ON CERTAIN FALLACIES OF SIGHT IN THE VISION OF SOLID BODIES.
In a preceding chapter I have explained a remarkable fallacy of sight
which takes place in the stereoscope when we interchange the binocular
pictures, that is, when we place the right-eye picture on the left
side, and the left-eye picture on the right side. The objects in the
foreground of the picture are thus thrown into the background, and,
_vice versa_, the same effect, as we have seen, takes place when we
unite the binocular pictures, in their usual position, by the ocular
stereoscope, that is, by converging the optic axes to a point between
the eye and the pictures. In both these cases the objects are only the
plane representations of solid bodies, and the change which is produced
by their union is not in their form but in their position. In certain
cases, however, when the object is of some magnitude in the picture,
the form is also changed in consequence of the inverse position of
its parts. That is, the drawings of objects that are naturally convex
will appear concave, and those which are naturally concave will appear
convex.
In these phenomena there is no mental illusion in their production. The
two similar points in each picture, if they are nearer to one another
than other two similar points, must, in conformity with the laws of
vision, appear nearer the eye when combined in the common stereoscope.
When this change of place and form does not appear, as in the case of
the human figure, previously explained, it is by a mental illusion that
the law of vision is controlled.
The phenomena which we are about to describe are, in several respects,
different from those to which we have referred. They are seen in
_monocular_ as well as in _binocular_ vision, and they are produced
in all cases under a mental illusion, arising either from causes over
which we have no control, or voluntarily created and maintained by
the observer. The first notice of this class of optical illusion was
given by Aguilonius in his work on optics, to which we have already
had occasion to refer.[69] After proving that convex and concave
surfaces appear plane when seen at a considerable distance, he shews
that the same surfaces, when seen at a moderate distance, frequently
appear what he calls _converse_, that is, the concave convex, and the
convex concave. This conversion of forms, he says, is often seen in
the globes or balls which are fixed on the walls of fortifications,
and he ascribes the phenomena to the circumstance of the mind being
imposed upon from not knowing in what direction the light falls upon
the body. He states that a concavity differs from a convexity only
in this respect, that if the shadow is on the same side as that from
which the light comes it is a concavity, and if it is on the opposite
side, it is a convexity. Aguilonius observes also, that in pictures
imitating nature, a similar mistake is committed as to the form of
surfaces. He supposes that a circle is drawn upon a table and shaded
on one side so as to represent a convex or a concave surface. When this
shaded circle is seen at a great distance, it appears a plane surface,
notwithstanding the shadow on one side of it; but when we view it at
a short distance, and suppose the light to come from the same side of
it as the part not in shadow, the plane circle will appear to be a
convexity, and if we suppose the light to come from the same side as
the shaded part, the circle will appear to be a concavity.
[69] See Chap. i. p. 15.
More than half a century after the time of Aguilonius, a member of the
Royal Society of London, at one of the meetings of that body, when
looking at a guinea through a compound microscope which inverted the
object, was surprised to see the head upon the coin depressed, while
other members were not subject to this illusion.
Dr. Philip Gmelin[70] of Wurtemberg, having learned from a friend,
that when a common seal is viewed through a compound microscope, the
depressed part of the seal appeared elevated, and the elevated part
depressed, obtained the same result, and found, as Aguilonius did, that
the effect was owing to the inversion of the shadow by the microscope.
One person often saw the phenomena and another did not, and no effect
was produced when a raised object was so placed between two windows as
to be illuminated on all sides.
[70] _Phil. Trans._ 1744.
In 1780 Mr. Rittenhouse, an American writer, repeated these experiments
with an inverting eye-tube, consisting of two lenses placed at a
distance greater than the sum of their focal lengths, and he found that
when a reflected light was thrown on a cavity, in a direction opposite
to that of the light which came from his window, the cavity was raised
into an elevation by looking through a tube without any lens. In this
experiment the shadow was inverted, just as if he had looked through
his inverting eye-tube.
In studying this subject I observed a number of singular phenomena,
which I have described in my _Letters on Natural Magic_,[71] but as
they were not seen by binocular vision I shall mention only some of
the more important facts. If we take one of the intaglio moulds used
by the late Mr. Henning for his bas-reliefs, and direct the eye to it
steadily, without noticing surrounding objects, we may distinctly see
it as a bas-relief. After a little practice I have succeeded in raising
a complete hollow mask of the human face, the size of life, into a
projecting head. This result is very surprising to those who succeed in
the experiment, and it will no doubt be regarded by the sculptor who
can use it as an auxiliary in his art.
[71] _Letter_ v. pp. 98-107. See also the _Edinburgh Journal of
Science_, Jan. 1826, vol. iv. p. 99.
Till within the last few years, no phenomenon of this kind, either
as seen with one or with two eyes, had been noticed by the casual
observer. Philosophers alone had been subject to the illusion, or
had subjected others to its influence. The following case, however,
which occurred to Lady Georgiana Wolff, possesses much interest, as it
could not possibly have been produced by any voluntary effort. “Lady
Georgiana,” says Dr. Joseph Wolff in his _Journal_, “observed a curious
optical deception in the sand, about the middle of the day, when the
sun was strong: _all the foot-prints, and other marks that are indented
in the sand, had the appearance of being raised out of it_. At these
times there was such a glare, that it was unpleasant for the eye.”[72]
Having no doubt of the correctness of this observation, I have often
endeavoured, though in vain, to witness so remarkable a phenomenon.
In walking, however, in the month of March last, with a friend on the
beach at St. Andrews, the phenomenon presented itself, at the same
instant, to myself and to a lady who was unacquainted with this class
of illusions. The impressions of the feet of men and of horses were
distinctly raised out of the sand. In a short time they resumed their
hollow form, but at different places the phenomenon again presented
itself, sometimes to myself, sometimes to the lady, and sometimes
to both of us simultaneously. The sun was near the horizon on our
left hand, and the white surf of the sea was on our right, strongly
reflecting the solar rays. It is very probable that the illusion arose
from our considering the light as coming from the white surf, in which
case the shadows in the hollow foot-prints were such as could only
be produced by foot-prints raised from the sand, as if they were in
relief. It is possible that, when the phenomenon was observed by Lady
Georgiana Wolff, there may have been some source of direct or reflected
light opposite to the sun, or some unusual brightness of the clouds, if
there were any in that quarter, which gave rise to the illusion.
[72] _Journal_, 1839, p, 189.
When these illusions, whether monocular or binocular, are produced by
an inversion of the shadow, either real or supposed, they are instantly
dissipated by holding a pin in the field of view, so as to indicate by
its shadow the real place of the illuminating body. The figure will
appear raised or depressed, according to the knowledge which we obtain
of the source of light, by introducing or withdrawing the pin. When the
inversion is produced by the eye-piece of a telescope, or a compound
microscope, in which the field of view is necessarily small, we cannot
see the illuminating body and the convex or concave object (the
cameo or intaglio) at the same time; but if we use a small inverting
telescope, 1½ or 2 inches long, such as that shewn at MN, Fig. 36, we
obtain a large field of view, and may see at the same time the object
and a candle placed beside it. In this case the illusion will take
place according as the candle is seen beside the object or withdrawn.
If the object is a white tea-cup, or bowl, however large, and if it is
illuminated from behind the observer, the reflected image of the window
will be in the concave bottom of the tea-cup, and it will not rise into
a convexity if the illumination from surrounding objects is uniform;
but if the observer moves a little to one side, so that the reflected
image of the window passes from the centre of the cup, then the cup
will rise into a convexity, when seen through the inverting telescope,
in consequence of the position of the luminous image, which could
occupy its place only upon a convex surface. If the concave body were
cut out of a piece of chalk, or pure unpolished marble, it would appear
neither convex nor concave, but flat.
Very singular illusions take place, both with one and two eyes, when
the object, whether concave or convex, is a hollow or an elevation
in or upon a limited or extended surface—that is, whether the
surface occupies the whole visible field, or only a part of it. If
we view, through the inverting telescope or eye-piece, a dimple or a
hemispherical cavity in a broad piece of wood laid horizontally on the
table, and illuminated by _quaquaversus light_, like that of the sky,
it will instantly rise into an elevation, the end of the telescope or
eye-piece resting on the surface of the wood. The change of form is,
therefore, not produced by the inversion of the shadow, but by another
cause. The surface in which the cavity is made is obviously inverted
as well as the cavity, that is, it now looks downward in place of
upward; but it does not appear so to the observer leaning upon the
table, and resting the end of his eye-piece upon the wooden surface in
which the cavity is made. The surface seems to him to remain where it
was, and still to look upwards, in place of looking downwards. If the
observer strikes the wooden surface with the end of the eye-piece, this
conviction is strengthened, and he believes that it is the lower edge
of the field of view, or object-glass, that strikes the apparent wooden
surface or rests upon it, whereas the wooden surface has been inverted,
and optically separated from the lower edge of the object-glass.
In order to make this plainer, place a pen upon a sheet of paper with
the quill end nearest you, and view it through the inverting telescope:
The quill end will appear farthest from you, and the paper will not
appear inverted. In like manner, the letters on a printed page are
inverted, the top of each letter being nearest the observer, while the
paper seems to retain its usual place. Now in both these cases the
paper is inverted as well as the quill and the letters, and in reality
the image of the quill and of the pen, and of the lower end of the
letters, is nearest the observer. Let us next place a tea-cup on its
side upon the table, with its concavity towards the observer, and view
it through the inverting telescope. It will rise into a convexity, the
nearer margin of the cup appearing farther off than the bottom. If we
place a short pen within the cup, measuring as it were its depth, and
having its quill end nearest the observer, the pen will be inverted,
in correspondence with the conversion of the cup into a convexity, the
quill end appearing more remote, like the margin of the cup which it
touches, and the feather end next the eye like the summit of the convex
cup on which it rests.
In these experiments, the conversion of the concavity into a convexity
depends on two separate illusions, one of which springs from the other.
The _first_ illusion is the erroneous conviction that the surface of
the table is looking upwards as usual, whereas it is really inverted;
and the _second_ illusion, which arises from the first, is, that the
_nearest_ point of the object appears _farthest_ from the eye, whereas
it is _nearest_ to it. All these observations are equally applicable to
the vision of convexities, and hence it follows, that the conversion of
relief, caused by the use of an inverting eye-piece, is not produced
directly by the inversion, but by an illusion arising from the
inversion, in virtue of which we believe that the remotest side of the
convexity is nearer our eye than the side next us.
In order to demonstrate the correctness of this explanation, let the
hemispherical cavity be made in a stripe of wood, narrower than the
field of the inverting telescope with which it is viewed. It will then
appear really inverted, and free from both the illusions which formerly
took place. The thickness of the stripe of wood is now distinctly seen,
and the inversion of the surface, which now looks downward, immediately
recognised. The edge of the cavity now appears _nearest_ the eye, as
it really is, and _the concavity, though inverted, still appears a
concavity_. The same effect is produced when a convexity is placed on a
narrow stripe of wood.
Some curious phenomena take place when we view, at different degrees
of obliquity, a hemispherical cavity raised into a convexity. At every
degree of obliquity from 0° to 90°, that is, from a vertical to a
horizontal view of it, _the elliptical margin of the convexity will
always be visible_, which is impossible in a real convexity, and the
elevated apex will gradually sink till the elliptical margin becomes
a straight line, and _the imaginary convexity completely levelled_.
The struggle between truth and error is here so singular, that while
one part of the object has become concave, the other part retains its
convexity!
In like manner, when a convexity is seen as a concavity, the concavity
loses its true shape as it is viewed more and more obliquely, till
its remote elliptical margin is encroached upon, or eclipsed, by the
apex of the convexity; and towards an inclination of 90° the concavity
disappears altogether, under circumstances analogous to those already
described.
If in place of using an inverting telescope we invert the concavity, by
looking at its inverted image in the focus of a convex lens, it will
sometimes appear a convexity and sometimes not. In this form of the
experiment the image of the concavity, and consequently its apparent
depth, is greatly diminished, and therefore any trivial cause, such
as a preconception of the mind, or an approximation to a shadow, or a
touch of the concavity by the point of the finger, will either produce
a conversion of form or dissipate the illusion when it is produced.
In the preceding Chapter we have supposed the convexity to be high and
the concavity deep and circular, and we have supposed them also to be
shadowless, or illuminated by a _quaquaversus_ light, such as that
of the sky in the open fields. This was done in order to get rid of
all secondary causes which might interfere with and modify the normal
cause, when the concavities are shallow, and the convexities low and
have distinct shadows, or when the concavity, as in seals, has the
shape of an animal or any body which we are accustomed to see in relief.
Let us now suppose that a strong shadow is thrown upon the
concavity. In this case the normal experiment is much more perfect
and satisfactory. The illusion is complete and invariable when the
concavity is in or upon an extended surface, and it as invariably
disappears, or rather is not produced, when it is in a narrow stripe.
In the secondary forms of the experiment, the inversion of the shadow
becomes the principal cause of the illusion; but in order that the
result may be invariable, or nearly so, the concavities must be shallow
and the convexities but slightly raised. At great obliquities, however,
this cause of the conversion of form ceases to produce the illusion,
and in varying the inclination from 0° to 90° the cessation takes place
sooner with deep than with shallow cavities. The reason of this is that
the shadow of a concavity is very different at great obliquities from
the shadow of a convexity. The shadow never can emerge out of a cavity
so as to darken the surface in which the cavity is made, whereas the
shadow of a convexity soon extends beyond the outline of its base, and
finally throws a long stripe of darkness over the surface on which it
rests. Hence it is impossible to mistake a convexity for a concavity
when its shadow extends beyond its base.
When the concavity upon a seal is a horse, or any other animal, it will
often rise into a convexity _when seen through a single lens_, which
does not invert it; but the illusion disappears at great obliquities.
In this case, the illusion is favoured or produced by two causes; the
first is, that the form of the horse or other animal in relief is the
one which the mind is most disposed to seize, and the second is, that
we use only one eye, with which we cannot measure depths as well as
with two. The illusion, however, still takes place when we employ a
lens three or more inches wide, so as to permit the use of both eyes,
but it is less certain, as the binocular vision enables us in some
degree to keep in check the other causes of illusion.
The influence of these secondary causes is strikingly displayed in the
following experiment. In the armorial bearings upon a seal, the shield
is often more deeply cut than the surrounding parts. With binocular
vision, the shallow parts rise into relief sooner than the shield, and
continue so while the shield remains depressed; but if we shut one eye
the shield then rises into relief like the rest. In these experiments
with a single lens a slight variation in the position of the seal, or
a slight change in the intensity or direction of the illumination,
or particular reflexions from the interior of the stone, if it is
transparent, will favour or oppose the illusion. In viewing the shield
at the deepest portion with a single lens, a slight rotation of the
seal round the wrist, backwards and forwards, will remove the illusion,
in consequence of the eye perceiving that the change in the perspective
is different from what it ought to be.
In my _Letters on Natural Magic_, I have described several cases of
the conversion of form in which inverted vision is not employed.
Hollows in mother-of-pearl and other semi-transparent bodies often
rise into relief, in consequence of a quantity of light, occasioned by
refraction, appearing on the side next the light, where there should
have been a shadow in the case of a depression. Similar illusions take
place in certain pieces of polished wood, calcedony, mother-of-pearl,
and other shells, where the surface is perfectly plane. This arises
from there being at that place a knot, or growth, or nodule, differing
in transparency from the surrounding mass. The thin edge of the knot,
&c., opposite the candle, is illuminated by refracted light, so that
it takes the appearance of a concavity. From the same cause arises
the appearance of dimples in certain plates of calcedony, which have
received the name of _hammered calcedony_, or _agate_, from their
having the look of being dimpled with a hammer. The surface on which
these cavities are seen contains sections of small spherical formations
of siliceous matter, which exhibit the same illusion as the cavities
in wood. Mother-of-pearl presents similar phenomena, and so common are
they in this substance that it is difficult to find a mother-of-pearl
button or counter which seems to have its surface flat, although it
is perfectly so when examined by the touch. Owing to the different
refractions of the incident light by the different growths of the
shell, cut in different directions by the artificial surface, like the
annual growth of wood in a dressed plank, the surface of the mineral
has necessarily an inequal and undulating appearance.
In viewing good photographic or well-painted miniature portraits in an
erect and inverted position, and with or without a lens, considerable
changes take place in the apparent relief. Under ordinary vision there
is a certain amount of relief depending upon the excellence of the
picture. If we invert the picture, by turning it upside down, the
relief is perceptibly increased. If we view it when erect, with a
lens of about an inch in focal length, the relief is still greater;
but if we view it when inverted with the same lens the relief is very
considerably diminished.
[Illustration: FIG. 51.]
A very remarkable illusion, affecting the apparent position of the
drawings of geometrical solids, was first observed by the late
Professor Neckar, of Geneva, who communicated it to me personally in
1832.[73] “The rhomboid AX,” (Fig. 51,) he says, “is drawn so that the
solid angle A should be seen nearest to the spectator, and the solid
angle X the farthest from him, and that the face ACBD should be the
foremost, while the face XDC is behind. But in looking repeatedly at
the same figure, you will perceive that at times the apparent position
of the rhomboid is so changed that the solid angle X will appear the
nearest, and the solid angle A the farthest, and that the face ACDB
will recede behind the face XDC, which will come forward,—which effect
gives to the whole solid a quite contrary apparent inclination.”
Professor Neckar observed this change “as well with one as with both
eyes,” and he considered it as owing “to an involuntary change in the
adjustment of the eye for obtaining distinct vision. And that whenever
the point of distinct vision on the retina was directed to the angle
A for instance, this angle, seen more distinctly than the other, was
naturally supposed to be nearer and foremost, while the other angles,
seen indistinctly, were supposed to be farther away and behind. The
reverse took place when the point of distinct vision was brought to
bear upon the angle X. What I have said of the solid angles (A and
X) is equally true of the edges, those edges upon which the axis of
the eye, or the central hole of the retina, are directed, will always
appear forward; so that now it seems to me certain that this little, at
first so puzzling, phenomenon depends upon the law of distinct vision.”
[73] See _Edinburgh Philosophical Journal_, November 1832, vol. i. p.
334.
In consequence of completely misunderstanding Mr. Neckar’s explanation
of this illusion, Mr. Wheatstone has pronounced it to be erroneous,
but there can be no doubt of its correctness; and there are various
experiments by which the principle may be illustrated. By hiding with
the finger _one_ of the solid angles, or making it indistinct, by
a piece of dimmed glass, or throwing a slight shadow over it, the
_other_ will appear foremost till the obscuring cause is removed. The
experiment may be still more satisfactorily made by holding above the
rhomboid a piece of finely ground-glass, the ground side being farthest
from the eye, and bringing one edge of it gradually down till it
touches the point A, the other edge being kept at a distance from the
paper. In this way all the lines diverging from A will become dimmer
as they recede from A, and consequently A will appear the most forward
point. A similar result will be obtained by putting a black spot upon
A, which will have the effect of drawing our attention to A rather than
to X.
From these experiments and observations, it will be seen that the
conversion of form, excepting in the normal case, depends upon various
causes, which are influential only under particular conditions, such as
the depth of the hollow or the height of the relief, the distance of
the object, the sharpness of vision, the use of one or both eyes, the
inversion of the shadow, the nature of the object, and the means used
by the mind itself to produce the illusion. In the normal case, where
the cavity or convexity is shadowless, and upon an extended surface,
and where inverted vision is used, the conversion depends solely on the
illusion, which it is impossible to resist, that the side of the cavity
or elevation next the eye is actually farthest from it, an illusion not
produced by inversion, but by a false judgment respecting the position
of the surface in which the cavity is made, or upon which it rests.