) 

b. Second Static 

FIGURE 3. The relation between perceived size S' (per unit of retinal size ()) and perceived distance D', for the 

first and second set of static situations. 

the results obtained from all three retinal sizes 

for the 20 0 's in the first or second set of static 

presentations who started their series of judgments with a playing card of the indicated angular size ( 1.4°, 2.3°, or 5.9°). In Figure 3, the 

smallest starting sizes in both the first and second set of static situations (1.9° and 1.4°) tended 

11 

to result in smaller values of D' per value of S' j() 

than did the largest starting sizes (7.3° and 

5.0°). Also, in agreement with Figure 2, considering Figures 3a and 3b together, no consistent differentiation occurred between the middle 

starting sizes (3.9° and 2.3°) and the largest 

starting sizes (7.3° and 5.9°). 
Another possible explanation of the difference 

obtained between the large and small' starting 

sizes shown in Figure 2 is in terms of an anticipatory response; i.e., a tendency for 0 to stop the 

apparent movement before reaching the appropriate perceived position. Against this explanation is ( 1) the large differences between some of 

the curves of Figure 2, (2) the similar effects 

that occurred in the static situations (Figure 3), 

and ( 3) the consistent variation in the effect of 

starting size with perceived distance (task) and 

not with the magnitude of the adjustment from 

400 

300 

-o 

0 

~ 

': 

E 

u 200 

Q) 

(/) ' 

100 

0 

0 100 200 300 

D' (em.) 

a. No Comparison Field Group 

the starting pbsition. Both the first set of static 

and the first set of dynamic situations provide 

strong evidence for the perceptual interaction of 

successive stimuli whether these stimuli are 

changing discretely or continuously. 

The average results from the 51 O's in the 

second set of dynamic situations are shown in 

Figure 4. Figure 4a contains the results from 

27 O's who, prior to the dynamic adjustments, 

made size and distance judgments with the comparison field, while Figure 4b contains the results 

from the 24 O's who never were presented with 

600 

500 

400 

300 

200 

100 

0 

0 100 200 300 

D' {em.) 

b. Comparison Field Group 

FIGURE 4. The relation between perceived size S' (per unit of retinal size ()) and perceived distance D', in the 

second set of dynamic situations for the same two groups of O's used in Figure 1.. The "comparison-field 

group" made judgments of perceived size and distance in the comparison field immediately prior to the 

judgments in the second dynamic situation, whereas the "no comparison field group" did not. 

12 
the compar1s10n field. The data are presented 

separately for the six values of starting size. 

Although Figure 4a is much like Figure 2a, 

Figure 4b differs markedly from Figure 2b. It 

appears that the experience with the comparison 

field affected the subsequent judgments with respect to the playing card. This occurred even 

though the 0, in adjusting the apparent distance 

of the card, was not given the task of judging 

the card with respect to the comparison field. 

The major effect of the comparison field in this 

portion of the experiment seems to have been 

the distruption of the generally orderly displacements of the curves resulting from the different 

starting positions. This disruption did not seem 

to occur with the static situations, as would be indicated if the data curves from the static situations were plotted separately for the groups that 

did or did not experience the comparison field. 

The significance of the disruption in the dynamic 

situations was calculated by using the variability 

of the distributions described previously, in 

which the results from the smaller of the two 

starting sizes used with a particular distance adjustment was subtracted from the results for the 

larger of the two starting sizes, and the differences were averaged over the three distance 

tasks for all 51 O's. The difference in this variability between the first and second sets of dynamic situations is statistically significant for 

those O's who experienced the comparison field 

(F=3.34, df=26,26) but not for those O's who 

did not (F=1.93, df=23,23). The judgments 

made in the comparison field had a significant 

effect upon subsequent judgments made in the 

dynamic situations. 

The adjustment by 0 of the size of the image 

of the playing card on the screen in the dynamic 

situations can be expressed in terms of the distance (D) at which a normal-sized card (5.7 em 

wide) would have to be located in order to subtend that visual angle. The results expressed in 

this fashion give the distances that would have 

been adjusted if a normal-sized card of constant 

physical size had actually been moved in physical 

depth. The average values of D from the first 

and the second set of dynamic situations for each 

of the six starting sizes are given in Table 3. 

The average perceived width (S') of the playing 

card as determined by the kinesthetic (hand) adjustments was 6.2 em for the first and 7.0 em for 

the second dynamic situation. In agreement with 

Figures 2, 3, and 4, the effect of starting sizes 

as shown in Table 3 by the increase in D with 

increases in starting sizes is clear. 

C. Results from the Comparison Field and Calibration Situation. Table 4 gives the results from 

the comparison and calibration fields. Each mean 

and standard deviation is based on 30 scores in 

the case of the comparison field and 60 scores 

TABLE 3. Average results D and standard deviations (a) in centimeters from adjusting 

the playing card to a perceived distance of 3, 6, or 9 feet for six values of starting 

sizes or starting distances with N observers. 

First set of dynamic situations 

Starting Starting 3 teet 6 teet 9 teet 

size distance 

(degrees) (em) N D 0' N D 0' N D 0' 

7.3 45 15 72 23 18 127 27 18 179 53 

6.3 52 17 76 16 17 129 46 17 184 59 

4.7 70 19 80 19 15 123 23 17 194 49 

3.1 107 17 92 18 16 149 25 18 205 62 

1.5 218 16 124 36 17 183 49 18 259 54 

0.8 401 18 128 27 19 228 77 14 310 55 

Second set of dynamic situations 

Starting Starting 3 teet 6 feet 9 feet 

size distance 

(degrees) (em) N D 0' N D 0' N D 0' 

7.3 45 18 76 38 17 110 32 16 181 52 

6.3 52 16 66 16 19 123 26 16 182 55 

4.7 70 19 81 17 15 115 26 17 176 46 

3.1 107 17 95 16 16 139 33 18 210 61 

1.5 218 17 107 24 16 182 30 18 258 40 

0.8 401 15 114 25 19 211 43 17 328 57 

13 
of judgmehts will differ, depending on a number 

of factors, such as the temporal characteristics 

of the sequence and the range of stimuli sizes 

used. Therefore, it is unlikely that Equation (2) 

or any similar equation is capable of describing 

the perceived distance resulting from familiar 

size under a wide variety of conditions. 

D. Effect of Comparison Fields. The repeated 

interpolation of the comparison field in the second 

set of static presentations had no obvious effect 

upon the judgments of the perceived distances 

of the playing card; however, the completion of 

size and distance judgments in the comparison 

field prior to the presentation of the second set 

of dynamic situations had a disruptive effect 

upon the judgments. Several factors can be considered that possibly might have been important 

in determining the effect of the comparison field 

on subsequent judgments of the playing card. 

In view of the significance of sequential relations 

in this experiment, it is clear that the comparison 

field must be considered as only one of a number 

of visual stimuli inserted into an ongoing series 

of relational judgments of distance. As such, 

the comparison field and the previous series of 

judgments would be competitive in terms of influencing the subsequent judgments. In order for 

the comparison field to have an influence different from that of the previous series the K value 

of the comparison field and the previous series 

should differ. That this is indeed the case can 

be seen by comparing the slope of the curves of 

Figures 2 and 3 with the slope that would result 

from plotting in a similar manner the comparison 

field data of Table 4. It might be reasonable to 

expect that the effect of the comparison field upon 

the subsequent judgments would be greater than 

that of the previous series because it was temporarily more adjacent to the subsequent judgments. 

A factor that might, however, reduce the in: 

fluence of the comparison field relative to that of 

the prior series is that playing cards were used 

in the prior series and in the subsequent judgments but not in the comparison field. Perhaps 

the disruptive effect of the interpolated comparison field shown in Figure 4b is a consequence 

of the competitive effects of the prior series relative to that of the comparison field. 

VII. Summary. 

The relation between the retinal size of a 

familiar object and its perceived distance was 

16 

s~udied using a point-source system of projec-

~Ion to p~oduce an image of a ten-of-clubs playmg card m an otherwise completely dark visual 

field. Both static (stationary) and dynamic 

(moving) presentations of the playing card 

were used. The O's made size and distance judgments with respect to image sizes equivalent to a 

normal-sized playing card at 45, 85, and 174 em 

with the first set and 55, 144, and 234 em with 

t?e second set of static presentations. The image 

SIZe that was presented first in each set of static 

situations was different for each of the three 

groups of 20 O's. The distance judgments consisted of verbal reports, and the size judgments 

were made kinesthetically. In two sets of dynamic situations, the O's adjusted the size of the 

image of the playing card until the card appeared 

to be at 3, 6, or 9 feet from themselves and made 

kinesthetic judgments of its apparent size. A 

visual field containing many objects (a comparison field) was presented following the first set of 

static or dynamic presentations for half the O's. 

In the second static situation, the comparison 

field was viewed prior to each distance judgment. 

In the second dynamic situation, judgments of 

size and distance were completed in the comparison field prior to the dynamic judgments. J udgments of size and distance made at the end of the 

experiment in a full-cue situation indicated that 

the method of measuring size and distance used 

in the experiment was valid in that these measures were proportional to perceived size and distance. 

The average results from the first presentations of the first set of static conditions (the 

initial presentations of the experiment) were not 

found to be significantly different when only the 

judgments of perceived distance are considered. 

When both the size and distance judgments are 

c?nsidered together, however, the largest image 

size of the cards was perceptually differentiated 

from each. of the two smaller sizes, but not the 

two smaller sizes from each other. These results 

are interpreted to mean that perceived size as 

well as retinal size should be considered in predicting the perceived distance resulting from 

familiar obj~cts. When considering the judgments made m the first set of static conditions . ' It was concluded that the distance judgments 

made with respect to successive presentations 

were dependent upon the prior presentations. It 

was a though the distance judgment, for example, 
with respect to a second presentation was the sum 

of the perceived distance to the first presentation 

of the card plus the perceived depth between the 

two presentations. This view of the sequential 

effect of successive judgments was supported by 

the results from the dynamic adjustments in that 

the judgments associated with the dynamic situations were modified as a function of starting size. 

The introduction of the comparison field 

seemed to have had no effect upon the second 

set of static judgments and to have h~d a dis· 

ruptive effect upon the second set of dynamic 

adjustments. It is concluded that the effect of 

comparison fields must be understood as part of 

the total sequence of experimental presentations. 

The factors determining such sequential interactions require further study. 

REFERENCES 

1. BoRING, E. G. : The Moon Illusion. Amer. J. Phys., 

11 : 55-60, 1943. 

2. GoGEL, W. C. : The Visual Perception of Size and 

Distance. Vision Res., 3: 101-120, 1963. 

3. KILPATRICK; F. P., and ITTELSON, W. H.: The Sizedistance Invariance Hypothesis. Psychol. Rev., 60 : 

223-231, 1953. 

4. GoGEL, w. C., Wist, E. R., and HARKER, G. S. : A 

Test of the Invariance of the Ratio of Perceived Size 

to Perceived Distance. A mer. J. Psychol., 76: 537-553, 

1963. 

5. EPsTEIN, w .. , PARK, J., and CAsEY, A.: The Current 

Status of the 'Size-distance Hypothesis. Psychol. Bull., 

58 : 491-514, 1961. 

6. McKENNELL, A. C. : Visual Size and Familiar Size : 

Individual Differences. Brit. J. Psychol., 51 : 27-35, 

1960. 

7. GoGEL, W. C. : Size Cue to visually Perceived Distance. Psychol. Bull., 62: 217-234, 1964. 

17 

8. GoGEL, W. C., HARTMAN, B. 0., and HARKER, G. S.: 

The Retinal Size of a Familiar Object as a Determiner of Apparent Distance. Psychol. Monogr., 71, 

No. 13: 1-16, 1957. 

9. BAIRD, J. C. : Retinal and Assumed S'ize Cues as determinants of Size and Distance Perception. J. emp. 

Psychol., 66: 155-162, 1963. 

10. EPSTEIN, W. : The Influence of Assumed Size on Apparent Distance. A mer. J. Psychol., 76: 257-265, 1963. 

11. EPSTEIN, w .. : Nonrelational Judgments of Size and 

Distauce. Amer. J. Psychol., 78: 12Q-123, 1965. 

12. GoGEL, W. C., and MERTENS, H. w, : A Method of 

Simulating Objects Moving in Depth. Federal Aviation Agency Office of Aviation Medicine Report AM 

65-32, 1965. 

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