Six experiments were conducted to test the hypothesis that overestimation of vertical distance

 Six experiments were conducted to test the hypothesis that
overestimation of vertical distance is a pervasive phenomenon. The experiments involved judgments of: (a) vertical
distance looking upward; (b) vertical distance looking downward; (c) the slope of a real hill; (d) the recalled slopes
of streets; (e) the magnitudes of angles drawn on paper;
rn the distances to afterimages projected into the sky.
The results showed that a very strong illusion of overestimation of both vertical distance and slope occurred
in all situations except for the judgments of drawn angles
by males. Furthermore, in five of the six experiments females
showed a greater amount of the iIIusion than males. The
discussion pointed out the difficulty of explaining the moon
illusion by the assumptions of a flattened sky surface and
Emmert's law in light of the data. 

At present there exist two tenable theories of the moon
illusion which. however. make opposite assumptions
about the perception of distances in vertical or elevated
directions. The theory of Kaufman and Rock (1962)
assumes that. perceptually speaking. the sky is a surface which has the shape of a "flattened dome." This
phrase indicates that the sky surface is perceived to
be farther away at the horizon than when it is overhead
as a result of the visible terrain. The larger apparent
size of the moon (or sun) at the horizon is derived
from this greater apparent distance. by the logic of
Emmert's law for afterimages.2 This same argument
was advanced by King and Gruber (1962) who showed
that the size illusion also held for negative afterimages
projected into the sky at the jlorizon and at 45 deg

Thor and Wood (1966) have taken the position that vertical distances are typically overestimated
relative to horizontal distances. This "heightened arch"
view of visual space implies that targets at high elevations in the sky are seen as farther away. as well as
smaller. which is a direct reversal of the positive
correlation of size and distance as given in Emmert's
law. Since the sky is not. in fact. a surface with normal
cues to its distance, it is not necessary that Emmert's
law should apply. even for afterimages. Furthermore.
Thor and Wood reported vertical distance overestimation in experiments in both a lighted and darkened

They concluded from their investigation that the
moon illusion is one case of visual distortion produced
by stimulation coming from the vestibular system
accompanying the tilting of the head.
The purpose of this paperis to report several experiments which were designed to find out how pervasive
is the tendency, as suggested by the Thor and Wood
hypothesis, for observers to overestimate vertical distances. The present studies examined vertical distance
judgments in both upward and downward directions. the
perceived and recalled slopes of hills. the magnitudes
of drawn angles, and the apparent distances to afterimages projected into the sky. The data were analyzed
by the sex of the subject in each situation. Since each
experiment measured an apparent vertical distance
relative to an apparent horizontal distance, it would
be equally possible to call the phenomenon horizontal
underestimation, although some anecdotal data couldbe
offered to support the term chosen.
In all of the six experiments run. the Ss were undergraduate students at Oakland University. and except
for five female Ss who participated in Experiments
2. 3, and 6, no Ss were used in more than one experimental condition. In all experiments requiring target
perception. the S was free to use binocular vision under
normal indoor or outdoor lighting conditions.
Experiment 1: Distance Upward
The purpose of this experiment was to replicate
and quantify the Thor and Wood report thatthe distance
to the ceiling of a room is overestimated relative to
the distance to the wall. The room used had a ceiling
height of 13.4 it (the front of a small classroom auditorium) with cream colored walls and ceiling.
In the first version (a) of the experiment. the S
was first shown a plain white paper plate suspended
at eye level on the far wall. Directly above this on
the ceiling. in a line perpendicular to the wall was
mounted a row of eleven identical paper plates. These
plates ran from .90 it from the wall. at 1.74 it intervals. to a final distance of 18.30 it for the 11th plate.
The S was asked to walk back and forth beneath the
row of ceiling plates until he found one to stand under
such that the distance from his eyes to the wall plate
was equal to the distance from his eyes (emphasized)
to the chosen plate on the ceiling. At that time his eye
height was measured. and with .10 ft added to compensate for the upward tilting of the head, the actual
distance from eyes to ceiling could be obtained by
subtracting the corrected eye height from the total
room height. If the S chose a paper plate which was
farther from the wall than the distance from eyes
to ceiling, he was said to overestimate the vertical
distance accordingly.
In the second version (b) of the experiment, all paper
Perception & Psychophysics. 1967, Vol. 2 (12) Copuruih! 1967, Peuctionomic Prcs«, Goleta, Calif.
.. 21.7'
Fig. 1. Diagram of Ute physical
situation for Ute vertical-horizontal
distance comparison in Experiment
2, and of Ute slope judged in Experiment 3.
plates were removed and a path perpendicular to the
wall was marked by two chalk lines on the floor. Again
each S was asked to walk back and forth in the path
until he found a place to stand such that the eye-wall
distance matched the eye-ceiling distance. In this case
it was necessary to measure not only the S's eye height
but also the distance from the wall to his eyes. A different sample of Ss was used in each version of the
Experiment 2:

 Distance Downward
This study examined vertical distance judgments in
which the S had to look downward instead of upward.
Each S was stationed near the center of a bridge walkway leading from a 19.2 ft hill to the third floor of
the Van Wagoner dormitory. The situation is shown in
Fig. 1. The S was asked to bend over until his eyes
were level with the bridge railing and to observe the
distance from his eyes to the ground below (which was
level). He was then asked to straighten up and observe
the distance to the E who had taken a position at the
open end of the bridge. Ss were encouraged to look
down and forth again and then to report which distance was greater. After a choice was made, they were
asked "greater by what per cent?"

 The actual distance
from eyes to ground was 22.9 ft and the distance to
the E was 28.7 ft, for a physical vertical-horizontal
distance ratio of .80.
Experiment 3: The Slope of a 34°Hill
It followed that if the Ss overestimated the vertical
distance from the bridge to the ground in Experiment 2,
they should also overestimate the slope of the 34 deg
grass hill which fell from bridge level to ground level
underneath the forward section of the bridge (Fig. 1).
In order to ensure that the S understood the judgmental
task, he was first shown a line diagram of two hills
of 30 deg and 60 deg, each labeled only by an arrow
and the symbol 9 which identified the angle of interest.
For further anchoring, a 0 deg hill was verbally
defined as level ground with no slope and a 90 deg hill
as a straight up and down cliff wall. The S was then
asked to walk wherever he wished and to report back
with his best estimate of the slope of the hill in degrees.
No S reported difficulty in understanding the task.
Experiment 4:

 Memory for Steep Streets
In order to ensure that the resultsfrom Experiment 3
would not be peculiar to that visual scene, a questionnaire was distributed to an introductory psychology class
during the first week of the course. The questionnaire
showed a line diagram of a hill with the 45 deg angle
under the hill numerically labeled. The verbal definitions of 0 deg and 90 deg slopes as in Experiment 3
were included. The questionnaire asked the Ss to report, in degrees, the steepest streets they had ever
driven on, walked on, and seen, with the location of
the streets requested in each case. Only the data
from steepest streets ever driven on are reported
here; these data show the least amount of overestimation of the three questions.
In order to calculate the amount of overestimation,
it was necessary to decide upon some maximum feasible slope as a baseline, for which purpose 25 deg was
decided to be a generous estimate after an examination
of several highway engineering manuals which made no
reference to grades above 15 deg. Furthermore, it
was established through the San Francisco Bureau of
Engineering, Divtston of Grades, that the steepest segment of passable street in that city was 17.5 deg,
Those sa who located their steepest street experiences
in San Francisco were then used as a subsarnple for
comparison with this more objective baseline

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