DESCRIPTION OF THE OCULAR, THE REFLECTING, AND THE LENTICULAR
STEREOSCOPES.
Although it is by the combination of two plane pictures of an object,
as seen by each eye, that we see the object in relief, yet the relief
is not obtained from the mere combination or superposition of the two
dissimilar pictures. The superposition is effected by turning each eye
upon the object, but the relief is given by the play of the optic axes
in uniting, in rapid succession, similar points of the two pictures,
and placing them, for the moment, at the distance from the observer of
the point to which the axes converge. If the eyes were to unite the two
images into one, and to retain their power of distinct vision, while
they lost the power of changing the position of their optic axes, no
relief would be produced.
This is equally true when we unite two dissimilar photographic pictures
by fixing the optic axes on a point nearer to or farther from the eye.
Though the pictures apparently coalesce, yet the relief is given by the
subsequent play of the optic axes varying their angles, and converging
themselves successively upon, and uniting, the similar points in each
picture that correspond to different distances from the observer.
As very few persons have the power of thus uniting, by the eyes alone,
the two dissimilar pictures of the object, the stereoscope has been
contrived to enable them to combine the two pictures, but it is not
the stereoscope, as has been imagined, that gives the relief. The
instrument is merely a substitute for the muscular power which brings
the two pictures together. The relief is produced, as formerly,
solely by the subsequent play of the optic axes. If the relief were
the effect of the apparent union of the pictures, we should see it by
looking with one eye at the combined binocular pictures—an experiment
which could be made by optical means; but we should look for it in
vain. The combined pictures would be as flat as the combination of two
similar pictures. These experiments require to be made with a thorough
knowledge of the subject, for when the eyes are converged on one point
of the combined picture, this point has the relief, or distance from
the eye, corresponding to the angle of the optic axes, and therefore
the adjacent points are, as it were, brought into a sort of indistinct
relief along with it; but the optical reader will see at once that
the true binocular relief cannot be given to any other parts of the
picture, till the axes of the eyes are converged upon them. These
views will be more readily comprehended when we have explained, in a
subsequent chapter, the theory of stereoscopic vision.
_The Ocular Stereoscope._
We have already stated that objects are seen in perfect relief when
we unite two dissimilar photographic pictures of them, either by
converging the optic axes upon a point so far in front of the pictures
or so far beyond them, that two of the four images are combined.
In both these cases each picture is seen double, and when the two
innermost of the four, thus produced, unite, the original object is
seen in relief. The simplest of these methods is to converge the
optical axes to a point nearer to us than the pictures, and this may
be best done by holding up a finger between the eyes and the pictures,
and placing it at such a distance that, when we see it single, the two
innermost of the four pictures are united. If the finger is held up
near the dissimilar pictures, they will be slightly doubled, the two
images of each overlapping one other; but by bringing the finger nearer
the eye, and seeing it singly and distinctly, the overlapping images
will separate more and more till they unite. We have, therefore, made
our eyes a stereoscope, and we may, with great propriety, call it the
_Ocular Stereoscope_. If we wish to magnify the picture in relief, we
have only to use convex spectacles, which will produce the requisite
magnifying power; or what is still better, to magnify the united
pictures with a powerful reading-glass. The two single images are hid
by advancing the reading-glass, and the other two pictures are kept
united with a less strain upon the eyes.
As very few people can use their eyes in this manner, some instrumental
auxiliary became necessary, and it appears to us strange that the
simplest method of doing this did not occur to Mr. Elliot and Mr.
Wheatstone, who first thought of giving us the help of an instrument.
By enabling the left eye to place an image of the left-hand picture
upon the right-hand picture, as seen by the naked eye, we should have
obtained a simple instrument, which might be called the _Monocular
Stereoscope_, and which we shall have occasion to describe. The same
contrivance applied also to the right eye, would make the instrument
_Binocular_. Another simple contrivance for assisting the eyes would
have been to furnish them with a minute opera-glass, or a small
astronomical telescope about an inch long, which, when held in the hand
or placed in a pyramidal box, would unite the dissimilar pictures with
the greatest facility and perfection. This form of the stereoscope will
be afterwards described under the name of the _Opera-Glass Stereoscope_.
[Illustration: FIG. 8.]
_Description of the Ocular Stereoscope._
A stereoscope upon the principle already described, in which the eyes
alone are the agent, was contrived, in 1834, by Mr. Elliot, as we
have already had occasion to state. He placed the binocular pictures,
described in Chapter I., at one end of a box, and without the aid
either of lenses or mirrors, he obtained a landscape in perfect relief.
I have examined this stereoscope, and have given, in Fig. 8, an
accurate though reduced drawing of the binocular pictures executed and
used by Mr. Elliot. I have also united the two original pictures by
the convergency of the optic axes beyond them, and have thus seen the
landscape in true relief. To delineate these binocular pictures upon
stereoscopic principles was a bold undertaking, and establishes, beyond
all controversy, Mr. Elliot’s claim to the invention of the ocular
stereoscope.
If we unite the two pictures in Fig. 8, by converging the optic axes to
a point _nearer_ the eye than the pictures, we shall see distinctly the
stereoscopic relief, the moon being in the remote distance, the cross
in the middle distance, and the stump of a tree in the foreground.
If we place the two pictures as in Fig. 9, which is the position they
had in Mr. Elliot’s box, and unite them, by looking at a point beyond
them we shall also observe the stereoscopic relief. In this position
Mr. Elliot saw the relief without any effort, and even without being
conscious that he was not viewing the pictures under ordinary vision.
This tendency of the optic axes to a distant convergency is so rare
that I have met with it only in one person.
[Illustration: FIG. 9.]
As the relief produced by the union of such imperfect pictures was
sufficient only to shew the correctness of the principle, the friends
to whom Mr. Elliot shewed the instrument thought it of little interest,
and he therefore neither prosecuted the subject, nor published any
account of his contrivance.
Mr. Wheatstone suggested a similar contrivance, without either mirrors
or lenses. In order to unite the pictures by converging the optic axes
to a point between them and the eye, he proposed to place them in a
box to hide the lateral image and assist in making them unite with
the naked eyes. In order to produce the union by looking at a point
beyond the picture, he suggested the use of “a pair of tubes capable
of being inclined to each other at various angles,” the pictures being
placed on a stand in front of the tubes. These contrivances, however,
though auxiliary to the use of the naked eyes, were superseded by the
Reflecting Stereoscope, which we shall now describe.
_Description of the Reflecting Stereoscope._
This form of the stereoscope, which we owe to Mr. Wheatstone, is shewn
in Fig. 10, and is described by him in the following terms:—“AA′ are
two plane mirrors, (whether of glass or metal is not stated,) about
four inches square, inserted in frames, and so adjusted that their
backs form an angle of 90° with each other; these mirrors are fixed
by their common edge against an upright B, or, which was less easy to
represent in the drawing against the middle of a vertical board, cut
away in such a manner as to allow the eyes to be placed before the
two mirrors. C, C′ are two sliding boards, to which are attached the
upright boards D, D′, which may thus be removed to different distances
from the mirrors. In most of the experiments hereafter to be detailed
it is necessary that each upright board shall be at the same distance
from the mirror which is opposite to it. To facilitate this double
adjustment, I employ a right and a left-handed wooden screw, _r_, _l_;
the two ends of this compound screw pass through the nuts _e_, _e′_,
which are fixed to the lower parts of the upright boards D, D, so that
by turning the screw pin _p_ one way the two boards will approach,
and by turning them the other they will recede from each other, one
always preserving the same distance as the other from the middle line
_f_; E, E′ are pannels to which the pictures are fixed in such manner
that their corresponding horizontal lines shall be on the same level;
these pannels are capable of sliding backwards or forwards in grooves
on the upright boards D, D′. The apparatus having been described, it
now remains to explain the manner of using it. The observer must place
his eyes as near as possible to the mirrors, the right eye before the
right-hand mirror, and the left eye before the left-hand mirror, and
he must move the sliding pannels E, E′ to or from him till the two
reflected images coincide at the intersection of the optic axes, and
form an image of the same apparent magnitude as each of the component
pictures. The picture will, indeed, coincide when the sliding pannels
are in a variety of different positions, and, consequently, when viewed
under different inclinations of the optic axes, but there is only one
position in which the binocular image will be immediately seen single,
of its proper magnitude, and without fatigue to the eyes, because in
this position only the ordinary relations between the magnitude of the
pictures on the retina, the inclination of the optic axes, and the
adaptation of the eye to distinct vision at different distances, are
preserved. In all the experiments detailed in the present memoir I
shall suppose these relations to remain undisturbed, and the optic axes
to converge about six or eight inches before the eyes.
[Illustration: FIG. 10.]
“If the pictures are all drawn to be seen with the same inclination of
the optic axes the apparatus may be simplified by omitting the screw
_rl_, and fixing the upright boards D, D′ at the proper distance. The
sliding pannels may also be dispensed with, and the drawings themselves
be made to slide in the grooves.”
The figures to which Mr. Wheatstone applied this instrument were pairs
of outline representations of objects of three dimensions, such as
a cube, a cone, the frustum of a square pyramid, which is shewn on
one side of E, E′ in Fig. 10, and in other figures; and he employed
them, as he observes, “for the purpose of illustration, for had either
shading or colouring been introduced it might be supposed that the
effect was wholly or in part due to these circumstances, whereas, by
leaving them out of consideration, no room is left to doubt that the
entire effect of relief is owing to the simultaneous perception of the
two monocular projections, one on each retina.”
“Careful attention,” he adds, “would enable an artist to draw and
paint the two component pictures, so as to present to the mind of the
observer, in the resultant perception, perfect identity with the object
represented. Flowers, crystals, busts, vases, instruments of various
kinds, &c., might thus be represented, _so as not to be distinguished
by sight from the real objects themselves_.”
This expectation has never been realized, for it is obviously beyond
the reach of the highest art to draw two copies of a flower or a
bust with such accuracy of outline or colour as to produce “perfect
identity,” or anything approaching to it, “with the object represented.”
Photography alone can furnish us with such representations of natural
and artificial objects; and it is singular that neither Mr. Elliot
nor Mr. Wheatstone should have availed themselves of the well-known
photographic process of Mr. Wedgewood and Sir Humphry Davy, which, as
Mr. Wedgewood remarks, wanted only “a method of preventing the unshaded
parts of the delineation from being coloured by exposure to the day, to
render the process as useful as it is elegant.” When the two dissimilar
photographs were taken they could have been used in the stereoscope in
candle-light, or in faint daylight, till they disappeared, or permanent
outlines of them might have been taken and coloured after nature.
Mr. Fox Talbot’s beautiful process of producing permanent photographs
was communicated to the Royal Society in January 1839, but no attempt
was made till some years later to make it available for the stereoscope.
In a chapter on binocular pictures, and the method of executing them
in order to reproduce, with perfect accuracy, the objects which they
represent, we shall recur to this branch of the subject.
Upon obtaining one of these reflecting stereoscopes as made by the
celebrated optician, Mr. Andrew Ross, I found it to be very ill adapted
for the purpose of uniting dissimilar pictures, and to be imperfect in
various respects. Its imperfections may be thus enumerated:—
1. It is a clumsy and unmanageable apparatus, rather than an instrument
for general use. The one constructed for me was 16½ inches long, 6
inches broad, and 8½ inches high.
2. The loss of light occasioned by reflection from the mirrors is
very great. In all optical instruments where images are to be formed,
and light is valuable, mirrors and specula have been discontinued.
Reflecting microscopes have ceased to be used, but large telescopes,
such as those of Sir W. and Sir John Herschel, Lord Rosse, and Mr.
Lassel, were necessarily made on the reflecting principle, from the
impossibility of obtaining plates of glass of sufficient size.
3. In using glass mirrors, of which the reflecting stereoscope is
always made, we not only lose much more than half the light by the
reflections from the glass and the metallic surface, and the absorbing
power of the glass, but the images produced by reflection are made
indistinct by the oblique incidence of the rays, which separates the
image produced by the glass surface from the more brilliant image
produced by the metallic surface.
4. In all reflections, as Sir Isaac Newton states, the errors are
greater than in refraction. With glass mirrors in the stereoscope,
we have _four_ refractions in each mirror, and the light transmitted
through _twice_ the thickness of the glass, which lead to two sources
of error.
5. Owing to the exposure of the eye and every part of the apparatus
to light, the eye itself is unfitted for distinct vision, and
the binocular pictures become indistinct, especially if they are
Daguerreotypes,[34] by reflecting the light incident from every part of
the room upon their glass or metallic surface.
[34] Mr. Wheatstone himself says, “that it is somewhat difficult to
render the two Daguerreotypes equally visible.”—_Phil. Trans._, 1852,
p. 6.
6. The reflecting stereoscope is inapplicable to the beautiful
binocular slides which are now being taken for the lenticular
stereoscope in every part of the world, and even if we cut in two
those on paper and silver-plate, they would give, in the reflecting
instrument, _converse_ pictures, the right-hand part of the picture
being placed on the left-hand side, and _vice versa_.
7. With transparent binocular slides cut in two, we could obtain
pictures by reflection that are not converse; but in using them, we
would require to have two lights, one opposite each of the pictures,
which can seldom be obtained in daylight, and which it is inconvenient
to have at night.
Owing to these and other causes, the reflecting stereoscope never came
into use, even after photography was capable of supplying binocular
pictures.
As a set-off against these disadvantages, it has been averred that in
the reflecting stereoscope we can use larger pictures, but this, as we
shall shew in a future chapter, is altogether an erroneous assertion.
_Description of the Lenticular Stereoscope._
Having found that the reflecting stereoscope, when intended to produce
accurate results, possessed the defects which I have described, and
was ill fitted for general use, both from its size and its price, it
occurred to me that the union of the dissimilar pictures could be
better effected by means of lenses, and that a considerable magnifying
power would be thus obtained, without any addition to the instrument.
[Illustration: FIG. 11.]
If we suppose A, B, Fig. 11, to be two portraits,—A a portrait of a
gentleman, as seen by the left eye of a person viewing him at the
proper distance and in the best position, and B his portrait as seen
by the right eye, the purpose of the stereoscope is to place these two
pictures, or rather their images, one above the other. The method of
doing this by lenses may be explained, to persons not acquainted with
optics, in the following manner:—
If we look at A with one eye through the _centre_ of a convex glass,
with which we can see it distinctly at the distance of 6 inches, which
is called its _focal distance_, it will be seen in its place at A. If
we now move the lens from _right to left_, the image of A will move
towards B; and when it is seen through the _right_-hand edge of the
lens, the image of A will have reached the position C, half-way between
A and B. If we repeat this experiment with the portrait B, and move
the lens from _left to right_, the image of B will move towards A; and
when it is seen through the _left_-hand edge of the lens, the image
of B will have reached the position C. Now, it is obviously by the
_right_-hand half of the lens that we have transferred the image of A
to C, and by the _left_-hand half that we have transferred the image of
B to C. If we cut the lens in two, and place the halves—one in front of
each picture at the distance of 2½ inches—in the same position in which
they were when A was transferred to C and B to C, they will stand as in
Fig. 12, and we shall see the portraits A and B united into one at C,
and standing out in beautiful relief,—a result which will be explained
in a subsequent chapter.
[Illustration: FIG. 12.]
The same effect will be produced by quarter lenses, such as those shewn
in Fig. 13. These lenses are cut into a round or square form, and
placed in tubes, as represented at R, L, in Fig. 14, which is a drawing
of the _Lenticular Stereoscope_.
[Illustration: FIG. 13.]
This instrument consists of a pyramidal box, Fig. 14, blackened inside,
and having a lid, CD, for the admission of light when required. The
top of the box consists of two parts, in one of which is the right-eye
tube, R, containing the lens G, Fig. 13, and in the other the left-eye
tube, L, containing the lens H. The two parts which hold the lenses,
and which form the top of the box, are often made to slide in grooves,
so as to suit different persons whose eyes, placed at R, L, are more
or less distant. This adjustment may be made by various pieces of
mechanism. The simplest of these is a jointed parallelogram, moved by
a screw forming its longer diagonal, and working in nuts fixed on the
top of the box, so as to separate the semi-lenses, which follow the
movements of the obtuse angles of the parallelogram. The tubes R, L
move up and down, in order to suit eyes of different focal lengths, but
they are prevented from turning round by a brass pin, which runs in a
groove cut through the movable tube. Immediately below the eye-tubes
R, L, there should be a groove, G, for the introduction of convex or
concave lenses, when required for very long-sighted or short-sighted
persons, or for coloured glasses and other purposes.
[Illustration: FIG. 14.]
If we now put the slide AB, Fig. 11, into the horizontal opening at
S, turning up the sneck above S to prevent it from falling out, and
place ourselves behind R, L, we shall see, by looking through R with
the right eye and L with the left eye, the two images A, B united in
one, and in the same relief as the living person whom they represent.
No portrait ever painted, and no statue ever carved, approximate in
the slightest degree to the living reality now before us. If we shut
the right eye R we see with the left eye L merely the portrait A, but
it has now sunk into a flat picture, with only _monocular relief_.
By closing the left eye we shall see merely the portrait B, having,
like the other, only monocular relief, but a relief greater than the
best-painted pictures can possibly have, when seen even with one eye.
When we open both eyes, the two portraits instantly start into all the
roundness and solidity of life.
Many persons experience a difficulty in seeing the portraits single
when they first look into a stereoscope, in consequence of their eyes
having less power than common over their optic axes, or from their
being more or less distant than two and a half inches, the average
distance. The two images thus produced frequently disappear in a few
minutes, though sometimes it requires a little patience and some
practice to see the single image. We have known persons who have lost
the power of uniting the images, in consequence of having discontinued
the use of the instrument for some months; but they have always
acquired it again after a little practice.
If the portraits or other pictures are upon opaque paper or
silver-plate, the stereoscope, which is usually held in the left hand,
must be inclined so as to allow the light of the sky, or any other
light, to illuminate every part of the pictures. If the pictures are
on transparent paper or glass, we must shut the lid CD, and hold up
the stereoscope against the sky or the artificial light, for which
purpose the bottom of the instrument is made of glass finely ground on
the outside, or has two openings, the size of each of the binocular
pictures, covered with fine paper.
In using the stereoscope the observer should always be seated, and it
is very convenient to have the instrument mounted like a telescope,
upon a stand, with a weight and pulley for regulating the motion of the
lid CD.
The lenticular stereoscope may be constructed of various materials
and in different forms. I had them made originally of card-board,
tin-plate, wood, and brass; but wood is certainly the best material
when cheapness is not an object.
[Illustration: FIG. 15.]
One of the earliest forms which I adopted was that which is shewn
in Fig. 15, as made by M. Duboscq in Paris, and which may be called
_stereoscopic spectacles_. The two-eye lenses L, R are held by the
handle H, so that we can, by moving them to or from the binocular
pictures, obtain distinct vision and unite them in one. The effect,
however, is not so good as that which is produced when the pictures are
placed in a box.
The same objection applies to a form otherwise more convenient, which
consists in fixing a cylindrical or square rod of wood or metal to C,
the middle point between L and R. The binocular slide having a hole
in the middle between the two pictures is moved along this rod to its
proper distance from the lenses.
[Illustration: FIG. 16.]
Another form, analogous to this, but without the means of moving the
pictures, is shewn in Fig. 16, as made by M. Duboscq. The adjustment
is effected by moving the eye-pieces in their respective tubes, and by
means of a screw-nut, shewn above the eye-pieces, they can be adapted
to eyes placed at different distances from one another. The advantage
of this form, if it is an advantage, consists in allowing us to use
larger pictures than can be admitted into the box-stereoscope of the
usual size. A box-stereoscope, however, of the same size, would have
the same property and other advantages not possessed by the open
instrument.
Another form of the lenticular stereoscope, under the name of the
cosmorama stereoscope, has been adopted by Mr. Knight. The box is
rectangular instead of pyramidal, and the adjustment to distinct
vision is made by pulling out or pushing in a part of the box, instead
of the common and better method of moving each lens separately. The
illumination of the pictures is made in the same manner as in the
French instrument, called the cosmorama, for exhibiting dissolving
views. The lenses are large in surface, which, without any reason, is
supposed to facilitate the view of the binocular pictures, and the
instrument is supported in a horizontal position upon a stand. There
is no contrivance for adjusting the distance of the lenses to the
distance between the eyes, and owing to the quantity of light which
gets into the interior of the box, the stereoscopic picture is injured
by false reflections, and the sensibility of the eyes diminished. The
exclusion of all light from the eyes, and of every other light from the
picture but that which illuminates it, is essentially necessary to the
perfection of stereoscopic vision.
When by means of any of these instruments we have succeeded in forming
a single image of the two pictures, we have only, as I have already
explained, placed the one picture above the other, in so far as the
stereoscope is concerned. It is by the subsequent action of the two
eyes that we obtain the desired relief. Were we to unite the two
pictures when transparent, and take a copy of the combination by the
best possible camera, the result would be a blurred picture, in which
none of the points or lines of the one would be united with the points
or lines of the other; but were we to look at the combination with both
eyes the blurred picture would start into relief, the eyes uniting in
succession the separate points and lines of which it is composed.
Now, since, in the stereoscope, when looked into with two eyes, we see
the picture in relief with the same accuracy as, in ordinary binocular
vision, we see the same object in relief by uniting on the retina two
pictures exactly the same as the binocular ones, the mere statement of
this fact has been regarded as the theory of the stereoscope. We shall
see, however, that it is not, and that it remains to be explained, more
minutely than we have done in Chapter III., both how we see objects
in relief in ordinary binocular vision, and how we see them in the
same relief by uniting ocularly, or in the stereoscope, two dissimilar
images of them.
Before proceeding, however, to this subject, we must explain the manner
in which half and quarter lenses unite the two dissimilar pictures.
[Illustration: FIG. 17.]
In Fig. 17 is shewn a semi-lens MN, with its section M′N′. If we look
at any object successively through the portions AA′A″ in the semi-lens
MN, corresponding to _aa′a″_ in the section M′N′, which is the same as
in a quarter-lens, the object will be magnified equally in all of them,
but it will be more displaced, or more refracted, towards N, by looking
through A′ or _a′_ than through A or _a_, and most of all by looking
through A″ or _a″_, the refraction being greatest at A″ or _a″_, less
at A′ or _a′_, and still less at A or _a_. By means of a semi-lens,
or a quarter of a lens of the size of MN, we can, with an aperture
of the size of A, obtain three different degrees of displacement or
refraction, without any change of the magnifying power.
If we use a thicker lens, as shewn at M′N′_nm_, keeping the curvature
of the surface the same, we increase the refracting angle at its margin
N′_n_, we can produce any degree of displacement we require, either for
the purposes of experiment, or for the duplication of large binocular
pictures.
When two half or quarter lenses are used as a stereoscope, the
displacement of the two pictures is produced in the manner shewn in
Fig. 18, where LL is the lens for the left eye E, and L′L′ that for
the right eye E′, placed so that the middle points, _no_, _n′o′_,
of each are 2½ inches distant, like the two eyes. The two binocular
pictures which are to be united are shewn at _ab_, AB, and placed at
nearly the same distance. The pictures being fixed in the focus of the
lenses, the pencils _ano_, A′_n′o′_, _bno_, B′_n′o′_, will be refracted
at the points _n_, _o_, _n′_, _o′_, and at their points of incidence
on the second surface, so as to enter the eyes, E, E′, in parallel
directions, though not shewn in the Figure. The points _a_, A, of one
of the pictures, will therefore be seen distinctly in the direction of
the refracted ray—that is, the pencils _an_, _ao_, issuing from _a′_,
will be seen as if they came from _a′_, and the pencils _bn_, _bo_, as
if they came from _b′_, so that _ab_ will be transferred by refraction
to _a′b′_. In like manner, the picture AB will be transferred by
refraction to A′B′, and thus united with _a′b′_.
[Illustration: FIG. 18]
The pictures _ab_, ABB thus united are merely circles, and will
therefore be seen as a single circle at A′B′. But if we suppose _ab_ to
be the base of the frustum of a cone, and _cd_ its summit, as seen by
the left eye, and the circles AB, CD to represent the base and summit
of the same solid as seen by the right eye, then it is obvious that
when the pictures of _cd_ and CD are similarly displaced or refracted
by the lenses LL L′L′, so that _cc′_ is equal to _a_A′ and DD′ to
BB′, the circles will not be united, but will overlap one another
as at C′D′, _c′d′_, in consequence of being carried _beyond_ their
place of union. The eyes, however, will instantly unite them into one
by converging their axes to a remoter point, and the united circles
will rise from the paper, or from the base A′B′, and place the single
circle at the point of convergence, as the summit of the frustum of a
hollow cone whose base is A′B′. If _cd_, CD had been _farther_ from
one another than _ab_, AB, as in Figs. 20 and 21, they would still
have overlapped though not carried up to their place of union. The
eyes, however, will instantly unite them by converging their axes to
a _nearer_ point, and the united circles will rise from the paper, or
from the base AB, and form the summit of the frustum of a _raised_ cone
whose base is A′B′.
In the preceding illustration we have supposed the solid to consist
only of a base and a summit, or of parts at _two_ different distances
from the eye; but what is true of two distances is true of any number,
and the instant that the two pictures are combined by the lenses they
will exhibit in relief the body which they represent. If the pictures
are refracted too little, or if they are refracted too much, so as
not to be united, their tendency to unite is so great, that they are
soon brought together by the increased or diminished convergency of
the optic axes, and the stereoscopic effect is produced. Whenever two
pictures are seen, no relief is visible; when only one picture is
distinctly seen, the relief must be complete.
In the preceding diagram we have not shewn the refraction at the second
surface of the lenses, nor the parallelism of the rays when they enter
the eye,—facts well known in elementary optics.