Transcriber’s Notes:

  Underscores “_” before and after a word or phrase indicate _italics_
    in the original text.
  Equal signs “=” before and after a word or phrase indicate =bold=
    in the original text.
  Small capitals have been converted to SOLID capitals.
  Illustrations and footnotes have been moved so they do not break up
    paragraphs.
  Antiquated spellings have been preserved.
  Typographical and punctuation errors have been silently corrected.
  In the Table of Contents, Chapters XV and XVI were corrected from page
    200 to 211 and 216 respectively.
  Figure 46 was incorrectly labelled Figure 45, this has been corrected.




                              THE STEREOSCOPE

                   ITS HISTORY, THEORY, AND CONSTRUCTION

             WITH ITS APPLICATION TO THE FINE AND USEFUL ARTS
                             AND TO EDUCATION.

                                    BY
            SIR DAVID BREWSTER, K.H., D.C.L., F.R.S., M.R.I.A.,

    VICE-PRESIDENT OF THE ROYAL SOCIETY OF EDINBURGH, ONE OF THE EIGHT
      ASSOCIATES OF THE IMPERIAL INSTITUTE OF FRANCE, OFFICER OF THE
        LEGION OF HONOUR, CHEVALIER OF THE PRUSSIAN ORDER OF MERIT,
             HONORARY OR CORRESPONDING MEMBER OF THE ACADEMIES
                OF PETERSBURGH, VIENNA, BERLIN, COPENHAGEN,
                  STOCKHOLM, BRUSSELS, GÖTTINGEN, MODENA,
                     AND OF THE NATIONAL INSTITUTE OF
                             WASHINGTON, ETC.

                        WITH FIFTY WOOD ENGRAVINGS.

                                  LONDON:
                      JOHN MURRAY, ALBEMARLE STREET.
                                   1856.

              [_The Right of Translation is reserved._]

                                EDINBURGH:
                   T. CONSTABLE, PRINTER TO HER MAJESTY.




                           CONTENTS


                                                                 PAGE
    INTRODUCTION,                                                  1
    CHAP. I.—HISTORY OF THE STEREOSCOPE,                           5
         II.—ON MONOCULAR VISION, OR VISION WITH ONE EYE,         38
        III.—ON BINOCULAR VISION, OR VISION WITH TWO EYES,        47
         IV.—DESCRIPTION OF THE OCULAR, REFLECTING,
               AND LENTICULAR STEREOSCOPES,                       53
          V.—ON THE THEORY OF THE STEREOSCOPIC VISION,            76
         VI.—ON THE UNION OF SIMILAR PICTURES IN
               BINOCULAR VISION,                                  90
        VII.—DESCRIPTION OF DIFFERENT STEREOSCOPES,              107
       VIII.—METHOD OF TAKING PICTURES FOR THE STEREOSCOPE,      131
         IX.—ON THE ADAPTATION OF THE PICTURES TO
               THE STEREOSCOPE.—THEIR SIZE, POSITION,
               AND ILLUMINATION,                                 159
          X.—APPLICATION OF THE STEREOSCOPE TO PAINTING,         166
         XI.—APPLICATION OF THE STEREOSCOPE TO SCULPTURE,
               ARCHITECTURE, AND ENGINEERING,                    183
        XII.—APPLICATION OF THE STEREOSCOPE TO NATURAL HISTORY,  189
       XIII.—APPLICATION OF THE STEREOSCOPE TO
               EDUCATIONAL PURPOSES,                             193
        XIV.—APPLICATION OF THE STEREOSCOPE TO PURPOSES
               OF AMUSEMENT,                                     204
         XV.—ON THE PRODUCTION OF STEREOSCOPIC
               PICTURES FROM A SINGLE PICTURE,                   211
        XVI.—ON CERTAIN FALLACIES OF SIGHT IN THE
               VISION OF SOLID BODIES,                           216
       XVII.—ON CERTAIN DIFFICULTIES EXPERIENCED IN
               THE USE OF THE STEREOSCOPE,                       231




ON THE STEREOSCOPE.




INTRODUCTION.


The _Stereoscope_, a word derived from =στέρεος=, _solid_, and
σκόπειν, to _see_, is an optical instrument, of modern invention, for
representing, in apparent relief and solidity, all natural objects and
all groups or combinations of objects, by uniting into one image two
plane representations of these objects or groups as seen by each eye
separately. In its most general form the Stereoscope is a _binocular_
instrument, that is, is applied to _both_ eyes; but in two of its
forms it is _monocular_, or applied only to _one_ eye, though the use
of the other eye, without any instrumental aid, is necessary in the
combination of the two plane pictures, or of one plane picture and its
reflected image. The Stereoscope, therefore, cannot, like the telescope
and microscope, be used by persons who have lost the use of one eye,
and its remarkable effects cannot be properly appreciated by those
whose eyes are not equally good.

When the artist represents living objects, or groups of them, and
delineates buildings or landscapes, or when he copies from statues or
models, he produces apparent solidity, and difference of distance from
the eye, by light and shade, by the diminished size of known objects as
regulated by the principles of geometrical perspective, and by those
variations in distinctness and colour which constitute what has been
called aerial perspective. But when all these appliances have been
used in the most skilful manner, and art has exhausted its powers,
we seldom, if ever, mistake the plane picture for the solid which it
represents. The two eyes scan its surface, and by their distance-giving
power indicate to the observer that every point of the picture is
nearly at the same distance from his eye. But if the observer closes
one eye, and thus deprives himself of the power of determining
differences of distance by the convergency of the optical axes, the
relief of the picture is increased. When the pictures are truthful
photographs, in which the variations of light and shade are perfectly
represented, a very considerable degree of relief and solidity is
thus obtained; and when we have practised for a while this species of
monocular vision, the drawing, whether it be of a statue, a living
figure, or a building, will appear to rise in its different parts from
the canvas, though only to a limited extent.

In these observations we refer chiefly to ordinary drawings held in the
hand, or to portraits and landscapes hung in rooms and galleries, where
the proximity of the observer, and lights from various directions,
reveal the surface of the paper or the canvas; for in panoramic and
dioramic representations, where the light, concealed from the observer,
is introduced in an oblique direction, and where the distance of the
picture is such that the convergency of the optic axes loses much of
its distance-giving power, the illusion is very perfect, especially
when aided by correct geometrical and aerial perspective. But when
the panorama is illuminated by light from various directions, and the
slightest motion imparted to the canvas, its surface becomes distinctly
visible, and the illusion instantly disappears.

The effects of stereoscopic representation are of a very different
kind, and are produced by a very different cause. The singular relief
which it imparts is independent of light and shade, and of geometrical
as well as of aerial perspective. These important accessories, so
necessary in the visual perception of the drawings _in plano_, avail
nothing in the evolution of their _relievo_, or third dimension. They
add, doubtless, to the beauty of the binocular pictures; but the
stereoscopic creation is due solely to the superposition of the two
plane pictures by the optical apparatus employed, and to the distinct
and instantaneous perception of distance by the convergency of the
optic axes upon the similar points of the two pictures which the
stereoscope has united.

If we close one eye while looking at photographic pictures in the
stereoscope, the perception of relief is still considerable, and
approximates to the binocular representation; but when the pictures are
mere diagrams consisting of white lines upon a black ground, or black
lines upon a white ground, the relief is instantly lost by the shutting
of the eye, and it is only with such binocular pictures that we see the
true power of the stereoscope.

As an amusing and useful instrument the stereoscope derives much of
its value from photography. The most skilful artist would have been
incapable of delineating two equal representations of a figure or a
landscape as seen by two eyes, or as viewed from two different points
of sight; but the binocular camera, when rightly constructed, enables
us to produce and to multiply photographically the pictures which we
require, with all the perfection of that interesting art. With this
instrument, indeed, even before the invention of the Daguerreotype and
the Talbotype, we might have exhibited temporarily upon ground-glass,
or suspended in the air, the most perfect stereoscopic creations, by
placing a Stereoscope behind the two dissimilar pictures formed by the
camera.




CHAPTER I.

HISTORY OF THE STEREOSCOPE.


When we look with both eyes open at a sphere, or any other solid
object, we see it by uniting into one two pictures, one as seen by the
right, and the other as seen by the left eye. If we hold up a thin book
perpendicularly, and midway between both eyes, we see distinctly the
back of it and both sides with the eyes open. When we shut the right
eye we see with the left eye the back of the book and the left side of
it, and when we shut the left eye we see with the right eye the back of
it and the right side. The picture of the book, therefore, which we see
with both eyes, consists of _two_ dissimilar pictures united, namely, a
picture of the back and the left side of the book as seen by the left
eye, and a picture of the back and right side of the book as seen by
the right eye.

In this experiment with the book, and in all cases where the object is
near the eye, we not only see _different pictures_ of the same object,
but we see _different things_ with each eye. Those who wear spectacles
see only the left-hand spectacle-glass with the left eye, on the left
side of the face, while with the right eye they see only the right-hand
spectacle-glass on the right side of the face, both glasses of the
spectacles being seen united midway between the eyes, or above the
nose, when both eyes are open. It is, therefore, a fact well known to
every person of common sagacity that _the pictures of bodies seen by
both eyes are formed by the union of two dissimilar pictures formed by
each_.

This palpable truth was known and published by ancient mathematicians.
Euclid knew it more than two thousand years ago, as may be seen in the
26th, 27th, and 28th theorems of his Treatise on Optics.[1] In these
theorems he shews that the part of a sphere seen by both eyes, and
having its diameter equal to, or greater or less than the distance
between the eyes, is equal to, and greater or less than a hemisphere;
and having previously shewn in the 23d and 24th theorems how to find
the part of any sphere that is seen by one eye at different distances,
it follows, from constructing his figure, that each eye sees different
portions of the sphere, and that it is seen by both eyes by the union
of these two dissimilar pictures.

[1] Edit. of Pena, pp. 17, 18, Paris, 1577; or _Opera_, by Gregory, pp.
619, 620. Oxon. 1703.

More than _fifteen hundred_ years ago, the celebrated physician Galen
treated the subject of binocular vision more fully than Euclid. In
the _twelfth_ chapter of the tenth book of his work, _On the use of
the different parts of the Human Body_, he has described with great
minuteness the various phenomena which are seen when we look at
bodies with both eyes, and alternately with the right and the left.
He shews, by diagrams, that dissimilar pictures of a body are seen
in each of these three modes of viewing it; and, after finishing his
demonstration, he adds,—

    “But if any person does not understand these
    demonstrations by means of lines, he will finally
    give his assent to them when he has made the
    following experiment:—Standing near a column, and
    shutting each of the eyes in succession;—when the
    _right_ eye is shut, some of those parts of the
    column which were previously seen by the _right_ eye
    on the _right_ side of the column, will not now be
    seen by the _left_ eye; and when the _left_ eye is
    shut, some of those parts which were formerly seen
    by the _left_ eye on the _left_ side of the column,
    will not now be seen by the _right_ eye. But when we,
    at the same time, open both eyes, both these will be
    seen, for a greater part is concealed when we look
    with either of the two eyes, than when we look with
    both at the same time.”[2]

[2] _De Usu Partium Corporis Humani_, edit. Lugduni, 1550, p. 593.

In such distinct and unambiguous terms, intelligible to the meanest
capacity, does this illustrious writer announce the fundamental law
of binocular vision—the grand principle of the Stereoscope, namely,
that _the picture of the solid column which we see with both eyes is
composed of two dissimilar pictures, as seen by each eye separately_.
As the vision of the solid column, therefore, was obtained by the union
of these dissimilar pictures, an instrument only was wanted to take
such pictures, and another to combine them. The Binocular Photographic
Camera was the one instrument, and the Stereoscope the other.

The subject of binocular vision was studied by various optical writers
who have flourished since the time of Galen. Baptista Porta, one of
the most eminent of them, repeats, in his work _On Refraction_, the
propositions of Euclid on the vision of a sphere with one and both
eyes, and he cites from Galen the very passage which we have given
above on the dissimilarity of the three pictures seen by each eye and
by both. Believing that we see only with one eye at a time, he denies
the accuracy of Euclid’s theorems, and while he admits the correctness
of the observations of Galen, he endeavours to explain them upon other
principles.

[Illustration: FIG. 1.]

In illustrating the views of Galen on the dissimilarity of the three
pictures which are requisite in binocular vision, he employs a much
more distinct diagram than that which is given by the Greek physician.
“Let A,” he says, “be the pupil of the right eye, B that of the left,
and DC the body to be seen. When we look at the object with both eyes
we see DC, while with the left eye we see EF, and with the right eye
GH. But if it is seen with one eye, it will be seen otherwise, for when
the left eye B is shut, the body CD, on the left side, will be seen in
HG; but when the right eye is shut, the body CD will be seen in FE,
whereas, when both eyes are opened at the same time, it will be seen
in CD.” These results are then explained by copying the passage from
Galen, in which he supposes the observer to repeat these experiments
when he is looking at a solid column.

In looking at this diagram, we recognise at once not only the
principle, but the construction of the stereoscope. The double
stereoscopic picture or slide is represented by HE; the right-hand
picture, or the one seen by the right eye, by HF; the left-hand
picture, or the one seen by the left eye, by GE; and the picture of the
solid column in full relief by DC, as produced midway between the other
two dissimilar pictures, HF and GE, by their union, precisely as in the
stereoscope.[3]

[3] Joan. Baptistæ Portæ Neap., _De Refractione Optices parte_, lib. v.
p. 132, and lib. vi. pp. 143-5. Neap. 1593.

Galen, therefore, and the Neapolitan philosopher, who has employed
a more distinct diagram, certainly knew and adopted the fundamental
principle of the stereoscope; and nothing more was required, for
producing pictures in full relief, than a simple instrument for uniting
HF and GE, the right and left hand dissimilar pictures of the column.

[Illustration: FIG. 2.]

In the treatise on painting which he left behind him in MS.,[4]
Leonardo da Vinci has made a distinct reference to the dissimilarity
of the pictures seen by each eye as the reason why “a painting, though
conducted with the greatest art, and finished to the last perfection,
both with regard to its contours, its lights, its shadows, and its
colours, can never shew a _relievo_ equal to that of the natural
objects, unless these be viewed at a distance and with a single
eye,”[5] which he thus demonstrates. “If an object C be viewed by a
single eye at A, all objects in the space behind it—included, as it
were, in a shadow ECF, cast by a candle at A—are invisible to an eye at
A; but when the other eye at B is opened, part of these objects become
visible to it; those only being hid from both eyes that are included,
as it were, in the double shadow CD, cast by two lights at A and B and
terminated in D; the angular space EDG, beyond D, being always visible
to both eyes. And the hidden space CD is so much the shorter as the
object C is smaller and nearer to the eyes. Thus he observes that
the object C, seen with both eyes, becomes, as it were, transparent,
according to the usual definition of a transparent thing, namely, that
which hides nothing beyond it. But this cannot happen when an object,
whose breadth is bigger than that of the pupil, is viewed by a single
eye. The truth of this observation is, therefore, evident, because a
painted figure intercepts all the space behind its apparent place, so
as to preclude the eyes from the sight of every part of the imaginary
ground behind it. Hence,” continues Dr. Smith, “we have one help to
distinguish the place of a near object more accurately _with both eyes
than with one_, inasmuch as we see it more detached from other objects
beyond it, _and more of its own surface, especially if it be roundish_.”

[4] _Trattata della Pictura, Scultura, ed Architettura._ Milan, 1584.

[5] Dr. Smith’s _Compleat System of Opticks_, vol. ii., Remarks, pp. 41
and 244.

We have quoted this passage, not from its _proving_ that Leonardo da
Vinci was acquainted with the fact that each eye, A, B, sees dissimilar
pictures of the sphere C, but because it has been referred to by Mr.
Wheatstone as the only remark on the subject of binocular vision which
he could find “after looking over the works of many authors who might
be expected to have made them.” We think it quite clear, however, that
the Italian artist knew as well as his commentator Dr. Smith, that each
eye, A and B, sees dissimilar parts of the sphere C. It was not his
purpose to treat of the binocular pictures of C, but his figure proves
their dissimilarity.

The subject of binocular vision was successfully studied by Francis
Aguillon or Aguilonius,[6] a learned Jesuit, who published his Optics
in 1613. In the first book of his work, where he is treating of the
vision of solids of all forms, (_de genere illorum quæ τὰ στέρεα [ta
sterea] nuncupantur_,) he has some difficulty in explaining, and fails
to do it, why the two dissimilar pictures of a solid, seen by each
eye, do not, when united, give a confused and imperfect view of it.
This discussion is appended to the demonstration of the theorem, “that
when an object is seen with two eyes, two optical pyramids are formed
whose common base is the object itself, and whose vertices are in the
eyes,”[7] and is as follows:—

[6] _Opticorum Libri Sex Philosophis juxta ac Mathematicis utiles._
Folio. Antverpiæ, 1613.

[7] In FIG. 1, AHF is the optical pyramid seen by the eye A, and BGE
the optical pyramid seen by the eye B.

“When one object is seen with two eyes, the angles at the vertices of
the optical pyramids (namely, HAF, GBE, Fig. 1) are not always equal,
for beside the direct view in which the pyramids ought to be equal,
into whatever direction both eyes are turned, they receive pictures of
the object under inequal angles, the greatest of which is that which
is terminated at the nearer eye, and the lesser that which regards the
remoter eye. This, I think, is perfectly evident; but I consider it as
worthy of admiration, how it happens that bodies seen by both eyes are
not all confused and shapeless, though we view them by the optical axes
fixed on the bodies themselves. For greater bodies, seen under greater
angles, appear lesser bodies under lesser angles. If, therefore, one
and the same body which is in reality greater with one eye, is seen
less on account of the inequality of the angles in which the pyramids
are terminated, (namely, HAF, GBE,[8]) the body itself must assuredly
be seen greater or less at the same time, and to the same person that
views it; and, therefore, since the images in each eye are dissimilar
(_minime sibi congruunt_) the representation of the object must appear
confused and disturbed (_confusa ac perturbata_) to the primary sense.”

[8] These angles are equal in this diagram and in the vision of a
sphere, but they are inequal in other bodies.

“This view of the subject,” he continues, “is certainly consistent with
reason, but, what is truly wonderful is, that it is not correct, for
bodies are seen clearly and distinctly with both eyes when the optic
axes are converged upon them. The reason of this, I think, is, that
the bodies do not appear to be single, because the apparent images,
which are formed from each of them in separate eyes, exactly coalesce,
(_sibi mutuo exacte congruunt_,) but because the common sense imparts
its aid equally to each eye, exerting its own power equally in the
same manner as the eyes are converged by means of their optical axes.
Whatever body, therefore, each eye sees with the eyes conjoined, the
common sense makes a single notion, not composed of the two which
belong to each eye, but belonging and accommodated to the imaginative
faculty to which it (the common sense) assigns it. Though, therefore,
the angles of the optical pyramids which proceed from the same object
to the two eyes, viewing it obliquely, are inequal, and though the
object appears greater to one eye and less to the other, yet the same
difference does not pass into the primary sense if the vision is made
only by the axes, as we have said, but if the axes are converged on
this side or on the other side of the body, the image of the same body
will be seen double, as we shall shew in Book iv., on the fallacies of
vision, and the one image will appear greater and the other less on
account of the inequality of the angles under which they are seen.”[9]

[9] Aguilonius, _Opticorum_, lib. ii. book xxxviii. pp. 140, 141.

Such is Aguilonius’s theory of binocular vision, and of the union
of the two dissimilar pictures in each eye by which a solid body is
seen. It is obviously more correct than that of Dr. Whewell and Mr.
Wheatstone. Aguilonius affirms it to be contrary to reason that two
dissimilar pictures can be united into a clear and distinct picture,
as they are actually found to be, and he is therefore driven to call
in the aid of what does not exist, a _common sense_, which rectifies
the picture. Dr. Whewell and Mr. Wheatstone have cut the Gordian knot
by maintaining what is impossible, that in binocular and stereoscopic
vision a long line is made to coincide with a short one, and a large
surface with a small one; and in place of conceiving this to be done by
a common sense overruling optical laws, as Aguilonius supposes, they
give to the tender and pulpy retina, the recipient of ocular pictures,
the strange power of contracting or expanding itself in order to
equalize inequal lines and inequal surfaces!

[Illustration: FIG. 3.]

In his fourth and very interesting book, on the fallacies of distance,
magnitude, position, and figure, Aguilonius resumes the subject of the
vision of solid bodies. He repeats the theorems of Euclid and Gassendi
on the vision of the sphere, shewing how much of it is seen by each
eye, and by both, whatever be the size of the sphere, and the distance
of the observer. At the end of the theorems, in which he demonstrates
that when the diameter of the sphere is equal to the distance between
the eyes we see exactly a hemisphere, he gives the annexed drawing
of the mode in which the sphere is seen by each eye, and by both. In
this diagram E is the right eye and D the left, CHFI the section of
that part of the sphere BC which is seen by the right eye E, BHGA the
section of the part which is seen by the left eye D, and BLC the half
of the great circle which is the section of the sphere as seen by both
eyes.[10] These three pictures of the solids are all dissimilar. The
right eye E does not see the part BLCIF of the sphere; the left eye
does not see the part BLCGA, while the part seen with both eyes is the
hemisphere BLCGF, the dissimilar segments BFG, CGF being united in its
vision.[11]

After demonstrating his theorems on the vision of spheres with one
and both eyes,[12] Aguilonius informs us, before he proceeds to the
vision of cylinders, that it is agreed upon that it is not merely true
with the sphere, but also with the cylinder, the cone, and all bodies
whatever, that the part which is seen is comprehended by tangent rays,
such as EB, EC for the right eye, in Fig. 3. “For,” says he, “since
these tangent lines are the outermost of all those which can be drawn
to the proposed body from the same point, namely, that in which the
eye is understood to be placed, it clearly follows that the part of
the body which is seen must be contained by the rays touching it on
all sides. For in this part no point can be found from which a right
line cannot be drawn to the eye, by which the correct visible form is
brought out.”[13]

[10] It is obvious that a complete hemisphere is not seen with both
eyes.

[11] Aguilonius, _Opticorum_, lib. iv. pp. 306, 307.

[12] In the last of these theorems Aguilonius describes and explains,
we believe for the first time, the _conversion of relief_ in the vision
of convex and concave surfaces. See Prop. xciv. p. 312.

[13] Id., p. 313.

Optical writers who lived after the time of Aguilonius seem to have
considered the subject of binocular vision as exhausted in his
admirable work. Gassendi,[14] though he treats the subject very
slightly, and without any figures, tells us that we see the left side
of the nose with the left eye, and the right side of it with the
right eye,—two pictures sufficiently dissimilar. Andrew Tacquet,[15]
though he quotes Aguilonius and Gassendi on the subject of seeing
distances with both eyes, says nothing on the binocular vision of
solids; and Smith, Harris, and Porterfield, only touch upon the subject
incidentally. In commenting on the passage which we have already
quoted from Leonardo da Vinci, Dr. Smith says, “Hence we have one help
to distinguish the place of a near object more accurately with both
eyes than with one, inasmuch as we see it more detached from other
objects beyond it, _and more of its own surface, especially if it be
roundish_.”[16] If any farther evidence were required that Dr. Smith
was acquainted with the dissimilarity of the images of a solid seen by
each eye, it will be found in his experiment with a “long ruler placed
between the eyebrows, and extended directly forward with its flat
sides, respecting the right hand and the left.” “By directing the eyes
to a remote object,” he adds, “the _right side of the ruler seen by
the right eye_ will appear on the left hand, and _the left side on the
right hand_, as represented in the figure.”[17]

[14] _Opera_, tom. ii. p. 394. Lugduni, 1658.

[15] _Opera Mathematica Optica_, tribus libris exposita, p. 136.

[16] _Opticks_, vol. ii., Remarks, pp. 41 and 245.

[17] Id., vol. i. p. 48, Fig. 196.

In his Treatise on Optics, published in 1775, Mr. Harris, when speaking
of the visible or apparent figures of objects, observes, that “we have
other helps for distinguishing _prominences of small parts_ besides
those by which we distinguish distances in general, as their degrees
of light and shade, and _the prospect we have round them_.” _And by
the parallax, on account of the distance betwixt our eyes, we can
distinguish besides the front part of the two sides of a near object
not thicker than the said distance, and this gives a visible relievo
to such objects, which helps greatly to raise or detach them from the
plane in which they lie. Thus the nose on a face is the more remarkably
raised by our seeing both sides of it at once._“[18] _That is, the
relievo is produced by the combination of the two dissimilar pictures
given by each eye._

Without referring to a figure given by Dr. Porterfield, in which he
actually gives drawings of an object as seen by each eye in binocular
vision,[19] the one exhibiting the object as seen endwise by the right
eye, and the other the same object as seen laterally by the left eye,
we may appeal to the experience of every optical, or even of every
ordinary observer, in support of the fact, that the dissimilarity of
the pictures in each eye, by which we see solid objects, is known to
those who have never read it in Galen, Porta, or Aguilonius. Who has
not observed the fact mentioned by Gassendi and Harris, that their left
eye sees only the left side of their nose, and their right eye the
right side, two pictures sufficiently dissimilar? Who has not noticed,
as well as Dr. Smith, that when they look at any thin, flat body, such
as a thin book, they see both sides of it—_the left eye only the left
side of it, and the right eye only the right side_, while the back, or
the part nearest the face, is seen by each eye, and both the sides and
the back by both the eyes? What student of perspective is there—master
or pupil, male or female—who does not know, as certainly as he knows
his alphabet, that the picture of a chair or table, or anything else,
drawn from _one point of sight_, or as seen by one eye placed in that
point, is _necessarily dissimilar_ to another drawing of the same
object taken from another point of sight, or as seen by the other eye
placed in a point 2½ inches distant from the first? If such a person is
to be found, we might then admit that the dissimilarity of the pictures
in each eye was not known to every student of perspective.[20]

[18] _Treatise on Optics_, p. 171; see also sect. 64, p. 113.

[19] _Treatise on the Eye_, vol i. p. 412, Plate 5, Fig. 37.

[20] As Mr. Wheatstone himself describes the dissimilar pictures or
drawings as “two different projections of the same object seen from
_two points of sight_, the distance between which is equal to the
interval between the eyes of the observer,” it is inconceivable on what
ground he could imagine himself to be the discoverer of so palpable and
notorious a fact as that the pictures of a body seen by two eyes—_two
points of sight_, must be dissimilar.

Such was the state of our knowledge of binocular vision when two
individuals, Mr. Wheatstone, and Mr. Elliot, now Teacher of Mathematics
in Edinburgh, were directing their attention to the subject. Mr.
Wheatstone communicated an important paper on the Physiology of Vision
to the British Association at Newcastle in August 1838, and exhibited
an instrument called a Stereoscope, by which he united the two
dissimilar pictures of solid bodies, the =τὰ στέρεα=, (_ta sterea_ of
Aguilonius,) and thus reproduced, as it were, the bodies themselves.
Mr. Wheatstone’s paper on the subject, which had been previously
read at the Royal Society on the 21st of June, was printed in their
Transactions for 1838.[21]

[21] _Phil. Trans._, 1838, pp. 371-394.

Mr. Elliot was led to the study of binocular vision in consequence
of having written an Essay, so early as 1823, for the Class of Logic
in the University of Edinburgh, “On the means by which we obtain
our knowledge of distances by the Eye.” Ever since that date he was
familiar with the idea, that the relief of solid bodies seen by the
eye was produced by the union of the dissimilar pictures of them in
each eye, but he never imagined that this idea was his own, believing
that it was known to every student of vision. Previous to or during the
year 1834, he had resolved to construct an instrument for uniting two
dissimilar pictures, or of constructing a stereoscope; but he delayed
doing this till the year 1839, when he was requested to prepare an
original communication for the Polytechnic Society, which had been
recently established in Liverpool. He was thus induced to construct
the instrument which he had projected, and he exhibited it to his
friends, Mr. Richard Adie, optician, and Mr. George Hamilton, lecturer
on chemistry in Liverpool, who bear testimony to its existence at that
date. This simple stereoscope, without lenses or mirrors, consisted of
a wooden box 18 inches long, 7 broad, and 4½ deep, and at the bottom
of it, or rather its farther end, was placed a slide containing two
dissimilar pictures of a landscape as seen by each eye. Photography did
not then exist, to enable Mr. Elliot to procure two views of the same
scene, as seen by each eye, but he drew the transparency of a landscape
with three distances. The _first_ and most remote was the moon and
the sky, and a stream of water from which the moon was reflected, the
two moons being placed nearly at the distance of the two eyes, or 2½
inches, and the two reflected moons at the same distance. The _second_
distance was marked by an old cross about a hundred feet off; and the
_third_ distance by the withered branch of a tree, thirty feet from the
observer. In the right-hand picture, one arm of the cross just touched
the disc of the moon, while, in the left-hand one, it projected over
one-third of the disc. The branch of the tree touched the outline of a
distant hill in the one picture, but was “a full moon’s-breadth” from
it on the other. When these dissimilar pictures were united by the
eyes, a landscape, certainly a very imperfect one, was seen in relief,
composed of three distances.

Owing, no doubt, to the difficulty of procuring good binocular
pictures, Mr. Elliot did not see that his contrivance would be very
popular, and therefore carried it no farther. He had never heard of Mr.
Wheatstone’s stereoscope till he saw his paper on Vision reprinted in
the _Philosophical Magazine_ for March 1852, and having perused it, he
was convinced not only that Mr. Wheatstone’s theory of the instrument
was incorrect, but that his claim to the discovery of the dissimilarity
of the images in each eye had no foundation. He was, therefore, led
to communicate to the same journal the fact of his having himself,
thirteen years before, constructed and used a stereoscope, which was
still in his possession. In making this claim, Mr. Elliot had no
intention of depriving Mr. Wheatstone of the credit which was justly
due to him; and as the claim has been publicly made, we have described
the nature of it as a part of scientific history.

In Mr. Wheatstone’s ingenious paper of 1838, the subject of binocular
vision is treated at considerable length. He gives an account of
the opinions of previous writers, referring repeatedly to the works
of Aguilonius, Gassendi, and Baptista Porta, in the last of which
the views of Galen are given and explained. In citing the passage
which we have already quoted from Leonardo da Vinci, and inserting
the figure which illustrates it, he maintains that Leonardo da Vinci
was not aware “that the object (C in Fig. 2) presented a different
appearance to each eye.” “_He failed_,” he adds, “_to observe this,
and no subsequent writer, to my knowledge, has supplied the omission.
The projection of two obviously dissimilar pictures on the two retinæ,
when a single object is viewed, while the optic axes converge, must
therefore be regarded as a new fact in the theory of vision._” Now,
although Leonardo da Vinci does not state in so many words that he was
aware of the dissimilarity of the two pictures, the fact is obvious in
his own figure, and he was not led by his subject to state the fact
at all. But even if the fact had not stared him in the face he must
have known it from the Optics of Euclid and the writings of Galen,
with which he could not fail to have been well acquainted. That the
dissimilarity of the two pictures is _not a new fact_ we have already
placed beyond a doubt. The fact is expressed in words, and delineated
in drawings, by Aguilonius and Baptista Porta. It was obviously known
to Dr. Smith, Mr. Harris, Dr. Porterfield, and Mr. Elliot, before it
was known to Mr. Wheatstone, and we cannot understand how he failed
to observe it in works which he has so often quoted, and in which he
professes to have searched for it.

This remarkable property of binocular vision being thus clearly
established by preceding writers, and admitted by himself, as the cause
of the vision of solidity or distance, Mr. Wheatstone, as Mr. Elliot
had done before him, thought of an instrument for uniting the two
dissimilar pictures optically, so as to produce the same result that is
obtained by the convergence of the optical axes. Mr. Elliot thought of
doing this by the eyes alone; but Mr. Wheatstone adopted a much better
method of doing it by reflexion. He was thus led to construct an
apparatus, to be afterwards described, consisting of two plane mirrors,
placed at an angle of 90°, to which he gave the name of _stereoscope_,
anticipating Mr. Elliot both in the construction and publication of his
invention, but not in the general conception of a stereoscope.

After describing his apparatus, Mr. Wheatstone proceeds to consider
(in a section entitled, “Binocular vision of objects of different
magnitudes”) “what effects will result from presenting similar images,
differing only in magnitude, to analogous parts of the retina.” “For
this purpose,” he says, “two squares or circles, _differing obviously_
but not extravagantly in size, may be drawn on two separate pieces of
paper, and placed in the stereoscope, so that the reflected image of
each shall be equally distant from the eye by which it is regarded. _It
will then be seen that notwithstanding this difference they coalesce
and occasion a single resultant perception._” The fact of coalescence
being supposed to be perfect, the author next seeks to determine the
difference between the length of two lines which the eye can force
into coalescence, or “the limits within which the single appearance
subsists.” He, therefore, unites two images of equal magnitude, by
making one of them visually less from distance, and he states that,
“by this experiment, _the single appearance of two images of different
size is demonstrated_.” Not satisfied with these erroneous assertions,
he proceeds to give a sort of rule or law for ascertaining the
relative size of the two unequal pictures which the eyes can force
into coincidence. The inequality, he concludes, must not exceed the
difference “between the projections of the same object when seen in the
most oblique position of the eyes (_i.e._, both turned to the extreme
right or the extreme left) ordinarily employed.” Now, this rule, taken
in the sense in which it is meant, is simply _a truism_. It merely
states that the difference of the pictures which the eyes _can_ make to
coalesce is equal to the difference of the pictures which the eyes do
make to coalesce in their most oblique position; but though _a truism_
it is not _a truth_, first, because no real coincidence ever can take
place, and, secondly, because no apparent coincidence is effected when
the difference of the picture is greater than what is above stated.

From these principles, which will afterwards be shewn to be erroneous,
Mr. Wheatstone proceeds “to examine _why_ two dissimilar pictures
projected on the two retinæ _give_ rise to the perception _of an object
in relief_.” “I will not attempt,” he says, “at present to give the
complete solution of this question, which is far from being so easy
as at first glance it may appear to be, and is, indeed, _one of great
complexity_. I shall, in this case, merely consider the most obvious
explanations which might be offered, and shew their insufficiency to
explain the whole of the phenomena.

“_It may be supposed_ that we see only one point of a field of view
distinctly at the same instant, the one, namely, to which the optic
axes are directed, while all other points are seen so indistinctly that
the mind does not recognise them to be either single or double, and
that the figure is appreciated by successively directing the point of
convergence of the optic axes successively to a sufficient number of
its points to enable us to judge accurately of its form.

“That there is _a degree of indistinctness_ in those parts of the field
of view to which the eyes are not immediately directed, and which
increases with the distance from that point, cannot be doubted; and
it is also true that the objects there obscurely seen are _frequently
doubled_. In _ordinary_ vision, it may be said, this indistinctness and
duplicity are not attended to, because the eyes shifting continually
from point to point, every part of the object is successively rendered
distinct, and the perception of the object is not the consequence
of a single glance, during which _a small part of it only is seen
distinctly_, but is formed from a comparison of all the pictures
successively seen, while the eyes were changing from one point of an
object to another.

“_All this is_ IN SOME DEGREE _true, but were it entirely so_ no
appearance of relief should present itself when the eyes remain
intently fixed on one point of a binocular image in the stereoscope.
But in performing the experiment carefully, it will be found, provided
the picture do not extend far beyond the centres of distinct vision,
that the image is still seen single, and in relief, when in this
condition.”[22]

[22] _Phil. Trans._, 1838, pp. 391, 392.

In this passage the author makes a distinction between _ordinary
binocular vision_, and binocular vision through the stereoscope,
whereas in reality there is none. The theory of both is exactly the
same. The muscles of the two eyes unite the two dissimilar pictures,
and exhibit the solid, in ordinary vision; whereas in stereoscopic
vision the images are united by reflexion or refraction, the eyes in
both cases obtaining the vision of different distances by rapid and
successive convergences of the optical axes. Mr. Wheatstone notices
_the degree of indistinctness_ in the parts of the picture to which
the eyes are not immediately directed; but he does not notice the
“_confusion and incongruity_” which Aguilonius says ought to exist,
in consequence of some parts of the resulting relievo being seen of
one size by the left eye alone,—other parts of a different size by the
right eye alone, and other parts by both eyes. This confusion, however,
Aguilonius, as we have seen, found not to exist, and he ascribes it to
the influence of a _common sense_ overruling the operation of physical
laws. Erroneous as this explanation is, it is still better than that of
Mr. Wheatstone, which we shall now proceed to explain.

In order to disprove the theory referred to in the preceding extract,
Mr. Wheatstone describes two experiments, which he says _are equally
decisive against it_, the first of them only being subject to rigorous
examination. With this view he draws “two lines about two inches long,
and inclined towards each other, on a sheet of paper, and having
caused them to coincide by converging the optic axes to a point nearer
than the paper, he looks intently on the upper end of the resultant
line without allowing the eyes to wander from it for a moment. The
_entire line will appear single_, and in its proper relief, &c....
The eyes,” he continues, “sometimes become fatigued, which causes the
line to become double at those parts to which the optic axes are not
fixed, _but in such case all appearance of relief vanishes_. The same
experiment may be tried with small complex figures, but the pictures
should not extend too far beyond the centre of the retinæ.”

Now these experiments, if rightly made and interpreted, are not
_decisive against_ the theory. It is not true that the entire line
appears single when the axes are converged upon the upper end of the
resultant line, and it is not true that the disappearance of the
relief when it does disappear arises from the eye being fatigued.
In the combination of more complex figures, such as two similar
rectilineal figures contained by lines of unequal length, neither the
inequalities nor the entire figure will appear single when the axes are
converged upon any one point of it.

In the different passages which we have quoted from Mr. Wheatstone’s
paper, and in the other parts of it which relate to binocular vision,
he is obviously halting between truth and error, between theories
which he partly believes, and ill-observed facts which he cannot
reconcile with them. According to him, certain truths “may be supposed”
to be true, and other truths may be “in some degree true,” but “not
entirely so;” and thus, as he confesses, the problem of binocular and
stereoscopic vision “is indeed one of great complexity,” of which “he
will not attempt at present to give the complete solution.” If he had
placed a proper reliance on the law of visible direction which he
acknowledges I have established, and “with which,” he says, “the laws
of visible direction for binocular vision ought to contain nothing
inconsistent,” he would have seen the impossibility of the two eyes
uniting two lines of inequal length; and had he believed in the law of
distinct vision he would have seen the impossibility of the two eyes
obtaining single vision of any more than one point of an object at a
time. These laws of vision are as rigorously true as any other physical
laws,—as completely demonstrated as the law of gravity in Astronomy,
or the law of the Sines in Optics; and the moment we allow them to be
tampered with to obtain an explanation of physical puzzles, we convert
science into legerdemain, and philosophers into conjurors.

Such was the state of our stereoscopic knowledge in 1838, after the
publication of Mr. Wheatstone’s interesting and important paper.
Previous to this I communicated to the British Association at
Newcastle, in August 1838, a paper, in which I established the law
of visible direction already mentioned, which, though it had been
maintained by preceding writers, had been proved by the illustrious
D’Alembert to be incompatible with observation, and the admitted
anatomy of the human eye. At the same meeting Mr. Wheatstone exhibited
his stereoscopic apparatus, which gave rise to an animated discussion
on the theory of the instrument. Dr. Whewell maintained that the
retina, in uniting, or causing to coalesce into a single resultant
impression two lines of different lengths, had the power either of
contracting the longest, or lengthening the shortest, or what might
have been suggested in order to give the retina only half the trouble,
that it contracted the long line as much as it expanded the short one,
and thus caused them to combine with a less exertion of muscular power!
In opposition to these views, I maintained that the retina, a soft
pulpy membrane which the smallest force tears in pieces, had no such
power,—that a hypothesis so gratuitous was not required, and that the
law of visible direction afforded the most perfect explanation of all
the stereoscopic phenomena.

In consequence of this discussion, I was led to repeat my experiments,
and to inquire whether or not the eyes in stereoscopic vision _did
actually_ unite the two lines of different lengths, or of different
apparent magnitudes. I found that they did not, and that no such union
was required to convert by the stereoscope two plane pictures into
the apparent whole from which they were taken as seen by each eye.
These views were made public in the lectures on the _Philosophy of the
Senses_, which I occasionally delivered in the College of St. Salvator
and St. Leonard, St. Andrews, and the different stereoscopes which I
had invented were also exhibited and explained.

In examining Dr. Berkeley’s celebrated Theory of Vision, I saw the vast
importance of establishing the law of visible direction, and of proving
by the aid of binocular phenomena, and in opposition to the opinion of
the most distinguished metaphysicians, that we actually see a third
dimension in space, I therefore submitted to the Royal Society of
Edinburgh, in January 1843, a paper _On the law of visible position in
single and binocular vision, and on the representation of solid figures
by the union of dissimilar plane pictures on the retina_. More than
twelve years have now elapsed since this paper was read, and neither
Mr. Wheatstone nor Dr. Whewell have made any attempt to defend the
views which it refutes.

In continuing my researches, I communicated to the Royal Society of
Edinburgh, in April 1844, a paper _On the knowledge of distance as
given by binocular vision_, in which I described several interesting
phenomena produced by the union of _similar_ pictures, such as those
which form the patterns of carpets and paper-hangings. In carrying on
these inquiries I found the reflecting stereoscope of little service,
and ill fitted, not only for popular use, but for the application
of the instrument to various useful purposes. I was thus led to the
construction of several new stereoscopes, but particularly to the
_Lenticular Stereoscope_, now in universal use. They were constructed
in St. Andrews and Dundee, of various materials, such as wood,
tin-plate, brass, and of all sizes, from that now generally adopted,
to a microscopic variety which could be carried in the pocket. New
geometrical drawings were executed for them, and binocular pictures
taken by the sun were lithographed by Mr. Schenck of Edinburgh.
Stereoscopes of the lenticular form were made by Mr. Loudon, optician,
in Dundee, and sent to several of the nobility in London, and in other
places, and an account of these stereoscopes, and of a binocular camera
for taking portraits, and copying statues, was communicated to the
Royal Scottish Society of Arts, and published in their Transactions.

It had never been proposed to apply the reflecting stereoscope to
portraiture or sculpture, or, indeed, to any useful purpose; but it was
very obvious, after the discovery of the Daguerreotype and Talbotype,
that binocular drawings could be taken with such accuracy as to
exhibit in the stereoscope excellent representations in relief, both
of living persons, buildings, landscape scenery, and every variety of
sculpture. In order to shew its application to the most interesting of
these purposes, Dr. Adamson of St. Andrews, at my request, executed
two binocular portraits of himself, which were generally circulated
and greatly admired. This successful application of the principle to
portraiture was communicated to the public, and recommended as an art
of great domestic interest.

After endeavouring in vain to induce opticians, both in London and
Birmingham, (where the instrument was exhibited in 1849 to the
British Association,) to construct the lenticular stereoscope, and
photographers to execute binocular pictures for it, I took with me
to Paris, in 1850, a very fine instrument, made by Mr. Loudon in
Dundee, with the binocular drawings and portraits already mentioned.
I shewed the instrument to the Abbé Moigno, the distinguished author
of _L’Optique Moderne_, to M. Soleil and his son-in-law, M. Duboscq,
the eminent Parisian opticians, and to some members of the Institute
of France. These gentlemen saw at once the value of the instrument,
not merely as one of amusement, but as an important auxiliary in the
arts of portraiture and sculpture. M. Duboscq immediately began to make
the lenticular stereoscope for sale, and executed a series of the most
beautiful binocular Daguerreotypes of living individuals, statues,
bouquets of flowers, and objects of natural history, which thousands of
individuals flocked to examine and admire. In an interesting article
in _La Presse_,[23] the Abbé Moigno gave the following account of the
introduction of the instrument into Paris:—

[23] December 28, 1550.

“In his last visit to Paris, Sir David Brewster intrusted the models
of his stereoscope to M. Jules Duboscq, son-in-law and successor of M.
Soleil, and whose intelligence, activity, and affability will extend
the reputation of the distinguished artists of the Rue de l’Odeon, 35.
M. Jules Duboscq has set himself to work with indefatigable ardour.
Without requiring to have recourse to the binocular camera, he has,
with the ordinary Daguerreotype apparatus, procured a great number
of dissimilar pictures of statues, bas-reliefs, and portraits of
celebrated individuals, &c. His stereoscopes are constructed with more
elegance, and even with more perfection, than the original English
(Scotch) instruments, and while he is shewing their wonderful effects
to natural philosophers and amateurs who have flocked to him in crowds,
there is a spontaneous and unanimous cry of admiration.”

While the lenticular stereoscope was thus exciting much interest in
Paris, not a single instrument had been made in London, and it was not
till a year after its introduction into France that it was exhibited in
England. In the fine collection of philosophical instruments which M.
Duboscq contributed to the Great Exhibition of 1851, and for which he
was honoured with a Council medal, he placed a lenticular stereoscope,
with a beautiful set of binocular Daguerreotypes. This instrument
attracted the particular attention of the Queen, and before the closing
of the Crystal Palace, M. Duboscq executed a beautiful stereoscope,
which I presented to Her Majesty in his name. In consequence of this
public exhibition of the instrument, M. Duboscq received several orders
from England, and a large number of stereoscopes were thus introduced
into this country. The demand, however, became so great, that opticians
of all kinds devoted themselves to the manufacture of the instrument,
and photographers, both in Daguerreotype and Talbotype, found it a most
lucrative branch of their profession, to take binocular portraits of
views to be thrown into relief by the stereoscope. Its application to
sculpture, which I had pointed out, was first made in France, and an
artist in Paris actually copied a statue from the _relievo_ produced by
the stereoscope.

Three years after I had published a description of the lenticular
stereoscope, and after it had been in general use in France and
England, and the reflecting stereoscope forgotten,[24] Mr. Wheatstone
printed, in the _Philosophical Transactions_ for 1852, a paper on
Vision, in which he says that he had previously used “an apparatus in
which prisms were employed to deflect the rays of light proceeding from
the pictures, so as to make them appear to occupy the same place;” and
he adds, “I have called it the _refracting_ stereoscope.”[25] Now,
whatever Mr. Wheatstone may have done with prisms, and at whatever time
he may have done it, I was the first person who published a description
of stereoscopes both with _refracting_ and reflecting prisms; and
during the three years that elapsed after he had read my paper, he made
no claim to the suggestion of prisms till after the great success of
the lenticular stereoscope. The reason why he then made the claim, and
the only reason why we do not make him a present of the suggestion,
will appear from the following history:—

[24] “Le fait est,” says the Abbé Moigno, “_que le stéréoscope par
réflexion était presque complètement oublié_, lorsque Sir David
Brewster construisit son stéréoscope par refraction que nous allons
décrire.”—_Cosmos_, vol. i. p. 4, 1852.

[25] _Phil. Trans._, 1852, p. 6.

In the paper above referred to, Mr. Wheatstone says,—“I recommend, as
a convenient arrangement of the _refracting_ stereoscope for viewing
Daguerreotypes of small dimensions, the instrument represented, (Fig.
4,) shortened in its length from 8 inches to 5, and lenses 5 inches
focal distance, placed before and close to the prisms.”[26] Although
this refracting apparatus, which is simply a _deterioration_ of the
lenticular stereoscope, is recommended by Mr. Wheatstone, nobody
either makes it or uses it. The semi-lenses or quarter-lenses of the
lenticular stereoscope _include a virtual and absolutely perfect
prism_, and, what is of far more consequence, each lens is a variable
lenticular prism, so that, when the eye-tubes are placed at different
distances, the lenses have different powers of displacing the pictures.
They can thus unite pictures placed at different distances, which
cannot be done by any combination of whole lenses and prisms.

[26] _Ibid._, pp. 9, 10.

In the autumn of 1854, after all the facts about the stereoscope
were before the public, and Mr. Wheatstone in full possession of all
the merit of having anticipated Mr. Elliot in the publication of
his stereoscopic apparatus, and of his explanation of the theory of
stereoscopic relief, such as it was, he thought it proper to revive
the controversy by transmitting to the Abbé Moigno, for publication in
Cosmos, an extract of a letter of mine dated 27th September 1838. This
extract was published in the _Cosmos_ of the 15th August 1854,[27] with
the following illogical commentary by the editor.

    “Nous avons eu tort mille fois d’accorder à notre
    illustre ami, Sir David Brewster, l’invention du
    stéréoscope par réfraction. M. Wheatstone, en effet,
    a mis entre nos mains une lettre datée, le croirait
    on, du 27 Septembre 1838, dans lequel nous avons
    lû ces mots écrits par l’illustre savant Ecossais:
    ‘I have also stated that you promised to order
    for me your stereoscope, both with reflectors and
    PRISMS. J’ai aussi dit (à Lord Rosse[28])
    que vous aviez promis de commander pour moi votre
    stéréoscope, celui avec réflecteurs et celui avec
    prismes.’ Le stéréoscope par réfraction est donc,
    aussi bien que le stéréoscope par réflexion, le
    stéréoscope de M. Wheatstone, qui l’avait inventé
    en 1838, et le faisait construire à cette époque
    pour Sir David Brewster lui-même. Ce que Sir
    David Brewster a imaginée, et c’est une idée très
    ingénieuse, dont M. Wheatstone ne lui disputât
    jamais la gloire, c’est de former les deux prismes
    du stéréoscope par réfraction avec les deux moitiés
    d’une même lentille.”

[27] Vol. v. livre viii. p. 241.

[28] Mr. Andrew Ross, the celebrated optician!

That the reader may form a correct idea of the conduct of Mr.
Wheatstone in making this claim indirectly, and in a foreign journal,
whose editor he has willingly misled, I must remind him that I
first saw the reflecting stereoscope at the meeting of the British
Association at Newcastle, in the middle of _August 1838_. It is proved
by my letter that he and I then conversed on the subject of _prisms_,
which at that time he had never thought of. I suggested prisms for
displacing the pictures, and Mr. Wheatstone’s natural reply was, that
they must be _achromatic prisms_. This fact, if denied, may be proved
by various circumstances. His paper of 1838 contains no reference to
prisms. If he had suggested the use of prisms in August 1838, he would
have inserted his suggestion in that paper, which was then unpublished;
and if he had _only once_ tried a prism stereoscope, he never would
have used another. On my return to Scotland, I ordered from Mr. Andrew
Ross one of the reflecting stereoscopes, and one made with achromatic
prisms; but my words do not imply that Mr. Wheatstone was the first
person who suggested prisms, and still less that he ever made or used
a stereoscope with prisms. But however this may be, it is a most
extraordinary statement, which he allows the Abbé Moigno to make, and
which, though made a year and a half ago, he has not enabled the Abbé
to correct, _that a stereoscope with prisms was made for me_ (or for
any other person) _by Mr. Ross_. I never saw such an instrument, or
heard of its being constructed: I supposed that after our conversation
Mr. Wheatstone might have tried achromatic prisms, and in 1848, when I
described my single prism stereoscope, I stated what I now find is not
correct, that _I believed_ Mr. Wheatstone had used _two_ achromatic
prisms. The following letter from Mr. Andrew Ross will prove the main
fact that he never constructed for me, or for Mr. Wheatstone, any
refracting stereoscope:—

                    ”2, FEATHERSTONE BUILDINGS,
                             _28th September 1854_.

    “DEAR SIR,—In reply to yours of the 11th
    instant, I beg to state that I never supplied you
    with a stereoscope in which prisms were employed in
    place of plane mirrors. I have a perfect recollection
    of being called upon either by yourself or Professor
    Wheatstone, some fourteen years since, to make
    achromatized prisms for the above instrument. I also
    recollect that I did not proceed to manufacture them
    in consequence of the great bulk of an achromatized
    prism, with reference to their power of deviating a
    ray of light, and at that period glass sufficiently
    free from striæ could not readily be obtained, and
    was consequently very high-priced.—I remain, &c. &c.

                                  “ANDREW ROSS.
    “To Sir David Brewster.”

Upon the receipt of this letter I transmitted a copy of it to the Abbé
Moigno, to shew him how he had been misled into the statement, “that
Mr. Wheatstone had caused a stereoscope with prisms to be constructed
for me;” but neither he nor Mr. Wheatstone have felt it their duty to
withdraw that erroneous statement.

In reference to the comments of the Abbé Moigno, it is necessary to
state, that when he wrote them he had in his possession my printed
description of the single-prism, and other stereoscopes,[29] in which
I mention my belief, now proved to be erroneous, that Mr. Wheatstone
had used achromatic prisms, so that he had, on my express authority,
the information which surprised him in my letter. The Abbé also must
bear the responsibility of a glaring misinterpretation of my letter
of 1838. In that letter I say that Mr. Wheatstone promised _to order
certain things from Mr. Ross_, and the Abbé declares, contrary to the
express terms of the letter, as well as to fact, _that these things
were actually constructed for me_. The letter, on the contrary, does
not even state that Mr. Wheatstone complied with my request, and it
does not even appear from it that the reflecting stereoscope was made
for me by Mr. Ross.

[29] The Abbé gave an abstract of this paper in the French journal _La
Presse_, December 28, 1850.

Such is a brief history of the lenticular stereoscope, of its
introduction into Paris and London, and of its application to
portraiture and sculpture. It is now in general use over the whole
world, and it has been estimated that upwards of half a million
of these instruments have been sold. A Stereoscope Company has
been established in London[30] for the manufacture and sale of the
lenticular stereoscope, and for the production of binocular pictures
for educational and other purposes. Photographers are now employed
in every part of the globe in taking binocular pictures for the
instrument,—among the ruins of Pompeii and Herculaneum—on the glaciers
and in the valleys of Switzerland—among the public monuments in the
Old and the New World—amid the shipping of our commercial harbours—in
the museums of ancient and modern life—in the sacred precincts of
the domestic circle—and among those scenes of the picturesque and the
sublime which are so affectionately associated with the recollection of
our early days, and amid which, even at the close of life, we renew,
with loftier sentiments and nobler aspirations, the youth of our being,
which, in the worlds of the future, is to be the commencement of a
longer and a happier existence.

[30] No. 54, Cheapside, and 313, Oxford Street. The prize of twenty
guineas which they offered for the best short popular treatise on the
Stereoscope, has been adjudged to Mr. Lonie, Teacher of Mathematics in
the Madras Institution, St. Andrews. The second prize was given to the
Rev. R. Graham, Abernyte, Perthshire.




CHAPTER II.

ON MONOCULAR VISION, OR VISION WITH ONE EYE.


In order to understand the theory and construction of the stereoscope
we must be acquainted with the general structure of the eye, with the
mode in which the images of visible objects are formed within it, and
with the laws of vision by means of which we see those objects in
the position which they occupy, that is, in the direction and at the
distance at which they exist.

Every visible object radiates, or throws out in all directions,
particles or rays of light, by means of which we see them either
directly by the images formed in the eye, or indirectly by looking at
images of them formed by their passing through a small hole, or through
a lens placed in a dark room or _camera_, at the end of which is a
piece of paper or ground-glass to receive the image.

In order to understand this let H be a very small pin-hole in a shutter
or camera, MN, and let RYB be any object of different colours, the
upper part, R, being _red_, the middle, Y, _yellow_, and the lower
part, B, _blue_. If a sheet of white paper, _br_, is placed behind
the hole H, at the same distance as the object RB is before it, an
image, _br_, will be formed of the same ray and the same colours as the
object RB. As the particles or rays of light move in straight lines,
a _red_ ray from the middle part of R will pass through the hole H and
illuminate the point _r_ with _red_ light. In like manner, rays from
the middle points of Y and B will pass through H and illuminate with
_yellow_ and _blue_ light the points _y_ and _b_. Every other point
of the coloured spaces, R, Y, and B, will, in the same manner, paint
itself, as it were, on the paper, and produce a coloured image, _byr_,
exactly the same in form and colour as the object RYB. If the hole H
is sufficiently small no ray from any one point of the object will
interfere with or mix with any other ray that falls upon the paper.
If the paper is held at _half_ the distance, at _b′y′_ for example, a
coloured image, _b′y′r′_, of half the size, will be formed, and if we
hold it at twice the distance, at _b″r″_ for example, a coloured image,
_b″y″r″_, of _twice_ the size, will be painted on the paper.

[Illustration: FIG. 4.]

As the hole H is supposed to be so small as to receive only one ray
from every point of the object, the images of the object, viz., _br_,
_b′r′_, _b″r″_, will be very faint. By widening the hole H, so as
to admit more rays from each luminous point of RB, the images would
become brighter, but they would become at the same time indistinct,
as the rays from one point of the object would mix with those from
adjacent points, and at the boundaries of the colours R, Y, and B, the
one colour would obliterate the other. In order, therefore, to obtain
sufficiently bright images of visible objects we must use _lenses_,
which have the property of forming distinct images behind them, at a
point called their focus. If we widen the hole H, and place in it a
lens whose focus is at _y_, for an object at the same distance, HY, it
will form a bright and distinct image, _br_, of the same size as the
object RB. If we remove the lens, and place another in H, whose focus
is at _y′_, for a distance HY, an image, _b′r′_, half of the size of
RB, will be formed at that point; and if we substitute for this lens
another, whose focus is at _y″_, a distinct image, _b″r″_, _twice_ the
size of the object, will be formed, the size of the image being always
to that of the object as their respective distances from the hole or
lens at H.

With the aid of these results, which any person may confirm by making
the experiments, we shall easily understand how we see external objects
by means of the images formed in the eye. The human eye, a section
and a front view of which is shewn in Fig. 5, A, is almost a sphere.
Its outer membrane, ABCDE, or MNO, Fig. 5, B, consists of a tough
substance, and is called the _sclerotic_ coat, which forms the _white
of the eye_, A, seen in the front view. The front part of the eyeball,
C_x_D, which resembles a small watch-glass, is perfectly transparent,
and is called the _cornea_. Behind it is the _iris_, _cabe_, or C in
the front view, which is a circular disc, with a hole, _ab_, in its
centre, called the _pupil_, or _black of the eye_. It is, as it were,
the _window_ of the eye, through which all the light from visible
objects must pass. The _iris_ has different colours in different
persons, _black_, _blue_, or _grey_; and the pupil, _ab_, or H, has
the power of contracting or enlarging its size according as the light
which enters it is more or less bright. In sunlight it is very small,
and in twilight its size is considerable. Behind the iris, and close
to it, is a doubly convex lens, _df_, or LL in Fig. 5, B, called the
_crystalline lens_. It is more convex or round on the inner side, and
it is suspended by the _ciliary_ processes at LC, LC′, by which it
is supposed to be moved towards and from H, in order to accommodate
the eye to different distances, or obtain distinct vision at these
distances. At the back of the eye is a thin pulpy transparent membrane,
_rr_ O _rr_, or _vvv_, called the _retina_, which, like the ground
glass of a camera obscura, receives the images of visible objects.
This membrane is an expansion of the optic nerve O, or A in Fig. 5, A,
which passes to the brain, and, by a process of which we are ignorant,
gives us vision of the objects whose images are formed on its expanded
surface. The globular form of the eye is maintained by two fluids which
fill it,—the _aqueous humour_, which lies between the crystalline lens
and the cornea, and the _vitreous humour_, ZZ, which fills the back of
the eye.

[Illustration: FIG. 5, A.]

[Illustration: FIG. 5, B.]

But though we are ignorant of the manner in which the mind takes
cognizance through the brain of the images on the retina, and may
probably never know it, we can determine experimentally the laws by
which we obtain, through their images on the retina, a knowledge of the
direction, the position, and the form of external objects.

If the eye MN consisted only of a hollow ball with a small aperture H,
an inverted image, _ab_, of any external object AB would be formed on
the retina _r_O_r_, exactly as in Fig. 4. A ray of light from A passing
through H would strike the retina at _a_, and one from B would strike
the retina at _b_. If the hole H is very small the inverted image
_ab_ would be very distinct, but very obscure. If the hole were the
size of the pupil the image would be sufficiently luminous, but very
indistinct. To remedy this the crystalline lens is placed behind the
pupil, and gives distinctness to the image _ab_ formed in its focus.
The image, however, still remains inverted, a ray from the _upper_ part
A of the object necessarily falling on the _lower_ part _a_ of the
retina, and a ray from the _lower_ part B of the object upon the upper
part _b_ of the retina. Now, it has been proved by accurate experiments
that in whatever direction a ray AH_a_ falls upon the retina, it gives
us the vision of the point A from which it proceeds, or causes us to
see that point, in a direction perpendicular to the retina at _a_, the
point on which it falls. It has also been proved that the human eye is
nearly spherical, and that a line drawn perpendicular to the retina
from any point _a_ of the image _ab_ will very nearly pass through the
corresponding point A of the object AB,[31] so that the point A is, in
virtue of this law, which is called the _Law of visible direction_,
seen in nearly its true direction.

[31] _Edinburgh Transactions_, vol. xv. p. 349, 1843; or _Philosophical
Magazine_, vol. xxv. pp. 356, 439, May and June 1844.

When we look at any object, AB, for example, we see only one point
of it distinctly. In Fig. 5 the point D only is seen distinctly, and
every point from D to A, and from D to B, less distinctly. The point of
distinct vision on the retina is at _d_, corresponding with the point D
of the object which is seen distinctly. This point _d_ is the centre of
the retina at the extremity of the line AH_a_, called the optical axis
of the eye, passing through the centre of the lens L_h_, and the centre
of the pupil. The point of distinct vision _d_ corresponds with a small
hole in the retina called the _Foramen centrale_, or _central hole_,
from its being in the centre of the membrane. When we wish to see the
points A and B, or any other point of the object, we turn the eye upon
them, so that their image may fall upon the central point _d_. This
is done so easily and quickly that every point of an object is seen
distinctly in an instant, and we obtain the most perfect knowledge
of its form, colour, and direction. The law of distinct vision may be
thus expressed. Vision is most distinct when it is performed by the
central point of the retina, and the distinctness decreases with the
distance from the central point. It is a curious fact, however, that
the most _distinct point d is the least sensitive to light_, and that
the sensitiveness increases with the distance from that point. This is
proved by the remarkable fact, that when an astronomer cannot see a
very minute star by looking at it directly along the optical axis _d_D,
he can see it _by looking away from it_, and bringing its image upon a
more sensitive part of the retina.

But though we see with one eye the direction in which any object or
point of an object is situated, we do not see its position, or the
distance from the eye at which it is placed. If a small luminous point
or flame is put into a dark room by another person, we cannot with one
eye form anything like a correct estimate of its distance. Even in good
light we cannot with one eye snuff a candle, or pour wine into a small
glass at arm’s length. In monocular vision, we learn from experience to
estimate all distances, but particularly great ones, by various means,
which are called the _criteria of distance_; but it is only with both
eyes that we can estimate with anything like accuracy the distance of
objects not far from us.

The _criteria of distance_, by which we are enabled with one eye to
form an approximate estimate of the distance of objects are five in
number.

1. The interposition of numerous objects between the eye and the object
whose distance we are appreciating. A distance at sea appears much
shorter than the same distance on land, marked with houses, trees, and
other objects; and for the same reason, the sun and moon appear more
distant when rising or setting on the horizon of a flat country, than
when in the zenith, or at great altitudes.

2. The variation in the apparent magnitude of known objects, such as
man, animals, trees, doors and windows of houses. If one of two men,
placed at different distances from us, appears only half the size of
the other, we cannot be far wrong in believing that the smallest in
appearance is at twice the distance of the other. It is possible that
the one may be a dwarf, and the other of gigantic stature, in which
case our judgment would be erroneous, but even in this case other
criteria might enable us to correct it.

3. The degree of vivacity in the colours and tints of objects.

4. The degree of distinctness in the outline and minute parts of
objects.

5. To these criteria we may add the sensation of muscular action, or
rather effort, by which we close the pupil in accommodating the eye to
near distances, and produce the accommodation.

With all these means of estimating distances, it is only by binocular
vision, in which we converge the optical axes upon the object, that we
have the power of _seeing distance_ within a limited range.

But this is the only point in which Monocular is _inferior_ to
Binocular vision. In the following respects it is _superior_ to it.

1. When we look at oil paintings, the varnish on their surface reflects
to each eye the light which falls upon it from certain parts of the
room. By closing one eye we shut out the quantity of reflected light
which enters it. Pictures should always be viewed by the eye farthest
from windows or lights in the apartment, as light diminishes the
sensibility of the eye to the red rays.

2. When we view a picture with both eyes, we discover, from the
convergency of the optic axes, that the picture is on a plane surface,
every part of which is nearly equidistant from us. But when we shut one
eye, we do not make this discovery; and therefore the effect with which
the artist gives relief to the painting exercises its whole effect in
deceiving us, and hence, in monocular vision, the _relievo_ of the
painting is much more complete.

This influence over our judgment is beautifully shewn in viewing,
with one eye, photographs either of persons, or landscapes, or solid
objects. After a little practice, the illusion is very perfect, and
is aided by the correct geometrical perspective and _chiaroscuro_ of
the Daguerreotype or Talbotype. To this effect we may give the name of
_Monocular Relief_, which, as we shall see, is necessarily inferior to
_Binocular Relief_, when produced by the stereoscope.

3. As it very frequently happens that one eye has not exactly the same
focal length as the other, and that, when it has, the vision by one eye
is less perfect than that by the other, the picture formed by uniting a
perfect with a less perfect picture, or with one of a different size,
must be more imperfect than the single picture formed by one eye.




CHAPTER III.

ON BINOCULAR VISION, OR VISION WITH TWO EYES.


We have already seen, in the history of the stereoscope, that in
the binocular vision of objects, each eye sees a different picture
of the same object. In order to prove this, we require only to look
attentively at our own hand held up before us, and observe how some
parts of it disappear upon closing each eye. This experiment proves, at
the same time, in opposition to the opinion of Baptista Porta, Tacquet,
and others, that we always see two pictures of the same object combined
in one. In confirmation of this fact, we have only to push aside one
eye, and observe the image which belongs to it separate from the other,
and again unite with it when the pressure is removed.

It might have been supposed that an object seen by both eyes would be
seen twice as brightly as with one, on the same principle as the light
of two candles combined is twice as bright as the light of one. That
this is not the case has been long known, and Dr. Jurin has proved
by experiments, which we have carefully repeated and found correct,
that the brightness of objects seen with two eyes is only ¹/₁₃th part
greater than when they are seen with one eye.[32] The cause of this
is well known. When both eyes are used, the pupils of each contract
so as to admit the proper quantity of light; but the moment we shut
the right eye, the pupil of the left dilates to nearly twice its size,
to compensate for the loss of light arising from the shutting of the
other.[33]

[32] Smith’s _Opticks_, vol. ii., Remarks, p. 107. Harris makes the
difference ¹/₁₀th or ¹/₁₁th; _Optics_, p. 117.

[33] This variation of the pupil is mentioned by Bacon.

[Illustration: FIG. 6.]

This beautiful provision to supply the proper quantity of light when
we can use only one eye, answers a still more important purpose, which
has escaped the notice of optical writers. In binocular vision, as we
have just seen, certain parts of objects are seen with both eyes, and
certain parts only with one; so that, if the parts seen with both eyes
were twice as bright, or even much brighter than the parts seen with
one, the object would appear spotted, from the different brightness of
its parts. In Fig. 6, for example, (see p. 14,) the areas BFI and CGI,
the former of which is seen only by the left eye, D, and the latter
only by the right eye, E, and the corresponding areas on the other side
of the sphere, would be only half as bright as the portion FIGH, seen
with both eyes, and the sphere would have a singular appearance.

It has long been, and still is, a vexed question among philosophers,
how we see objects single with two eyes. Baptista Porta, Tacquet, and
others, got over the difficulty by denying the fact, and maintaining
that we use only one eye, while other philosophers of distinguished
eminence have adopted explanations still more groundless. The law of
visible direction supplies us with the true explanation.

[Illustration: FIG. 7.]

Let us first suppose that we look with both eyes, R and L, Fig. 7, upon
a luminous point, D, which we see single, though there is a picture
of it on the retina of each eye. In looking at the point D we turn or
converge the optical axes _d_HD, _d′_H′ D, of each eye to the point D,
an image of which is formed at _d_ in the right eye R, and at _d′_ in
the left eye L. In virtue of the law of visible direction the point
D is seen in the direction _d_D with the eye R, and in the direction
_d′_D with the eye L, these lines being perpendicular to the retina
at the points _d_, _d′_. The one image of the point D is therefore
seen lying upon the other, and consequently seen single. Considering
D, then, as a single point of a visible object AB, the two eyes will
see the points A and B single by the same process of turning or
converging upon them their optical axes, and so quickly does the point
of convergence pass backward and forward over the whole object, that
it appears single, though in reality only one point of it can be seen
single at the same instant. The whole picture of the line AB, as seen
with one eye, _seems_ to coincide with the whole picture of it as seen
with the _other_, and to appear single. The same is true of a surface
or area, and also of a solid body or a landscape. Only one point of
each is seen single; but we do not observe that other points are
double or indistinct, because the images of them are upon parts of the
retina which do not give distinct vision, owing to their distance from
the _foramen_ or point which gives distinct vision. Hence we see the
reason why distinct vision is obtained only on one point of the retina.
Were it otherwise we should see every other point double when we look
fixedly upon one part of an object. If in place of _two_ eyes we had
a _hundred_, capable of converging their optical axes to one point,
we should, in virtue of the law of visible direction, see only _one_
object.

The most important advantage which we derive from the use of two
eyes is to enable us to _see distance_, or a third dimension in
space. That we have this power has been denied by Dr. Berkeley, and
many distinguished philosophers, who maintain that our perception of
distance is acquired by experience, by means of the criteria already
mentioned. This is undoubtedly true for great distances, but we
shall presently see, from the effects of the stereoscope, that the
successive convergency of the optic axes upon two points of an object
at different distances, exhibits to us the difference of distance when
we have no other possible means of perceiving it. If, for example, we
suppose G, D, Fig. 7, to be separate points, or parts of an object,
whose distances are GO, DO, then if we converge the optical axes HG,
H′ G upon G, and next turn them upon D, the points will appear to be
situated at G and D at the distance GD from each other, and at the
distances OG, OD from the observer, although there is nothing whatever
in the appearance of the points, or in the lights and shades of the
object, to indicate distance. That this vision of distance is not
the result of experience is obvious from the fact that distance is
seen as perfectly by children as by adults; and it has been proved
by naturalists that animals newly born appreciate distances with the
greatest correctness. We shall afterwards see that so infallible is
our vision of near distances, that a body whose real distance we can
ascertain by placing both our hands upon it, will appear at the greater
or less distance at which it is placed by the convergency of the
optical axes.

We are now prepared to understand generally, how, in binocular vision,
we see the difference between a picture and a statue, and between a
real landscape and its representation. When we look at a picture of
which every part is nearly at the same distance from the eyes, the
point of convergence of the optical axes is nearly at the same distance
from the eyes; but when we look at its original, whether it be a
living man, a statue, or a landscape, the optical axes are converged
in rapid succession upon the nose, the eyes, and the ears, or upon
objects in the foreground, the middle and the remote distances in the
landscape, and the relative distances of all these points from the eye
are instantly perceived. The _binocular relief_ thus seen is greatly
superior to the _monocular relief_ already described.

Since objects are seen in relief by the apparent union of two
dissimilar plane pictures of them formed in each eye, it was a
supposition hardly to be overlooked, that if we could delineate two
plane pictures of a solid object, as seen dissimilarly with each
eye, and unite their images by the convergency of the optical axes,
we should see the solid of which they were the representation. The
experiment was accordingly made by more than one person, and was found
to succeed; but as few have the power, or rather the art, of thus
converging their optical axes, it became necessary to contrive an
instrument for doing this.

The first contrivances for this purpose were, as we have already
stated, made by Mr. Elliot and Mr. Wheatstone. A description of these,
and of others better fitted for the purpose, will be found in the
following chapter.




CHAPTER IV.

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.




CHAPTER V.

ON THE THEORY OF STEREOSCOPIC VISION.


Having, in the preceding chapter, described the ocular, the reflecting,
and the lenticular stereoscopes, and explained the manner in which the
two binocular pictures are combined or laid upon one another in the
last of these instruments, we shall now proceed to consider the theory
of stereoscopic vision.

[Illustration: FIG. 19.]

In order to understand how the two pictures, when placed the one above
the other, rise into relief, we must first explain the manner in which
a solid object itself is, in ordinary vision, seen in relief, and
we shall then shew how this process takes place in the two forms of
the ocular stereoscope, and in the lenticular stereoscope. For this
purpose, let ABCD, Fig. 19, be a section of the frustum of a cone, that
is, a cone with its top cut off by a plane C_e_D_g_, and having AEBG
for its base. In order that the figure may not be complicated, it will
be sufficient to consider how we see, with two eyes, L and R, the cone
as projected upon a plane passing through its summit C_e_D_g_. The
points L, R being the points of sight, draw the lines RA, RB, which
will cut the plane on which the projection is to be made in the points
_a_, _b_, so that _ab_ will represent the line AB, and a circle, whose
diameter is _ab_, will represent the base of the cone, as seen by the
right eye R. In like manner, by drawing LA, LB, we shall find that
A′B′ will represent the line AB, and a circle, whose diameter is A′B′,
the base AEBG, as seen by the left eye. The summit, C_e_D_g_, of the
frustum being in the plane of projection, will be represented by the
circle C_e_D_g_. The representation of the frustum ABCD, therefore,
upon a plane surface, as seen by the left eye L, consists of two
circles, whose diameters are AB, CD; and, as seen by the right eye, of
other two circles, whose diameters are _ab_, CD, which, in Fig. 20,
are represented by AB, CD, and _ab_, _cd_. These plane figures being
also the representation of the solid on the retina of the two eyes,
how comes it that we see the solid and not the plane pictures? When
we look at the point B, Fig. 19, with both eyes, we converge upon it
the optic axes LB, RB, and we therefore see the point single, and at
the distances LB, RB from each eye. When we look at the point D, we
withdraw the optic axes from B, and converge them upon D. We therefore
see the point D single, and at the distances LD, RD from each eye;
and in like manner the eyes run over the whole solid, seeing every
point single and distinct upon which they converge their axes, and at
the distance of the point of convergence from the observer. During
this rapid survey of the object, the whole of it is seen distinctly
as a solid, although every point of it is seen double and indistinct,
excepting the point upon which the axes are for the instant converged.

[Illustration: FIG. 20.]

From these observations it is obvious, that when we look with both eyes
at any solid or body in relief, _we see more of the right side of it
by the right eye, and more of the left side of it by the left eye_. The
right side of the frustum ABCD, Fig. 19, is represented by the line
D_b_, as seen by the right eye, and by the shorter line DB′, as seen by
the left eye. In like manner, the left side AC is represented by CA′,
as seen by the left eye, and by the shorter line C_a′_, as seen by the
right eye.

When the body is hollow, like a wine glass, _we see more of the right
side with the left eye, and more of the left side with the right eye_.

If we now separate, as in Fig. 20, the two projections shewn together
on Fig. 19, we shall see that the two summits, CD, _cd_, of the frustum
are farther from one another than the more distant bases, AB, _ab_, and
it is true generally that _in the two pictures of any solid in relief,
the similar parts that are near the observer are more distant in the
two pictures than the remoter parts, when the plane of perspective is
beyond the object_. In the binocular picture of the human face the
distance between the two noses is greater than the distance between the
two right or left eyes, and the distance between the two right or left
eyes greater than the distance between the two remoter ears.

We are now in a condition to explain the process by which, with the
eyes alone, we can see a solid in relief by uniting the right and left
eye pictures of it,—or the theory ocular stereoscope. In order to
obtain the proper relief we must place the right eye picture on the
left side, and the left eye picture on the right side, as shewn in Fig.
21, by the pictures ABCD, _abcd_, of the frustum of a cone, as obtained
from Fig. 19.

[Illustration: FIG. 21.]

In order to unite these two dissimilar projections, we must converge
the optical axes to a point nearer the observer, or look at some point
about M. Both pictures will immediately be doubled. An image of the
figure _ab_ will advance towards P, and an image of AB will likewise
advance towards P; and the instant these images are united, the frustum
of a cone, which they represent, will appear in relief at MN, the
place where the optic axes meet or cross each other. At first the
solid figure will appear in the middle, between the two pictures from
which it is formed and of the same size, but after some practice it
will appear smaller and nearer the eye. Its smallness is an optical
illusion, as it has the same angle of apparent magnitude as the plane
figures, namely, _mn_L = ABL; but its position at MN is a reality, for
if we look at the point of our finger held beyond M the solid figure
will be seen nearer the eye. The difficulty which we experience in
seeing it of the size and in the position shewn in Fig. 21, arises from
its being seen along with its two plane representations, as we shall
prove experimentally when we treat in a future chapter of the union of
similar figures by the eye.

The two images being thus superimposed, or united, we shall now see
that the combined images are seen in relief in the very same way that
in ordinary vision we saw the real solid, ABCD, Fig. 19, in relief, by
the union of the two pictures of it on the retina. From the points A,
B, C, D, _a, b, c, d_, draw lines to L and R, the centres of visible
direction of each eye, and it will be seen that the circles AB, _ab_,
representing the base of the cone, can be united by converging the
optical axes to points in the line _mn_, and that the circles CD, _cd_,
which are more distant, can be united only by converging the optic axes
to points in the line _op_. The points A, _a_, for example, united by
converging the axes to _m_, are seen at that point single; the points
B, _b_ at _n_ single, the points C, _c_ at _o_ single, the points D,
_d_ at _p_ single, the centres S, _s_ of the base at M single, and the
centres S′, _s′_ of the summit plane at N single. Hence the eyes L and
R see the combined pictures at MN in relief, exactly in the same manner
as they saw in relief the original solid MN in Fig. 19.

In order to find the height MN of the conical frustum thus seen, let D
= distance OP; _d_ = S_s_, the distance of the two points united at M;
_d′_ = S′_s′_, the distance of the two points united at N; and C = LR =
2½ inches, the distance of the eyes. Then we have—

                       D_d_
                 MP = ———————
                      C + _d_

                       D_d′_
                 NP = ——————— , and
                      C + _d′_

                       D_d_       D_d′_
                 MN = ——————  -  ———————
                      C + _d_    C + _d′_

        If   D = 9·24 inches,
             C = 2·50, then
           _d_ = 2·14,
          _d′_ = 2·42, and
            MN = 0·283, the height of the cone.

                            DC
        When C = _d_, MP = ————
                            2C.

As the summit plane _op_ rises above the base _mn_ by the successive
convergency of the optic axes to different points in the line _o_N_p_,
it may be asked how it happens that the conical frustum still appears
a solid, and the plane _op_ where it is, when the optic axes are
converged to points in the line _m_M_n_, so as to see the base
distinctly? The reason of this is that the rays emanate from _op_
exactly in the same manner, and form exactly the same image of it,
on the two retinas as if it were the summit CD, Fig. 19, of the real
solid when seen with both eyes. The only effect of the advance of the
point of convergence from N to M is to throw the image of N a little
to the _right_ side of the optic axis of the left eye, and a little to
the _left_ of the optic axis of the right eye. The summit plane _op_
will therefore retain its place, and will be seen slightly doubled and
indistinct till the point of convergence again returns to it.

It has been already stated that the two dissimilar pictures may be
united by converging the optical axes to a point beyond them. In order
to do this, the distance SS′ of the pictures, Fig. 21, must be greatly
less than the distance of the eyes L, R, in order that the optic axes,
in passing through similar points of the two plane pictures, may meet
at a moderate distance beyond them. In order to explain how the relief
is produced in this case, let AB, CD, _ab_, _cd_, Fig. 22, be the
dissimilar pictures of the frustum of a cone whose summit is CD, as
seen by the right eye, and _cd_ as seen by the left eye. From L and R,
as before, draw lines through all the leading points of the pictures,
and we shall have the points A, _a_ united at _m_, the points B, _b_ at
_n_, the points C, _c_ at _o_, and the points D, _d_ at _p_, the points
S, _s_ at M, and the points S′, _s′_ at N, forming the cone _mnop_,
with its base _mn_ towards the observer, and its summit _op_ more
remote. If the cone had been formed of lines drawn from the outline of
the summit to the outline of the base, it would now appear _hollow_,
the inside of it being seen in place of the outside as before. If the
pictures AB, _ab_ are made to change places the combined picture would
be in relief, while in the case shewn in Fig. 21 it would have been
hollow. Hence the _right_-eye view of any solid must be placed on the
_left_ hand, and the _left_-eye view of it on the _right_ hand, when
we wish to obtain it in relief by converging the optic axes to a point
between the pictures and the eye, and _vice versa_ when we wish to
obtain it in relief by converging the optic axes to a point beyond the
pictures. In every case when we wish the combined pictures to represent
a _hollow_, or the converse of relief, their places must be exchanged.

[Illustration: FIG. 22.]

In order to find the height MN, or rather the depth of the cone in Fig.
22, let D, _d_, C, _c_, represent the same quantities as before, and we
shall have

          D_d_
    MP = ———————
         C - _d_

          D_d′_
    NP = ——————— , and
         C - _d′_

          D_d′_       D_d_
    OP = ———————  -  ——————
         C - _d′_    C - _d_

When D, C, _d_, _d′_ have the same values as before, we shall have MN =
18·7 feet!

When C = _d_, MP will be infinite.

We have already explained how the two binocular pictures are combined
or laid upon one another in the lenticular stereoscope. Let us now see
how the relief is obtained. The two plane pictures _abcd_, ABCD, in
Fig. 18, are, as we have already explained, combined or simply laid
upon one another by the lenses LL, L′L′, and in this state are shewn by
the middle circles at A_a_B_b_, C_c_D_d_. The images of the bases AB,
_ab_ of the cone are accurately united in the double base AB, _ab_, but
the summits of the conical frustum remain separate, as seen at C′D′,
_c′d′_. It is now the business of the eyes to unite these, or rather to
make them appear as united. We have already seen how they are brought
into relief when the summits are refracted so as to pass one another,
as in Fig. 18. Let us therefore take the case shewn in Fig. 20, where
the summits CD, _cd_ are more distant than the bases AB, _ab_. The
union of these figures is instantly effected, as shewn in Fig. 23, by
converging the optic axes to points _m_ and _n_ successively, and thus
uniting C and _c_ and D and _d_, and making these points of the summit
plane appear at _m_ and _n_, the points of convergence of the axes
L_m_, R_m_, and L_n_, R_n_. In like manner, every pair of points in the
summit plane, and in the sides A_m_, B_n_ of the frustum, are converged
to points corresponding to their distance from the base AB of the
original solid frustum, from which the plane pictures ABCD, _abcd_,
were taken. We shall, therefore, see in relief the frustum of a cone
whose section is A_mn_B.

[Illustration: FIG. 23.]

The theory of the stereoscope may be expressed and illustrated in the
following manner, without any reference to binocular vision:—

1. When a drawing of any object or series of objects is executed on a
plane surface from _one point of sight_, according to the principles
of geometrical perspective, every point of its surface that is visible
from the point of sight will be represented on the plane.

2. If another drawing of the same object or series of objects is
similarly executed on the same plane from _a second_ point of sight,
sufficiently distant from the first to make the two drawings separate
without overlapping, every point of its surface visible from this
second point of sight will also be represented on the plane, so that
we shall have two different drawings of the object placed, at a short
distance from each other, on the same plane.

[Illustration: FIG. 24.]

3. Calling these different points of the object 1, 2, 3, 4, &c., it
will be seen from Fig. 24, in which L, R are the two points of sight,
that the distances 1, 1, on the plane MN, of any pair of points in
the two pictures representing the point 1 of the object, will be to
the distance of any other pair 2, 2, representing the point 2, as the
distances 1′P, 2′P of the points of the object from the plane MN,
multiplied inversely by the distances of these points from the points
of sight L, R, or the middle point O between them.

4. If the sculptor, therefore, or the architect, or the mechanist, or
the surveyor, possesses two such pictures, either as drawn by a skilful
artist or taken photographically, he can, by measuring the distances of
every pair of points, obtain the relief or prominence of the original
point, or its distance from the plane MN or AB; and without the use
of the stereoscope, the sculptor may model the object from its plane
picture, and the distances of every point from a given plane. In like
manner, the other artists may determine distances in buildings, in
machinery, and in the field.

5. If the distance of the points of sight is equal to the distance of
the eyes L, R, the two plane pictures may be united and raised into
relief by the stereoscope, and thus give the sculptor and other artists
an accurate model, from which they will derive additional aid in the
execution of their work.

6. In stereoscopic vision, therefore, when we join the points 1, 1 by
converging the optic axes to 1′ in the line PQ, and the points 2, 2 by
converging them to 2′ in the same line, we place these points at the
distances O1, OO2, and _see the relief_, or the various differences of
distance which the sculptor and others obtained by the method which we
have described.

7. Hence we infer, that if the stereoscopic vision of relief had never
been thought of, the principles of the instrument are involved in the
geometrical relief which is embodied in the two pictures of an object
taken from two points of sight, and in the prominence of every part of
it obtained geometrically.




CHAPTER VI.

ON THE UNION OF SIMILAR PICTURES IN BINOCULAR VISION.


In uniting by the convergency of the optic axes two dissimilar
pictures, as shewn in Fig. 18, the solid cone MN ought to appear at MN
much nearer the observer than the pictures which compose it. I found,
however, that it never took its right position in absolute space,
the base MN of the solid seeming to rest on the same plane with its
constituent pictures AB, _ab_, whether it was seen by converging the
axes as in Fig. 18 or in Fig. 22. Upon inquiring into the reason of
this I found that the disturbing cause was simply the simultaneous
perception of other objects in the same field of view whose distance
was known to the observer.

In order to avoid all such influences I made experiments on large
surfaces covered with similar plane figures, such as flowers or
geometrical patterns upon paper-hangings and carpets. These figures
being always at equal distances from each other, and almost perfectly
equal and similar, the coalescence of any pair of them, effected by
directing the optic axes to a point between the paper-hanging and the
eye, is accompanied by the instantaneous coalescence of them all. If
we, therefore, look at a papered wall without pictures, or doors, or
windows, or even at a considerable portion of a wall, at the distance
of three feet, and unite two of the figures,—two flowers, for example,
at the distance of twelve inches from each other horizontally, the
whole wall or visible portion of it will appear covered with flowers as
before, but as each flower is now composed of two flowers united at the
point of convergence of the optic axes, _the whole papered wall with
all its flowers will be seen suspended in the air at the distance of
six inches from the observer_! At first the observer does not decide
upon the distance of the suspended wall from himself. It generally
advances slowly to its new position, and when it has taken its place it
has a very singular character. The surface of it seems slightly curved.
It has a silvery transparent aspect. It is more beautiful than the real
paper, which is no longer seen, and it moves with the slightest motion
of the head. If the observer, who is now three feet from the wall,
retires from it, the suspended wall of flowers will follow him, moving
farther and farther from the real wall, and also, but very slightly,
farther and farther from the observer. When he stands still, he may
stretch out his hand and place it on the other side of the suspended
wall, and even hold a candle on the other side of it to satisfy himself
that the ghost of the wall stands between the candle and himself.

In looking attentively at this strange picture some of the flowers have
the aspect of real flowers. In some the stalk retires from the plane of
the picture. In others it rises from it. One leaf will come farther out
than another. One coloured portion, _red_, for example, will be more
prominent than the _blue_, and the flower will thus appear thicker and
more solid, like a real flower compressed, and deviating considerably
from the plane representation of it as seen by one eye. All this
arises from slight and accidental differences of distance in similar
or corresponding parts of the united figures. If the distance, for
example, between two corresponding leaves is greater than the distance
between other two corresponding leaves, then the two first when united
will appear nearer the eye than the other two, and hence the appearance
of a flower in low relief, is given to the combination.

In continuing our survey of the suspended image another curious
phenomenon often presents itself. A part of one, or even two pieces
of paper, and generally the whole length of them from the roof to
the floor, will retire behind the general plane of the image, as if
there were a recess in the wall, or rise above it as if there were a
projection, thus displaying on a large scale the imperfection in the
workmanship which otherwise it would have been difficult to discover.
This phenomenon, or defect in the work, arises from the paper-hanger
having cut off too much of the margin of one or more of the adjacent
stripes or pieces, or leaving too much of it, so that, in the first
case, when the two halves of a flower are joined together, part of
the middle of the flower is left out, and hence, when this defective
flower is united binocularly with the one on the right hand of it,
and the one on the left hand united with the defective one, the
united or corresponding portion being at a less distance, will appear
farther from the eye than those parts of the suspended image which are
composed of complete flowers. The opposite effect will be produced
when the two portions of the flowers are not brought together, but
separated by a small space. All these phenomena may be seen, though
not so conveniently, with a carpet from which the furniture has been
removed. We have, therefore, an accurate method of discovering defects
in the workmanship of paper-hangers, carpet-makers, painters, and all
artists whose profession it is to combine a series of similar patterns
or figures to form an uniformly ornamented surface. The smallest defect
in the similarity or equality of the figures or lines which compose
a pattern, and any difference in the distance of single figures is
instantly detected, and what is very remarkable a small inequality
of distance in a line perpendicular to the axis of vision, or in one
dimension of space, is exhibited in a magnified form at a distance
coincident with the axis of vision, and in an opposite dimension of
space.

A little practice will enable the observer to realize and to maintain
the singular binocular vision which replaces the real picture.[35] The
occasional retention of the picture after one eye is closed, and even
after both have been closed and quickly reopened, shews the influence
of time over the evanescence as well as over the creation of this class
of phenomena. On some occasions, a singular effect is produced. When
the flowers or figures on the paper are distant _six_ inches, we may
either unite two six inches distant, or _two_ twelve inches distant,
and so on. In the latter case, when the eyes have been accustomed to
survey the suspended picture, I have found that, after shutting or
opening them, I neither saw the picture formed by the two flowers
_twelve_ inches distant, nor the papered wall itself, but a picture
formed by uniting all the flowers _six_ inches distant! The binocular
centre (the point to which the optic axes converged, and consequently
the locality of the picture) had shifted its place, and instead of
advancing to the real wall and seeing it, it advanced exactly as much
as to unite the nearest flowers, just as in a ratchet wheel, when the
detent stops one tooth at a time; or, to speak more correctly, the
binocular centre advanced in order to relieve the eyes from their
strain, and when the eyes were opened, it had just reached that point
which corresponded with the union of the flowers _six_ inches distant.

[35] A sheet of Queen’s heads may be advantageously used to accustom
the eyes to the union of similar figures.

[Illustration: FIG. 25.]

We have already seen, as shewn in Fig. 22, that when we fix the
binocular centre, that is, converge the optic axes on a point beyond
the dissimilar pictures, so as to unite them, they rise into relief
as perfectly as when the binocular centre, as shewn in Fig. 18, is
fixed between the pictures used and the eye. In like manner we may
unite similar pictures, but, owing to the opacity of the wall and the
floor, we cannot accomplish this with paper-hangings and carpets.
The experiment, however, may be made with great effect by looking
through transparent patterns cut out of paper or metal, such as those
in zinc which are used for larders and other purposes. Particular
kinds of trellis-work, and windows with small squares or rhombs of
glass, may also be used, and, what is still better, a screen might be
prepared, by cutting out the small figures from one or more pieces of
paper-hangings. The readiest means, however, of making the experiment,
is to use the cane bottom of a chair, which often exhibits a succession
of octagons with small luminous spaces between them. To do this, place
the back of the chair upon a table, the height of the eye either when
sitting or standing, so that the cane bottom with its luminous pattern
may have a vertical position, as shewn in Fig. 25, where MN is the
real bottom of the chair with its openings, which generally vary from
half an inch to three-fourths. Supposing the distance to be half an
inch, and the eyes, L, R, of the observer 12 inches distant from MN,
let L_ad_, L_be_ be lines drawn through the centres of two of the open
spaces _a_, _b_, and R_bd_, R_ce_ lines drawn through the centres of
_b_ and _c_, and meeting L_ad_, L_be_ at _d_ and _e, d_ being the
binocular centre to which the optic axes converge when we look at it
through _a_ and _b_, and _c_ the binocular centre when we look at it
through _b_ and _c_. Now, the right eye, R, sees the opening _b_ at
_d_, and the left eye sees the opening _a_ at _d_, so that the image
at _d_ of the opening consists of the similar images of _a_ and _b_
united, and so on with all the rest; so that the observer at L, R no
longer sees the real pattern MN, but an image of it suspended at _mn_,
three inches behind MN. If the observer now approaches MN, the image
_mn_ will approach to him, and if he recedes, _mn_ will recede also,
being 1½ inches behind MN when the observer is _six_ inches before it,
and _twelve_ inches behind MN when the observer is _forty-eight_ inches
before it, the image _mn_ moving from _mn_ with a velocity one-fourth
of that with which the observer recedes.

The observer resuming the position in the figure where his eyes, L,
R, are _twelve_ inches distant from MN, let us consider the important
results of this experiment. If he now grasps the cane bottom at MN,
his thumbs pressing upon MN, and his fingers trying to grasp _mn_,
he will then _feel what he does not see_, and _see what he does not
feel_! The real pattern is absolutely invisible at MN, where he feels
it, and it stands fixed at _mn_. The fingers may be passed through and
through between the real and the false image, and beyond it,—now seen
on this side of it, now in the middle of it, and now on the other side
of it. If we next place the palms of each hand upon MN, the real bottom
of the chair, feeling it all over, the result will be the same. No
knowledge derived from touch—no measurement of real distance—no actual
demonstration from previous or subsequent vision, that there is a real
solid body at MN, and nothing at all at _mn_, will remove or shake the
infallible conviction of the sense of sight that the cane bottom is at
_mn_, and that _d_L or _d_R is its real distance from the observer. If
the binocular centre be now drawn back to MN, the image _seen_ at _mn_
will disappear, and the real object be _seen and felt at_ MN. If the
binocular centre be brought further back to _f_, that is, if the optic
axes are converged to a point nearer the observer than the object, as
illustrated by Fig. 18, the cane bottom MN will again disappear, and
will be seen at _uv_, as previously explained.

This method of uniting small similar figures is more easily attained
than that of doing it by converging the axes to a point between the
eye and the object. It puts a very little strain upon the eyes, as we
cannot thus unite figures the distance of whose centre is equal to or
exceeds 2½ inches, as appears from Fig. 22.

In making these experiments, the observer cannot fail to be struck with
the remarkable fact, that though the openings MN, _mn_, _uv_, have all
the same apparent or angular magnitude, that is, subtend the same angle
at the eye, viz., _d_L_c_, _d_R_e_, yet those at _mn_ appear larger,
and those at _uv_ smaller, than those at MN. If we cause the image
_mn_ to recede and approach to us, the figures in _mn_ will invariably
_increase as they recede_, and those in _uv_ diminish as they approach
the eye, and their _visual magnitudes_, as we may call them, will
depend on the respective distances at which the observer, whether right
or wrong in his estimate, conceives them to be placed,—a result which
is finely illustrated by the different size of the moon when seen in
the horizon and in the meridian. The fact now stated is a general one,
which the preceding experiments demonstrate; and though our estimate of
magnitude thus formed is erroneous, yet it is one which neither reason
nor experience is able to correct.

It is a curious circumstance, that, previous to the publication of
these experiments, no examples have been recorded of false estimates
of the distance of near objects in consequence of the _accidental_
binocular union of similar images. In a room where the paper-hangings
have a small pattern, a short-sighted person might very readily turn
his eyes on the wall when their axes converged to some point between
him and the wall, which would unite one pair of the similar images,
and in this case he would see the wall nearer him than the real wall,
and moving with the motion of his head. In like manner a long-sighted
person, with his optical axes converged to a point beyond the wall,
might see an image of the wall more distant, and moving with the motion
of his head; or a person who has taken too much wine, which often fixes
the optical axes in opposition to the will, might, according to the
nature of his sight, witness either of the illusions above mentioned.

Illusions of both these kinds, however, have recently occurred. A
friend to whom I had occasion to shew the experiments, and who is
short-sighted, mentioned to me that he had on two occasions been
greatly perplexed by the vision of these suspended images. Having taken
too much wine, he saw the wall of a papered room suspended near him in
the air; and on another occasion, when kneeling, and resting his arms
on a cane-bottomed chair, he had fixed his eyes on the carpet, which
had accidentally united the two images of the open octagons, and thrown
the image of the chair bottom beyond the plane on which he rested his
arms.

After hearing my paper on this subject read at the Royal Society of
Edinburgh, Professor Christison communicated to me the following
interesting case, in which one of the phenomena above described was
seen by himself:—“Some years ago,” he observes, “when I resided in a
house where several rooms are papered with rather formally recurring
patterns, and one in particular with stars only, I used occasionally
to be much plagued with the wall suddenly standing out upon me,
and waving, as you describe, with the movements of the head. I was
sensible that the cause was an error as to the point of union of the
visual axes of the two eyes; but I remember it sometimes cost me a
considerable effort to rectify the error; and I found that the best
way was to increase still more the deviation in the first instance. As
this accident occurred most frequently while I was recovering from a
severe attack of fever, I thought my near-sighted eyes were threatened
with some new mischief; and this opinion was justified in finding that,
after removal to my present house, where, however, the papers have
no very formal pattern, no such occurrence has ever taken place. The
reason is now easily understood from your researches.”[36]

Other cases of an analogous kind have been communicated to me; and
very recently M. Soret of Geneva, in looking through a trellis-work in
metal stretched upon a frame, saw the phenomenon represented in Fig.
25, and has given the same explanation of it which I had published long
before.[37]

[36] See _Edin. Transactions_, 1846, vol. xv. p. 663, and _Phil. Mag._,
May 1847, vol. xxx. p. 305.

[37] _Bibl. Universelle_, October 1855, p. 136.

Before quitting the subject of the binocular union of _similar_
pictures, I must give some account of a series of curious phenomena
which I observed by uniting the images of lines meeting at an angular
point when the eye is placed at different heights above the plane of
the paper, and at different distances from the angular point.

[Illustration: FIG. 26.]

Let AC, BC, Fig. 26, be two lines meeting at C, the plane passing
through them being the plane of the paper, and let them be viewed by
the eyes successively placed at E‴, E″, E′, and E, at different heights
in a plane, GMN, perpendicular to the plane of the paper. Let R be the
right eye, and L the left eye, and when at E‴, let them be strained
so as to unite the points A, B. The united image of these points will
be seen at the binocular centre D‴, and the united lines AC, BC, will
have the position D‴C. In like manner, when the eye descends to E″, E′,
E, the united image D‴C will rise and diminish, taking the positions
D″C, D′C, DC, till it disappears on the line CM, when the eyes reach
M. If the eye deviates from the vertical plane GMN, the united image
will also deviate from it, and is always in a plane passing through the
common axis of the two eyes and the line GM.

If at any altitude EM, the eye advances towards ACB in the line EG, the
binocular centre D will also advance towards ACB in the line EG, and
the image DC will rise, and become shorter as its extremity D moves
along DG, and, after passing the perpendicular to GE, it will increase
in length. If the eye, on the other hand, recedes from ACB in the line
GE, the binocular centre D will also recede, and the image DC will
descend to the plane CM, and increase in length.

[Illustration: FIG. 27.]

The preceding diagram is, for the purpose of illustration, drawn in a
sort of perspective, and therefore does not give the true positions and
lengths of the united images. This defect, however, is remedied in Fig.
27, where E, E′, E″, E‴ is the middle point between the two eyes, the
plane GMN being, as before, perpendicular to the plane passing through
ACB. Now, as the distance of the eye from G is supposed to be the same,
and as AB is invariable as well as the distance between the eyes, the
distance of the binocular centres OO, D, D′, D″, D‴, P from G, will
also be invariable, and lie in a circle ODP, whose centre is G, and
whose radius is GO, the point O being determined by the formula

               GM × AB
    GO = GD = —————————
               AB + RL.

Hence, in order to find the binocular centres D, D′, D″, D‴, &c., at
any altitude, E, E′, &c., we have only to join EG, E′G, &c., and the
points of intersection D, D′, &c., will be the binocular centres,
and the lines DC, D′C, &c., drawn to C, will be the real lengths and
inclinations of the united images of the lines AC, BC.

When GO is greater than GC there is obviously some angle A, or E″GM, at
which D″C is perpendicular to GC.

This takes place when

              GC
    Cos. A = ————.
              GO

When O coincides with C, the images CD, CD′, &c., will have the same
positions and magnitudes as the chords of the altitudes A of the eyes
above the plane GC. In this case the raised or united images will just
reach the perpendicular when the eye is in the plane GCM, for since

    GC = GO, Cos. A = 1 and A = 0.

When the eye at any position, E″ for example, sees the points A and B
united at D″, it sees also the whole lines AC, BC forming the image
D″C. The binocular centre must, therefore, run rapidly along the line
D″C; that is, the inclination of the optic axes must gradually diminish
till the binocular centre reaches C, when all strain is removed. The
vision of the image D″C, however, is carried on so rapidly that the
binocular centre returns to D″ without the eye being sensible of the
removal and resumption of the strain which is required in maintaining
a view of the united image D″C. If we now suppose AB to diminish,
the binocular centre will advance towards G, and the length and
inclination of the united images DC, D′C, &c., will diminish also, and
_vice versa_. If the distance RL (Fig. 26) between the eyes diminishes,
the binocular centre will retire towards E, and the length and
inclination of the images will increase. Hence persons with eyes more
or less distant will see the united images in different places and of
different sizes, though the quantities A and AB be invariable.

While the eyes at E″ are running along the lines AC, BC, let us suppose
them to rest upon the points _ab_ equidistant from C. Join _ab_, and
from the point _g_, where _ab_ intersects GC, draw the line _g_E″, and
find the point _d″_ from the formula

            _g_E″ × _ab_
    _gd″_ = ———————————-.
             _ab_ + RL

Hence the two points _a_, _b_ will be united at _d″_, and when the
angle E″GC is such that the line joining D and C is perpendicular to
GC, the line joining _d″_C will also be perpendicular to GC, the loci
of the points D″_d″_, &c., will be in that perpendicular, and the image
DC, seen by successive movements of the binocular centre from D″ to C,
will be a straight line.

In the preceding observations we have supposed that the binocular
centre D″, &c., is between the eye and the lines AC, BC; but the points
A, C, and all the other points of these lines, may be united by fixing
the binocular centre beyond AB. Let the eyes, for example, be at E″;
then if we unite A, B when the eyes converge to a point, Δ″, (not seen
in the Figure) beyond G, we shall have

          GE × AB
    GΔ″ = ———————;
          RL - AB


and if we join the point Δ″ thus found and C, the line Δ′C will be
the united image of AC and BC, the binocular centre ranging from Δ″
to C, in order to see it as one line. In like manner, we may find the
position and length of the image Δ‴C, Δ′C, and ΔC, corresponding to
the position of the eyes at E‴E and E. Hence all the united images
of AC, BC, viz., CΔ‴, CΔ″, &c., will lie below the plane of ABC, and
extend beyond a vertical line NG continued; and they will grow larger
and larger, and approximate in direction to CG as the eyes descend from
E‴ to M. When the eyes are near to M, and a little above the plane of
ABC, the line, when not carefully observed, will have the appearance of
coinciding with CG, but stretching a great way beyond G. This extreme
case represents the celebrated experiment with the compasses, described
by Dr. Smith, and referred to by Professor Wheatstone. He took a pair
of compasses, which may be represented by ACB, AB being their points,
AC, BC their legs, and C their joint; and having placed his eyes about
E, above their plane, he made the following experiment:—“Having opened
the points of a pair of compasses somewhat wider than the interval
of your eyes, with your arm extended, hold the head or joint in the
ball of your hand, with the points outwards, and equidistant from your
eyes, and somewhat higher than the joint. Then _fixing your eyes upon
any remote object_ lying in the plane that bisects the interval of the
points, you will first perceive two pair of compasses, (each by being
doubled with their inner legs crossing each other, not unlike the old
shape of the letter W). But by compressing the legs with your hand the
two inner points will come nearer to each other; and when they unite
(having stopped the compression) the two inner legs will also entirely
coincide and bisect the angle under the outward ones, and will appear
more vivid, thicker, and larger, than they do, so as to reach from your
hand to the remotest object in view even in the horizon itself, if the
points be exactly coincident.”[38] Owing to his imperfect apprehension
of the nature of this phenomenon, Dr. Smith has omitted to notice that
the united legs of the compasses lie below the plane of ABC, and that
they never can extend further than the binocular centre at which their
points A and B are united.

There is another variation of these experiments which possesses some
interest, in consequence of its extreme case having been made the basis
of a new theory of visible direction, by the late Dr. Wells.[39] Let us
suppose the eyes of the observer to advance from E to N, and to descend
along the opposite quadrant on the left hand of NG, but not drawn in
Fig. 27, then the united image of AC, BC will gradually descend towards
CG, and become larger and larger. When the eyes are a very little
above the plane of ABC, and so far to the left hand of AB that CA
points nearly to the left eye and CB to the right eye, then we have the
circumstances under which Dr. Wells made the following experiment:—“If
we hold two thin rules in such a manner that their sharp edges (AC, BC
in Fig. 27) shall be in the optic axes, one in each, or rather a little
below them, _the two edges will be seen united in the common axis_, (GC
in Fig. 27;) and this apparent edge will seem of the same length with
that of either of the real edges, when seen alone by the eye in the
axis of which it is placed.” This experiment, it will be seen, is the
same with that of Dr. Smith, with this difference only, that the points
of the compasses are directed towards the eyes. Like Dr. Smith, Dr.
Wells has omitted to notice that the united image rises above GH, and
he commits the opposite error of Dr. Smith, in making the length of the
united image too short.

[38] Smith’s _Opticks_, vol. ii. p. 388, § 977.

[39] _Essay on Single Vision, &c._, p. 44.

If in this form of the experiment we fix the binocular centre beyond
C, then the united images of AC, and BC descend below GC, and vary in
their length, and in their inclination to GC, according to the height
of the eye above the plane of ABC, and its distance from AB.




CHAPTER VII.

DESCRIPTION OF DIFFERENT STEREOSCOPES.


Although the lenticular stereoscope has every advantage that such
an instrument can possess, whether it is wanted for experiments on
binocular vision—for assisting the artist by the reproduction of
objects in relief, or for the purposes of amusement and instruction,
yet there are other forms of it which have particular properties,
and which may be constructed without the aid of the optician, and of
materials within the reach of the humblest inquirers. The first of
these is—


1. _The Tubular Reflecting Stereoscope._

In this form of the instrument, shewn in Fig. 28, the pictures are seen
by reflexion from two specula or prisms placed at an angle of 90°, as
in Mr. Wheatstone’s instrument. In other respects the two instruments
are essentially different.

In Mr. Wheatstone’s stereoscope he employs two mirrors, each _four
inches_ square—that is, he employs _thirty-two_ square inches of
reflecting surface, and is therefore under the necessity of employing
glass mirrors, and making a clumsy, unmanageable, and unscientific
instrument, with all the imperfections which we have pointed out in a
preceding chapter. It is not easy to understand why mirrors of such a
size should have been adopted. The reason of their being made of common
looking-glass is, that metallic or prismatic reflectors of such a size
would have been extremely expensive.

[Illustration: FIG. 28.]

It is obvious, however, from the slightest consideration, that
reflectors of such a size are wholly unnecessary, and that _one
square_ inch of reflecting surface, in place of _thirty-two_, is quite
sufficient for uniting the binocular pictures. We can, therefore, at
a price as low as that of the 4-inch glass reflectors, use mirrors of
speculum metal, steel, or even silver, or rectangular glass prisms,
in which the images are obtained by total reflexion. In this way the
stereoscope becomes a real optical instrument, in which the reflexion
is made from surfaces single and perfectly flat, as in the second
reflexion of the Newtonian telescope and the microscope of Amici, in
which pieces of looking-glass were never used. By thus diminishing the
reflectors, we obtain a portable tubular instrument occupying nearly
as little room as the lenticular stereoscope, as will be seen from
Fig. 28, where ABCD is a tube whose diameter is equal to the largest
size of one of the binocular pictures which we propose to use, the
left-eye picture being placed at CD, and the right-eye one at AB. If
they are transparent, they will be illuminated through paper or ground
glass, and if opaque, through openings in the tube. The image of AB,
reflected to the left eye L from the small mirror _mn_, and that of
CD to the right eye R from the mirror _op_, will be united exactly
as in Mr. Wheatstone’s instrument already described. The distance of
the two ends, _n_, _p_, of the mirrors should be a little greater than
the smallest distance between the two eyes. If we wish to magnify the
picture, we may use two lenses, or substitute for the reflectors a
totally reflecting glass prism, in which one or two of its surfaces are
made convex.[40]

[40] We may use also the lens prism, which I proposed many years ago in
the _Edinburgh Philosophical Journal_.


2. _The Single Reflecting Stereoscope._

This very simple instrument, which, however, answers only for
symmetrical figures, such as those shewn at A and B, which must be
either two right-eye or two left-eye pictures, is shewn in Fig. 29.
A single reflector, MN, which may be either a piece of glass, or a
piece of mirror-glass, or a small metallic speculum, or a rectangular
prism, is placed at MN. If we look into it with the left eye L, we see,
by reflexion from its surface at C, a reverted image, or a right-eye
picture of the left-eye picture B, which, when seen in the direction
LCA, and combined with the figure A, seen directly with the right eye
R, produces a _raised_ cone; but if we turn the reflector L round, so
that the right eye may look into it, and combine a reverted image of
A, with the figure B seen directly with the left eye L, we shall see
a _hollow_ cone. As BC + CL is greater than RA, the reflected image
will be slightly less in size than the image seen directly, but the
difference is not such as to produce any perceptible effect upon the
appearance of the hollow or the raised cone. By bringing the picture
viewed by reflexion a little nearer the reflector MN, the two pictures
may be made to have the same apparent magnitude.

[Illustration: FIG. 29.]

If we substitute for the single reflector MN, two reflectors such as
are shewn at M, N, Fig. 30, or a prism P, which gives two internal
reflexions, we shall have a general stereoscope, which answers for
landscapes and portraits.

[Illustration: FIG. 30.]

The reflectors M, N or P may be fitted up in a conical tube, which has
an elliptical section to accommodate two figures at its farther end,
the major axis of the ellipse being parallel to the line joining the
two eyes.


3. _The Double Reflecting Stereoscope._

This instrument differs from the preceding in having a single
reflector, MN, M′N′, for each eye, as shewn in Fig. 31, and the effect
of this is to exhibit, _at the same time, the raised and the hollow
cone_. The image of B, seen by reflexion from MN at the point C, is
combined with the picture of A, seen directly by the _right_ eye R, and
forms a _hollow_ cone; while the image of A, seen by reflexion from
M′N′ at the point C′, is combined with the picture of B, seen directly
by the left eye L, and forms a _raised_ cone.

[Illustration: FIG. 31.]

[Illustration: FIG. 32.]

Another form of the double reflecting stereoscope is shewn in Fig. 32,
which differs from that shewn in Fig. 31 in the position of the two
reflectors and of the figures to be united. The reflecting faces of
the mirrors are turned outwards, their distance being less than the
distance between the eyes, and the effect of this is to exhibit at the
same time the _raised_ and the _hollow_ cone, the hollow cone being now
on the right-hand side.

If in place of two right or two left eye pictures, as shewn in Figs.
29, 31, and 32, we use one right eye and one left eye picture, and
combine the reflected image of the one with the reflected image of the
other, we shall have a _raised_ cone with the stereoscope, shewn in
Fig. 31, and a _hollow_ cone with the one in Fig. 32.

The double reflecting stereoscope, in both its forms, is a general
instrument for portraits and landscapes, and thus possesses properties
peculiar to itself.

The reflectors may be glass or metallic specula, or total reflexion
prisms.


4. _The Total Reflexion-Stereoscope._

This form of the stereoscope is a very interesting one, and possesses
valuable properties. It requires only a small prism and _one_ diagram,
or picture of the solid, as seen by one eye; the other diagram, or
picture which is to be combined with it, being created by total
reflexion from the base of the prism. This instrument is shewn in Fig.
33, where D is the picture of a cone as seen by the left eye L, and ABC
a prism, whose base BC is so large, that when the eye is placed close
to it, it may see, by reflexion, the whole of the diagram D. The angles
ABC, ACB must be equal, but may be of any magnitude. Great accuracy in
the equality of the angles is not necessary; and a prism constructed,
by a lapidary, out of a fragment of thick plate-glass, the face BC
being one of the surfaces of the plate, will answer the purpose. When
the prism is placed at _a_, Fig. 34, at one end of a conical tube LD,
and the diagram D at the other end, in a cap, which can be turned round
so as to have the line _mn_, Fig. 33, which passes through the centre
of the base and summit of the cone parallel to the line joining the two
eyes, the instrument is ready for use. The observer places his left
eye at L, and views with it the picture D, as seen by total reflexion
from the base BC of the prism, Figs. 33 and 35, while with his right
eye R, Fig. 33, he views the real picture directly. The first of these
pictures being the reverse of the second D, like all pictures formed
by one reflexion, we thus combine two dissimilar pictures into a
_raised_ cone, as in the figure, or into a _hollow_ one, if the picture
at D is turned round 180°. If we place the images of two diagrams,
one like one of those at A, Fig. 31, and the other like the one at B,
vertically above one another, we shall then see, at the same time,
the _raised_ and the _hollow_ cone, as produced in the lenticular
stereoscope by the three diagrams, two like those in Fig. 31, and a
third like the one at A. When the prism is good, the dissimilar image,
produced by the two refractions at B and C, and the one reflexion at
E, is, of course, more accurate than if it had been drawn by the most
skilful artist; and therefore this form of the stereoscope has in this
respect an advantage over every other in which two dissimilar figures,
executed by art, are necessary. In consequence of the length of the
reflected pencil DB + BE + EC + CL being a little greater than the
direct pencil of rays DR, the two images combined have not exactly the
same apparent magnitude; but the difference is not perceptible to the
eye, and a remedy could easily be provided were it required.

[Illustration: FIG. 33.]

[Illustration: FIG. 34.]

If the conical tube LD is held in the left hand, the left eye must be
used, and if in the right hand the right eye must be used, so that
the hand may not obstruct the direct vision of the drawing by the eye
which does not look through the prism. The cone LD must be turned round
slightly in the hand till the line _mn_ joining the centre and apex of
the figure is parallel to the line joining the two eyes. The same line
must be parallel to the plane of reflexion from the prism; but this
parallelism is secured by fixing the prism and the drawing.

It is scarcely necessary to state that this stereoscope is applicable
only to those diagrams and forms where the one image is the reflected
picture of the other.

[Illustration: FIG. 35.]

If we wish to make a microscopic stereoscope of this form, or to
magnify the drawings, we have only to cement plano-convex lenses,
of the requisite focal length, upon the faces AB, AC of the prism,
or, what is simpler still, to use a section of a deeply convex lens
ABC, Fig. 35, and apply the other half of the lens to the right eye,
the face BC having been previously ground flat and polished for the
prismatic lens. By using a lens of larger focus for the right eye, we
may correct, if required, the imperfection arising from the difference
of paths in the reflected and direct pencils. This difference, though
trivial, might be corrected, if thought necessary, by applying to the
right eye the central portion of the same lens whose margin is used for
the prism.

[Illustration: FIG. 36.]

If we take the drawing of a six-sided pyramid as seen by the right eye,
as shewn in Fig. 36, and place it in the total-reflexion stereoscope at
D, Fig. 33, so that the line MN coincides with _mn_, and is parallel to
the line joining the eyes of the observer, we shall perceive a perfect
raised pyramid of a given height, the reflected image of CD, Fig. 36,
being combined with AF, seen directly. If we now turn the figure round
30°, CD will come into the position AB, and unite with AB, and we shall
still perceive a raised pyramid, with less height and less symmetry. If
we turn it round 30° more, CD will be combined with BC, and we shall
still perceive a raised pyramid with still less height and still less
symmetry. When the figure is turned round other 30°, or 90° degrees
from its first position, CD will coincide with CD seen directly,
and the combined figures will be perfectly flat. If we continue the
rotation through other 30°, CD will coincide with DE, and a slightly
hollow, but not very symmetrical figure, will be seen. A rotation of
other 30° will bring CD into coalesence with EF, and we shall see a
still more hollow and more symmetrical pyramid. A further rotation of
other 30°, making 180° from the commencement, will bring CD into union
with AF; and we shall have a perfectly symmetrical hollow pyramid of
still greater depth, and the exact counterpart of the raised pyramid
which was seen before the rotation of the figure commenced. If the
pyramid had been square, the _raised_ would have passed into the
_hollow_ pyramid by rotations of 45° each. If it had been rectangular,
the change would have been effected by rotations of 90°. If the space
between the two circular sections of the cone in Fig. 31 had been
uniformly shaded, or if lines had been drawn from every degree of the
one circle to every corresponding degree in the other, in place of
from every 90th degree, as in the Figure, the raised cone would have
gradually diminished in height, by the rotation of the figure, till it
became flat, after a rotation of 90°; and by continuing the rotation it
would have become hollow, and gradually reached its maximum depth after
a revolution of 180°.


5. _The Single-Prism Stereoscope._

Although the idea of uniting the binocular pictures by a single
prism applied to one eye, and refracting one of the pictures so as
to place it upon the other seen directly by the other eye, or by a
prism applied to each eye, could hardly have escaped the notice of
any person studying the subject, yet the experiment was, so far as I
know, first made and published by myself. I found two prisms quite
unnecessary, and therefore abandoned the use of them, for reasons which
will be readily appreciated. This simple instrument is shewn in Fig.
37, where A, B are the dissimilar pictures, and P a prism with such
a refracting angle as is sufficient to lay the image of A upon B, as
seen by the right eye. If we place a _second_ prism before the eye
R, we require it only to have half the refracting angle of the prism
P, because each prism now refracts the picture opposite to it only
half way between A and B, where they are united. This, at first sight,
appears to be an advantage, for as there must always be a certain
degree of colour produced by a single prism, the use of two prisms,
with half the refracting angle, might be supposed to reduce the colour
one-half. But while the colour produced by each prism is thus reduced,
the colour over the whole picture is the same. Each luminous edge with
two prisms has both red and blue tints, whereas with one prism each
luminous edge has only one colour, either red or blue. If the picture
is very luminous these colours will be seen, but in many of the finest
opaque pictures it is hardly visible. In order, however, to diminish
it, the prism should be made of glass with the lowest dispersive power,
or with rock crystal. A single plane surface, ground and polished by
a lapidary, upon the edge of a piece of plate-glass, a little larger
than the pupil of the eye, will give a prism sufficient for every
ordinary purpose. Any person may make one in a few minutes for himself,
by placing a little bit of good window glass upon another piece
inclined to it at the proper angle, and inserting in the angle a drop
of fluid. Such a prism will scarcely produce any perceptible colour.

[Illustration: FIG. 37.]

If a single-prism reflector is to be made perfect, we have only to
make it achromatic, which could be done _extempore_, by correcting
the colour of the fluid prism by another fluid prism of different
refractive and dispersive power.

With a good achromatic prism the single-prism stereoscope is a very
fine instrument; and no advantage of any value could be gained by
using _two achromatic prisms_. In the article on New Stereoscopes,
published in the Transactions of the Royal Society of Arts for 1849,
and in the Philosophical Magazine for 1852, I have stated in a note
that _I believed_ that Mr. Wheatstone had used _two achromatic prisms_.
This, however, was a mistake, as already explained,[41] for such
an instrument was never made, and has never been named in any work
previous to 1849, when it was mentioned by myself in the note above
referred to.

[41] See Chap. i. pp. 33-36.

If we make a double prism, or join two, as shewn at P, P′ in Fig.
38, and apply it to two dissimilar figures A, B, one of which is the
reflected image of the other, so that with the left eye L and the prism
P we place the refracted image of A upon B, as seen by the right eye
R, we shall see a _raised_ cone, and if with the prism P′ we place
the image of B upon A we shall see a _hollow_ cone. If we place the
left eye L at O, behind the common base of the prism, we shall see with
one-half of the pupil the _hollow_ cone and with the other half the
_raised_ cone.

[Illustration: FIG. 38.]


6. _The Opera-Glass Stereoscope._

As the eyes themselves form a stereoscope to those who have the power
of quickly converging their axes to points nearer than the object which
they contemplate, it might have been expected that the first attempt
to make a stereoscope for those who do not possess such a power, would
have been to supply them with auxiliary eyeballs capable of combining
binocular pictures of different sizes at different distances from the
eye. This, however, has not been the case, and the stereoscope for this
purpose, which we are about to describe, is one of the latest of its
forms.

[Illustration: FIG. 39.]

[Illustration: FIG. 40.]

In Fig. 39, MN is a small inverting telescope, consisting of two
convex lenses M, N, placed at the sum of their focal distances, and
OP another of the same kind. When the two eyes, R, L, look through the
two telescopes directly at the dissimilar pictures A, B, they will see
them with perfect distinctness; but, by the slightest inclination of
the axes of the telescopes, the two images can be combined, and the
stereoscopic effect immediately produced. With the dissimilar pictures
in the diagram a _hollow_ cone is produced; but if we look at B with
the telescope M′N′, as in Fig. 40, and at A′ with O′P′, a _raised_ cone
will be seen. With the usual binocular slides containing portraits or
landscapes, the pictures are seen in relief by combining the right-eye
one with the left-eye one.

The instrument now described is nothing more than a double opera-glass,
which itself forms a good stereoscope. Owing, however, to the use of
a concave eye-glass, the field of view is very small, and therefore a
convex glass, which gives a larger field, is greatly to be preferred.

The little telescopes, MN, OP, may be made one and a half or even
one inch long, and fitted up, either at a fixed or with a variable
inclination, in a pyramidal box, like the lenticular stereoscope, and
made equally portable. One of these instruments was made for me some
years ago by Messrs. Horne and Thornthwaite, and I have described it in
the _North British Review_[42] as having the properties of a _Binocular
Cameoscope_, and of what has been absurdly called a _Pseudoscope_,
seeing that every inverting eye-piece and every stereoscope is entitled
to the very same name.

The little telescope may be made of one piece of glass, _convex_
at each end, or _concave_ at the eye-end if a small field is not
objectionable,—the length of the piece of glass, in the _first_
case, being equal to the _sum_, and, in the _second_ case, to the
_difference_ of the focal lengths of the virtual lenses at each end.[43]

[42] For 1852, vol. xvii. p. 200.

[43] These solid telescopes may be made achromatic by cementing concave
lenses of flint glass upon each end, or of crown glass if they are made
of flint glass.


7. _The Eye-Glass Stereoscope._

As it is impossible to obtain, by the ocular stereoscope, pictures in
relief from the beautiful binocular slides which are made in every
part of the world for the lenticular stereoscope, it is very desirable
to have a portable stereoscope which can be carried safely in our
purse, for the purpose of examining stereoscopically all such binocular
pictures.

If placed together with their plane sides in contact, a plano-convex
lens, AB, and a plano-concave one, CD, of the same glass and the same
focal length, will resemble a thick watch-glass, and on looking through
them, we shall see objects of their natural size and in their proper
place; but if we slip the concave lens, CD, to a side, as shewn in
Fig. 41, we merely displace the image of the object which we view, and
the displacement increases till the centre of the concave lens comes
to the margin of the convex one. We thus obtain a variable prism, by
means of which we can, with the left eye, displace one of the binocular
pictures, and lay it upon the other, as seen by the right eye. We may
use semi-lenses or quarters of lenses, and we may make them achromatic
or nearly so if we desire it. Double convex and double concave lenses
may also be used, and the motion of the concave one regulated by a
screw. In one which I constantly use, the concave lens slides in a
groove over a convex quarter-lens.

[Illustration: FIG. 41.]

By employing two of these variable prisms, we have an _Universal
Stereoscope_ for uniting pictures of various sizes and at various
distances from each other, and the prisms may be placed in a pyramidal
box, like the lenticular stereoscope.


8. _The Reading-Glass Stereoscope._

If we take a reading-glass whose diameter is not less than two inches
and three quarters, and look through it with both eyes at a binocular
picture in which the right-eye view is on the left hand, and the
left-eye view on the right hand, as in the ocular stereoscope, we shall
see each picture doubled, and the degree of separation is proportional
to the distance of the picture from the eye. If the distance of the
binocular pictures from each other is small, the two middle images of
the four will be united when their distance from the lens is not very
much greater than its focal length. With a reading-glass 4½ inches in
diameter, with a focal length of two feet, binocular pictures, in which
the distance of similar parts is _nine_ inches, are united without
any exertion of the eyes at the distance of eight feet. With the same
reading-glass, binocular pictures, at the usual distance of 2½ inches,
will be united at the distance of 2¼ or even 2½ feet. If we advance the
reading-glass when the distance is 2 or 3 feet, the picture in relief
will be magnified, but, though the observer may not notice it, the
separated images are now kept united by a slight convergency of the
optic axes. Although the pictures are placed so far beyond the anterior
focus of the lens, they are exceedingly distinct. The distinctness of
vision is sufficient, at least to long-sighted eyes, when the pictures
are placed within 16 or 18 inches of the observer, that is, 6 or 8
inches nearer the eye than the anterior focus of the lens. In this
case we can maintain the union of the pictures only when we begin to
view them at a distance of 2½ or 3 feet, and then gradually advance
the lens within 16 or 18 inches of the pictures. At considerable
distances, the pictures are most magnified by advancing the lens while
the head of the observer is stationary.


9. _The Camera Stereoscope._

The object of this instrument is to unite the transient pictures of
groups of persons or landscapes, as delineated in two dissimilar
pictures, on the ground-glass of a binocular camera. If we attach
to the back of the camera a lenticular stereoscope, so that the two
pictures on the ground-glass occupy the same place as its usual
binocular slides, we shall see the group of figures in relief under
every change of attitude, position, and expression. The two pictures
may be formed in the air, or, more curiously still, upon a wreath of
smoke. As the figures are necessarily inverted in the camera, they
will remain inverted by the lenticular and every other instrument but
the opera-glass stereoscope, which inverts the object. By applying
it therefore to the camera, we obtain an instrument by which the
photographic artist can make experiments, and try the effect which will
be produced by his pictures before he takes them. He can thus select
the best forms of groups of persons and of landscapes, and thus produce
works of great interest and value.


10. _The Chromatic Stereoscope._

The chromatic stereoscope is a form of the instrument in which relief
or apparent solidity is given to a single figure with different colours
delineated upon a plane surface.

If we look with both eyes through a lens LL, Fig. 42, about 2½ inches
in diameter or upwards, at any object having colours of different
degrees of refrangibility, such as the coloured boundary lines on
a map, a red rose among green leaves and on a blue background, or
any scarlet object whatever upon a violet ground, or in general any
two simple colours not of the same degree of refrangibility, _the
differently coloured parts of the object will appear at different
distances from the observer_.

[Illustration: FIG. 42.]

Let us suppose the rays to be _red_ and _violet_, those which differ
most in refrangibility. If the red rays radiate from the anterior focus
R, or red rays of the lens LL, they will emerge parallel, and enter the
eye at _m_; but the violet rays radiating from the same focus, being
more refrangible, will emerge in a state of convergence, as shewn at
_mv_, _nv_, the red rays being _mr_, _nr_. The part of the object,
therefore, from which the red rays come, will appear nearer to the
observer than the parts from which the violet rays come, and if there
are other colours or rays of intermediate refrangibilities, they will
appear to come from intermediate distances.

If we place a small _red_ and _violet_ disc, like the smallest
wafer, beside one another, so that the line joining their centres is
perpendicular to the line joining the eyes, and suppose that rays from
both enter the eyes with their optical axes parallel, it is obvious
that the distance between the violet images on each retina will be
_less_ than the distance between the _red_ images, and consequently the
eyes will require to converge their axes to a _nearer_ point in order
to unite the red images, than in order to unite the violet images. The
red images will therefore appear at this nearer point of convergence,
just as, in the lenticular stereoscope, the more distant pair of points
in the dissimilar images appear when united nearer to the eye. By the
two eyes alone, therefore, we obtain a certain, though a small degree
of relief from colours. With the lens LL, however, the effect is
greatly increased, and we have the _sum_ of the _two_ effects.

From these observations, it is manifest that the reverse effect must
be produced by a concave lens, or by the common stereoscope, when
_two_ coloured objects are employed or united. The _blue_ part of the
object will be seen _nearer_ the observer, and the red part of it
more _remote_. It is, however, a curious fact, and one which appeared
difficult to explain, that in the stereoscope the colour-relief was not
brought out as might have been expected. Sometimes the red was nearest
the eye, and sometimes the blue, and sometimes the object appeared
without any relief. The cause of this is, that the colour-relief given
by the common stereoscope was the opposite of that given by the eye,
and it was only the _difference_ of these effects that ought to have
been observed; and though the influence of the eyes was an inferior
one, it often acted alone, and sometimes ceased to act at all, in
virtue of that property of vision by which we see only with one eye
when we are looking with two.

In the chromatic stereoscope, Fig. 42, the intermediate part _mn_ of
the lens is of no use, so that out of the margin of a lens upwards of
2½ inches in diameter, we may cut a dozen of portions capable of making
as many instruments. These portions, however, a little larger only than
the pupil of the eye, must be placed in the same position as in Fig. 42.

All the effects which we have described are greatly increased by using
lenses of highly-dispersing flint glass, oil of cassia, and other
fluids of a great dispersive power, and avoiding the use of compound
colours in the objects placed in the stereoscope.

It is an obvious result of these observations, that in painting, and in
coloured decorations of all kinds, the red or less refrangible colours
should be given to the prominent parts of the object to be represented,
and the _blue_ or more refrangible colours to the background and the
parts of the objects that are to retire from the eye.


11. _The Microscope Stereoscope._

The lenticular form of the stereoscope is admirably fitted for its
application to small and microscopic objects. The first instruments
of this kind were constructed by myself with quarter-inch lenses, and
were 3 inches long and only 1 and 1½ deep.[44] They may be carried in
the pocket, and exhibit all the properties of the instrument to the
greatest advantage. The mode of constructing and using the instrument
is precisely the same as in the common stereoscope; but in taking the
dissimilar pictures, we must use either a small binocular camera, which
will give considerably magnified representations of the objects, or
we must procure them from the compound microscope. The pictures may
be obtained with a small single camera, by first taking one picture,
and then shifting the object in the focus of the lens, through a space
corresponding with the binocular angle. To find this space, which we
may call _x_, make _d_ the distance of the object from the lens, _n_
the number of times it is to be magnified, or the distance of the image
behind the lens, and D the distance of the eyes; then we shall have

                                     D
    _nd_ : _d_ = D : _x_, and _x_ = ———.
                                    _n_

that is, the space is equal to the distance between the eyes divided by
the magnifying power.

[44] _Phil. Mag._, Jan. 1852, vol. iii. p. 19.

With the binocular microscope of Professor Riddell,[45] and the same
instrument as improved by M. Nachet, binocular pictures are obtained
directly by having them drawn, as Professor Riddell suggests, by the
camera lucida, but it would be preferable to take them photographically.

Portraits for lockets or rings might be put into a very small
stereoscope, by folding the one lens back upon the other.

[45] _American Journal of Science_, 1852, vol. xv. p. 68.




CHAPTER VIII.

METHOD OF TAKING PICTURES FOR THE STEREOSCOPE.


However perfect be the stereoscope which we employ, the effect which it
produces depends upon the accuracy with which the binocular pictures
are prepared. The pictures required for the stereoscope may be arranged
in four classes:—

1. The representations of geometrical solids as seen with two eyes.

2. Portraits, or groups of portraits, taken from living persons or
animals.

3. Landscapes, buildings, and machines or instruments.

4. Solids of all kinds, the productions of nature or of art. */

_Geometrical Solids._

Representations of geometrical solids, were, as we have already seen,
the only objects which for many years were employed in the reflecting
stereoscope. The figures thus used are so well known that it is
unnecessary to devote much space to their consideration. For ordinary
purposes they may be drawn by the hand, and composed of squares,
rectangles, and circles, representing quadrangular pyramids, truncated,
or terminating in a point, cones, pyramids with polygonal bases, or
more complex forms in which raised pyramids or cones rise out of
quadrangular or conical hollows. All these figures may be drawn by the
hand, and will produce solid forms sufficiently striking to illustrate
the properties of the stereoscope, though not accurate representations
of any actual solid seen by binocular vision.

If one of the binocular pictures is not equal to the other in its
base or summit, and if the lines of the one are made crooked, it is
curious to observe how the appearance of the resulting solid is still
maintained and varied.

The following method of drawing upon a plane the dissimilar
representations of solids, will give results in the stereoscope that
are perfectly correct:—

[Illustration: FIG. 43.]

Let L, R, Fig. 43, be the left and right eye, and A the middle point
between them. Let MN be the plane on which an object or solid whose
height is CB is to be drawn. Through B draw LB, meeting MN in _c_; then
if the object is a solid, with its apex at B, C_c_ will be the distance
of its apex from the centre C of its base, as seen by the left eye.
When seen by the right eye R, C_c′_ will be its distance, _c′_ lying
on the left side of C. Hence if the figure is a cone, the dissimilar
pictures of it will be two circles, in one of which its apex is placed
at the distance C_c_ from its centre, and in the other at the distance
C_c′_ on the other side of the centre. When these two plane figures are
placed in the stereoscope, they will, when combined, represent a raised
cone when the points _c_, _c′_ are nearer one another than the centres
of the circles representing the cone’s base, and a _hollow_ cone when
the figures are interchanged.

If we call E the distance between the two eyes, and _h_ the height of
the solid, we shall have

              E
    AB:_h_ = ——— : C_c_,
              2

               _h_E     5_h_
    and C_c_ = ————, or ————,
                2AB     4AB

which will give us the results in the following table, E being 2½, and
AC 8 inches:—

    Height of
     object.
     BC = _h_        AB = AC - _h_    C_c_
                                     Inches.
        1                 7           0.179
        2                 6           0.4166
        3                 5           0.75
        4                 4           1.25
        5                 3           2.083
        6                 2           3.75
        7                 1           8.75
        8                 0           Infinite.

If we now converge the optic axes to a point _b_, and wish to ascertain
the value of C_c_, which will give different _depths_, _d_, of the
_hollow_ solids corresponding to different values of C_b_, we shall have

         E
    A_b_:—— = _d_:C_c′_,
         2

                _d_E
    and C_c′_ = ————— AB,
                  2

which, making AC = 8 inches, as before, will give the following
results:—

       Depth.
    C_b_ = _d_     A_b_ = AC + _d_       C_c′_
                                        Inches.
         1               9               0.139
         2              10               0.25
         3              11               0.34
         4              12               0.4166
         5              13               0.48
         6              14               0.535
         7              15               0.58
         8              16               0.625
         9              17               0.663
        10              18               0.696
        11              19               0.723
        12              20               0.75

The values of _h_ and _d_ when C_c_, C_c′_ are known, will be found
from the formulæ

           2AB · C_c_
    _h_ = ————————————,
               E

              2AB · C_c′_
    and _d_ = ————————————.
                  E.


As C_c_ is always equal to C_c′_ in each pair of figures or dissimilar
pictures, the depth of the _hollow_ cone will always appear much
greater than the height of the raised one. When C_c_ = C_c′_ = 0.75,
_h_:_d_ = 3:12. When C_c_ = C_c′_ = 0.4166, _h_:_d_ = 2:4, and when
C_c_ = C_c′_ = 0.139, _h_:_d_ = 0.8:1.0.

When the solids of which we wish to have binocular pictures are
symmetrical, the one picture is the reflected image of the other, or
its reverse, so that when we have drawn the solid as seen by one eye,
we may obtain the other by copying its reflected image, or by simply
taking a copy of it as seen through the paper.

When the geometrical solids are not symmetrical, their dissimilar
pictures must be taken photographically from models, in the same manner
as the dissimilar pictures of other solids.


_Portraits of Living Persons or Animals._

Although it is possible for a clever artist to take two portraits, the
one as seen by his right, and the other as seen by his left eye, yet,
owing to the impossibility of fixing the sitter, it would be a very
difficult task. A bust or statue would be more easily taken by fixing
two apertures 2½ inches distant, as the two points of sight, but even
in this case the result would be imperfect. The photographic camera is
the only means by which living persons and statues can be represented
by means of two plane pictures to be combined by the stereoscope; and
but for the art of photography, this instrument would have had a very
limited application.

It is generally supposed that photographic pictures, whether in
Daguerreotype or Talbotype, are accurate representations of the human
face and form, when the sitter sits steadily, and the artist knows
the resources of his art. _Quis solem esse falsum dicere audeat?_
says the photographer, in rapture with his art. _Solem esse falsum
dicere audeo_, replies the man of science, in reference to the hideous
representations of humanity which proceed from the studio of the
photographer. The sun never errs in the part which he has to perform.
The sitter may sometimes contribute his share to the hideousness of his
portrait by involuntary nervous motion, but it is upon the artist or
his art that the blame must be laid.

If the single portrait of an individual is a misrepresentation of his
form and expression, the combination of two such pictures into a solid
must be more hideous still, not merely because the error in form and
expression is retained or doubled, but because the source of error
in the single portrait is incompatible with the application of the
stereoscopic principle in giving relief to the plane pictures. The art
of stereoscopic portraiture is in its infancy, and we shall therefore
devote some space to the development of its true principles and
practice.

In treating of the images of objects formed by lenses and mirrors
with spherical surfaces, optical writers have satisfied themselves by
shewing that the images of straight lines so formed are conic sections,
elliptical, parabolic, or hyperbolic. I am not aware that any writer
has treated of the images of solid bodies, and of their shape as
affected by the size of the lenses or mirrors by which they are formed,
or has even attempted to shew how a perfect image of any object can be
obtained. We shall endeavour to supply this defect.

In a previous chapter we have explained the manner in which images are
formed by a small aperture, H, in the side, MN, of a camera, or in the
window-shutter of a dark room. The rectangles _br_, _b′r′_, and _b″r″_,
are images of the object RB, according as they are received at the
same distance from the lens as the object, or at a less or a greater
distance, the size of the image being to that of the object as their
respective distances from the hole H. Pictures thus taken are accurate
representations of the object, whether it be lineal, superficial,
or solid, as seen from or through the hole H; and if we could throw
sufficient light upon the object, or make the material which receives
the image very sensitive, we should require no other camera for giving
us photographs of all sizes. The only source of error which we can
conceive, is that which may arise from the inflexion of light, but we
believe that it would exercise a small influence, if any, and it is
only by experiment that its effect can be ascertained.

[Illustration: FIG. 44.]

The Rev. Mr. Egerton and I have obtained photographs of a bust, in the
course of ten minutes, with a very faint sun, and through an aperture
less than the hundredth of an inch; and I have no doubt that when
chemistry has furnished us with a material more sensitive to light, a
camera without lenses, and with only a pin-hole, will be the favourite
instrument of the photographer. At present, no sitter could preserve
his composure and expression during the number of minutes which are
required to complete the picture.

But though we cannot use this theoretical camera, we may make some
approximation to it. If we make the hole H a quarter of an inch,
the pictures _br_, &c., will be faint and indistinct; but by
placing a thin lens a quarter of an inch in diameter in the hole
H, the distinctness of the picture will be restored, and, from the
introduction of so much light, the photograph may be completed in a
sufficiently short time. The lens should be made of rock crystal,
which has a small dispersive power, and the ratio of curvature of its
surfaces should be as six to one, the flattest side being turned to the
picture. In this way there will be very little colour and spherical
aberration, and no error produced by any striæ or want of homogeneity
in the glass.

As the hole H is nearly the same as the greatest opening of the pupil,
the picture which is formed by the enclosed lens will be almost
identical with the one we see in monocular vision, which is always the
most perfect representation of figures in relief.

[Illustration: FIG. 45.]

With this approximately perfect camera, let us now compare the
expensive and magnificent instruments with which the photographer
practises his art. We shall suppose his camera to have its lens or
lenses with an aperture of only _three_ inches, as shewn at LR in Fig.
45. If we cover the whole lens, or reduce its aperture to a quarter
of an inch, as shewn at _a_, we shall have a correct picture of the
sitter. Let us now take other _four_ pictures of the same person, by
removing the aperture successively to _b_, _c_, _d_, and _e_: It is
obvious that these pictures will all differ very perceptibly from each
other. In the picture obtained through _d_, we shall see parts on the
left side of the head which are not seen in the picture through _c_,
and in the one through _c_, parts on the right side of the head not
seen through _d_. In short, the pictures obtained through _c_ and _d_
are accurate dissimilar pictures, such as we have in binocular vision,
(the distance _cd_ being 2½ inches,) and fitted for the stereoscope. In
like manner, the pictures through _b_ and _e_ will be different from
the preceding, and different from one another. In the one through _b_,
we shall see parts _below_ the eyebrows, below the nose, below the
upper lip, and below the chin, which are not visible in the picture
through _e_, nor in those through _c_ and _d_; while in the picture
through _e_, we shall see parts above the brow, and above the upper
lip, &c., which are not seen in the pictures through _b_, _c_, and _d_.
In whatever part of the lens, LR, we place the aperture, we obtain
a picture different from that through any other part, and therefore
it follows, _that with a lens whose aperture is three inches, the
photographic picture is a combination of about one hundred and thirty
dissimilar pictures of the sitter, the similar parts of which are not
coincident_; or to express it in the language of perspective, _the
picture is a combination of about one hundred and thirty pictures of
the sitter, taken from one hundred and thirty different points of
sight_! If such is the picture formed by a _three_-inch lens, what must
be the amount of the _anamorphism_, or distortion of form, which is
produced by photographic lenses of diameters from _three_ to _twelve_
inches, actually used in photography?[46]

[46] See my _Treatise on Optics_, 2d edit., chap. vii. p. 65.

But it is not merely by the size of the lenses that hideous portraits
are produced. In cameras with two achromatic lenses, the rays which
form the picture pass through a large thickness of glass, which may
not be altogether homogeneous,—through _eight_ surfaces which may
not be truly spherical, and which certainly scatter light in all
directions,—and through an optical combination in which straight lines
in the object must be conic sections in the picture!

Photography, therefore, cannot even approximate to perfection till the
artist works with a camera furnished with a single quarter of an inch
lens of rock crystal, having its radii of curvature as six to one, or
what experience may find better, with an achromatic lens of the same
aperture. And we may state with equal confidence, that the photographer
who has the sagacity to perceive the defects of his instruments, the
honesty to avow it, and the skill to remedy them by the applications of
modern science, will take a place as high in photographic portraiture
as a Reynolds or a Lawrence in the sister art.

Such being the nature of single portraits, we may form some notion of
the effect produced by combining dissimilar ones in the stereoscope, so
as to represent the original in relief. The single pictures themselves,
including binocular and multocular representations of the individual,
must, when combined, exhibit a very imperfect portrait in relief,—so
imperfect, indeed, that the artist is obliged to take his two pictures
from points of sight different from the correct points, in order to
produce the least disagreeable result. This will appear after we have
explained the correct method of taking binocular portraits for the
stereoscope.

No person but a painter, or one who has the eye and the taste of
a painter, is qualified to be a photographer either in single or
binocular portraiture. The first step in taking a portrait or copying
a statue, is to ascertain in what aspect and at what distance from the
eye it ought to be taken.

In order to understand this subject, we shall first consider the
vision, with _one eye_, of objects of three dimensions, when of
different magnitudes and placed at different distances. When we thus
view a building, or a full-length or colossal statue, at a short
distance, a picture of all its visible parts is formed on the retina.
If we view it at a greater distance, certain parts cease to be seen,
and other parts come into view; and this change in the picture
will go on, but will become less and less perceptible as we retire
from the original. If we now look at the building or statue from a
distance through a telescope, so as to present it to us with the same
distinctness, and of the same apparent magnitude as we saw it at our
first position, the two pictures will be essentially different; all the
parts which ceased to be visible as we retired will still be invisible,
and all the parts which were not seen at our first position, but became
visible by retiring, will be seen in the telescopic picture. Hence
the parts seen by the near eye, and not by the distant telescope,
will be those towards the middle of the building or statue, whose
surfaces converge, as it were, towards the eye; while those seen by
the telescope, and not by the eye, will be the external parts of the
object, whose surfaces converge less, or approach to parallelism. It
will depend on the nature of the building or the statue which of these
pictures gives us the most favourable representation of it.

If we now suppose the building or statue to be reduced in the most
perfect manner,—to half its size, for example,—then it is obvious that
these two perfectly similar solids will afford a different picture,
whether viewed by the eye or by the telescope. In the reduced copy, the
inner surfaces visible in the original will disappear, and the outer
surfaces become visible; and, as formerly, it will depend on the nature
of the building or the statue whether the reduced or the original copy
gives the best picture.

If we repeat the preceding experiments with _two eyes_ in place of
_one_, the building or statue will have a different appearance;
surfaces and parts, formerly invisible, will become visible, and the
body will be better seen because we see more of it; but then the
parts thus brought into view being seen, generally speaking, with
one eye, will have less brightness than the rest of the picture. But
though we see more of the body in binocular vision, it is only parts
of vertical surfaces perpendicular to the line joining the eyes that
are thus brought into view, the parts of similar horizontal surfaces
remaining invisible as with one eye. It would require a pair of eyes
placed vertically, that is, with the line joining them in a vertical
direction, to enable us to see the horizontal as well as the vertical
surfaces; and it would require a pair of eyes inclined at all possible
angles, that is, a ring of eyes 2½ inches in diameter, to enable us to
have a perfectly symmetrical view of the statue.

These observations will enable us to answer the question, whether or
not a reduced copy of a statue, of precisely the same form in all
its parts, will give us, either by monocular or binocular vision,
a better view of it as a work of art. As it is the outer parts or
surfaces of a large statue that are invisible, its great outline and
largest parts must be best seen in the reduced copy; and consequently
its relief, or third dimension in space, must be much greater in the
reduced copy. This will be better understood if we suppose a _sphere_
to be substituted for the statue. If the sphere exceeds in diameter the
distance between the pupils of the right and left eye, or 2½ inches, we
shall not see a complete hemisphere, unless from an infinite distance.
If the sphere is very much larger, we shall see only a segment, whose
relief, in place of being equal to the radius of the sphere, is equal
only to the versed sine of half the visible segment. Hence it is
obvious that a reduced copy of a statue is not only better seen from
more of its parts being visible, but is also seen in stronger relief.


_On the Proper Position of the Sitter._

With these observations we are now prepared to explain the proper
method of taking binocular portraits for the stereoscope.

The first and most important step is to fix upon the position of
the sitter,—to select the best aspect of the face, and, what is of
more importance than is generally supposed, to determine the best
distance from the camera at which he should be placed. At a short
distance certain parts of one face and figure which should be seen are
concealed, and certain parts of other faces are concealed which should
be seen. Prominent ears may be either hid or made less prominent by
diminishing the distance, and if the sight of both ears is desirable
the distance should be increased. Prominent features become less
prominent by distance, and their influence in the picture is also
diminished by the increased vision which distance gives of the round
of the head. The outline of the face and head varies essentially with
the distance, and hence it is of great importance to choose the best. A
long and narrow face requires to be viewed at a different distance from
one that is short and round. Articles of dress even may have a better
or a worse appearance according to the distance at which we see them.

Let us now suppose the proper distance to be _six feet_, and since it
is impossible to give any rules for taking binocular portraits with
large lenses we must assume a standard camera with a lens a quarter of
an inch in diameter, as the only one which can give a correct picture
as seen with one eye. If the portrait is wanted for a ring, a locket,
or a binocular slide, its size is determined by its purpose, and the
photographer must have a camera (which he has not) to produce these
different pictures. His own camera will, no doubt, take a picture for a
ring, a locket, or a binocular slide, but he does this by placing the
sitter at different distances,—at a very great distance for the ring
picture, at a considerable distance for the locket picture, and at a
shorter distance for the binocular one; but none of these distances are
the distance which has been selected as the proper one. With a single
lens camera, however, he requires only several quarter-inch lenses
of different focal lengths to obtain the portrait of the sitter when
placed at the proper distance from the camera.

In order to take binocular portraits for the stereoscope a binocular
camera is required, having its lenses of such a focal length as to
produce two equal pictures of the same object and of the proper size.
Those in general use for the lenticular stereoscope vary from 2.1
inches to 2.3 in breadth, and from 2.5 inches to 2.8 in height, the
distance between similar points in the two pictures varying from 2.30
inches to 2.57, according to the different distances of the foreground
and the remotest object in the picture.

Having fixed upon the proper distance of the sitter, which we shall
suppose to be _six_ feet,—a distance very suitable for examining a
bust or a picture, we have now to take two portraits of him, which,
when placed in the stereoscope, shall have the same relief and the
same appearance as the sitter when viewed from the distance of _six
feet_. This will be best done by a binocular camera, which we shall now
describe.


_The Binocular Camera._

This instrument differs from the common camera in having two lenses
with the same aperture and focal length, for taking at the same instant
the picture of the sitter as seen at the distance of _six_ feet, or any
other distance. As it is impossible to grind and polish two lenses,
whether single or achromatic, of exactly the same focal length, even
when we have the same glass for both, we must bisect a good lens,
and use the two semi-lenses, ground into a circular form, in order
to obtain pictures of exactly the same size and definition. These
lenses should be placed with their diameters of bisection parallel to
one another, and perpendicular to the horizon, at the distance of 2½
inches, as shewn in Fig. 45, where MN is the camera, L, L′ the two
lenses, placed in two short tubes, so that by the usual mechanical
means they can be directed to the sitter, or have their axes converged
upon him, as shewn in the Figure, where AB is the sitter, _ab_ his
image as given by the lens L, and _a′b′_ as given by the lens L′. These
pictures are obviously the very same that would be seen by the artist
with his two eyes at L and L′, and as

    ALB = _a_L_b_ = _a′_L′_b′_,

the pictures will have the same apparent magnitude as the original, and
will in no respect differ from it as seen by each eye from E, E′, E_a_
being equal to _a_L, and E′_a′_ to _a_L.

[Illustration: FIG. 46.]

Since the publication in 1849 of my description of the _binocular
camera_, a similar instrument was proposed in Paris by a photographer,
M. Quinet, who gave it the name of _Quinetoscope_, which, as the Abbé
Moigno observes, means an instrument for seeing M. Quinet! I have not
seen this camera, but, from the following notice of it by the Abbé
Moigno, it does not appear to be different from mine:—“Nous avons été à
la fois surpris et très-satisfait de retrouver dans le _Quinetoscope_
la chambre binoculaire de notre ami Sir David Brewster, telle que nous
l’avons décrite après lui il y a dix-huit mois dans notre brochure
intitulée _Stéréoscope_.” Continuing to speak of M. Quinet’s camera,
the Abbé is led to criticise unjustly what he calls the limitation
of the instrument:—“En un mot, ce charmant appareil est aussi bien
construit qu’il peut être, et nous désirons ardemment qu’il se répand
assez pour récompenser M. Quinet de son habileté et de ses peines.
Employé dans les limites fixées à l’avance par son véritable inventeur,
Sir David Brewster; c’est-à-dire, employé _à reproduire des objets
de petite et moyenne grandeur, il donnera assez beaux résultats_.
_Il ne pourra pas servir, evidemment, il ne donnera pas bien l’effet
stéréoscopique voulu, quand on voudra l’appliquer à de très-grands
objets, on a des vues ou pay sages pris d’une très-grande distance;
mais il est de la nature des œuvres humaines d’être essentiellement
bornées._”[47] This criticism on the limitation of the camera is
wholly incorrect; and it will be made apparent, in a future part of
the Chapter, that for objects of all sizes and at all distances the
binocular camera gives the very representations which we see, and that
other methods, referred to as superior, give unreal and untruthful
pictures, for the purpose of producing a startling relief.

In stating, as he subsequently does, that the angles at which the
pictures should be taken “are too vaguely indicated by theory,”[48] the
Abbé cannot have appealed to his own optical knowledge, but must have
trusted to the practice of Mr. Claudet, who asserts “that there cannot
be any rule for fixing the binocular angle of camera obscuras. _It is
a matter of taste and artistic illusion._”[49] No question of science
can be a matter of taste, and no illusion can be artistic which is a
misrepresentation of nature.

[47] See _Cosmos_, vol. ii. pp. 622, 624.

[48] _Id._ vol. vii. p. 494.

[49] _Id._ vol. iii. p. 658.

When the artist has not a binocular camera he must place his single
camera successively in such positions that the axis of his lens may
have the directions EL, EL′ making an angle equal to LCL′, the angle
which the distance between the eyes subtends at the distance of the
sitter from the lenses. This angle is found by the following formula:—

               ½_d_   1.25
    Tang. ½A = ———— = ————
                D       D

_d_ being the distance between the eyes, D the distance of the sitter,
and A the angle which the distance between the eyes, = 2.5, subtends at
the distance of the sitter. These angles for different distances are
given in the following table:—

       D = Distance               A = Angle formed
        of Camera                    by the two
        from the                     directions
        Sitter.                    of the Camera.

          5 inches,                    28°  6′
          6,                           23  32
          7,                           20  14
          8,                           17  46
          9,                           15  48
         10,                           14  15
         11,                           13   0
         12, 1 foot,                   11  54
         13,                           11   0
         14,                           10  17
         15,                            9  32
         16,                            8  56
         17,                            8  24
         18,                            7  56
         19,                            7  31
         20,                            7  10
         24, 2 feet,                    5  58
         30,                            4  46
         36 inches, 3 feet,             3  59
         42,                            3  25
         48, 4 feet,                    2  59
         54,                            2  39
         60, 5 feet,                    2  23
         72, 6 feet,                    1  59
         84, 7 feet,                    1  42
         96, 8 feet,                    1  30
        108, 9 feet,                    1  20
        120, 10 feet,                   1  12

The numbers given in the greater part of the preceding table can be
of use only when we wish to take binocular pictures of small objects
placed at short distances from cameras of a diminutive size. In
photographic portraiture they are of no use. The correct angle for a
distance of _six_ feet must not exceed _two_ degrees,—for a distance
of _eight_ feet, _one and a half_ degrees, and for a distance of
_ten_ feet, _one and a fifth_ degree. Mr. Wheatstone has given quite
a different rule. He makes the angle to depend, not on the distance
of the sitter from the camera, but _on the distance of the binocular
picture in the stereoscope from the eyes of the observer_! According
to the rule which I have demonstrated, the angle of convergency for
a distance of _six feet_ must be 1° 59′, whereas in a stereoscope of
any kind, with the pictures _six_ inches from the eyes, Mr. Wheatstone
makes it 23° 32′! As such a difference is a scandal to science, we
must endeavour to place the subject in its true light, and it will
be interesting to observe how the problem has been dealt with by
the professional photographer. The following is Mr. Wheatstone’s
explanation of his own rule, or rather his mode of stating it:—

“With respect,” says he, “to the means of preparing the binocular
photographs, (and in this term I include both Talbotypes and
Daguerreotypes,) little requires to be said beyond a few directions as
to the proper positions in which it _is necessary_ to place the camera
in order to obtain the two required projections.

“We will suppose that the binocular pictures are required to be seen
in the stereoscope at a distance of eight inches before the eyes, in
which case the convergence of the optic axes is about 18°. To obtain
the proper projections for this distance, the camera must be placed
with its lens accurately directed towards the object successively in
two points of the circumference of a circle, of which the object is the
centre, and the points at which the camera is so placed must have the
angular distance of 18° from each other, exactly that of the optic axes
in the stereoscope. The distance of the camera from the object may be
taken arbitrarily, for so long as the same angle is employed, whatever
that distance may be, _the picture will exhibit in the stereoscope
the same relief_, and be seen at the same distance of eight inches,
_only_ the magnitude of the picture will appear different. Miniature
stereoscopic representations of buildings and full-sized statues are,
therefore, obtained merely by taking the two projections of the object
from a considerable distance, _but at the same time as if the object
were only eight inches distant_, that is, at an angle of 18°.”[50]

[50] _Phil. Trans._, 1852, p. 7.

Such is Mr. Wheatstone’s rule, for which he has assigned no reason
whatever. In describing the binocular camera, in which the lenses
must be only 2½ inches distant for portraits, I have shewn that the
pictures which it gives are perfect representations of the original,
and therefore pictures taken with _lenses_ or cameras at any other
distance, must be different from those which are seen by the artist
looking at the sitter from his camera. They are, doubtless, both
pictures of the sitter, but the picture taken by Mr. Wheatstone’s rule
is one which no man ever saw or can see, until he can place his eyes
at the distance of _twenty inches_! It is, in short, the picture of a
living doll, in which parts are seen which are never seen in society,
and parts hid which are always seen.

In order to throw some light upon his views, Mr. Wheatstone got “a
number of Daguerreotypes of the same bust taken at a variety of
different angles, so that he was enabled to place in the stereoscope
two pictures taken at any angular distance from 2° to 18°, the former
corresponding to a distance of about six feet, and the latter to a
distance of about eight inches.” In those taken at 2°, (the proper
angle,) there is “an undue elongation of lines joining two unequally
distant points, so that all the features of a bust appear to be
exaggerated in depth;” while in those taken at 18°, “there is an undue
shortening of the same lines, so that the appearance of a bas-relief is
obtained from the two projections of the bust, the apparent dimensions
in breadth and height remaining in both cases the same.”

Although Mr. Wheatstone speaks thus decidedly of the relative effect
produced by combining pictures taken at 2½° and 18°, yet in the very
next paragraph he makes statements entirely incompatible with his
previous observations. “When the optic axes,” he says, “are parallel,
_in strictness_ there should be no difference between the pictures
presented to each eye, and in this case _there would be no binocular
relief_, but I find _that an excellent effect_ is produced when the
axes are nearly parallel, by pictures taken at an inclination of 7° or
8°, and even a difference of 16° or 17° _has no decidedly bad effect_!”

That Mr. Wheatstone observed all these contradictory facts we do
not doubt, but why he observed them, and what was their cause, is
a question of scientific as well as of practical importance. Mr.
Wheatstone was not aware[51] that the Daguerreotype pictures which
he was combining, taken with _large lenses_, were not pictures as
seen with two human eyes, but were actually binocular and multocular
monstrosities, entirely unfit for the experiments he was carrying on,
and therefore incapable of testing the only true method of taking
binocular pictures which we have already explained.

[51] Mr. Wheatstone’s paper was published before I had pointed out the
deformities produced by large lenses. See p. 130.

Had Mr. Wheatstone combined pictures, each of which was a correct
monocular picture, as seen with each eye, and as taken with a small
aperture or a small lens, he would have found no discrepancy between
the results of observation and of science. From the same cause, we
presume, namely, the use of multocular pictures, Mr. Alfred Smee[52]
has been led to a singular method of taking binocular ones. In one
place he implicitly adopts Mr. Wheatstone’s erroneous rule. “The
pictures for the stereoscope,” he says, “are taken at two stations, at
a greater or less distance apart, according to the distance at which
they are to be viewed. For a distance of 8 inches the two pictures are
taken at angles of 18°, for 13 inches 10°, for 18 inches 8°, and for 4
feet 4°.” But when he comes to describe his own method he seems to know
and to follow the true method, if we rightly understand his meaning.
“To obtain a binocular picture of anybody,” he says, “the camera must
be employed to take half the impression, and then it must be moved
in the arc of a circle of which the distance from the camera to the
_point of sight_[53] is the radius for about 2½ inches when a second
picture is taken, and the two impressions conjointly form one binocular
picture. There are many ways by which this result may be obtained. A
spot may be placed on the ground-glass on which the point of sight
should be made exactly to fall. The camera may then be moved 2½ inches,
and adjusted till the point of sight falls again upon the same spot
on the ground-glass, when, if the camera has been moved in a true
horizontal plane _the effect of the double picture will be perfect_.”
This is precisely the true method of taking binocular pictures which we
had given long before, but it is true only when small lenses are used.
In order to obtain this motion in the true arc of a circle the camera
was moved on two cones which converged to the point of sight, and Mr.
Smee thus obtained pictures of the usual character. But in making
these experiments he was led to take pictures _when the camera was in
continual motion backwards and forwards for 2½ inches_, and he remarks
that “_in this case the picture was even more beautiful than when the
two images were superimposed_!” “This experiment,” he adds, “is very
remarkable, for who would have thought formerly that a picture could
possibly have been made with a camera in continual motion? Nevertheless
we accomplish it every day with ease, and the character of the likeness
is wonderfully improved by it.” We have now left the regions of
science, and have to adjudicate on a matter of opinion and taste. Mr.
Smee has been so kind as to send me a picture thus taken. It is a good
photograph with features enlarged in all azimuths, but it has no other
relief than that which we have described as monocular.

[52] _The Eye in Health and Disease_, by Alfred Smee, 2d edit. 1854,
pp. 85-95.

[53] This expression has a different meaning in perspective. We
understand it to mean here the point of the sitter or object, which is
to be the centre of the picture.

A singular effect of combining pictures taken at extreme angles has
been noticed by Admiral Lageol. Having taken the portrait of one of
his friends when his eyes were directed to the object-glass of the
camera, the Admiral made him look at an object 45°! to the right,
and took a second picture. When these pictures were placed in the
stereoscope, and viewed “without ceasing, turning first to the right
and then to the left, the eyes of the portrait follow this motion as
if they were animated.”[54] This fact must have been noticed in common
stereoscopic portraits by every person who has viewed them alternately
with each eye, but it is not merely the eyes which move. The nose, and
indeed every feature, changes its place, or, to speak more correctly,
the whole figure leaps from the one binocular position into the
other. As it is unpleasant to open and shut the eyes alternately, the
same effect may be more agreeably produced in ordinary portraits by
merely intercepting the light which falls upon each picture, or by
making an opaque screen pass quickly between the eyes and the lens,
or immediately below the lens, so as to give successive vision of
the pictures with each eye, and with both. The motion of the light
reflected from the round eyeball has often a striking effect.

[54] _Cosmos_, Feb. 29, 1856, vol. viii. p. 202.

From these discussions, our readers will observe that the science, as
well as the art of binocular portraiture for the stereoscope, is in a
transition state in which it cannot long remain. The photographer who
works with a very large lens chooses an angle which gives the least
unfavourable results; his rival, with a lens of less size, chooses,
on the same principle, a different angle; and the public, who are no
judges of the result, are delighted with their pictures in relief, and
when their noses are either pulled from their face, or flattened upon
their cheek, or when an arm or a limb threatens to escape from their
articulation, they are assured that nature and not art is to blame.

We come now to consider under what circumstances the photographer may
place the lenses of his binocular camera at a greater distance than 2½
inches, or his two cameras at a greater angle than that which we have
fixed.

1. In taking family portraits for the stereoscope, the cameras must be
placed at an angle of 2° for 6 feet, when the binocular camera is not
used.

2. In taking binocular pictures of any object whatever, when we wish
to see them exactly as we do with our two eyes, we must adopt the same
method.

3. If a portrait is wanted to assist a sculptor in modelling a statue,
a great angle might be adopted, in order to shew more of the head. But
in this case the best way would be to take the correct social likeness,
and then take photographs of the head in different azimuths.

If we wish to have a greater degree of relief than we have with our
two eyes, either in viewing colossal statues, or buildings, or
landscapes, where the deviation from nature does not, as in the human
face, affect the expression, or injure the effect, we must increase
the distance of the lenses in the binocular camera, or the angle of
direction of the common camera. Let us take the case of a colossal
statue 10 feet wide, and suppose that dissimilar drawings of it about
_three_ inches wide are required for the stereoscope. These drawings
are _forty_ times narrower than the statue, and must be taken at such
a distance, that with the binocular camera the relief would be almost
evanescent. We must therefore suppose the statue to be reduced _n_
times, and place the semi-lenses at the distance _n_ × 2½ inches. If
_n_ = 10, the statue 10 feet wide will be reduced to ¹⁰/₁₀, or to 1
foot, and _n_ × 2½, or the distance of the semi-lenses will be 25
inches. With the lenses at this distance, the dissimilar pictures of
the statue will reproduce, when combined, a statue one foot wide, which
will have exactly the same appearance and relief as if we had viewed
the colossal statue with eyes 25 inches distant. But the reproduced
statue will have also the same appearance and relief as a statue a foot
wide reduced from the colossal one with mathematical precision, and it
will therefore be a better or more relieved representation of the work
of art than if we had viewed the colossal original with our own eyes,
either under a greater, an equal, or a less angle of apparent magnitude.

We have supposed that a statue a foot broad will be seen in proper
relief by binocular vision; but it remains to be decided whether or
not it would be more advantageously seen if reduced with mathematical
precision to a breadth of 2½ inches, the width of the eyes, which
gives the vision of a hemisphere 2½ inches in diameter with the most
perfect relief.[55] If we adopt this principle, and call B the breadth
of the statue of which we require dissimilar pictures, we must make
_n_ = B/2½, and _n_ × 2½ = B, that is, the distance of the semi-lenses
in the binocular camera, or of the lenses in two cameras, must be made
equal to the breadth of the statue.

In concluding this chapter, it may be proper to remark, that unless
we require an increased relief for some special purpose, landscapes
and buildings should be taken with the normal binocular camera, that
is, with its lenses 2½ inches distant. Scenery of every kind, whether
of the picturesque, or of the sublime, cannot be made more beautiful
or grand than it is when seen by the traveller himself. To add an
artificial relief is but a trick which may startle the vulgar, but
cannot gratify the lover of what is true in nature and in art.


_The Single Lens Binocular Camera._

As every photographer possesses a camera with a lens between 2½ and 3
inches in diameter, it may be useful to him to know how he may convert
it into a binocular instrument.

In a cover for the lens take two points equidistant from each other,
and make two apertures, _c_, _d_, Fig. 43, ²/₁₀ths of an inch in
diameter, or of any larger size that may be thought proper, though
²/₁₀ is the proper size. Place the cover on the end of the tube, and
bring the line joining the apertures into a horizontal position.
Closing one aperture, take the picture of the sitter, or of the
statue, through the other, and when the picture is shifted aside by
the usual contrivances for this purpose, take the picture through the
other aperture. These will be good binocular portraits, fitted for
any stereoscope, but particularly for the Achromatic Reading Glass
Stereoscope. If greater relief is wanted, it may be obtained in larger
lenses by placing the two apertures at the greatest distance which the
diameter of the lens will permit.

[55] It is only in a horizontal direction that we can see 180° of the
hemisphere. We would require a circle of eyes 2½ inches distant to see
a complete hemisphere.


_The Binocular Camera made the Stereoscope._

If the lenses of the binocular camera, when they are whole lenses, be
made to separate a little, so that the distance between the centres of
their inner halves may be equal to 2½ inches, they become a lenticular
stereoscope, in which we may view the pictures which they themselves
create. The binocular pictures are placed in the camera in the very
place where their negatives were formed, and the observer, looking
through the halves of his camera lenses, will see the pictures united
and in relief. If the binocular camera is made of semi-lenses, we
have only to place them with their thin edges facing each other to
obtain the same result. It will appear, from the discussions in the
following chapter, that such a stereoscope, independently of its being
achromatic, if the camera is achromatic, will be the most perfect of
stereoscopic instruments.

The preceding methods are equally applicable to landscapes, machines,
and instruments, and to solid constructions of every kind, whether they
be the production of nature or of art.[56]

[56] See Chapters X. and XI.




CHAPTER IX.

ON THE ADAPTATION OF THE PICTURES TO THE STEREOSCOPE.

—THEIR SIZE, POSITION, AND ILLUMINATION.


Having described the various forms of the stereoscope, and the method
of taking the binocular portraits and pictures to which it is to be
applied, we have now to consider the relation that ought to exist
between the instrument and the pictures,—a subject which has not been
noticed by preceding writers.

If we unite two dissimilar pictures by the simple convergency of
the optical axes, we shall observe a certain degree of relief, at a
certain distance of the eyes from the pictures. If we diminish the
distance, the relief diminishes, and if we increase it, it increases.
In like manner, if we view the dissimilar pictures in the lenticular
stereoscope, they have a certain degree of relief; but if we use
lenses of a higher magnifying power, so as to bring the eyes nearer
the pictures, the relief will diminish, and if we use lenses of a less
magnifying power, the relief will increase. By bringing the eyes nearer
the pictures, which we do by magnifying them as well as by approaching
them, we increase the distance between similar points of the two
pictures, and therefore the distance of these points, when united,
from any plane in the picture, that is, its relief will be diminished.
For the same reason, the diminution of the distance between similar
points by the removal of the eyes from the picture, will produce an
increase of relief. This will be readily understood if we suppose the
eyes R, L, in Fig. 24, to be brought nearer the plane MN, to R′L′, the
points 1, 1 and 2, 2 will be united at points nearer MN than when the
eyes were at R, L, and consequently their relief diminished.

Now we have seen, that in taking portraits, as explained in Fig. 46, we
view the two pictures, _ab, a′b′_, with the eyes at E and E′, exactly,
and with the same relief in the air, as when we saw the original AB,
from L, L′, and therefore E_c_ is the distance at which the dissimilar
pictures should be viewed in the stereoscope, in order that we may see
the different parts of the solid figure under their proper relief. But
the distance E_c_ = L_c_ is the conjugate focal length of the lens L,
if one lens is used, or the conjugate equivalent focal length, if two
achromatic lenses are used; and consequently every picture taken for
the stereoscope should be taken by a camera, the conjugate focal length
of whose lens corresponding to the distance of the sitter, is equal to
_five_ inches, when it is to be used in the common stereoscope, which
has generally that depth.

Between the pictures and the purely optical part of the stereoscope,
there are other relations of very considerable importance. The
exclusion of all external objects or sources of light, excepting that
which illuminates the pictures, is a point of essential importance,
though its advantages have never been appreciated. The spectacle
stereoscope held in the hand, the reflecting stereoscope, and the
open lenticular stereoscope, are all, in this respect, defective.
The binocular pictures must be placed in a dark box, in order to
produce their full effect; and it would be a great improvement on
the lenticular stereoscope, if, on the left and right side of each
eye-tube, a piece of brass were to be placed, so as to prevent any
light from entering the left angle of the left eye, and the right angle
of the right eye.[57] The eyes, thus protected from the action of all
external light, and seeing nothing but the picture, will see it with a
distinctness and brilliancy which could not otherwise be obtained.

[57] When any external light falls upon the eye, its picture is
reflected back from the metallic surface of the Daguerreotype, and a
negative picture of the part of the Daguerreotype opposite each eye is
mixed with the positive picture of the same part.

The proper illumination of the picture, when seen by reflected light,
is also a point of essential importance. The method universally adopted
in the lenticular stereoscope is not good, and is not the one which I
found to be the best, and which I employed in the first-constructed
instruments. The light which falls upon the picture is prevented from
reaching the observer only by its being incident at an angle greater
or less than the angle of reflexion which would carry it to his eyes.
A portion of the scattered light, however, does reach the eye, and in
Daguerreotypes especially, when any part of the surface is injured,
the injury, or any other imperfection in the plate, is more distinctly
seen. The illumination should be lateral, either by a different form of
window in the front, or by openings on the two sides, or by both these
methods.

When the lenticular stereoscope is thus fitted up, and the pictures
in this manner illuminated, the difference of effect is equally great
as it is between a picture as commonly seen, and the same picture
exhibited as a panorama or a diorama, in which no light reaches the
eyes but that which radiates from the painting itself, the reflexion
from the varnish being removed by oblique or lateral illumination.

The great value of transparent binocular slides, when the picture
is to be upon glass, is obvious from the preceding considerations.
The illumination is uniform and excellent, but care must be taken to
have the ground-glass in front of the picture, or the paper, when it
is used, of a very fine grain, so that it may throw no black specks
upon the sky or the lights of the picture. Another advantage of the
transparent slides is, that the pictures are better protected from
injury than those upon paper.

It is obvious from these considerations that the size of the pictures
is determined, as well as the distance at which they are to be viewed.
Much ignorance prevails upon this subject, both among practical
photographers and optical writers. Large binocular pictures have been
spoken of as desirable productions, and it has been asserted, and
claimed too, as a valuable property of the reflecting stereoscope, that
it allows us to use larger pictures than other instruments. There never
was a greater mistake. If we take a large picture for the stereoscope
we must place it at a great distance from the eye, and consequently use
a large stereoscope. A small picture, seen distinctly near the eye, is
the very same thing as a large picture seen at a greater distance. The
size of a picture, speaking optically and correctly, is measured by the
angle which it subtends at the eye, that is its apparent magnitude. A
portrait three inches high, for example, and placed in the lenticular
stereoscope five inches from the eye, has the same apparent size as a
Kit Cat portrait in oil the size of life, three feet high, seen at the
distance of five feet, the distance at which it is commonly examined;
and if we increase the magnifying power so as to see the three-inch
picture at the distance of two inches, it will have the same apparent
size as the three feet oil portrait seen at the distance of two feet.
If the pictures used in the stereoscope were imperfect pictures that
would not bear being magnified, it would be improper to use them; but
the Daguerreotypes, and the transparent pictures, which are taken
by the first artists, for the lenticular stereoscope, will bear a
magnifying power ten times greater than that which is applied to them.

If we take a large picture for the stereoscope, we are compelled by
pictorial truth to place it at a distance from the eye equal to the
equivalent focal distance of the camera. Every picture in every camera
has the same apparent magnitude as the object which it represents;
whether it be a human figure, or the most distant landscape; and if
we desire to see it in its true relief in the stereoscope, we must
place it at a distance from the eye equal to the focal length of the
lens, whether it be an inch or a foot high. There is, therefore,
nothing gained by using large pictures. There is, on the contrary, much
inconvenience in their use. They are in themselves less portable, and
require a larger stereoscope; and we believe, no person whatever, who
is acquainted with the perfection and beauty of the binocular slides in
universal use, would either incur the expense, or take the trouble of
using pictures of a larger size.

In the beautiful combination of lenticular stereoscopes, which was
exhibited by Mr. Claudet, Mr. Williams, and others, in the Paris
Exhibition, and into which six or eight persons were looking at the
same time, binocular pictures of a larger size could not have been
conveniently used.

But, independently of these reasons, the question of large pictures
has been practically settled. No such pictures are taken by the
Daguerreotypists or Talbotypists, who are now enriching art with
the choicest views of the antiquities, and modern buildings, and
picturesque scenery of every part of the world; and even if they could
be obtained, there are no instruments fitted for their exhibition. In
the magnificent collection of stereoscopic pictures, amounting to above
a thousand, advertised by the London Stereoscopic Company, there are
no fewer than _sixty_ taken in Rome, and representing, better than a
traveller could see them there, the ancient and modern buildings of
that renowned city. Were these _sixty_ views placed on the sides of a
revolving polygon, with a stereoscope before each of its faces, a score
of persons might, in the course of an hour, see more of Rome, and see
it better, than if they had visited it in person. At all events, those
who are neither able nor willing to bear the expense, and undergo the
toil of personal travel, would, in such a panorama,—an analytical view
of Rome,—acquire as perfect a knowledge of its localities, ancient
and modern, as the ordinary traveller. In the same manner, we might
study the other metropolitan cities of the world, and travel from them
to its river and mountain scenery,—admiring its noble castles in our
descent of the Rhine,—its grand and wild scenery on the banks of the
Mississippi, or the Orinoco,—the mountain gorges, the glaciers, and the
peaks of the Alps and the Ural,—and the more sublime grandeur which
reigns among the solitudes of the Himalaya and the Andes.

The following general rule for taking and combining binocular pictures
is the demonstrable result of the principles explained in this chapter:—

_Supposing that the camera obscura employed to take binocular
portraits, landscapes, &c., gives perfect representations of them, the
relief picture in the stereoscope, produced by their superposition
and binocular union, will not be correct and truthful, unless the
dissimilar pictures are placed in the stereoscope at a distance from
the eyes, equal to the focal distance, real or equivalent, of the
object-glass or object-glasses of the camera, and, whatever be the size
of the pictures, they will appear, when they are so placed, of the same
apparent magnitude, and in the same relief, as when they were seen from
the object-glass of the camera by the photographer himself._




CHAPTER X.

APPLICATION OF THE STEREOSCOPE TO PAINTING.


Having explained the only true method of taking binocular portraits
which will appear in correct relief when placed in the stereoscope,
we shall proceed in this chapter to point out the application of the
stereoscope to the art of painting in all its branches. In doing this
we must not forget how much the stereoscope owes to photography, and
how much the arts of design might reasonably expect from the solar
pencil, when rightly guided, even if the stereoscope had never been
invented.

When the processes of the Daguerreotype and Talbotype, the sister arts
of Photography, were first given to the world, it was the expectation
of some, and the dread of others, that the excellence and correctness
of their delineations would cast into the shade the less truthful
representations of the portrait and the landscape painter. An invention
which supersedes animal power, or even the professional labour of man,
might have been justly hailed as a social blessing, but an art which
should supersede the efforts of genius, and interfere with the exercise
of those creative powers which represent to us what is beautiful and
sublime in nature, would, if such a thing were possible, be a social
evil.

The arts of painting, sculpture, and architecture have in every age,
and in every region of civilisation, called into exercise the loftiest
genius and the deepest reason of man. Consecrated by piety, and
hallowed by affection, the choicest productions of the pencil and the
chisel have been preserved by the liberality of individuals and the
munificence of princes, while the palaces of sovereigns, the edifices
of social life, the temples of religion, the watch-towers of war, the
obelisks of fame, and the mausolea of domestic grief, stand under the
azure cupola of heaven, to attest by their living beauty, or their
ruined grandeur, the genius and liberality which gave them birth. To
the cultivation and patronage of such noble arts, the vanity, the
hopes, and the holiest affections of man stand irrevocably pledged;
and we should deplore any invention or discovery, or any tide in the
nation’s taste, which should paralyse the artist’s pencil, or break the
sculptor’s chisel, or divert into new channels the genius which wields
them. But instead of superseding the arts of design, photography will
but supply them with new materials,—with collections of costume,—with
studies of drapery and of forms, and with scenes in life, and facts
in nature, which, if they possess at all, they possess imperfectly,
and without which art must be stationary, if she does not languish and
decline.

Sentiments analogous to these have been more professionally expressed
by M. Delaroche, a distinguished French artist,—by Sir Charles
Eastlake, whose taste and knowledge of art is unrivalled,—and by Mr.
Ruskin, who has already given laws to art, and whose genius is destined
to elevate and to reform it. M. Delaroche considers photography “as
carrying to such perfection certain of the essential principles of
art, that they must become subjects of study and observation, even
to the most accomplished artist.”... “The finish of inconceivable
minuteness,” he says, “disturbs in no respect the repose of the masses,
nor impairs in any way the general effect.... The correctness of the
lines, the precision of the forms in the designs of M. Daguerre, are
as perfect as it is possible they can be, and yet, at the same time,
we discover in them a broad and energetic manner, and a whole equally
rich in hue and in effect. The painter will obtain by this process
a quick method of making collections of studies, which he could not
otherwise procure without much time and labour, and in a style very far
inferior, whatever might be his talents in other respects.” In the same
spirit, Mr. Ruskin[58] considers “the art of photography as enabling
us to obtain as many memoranda of the facts of nature as we need;” and
long before Mr. Talbot taught us to fix upon paper the pictures of the
camera obscura, the Rev. John Thomson, one of the most distinguished of
our Scottish landscape painters, studied, in one of these instruments,
the forms and colours of the scenes which he was to represent. Other
artists, both in portrait and in landscape, now avail themselves of
photography, both as an auxiliary and a guide in their profession; but
there are certain difficulties and imperfections in the art itself,
and so many precautions required in its right application, whether we
use its pictures single, as representations on a plane, or take them
binocularly, to be raised into relief by the stereoscope, that we must
draw from the principles of optics the only rules which can be of real
services to the arts of design.

[58] _Modern Painters_, vol. iii., Preface, pp. 11, 12.

In painting a landscape, a building, a figure, or a group of figures,
the object of the artist is to represent it on his canvas _just as
he sees it_, having previously selected the best point of view, and
marked for omission or improvement what is not beautiful, or what would
interfere with the effect of his picture as a work of high art. His
first step, therefore, is to fix upon the size of his canvas, or the
distance at which the picture is to be seen, which determines its size.
His own eye is a camera obscura, and the relation between the picture
or image on its retina is such, that if we could view it from the
centre of curvature of the retina, (the centre of visible direction,)
a distance of half an inch, it would have precisely the same apparent
magnitude as the object of which it is the image. Let us now suppose
that the artist wishes to avail himself of the picture in the camera
obscura as received either on paper or ground-glass, or of a photograph
of the scene he is to paint. He must make use of a camera whose focal
length is equal to the distance at which his picture is to be seen,
and when the picture thus taken is viewed at this distance (suppose
_two_ feet) it will, as a whole, and in all its parts, have the same
apparent magnitude as the original object. This will be understood from
Fig. 47, in which we may suppose H to be the lens of the camera, RB the
object, and H_y′_ the distance at which it is to be viewed. The size
of the picture taken with a lens at H, whose focal length is H_y′_,
will be _b′r′_, and an eye placed at H will see the picture _b′r′_
under an angle _b′_H_r′_, equal to the angle RHB, under which the real
object RB was seen by the artist from H. In like manner, a larger
picture, _byr_, taken by a camera the focal distance of whose lens at
H is H_y_, will be an accurate representation of the object RB, when
viewed from H, and of the same apparent magnitude. If either of these
pictures, _b′r′_ or _br_, are viewed from greater or less distances
than H_y′_, or H_y_, they will not be correct representations of the
object RB, either in apparent magnitude or form. That they will be of
a different apparent magnitude, greater when viewed at less distances
than H_y′_, H_y_, and less when viewed at greater distances, is too
obvious to require any illustration. That they will differ in form, or
in the relative apparent size of their parts, has, so far as I know,
not been conjectured. In order to shew this, let us suppose a man _six_
feet high to occupy the foreground, and another of the same size to be
placed in the middle distance, the distance of the two from the artist
being ten and twenty feet. The apparent magnitudes of these two men
on the photograph will be as two to one; and if we look at it at any
distance greater or less than the focal length H_y′_ of the lens, the
same proportion of two to one will be preserved, whereas if we look at
the original figures at a greater or less distance from them than the
place of the artist, the ratio of their apparent magnitudes will be
altered. If the artist, for example, advances five feet, the nearest
man will be five feet distant and the other fifteen feet, so that their
apparent magnitude will now be as three to one.

[Illustration: FIG. 47.]

The same observations apply to a portrait of the human face. In looking
at a human profile let us suppose the breadth of the nose to be one
inch, that of the ear one inch, and that we view this profile at the
distance of _three_ feet from the ear, which is two inches nearer the
observer than the nose. The apparent magnitude of the ear and nose will
be as thirty-eight to thirty-six inches, whereas if we view the profile
from the distance of _one_ foot the ratio will be as fourteen to
twelve, that is, the ear will be increased in apparent size more than
the nose. Hence it follows that all pictures should be viewed under
the same angle of apparent magnitude under which they were seen by the
artist as taken photographically, for if we view them at a greater or
less angle than this we do not see the same picture as when we looked
at the original landscape or portrait, under the same angle of apparent
magnitude.

From the observations made in the preceding Chapter on photographic
and stereoscopic portraiture, the reader must have already drawn the
inference that the same landscape or building, seen at different
distances, varies essentially in its character,—beauties disclosing
themselves and defects disappearing as we approach or recede from them.
The picture in the camera, therefore, as used by Mr. Thomson, or, what
is still better, with the exception of colour, the photograph obtained
by the same instrument, will supply the artist with all the general
materials for his picture. The photograph will differ considerably
from any sketch which the artist may have himself made, owing to
certain optical illusions to which his eye is subject. The hills and
other vertical lines in the distance will be lower in the photograph
than in his sketch.[59] The vertical lines of buildings will converge
upwards in the photograph, as they ought to do, in receding from the
eye; and in the same picture there will be a confusion, as we shall
afterwards shew, in the delineation of near and minute objects in the
foreground, increasing with the size of the lens which he has employed.

[59] Sir Francis Chantrey, the celebrated sculptor, shewed me, many
years ago, a Sketch-Book, containing numerous drawings which he
had made with the _Camera Lucida_, while travelling from London to
Edinburgh by the Lakes. He pointed out to me the flatness, or rather
lowness, of hills, which to his own eye appeared much higher, but
which, notwithstanding, gave to him the idea of a greater elevation.
In order to put this opinion to the test of experiment, I had drawings
made by a skilful artist of the three Eildon hills opposite my
residence on the Tweed, and was surprised to obtain, by comparing them
with their true perspective outlines, a striking confirmation of the
observation made by Sir Francis Chantrey.

In his admirable chapter “On Finish,” Mr. Ruskin has established,
beyond a doubt, the most important principle in the art of painting.
“The finishing of nature,” he states, “consists not in the smoothing
of surface, but the filling of space, and the multiplication of life
and thought;” and hence he draws the conclusion, that “finishing
means, in art, simply telling more truth.” Titian, Tintoret, Bellini,
and Veronese have, as he has shewn, wrought upon this principle,
delineating vein by vein in the leaf of the vine, petal by petal in
the borage-blossoms, the very snail-shells on the ground, the stripe
of black bark in the birch-tree, and the clusters of the ivy-leaved
toad-flax in the rents of their walls; and we have seen that a modern
artist, Delaroche, considers a _finish_ of _inconceivable minuteness_
as neither disturbing the repose of the masses, nor interfering with
the general effect in a picture.

The Pre-Raphaelites, therefore, may appeal to high authority for
the cardinal doctrine of their creed; and whatever be their errors
in judgment or in taste, they have inaugurated a revolution which
will release art from its fetters, and give it a freer and a nobler
aim. Nature is too grand in her minuteness, and too beautiful in her
humility, to be overlooked in the poetry of art. If her tenderest and
most delicate forms are worthy of admiration, she will demand from the
artist his highest powers of design. If the living organizations of the
teeming earth, upon which we hourly tread, are matchless in structure,
and fascinating in colour, the palette of the painter must surrender
to them its choicest tints. In the foreground of the highest art, the
snail-shell may inoffensively creep from beneath the withered leaf or
the living blade; the harebell and the violet may claim a place in the
sylvan dell; the moss may display its tiny frond, the gnarled oak or
the twisted pine may demand the recognition of the botanist, while the
castle wall rises in grandeur behind them, and the gigantic cliffs or
the lofty mountain range terminate the scene.

If these views are sound, the man of taste will no longer endure
slovenliness in art. He will demand truth as well as beauty in the
landscape; and that painter may change his profession who cannot
impress geology upon his rocks, and botany upon his plants and trees,
or who refuses to display, upon his summer or his autumn tablet, the
green crop as well as the growing and the gathered harvest. Thus
enlarged in its powers and elevated in its purposes, the art of
painting will be invested with a new character, demanding from its
votaries higher skill and more extended knowledge. In former times, the
minute and accurate delineation of nature was a task almost impossible,
requiring an amount of toil which could hardly be repaid even when
slightly performed; but science has now furnished art with the most
perfect means of arresting, in their most delicate forms, every object,
however minute, that can enter into the composition of a picture. These
means are the arts of photography and stereoscopic re-combination,
when rightly directed, and it is the object of the present chapter
to shew how the artist may best avail himself of their valuable and
indispensable aid.

Every country and district, and even different parts of the same
district, have a Flora and Geology peculiar to themselves; and the
artist who undertakes to represent its beauties owes to truth the
same obligations as the botanist who is to describe its plants, or
the mineralogist its rocks and stones. The critic could not, in
former times, expect more details from his unaided pencil than it
has generally furnished; but with the means now at his command, he
must collect, like the naturalist, all the materials for his subject.
After the camera has given him the great features of his landscape, he
must appeal to it for accurate delineations of its minuter parts,—the
trunks, and stems, and leafage of his trees—the dipping strata of
its sandstone beds—the contortions of its kneaded gneiss, or the
ruder features of its trap and its granite. For the most important of
these details he will find the camera, as at present constructed, of
little service. It is fitted only to copy _surfaces_; and therefore,
when directed to solid bodies, such as living beings, statues, &c.,
it gives false and hideous representations of them, as I have shewn
in a preceding chapter. It is peculiarly defective when applied to
parts of bodies at different distances from it, and of a less diameter
than the lens. The photograph of a cube taken by a lens of a greater
diameter, will display _five_ of its sides in a position, when its true
perspective representation is simply a single square of its surface.
When applied to trees, and shrubs, and flowers, its pictures are still
more unsatisfactory. Every stem and leaf smaller than the lens, though
absolutely opaque, is transparent, and leaves and stems behind and
beyond are seen like ghosts through the photographic image.

[Illustration: FIG. 48.]

This will be understood from Fig. 48, in which LL is the lens of the
camera, AB the breadth of the trunk or stem of a tree less than LL in
width. Draw LA, LB, touching AB in the points A, B, and crossing at
C. Objects behind AB, and placed within the angle ACB, will not have
any images of them formed by the lens LL, because none of the rays
which proceed from them can fall upon the lens, but objects placed
within the angle ECF, however remote be their distance, will have
images of them formed by the lens. If D, for example, be a leaf or a
fruit, or a portion of a branch, the rays which it emits will fall
upon the portions L_m_, L_n_ of the lens, determined by drawing D_m_,
D_n_ touching AB, and an image of it will be formed in the centre of
the photographic image of AB, as if AB were transparent. This image
will be formed by all the portions of the surface of the lens on which
the shadow of AB, formed by rays emanating from D, would not fall. If
the object D is more remote, the shadow of AB will diminish in size,
and the image of the object will be formed by a greater portion of the
lens. If the sun were to be in the direction MN, his image would appear
in the centre of the trunk or stem, corresponding to AB, Fig. 49.

[Illustration: FIG. 49.]

If the stem occupies any other position, _ab_, Fig. 48, in the
landscape, objects, such as _d_, within the angle _ecf_, will have
images of them formed within the corresponding portion of the trunk or
stem. Hence, if AB, Fig. 49, represents the shadow of the stem across
the lens LL, the image of any object, which if luminous would give this
shadow, will be formed within the photographic image of the stem, and
as every part of it may have branches, or leaves, or fruit behind it,
its photographs will be filled with their pictures, which will have the
same distinctness as other equidistant parts of the landscape.

These observations are applicable to the limbs and slender parts of
animate and inanimate figures, when they are of a less size than the
lens with which their photograph is taken. They will be transparent
to all objects behind them, and their true forms and shades cannot be
taken with the cameras now in use.[60]

In order, therefore, to collect from nature the materials of his
profession, the artist must use a camera with a lens not much larger
than the pupil of his eye, and with such an instrument he will obtain
the most correct drawings of the trunks and stems of trees, of the
texture and markings of their bark, of the form of their leaves, and
of all those peculiarities of structure and of leafage by which alone
the trees of the forest can be distinguished. In like manner, he will
obtain the most correct representations of the rocks and precipices,
and the individual stones[61] which may enter into his picture,—of
the plants which spring from their crevices or grow at their base,
and of those flowers in their native grace and beauty, which hitherto
he has either drawn from recollection, or copied from the formal
representations of the botanist.

[60] By using large lenses, we may obtain the picture of an object
within the picture of an opaque one in front of it; and with a
telescope, we may see through opaque objects of a certain size. Many
singular experiments may be made by taking photographs of solid
objects, simple or compound, with lenses larger than the objects
themselves.

[61] In a landscape by Mr. Waller Paton, called the “Highland Stream,”
now in the Edinburgh Exhibition, the foreground consists principally
of a bed of water-worn stones, on the margin of a pool at the bottom
of a waterfall. The stones are so exquisitely painted, that nature
only could have furnished the originals. We may examine them at a few
inches’ distance, and recognise forms and structures with which we have
been long familiar. A water-ousel, peculiar to Scottish brooks and
rivers, perched upon one of them, looks as anxiously around as if a
schoolboy were about to avail himself of the missiles at his feet.

In addition to their correctness as true representations of natural
forms, photographs have a peculiar value, for which no labour or skill
on the part of the artist can compensate. In drawing the sketch of a
landscape, or delineating the trees, rocks, and foliage which are near
him, or the objects in the middle or remote distance, several hours
must be spent. During this period, the landscape and its individual
parts are undergoing no inconsiderable change. A breeze may disturb
the masses of his foliage, and bend his tree stems, and ruffle his
verdure, and throw new reflected lights upon the waving crops, while
every direct light is changing in intensity and direction during the
culmination or descent of the sun. What he has delineated in the
morning will hardly correspond with what he draws at noon, and the
distances which at one time are finely marked in aerial perspective,
will disappear, or even suffer inversion by variations in the intensity
and position of the haze. If cottages, or castles, or buildings of
any kind, enter into the picture, the shadows of their projections,
and the lights upon their walls and roofs will, in sunshine, undergo
still greater variations, and the artist will be perplexed with the
anachronisms and inconsistencies _of his choicest materials_. The
landscape thus composed in patches will, in its photograph, have a
very different aspect, as much in its forms as in its lights and
shadows. The truths of nature are fixed at one instant of time; the
self-delineated landscape is embalmed amid the co-existing events of
the physical and social world. If the sun shines, his rays throw their
gilding on the picture. If the rain-shower falls, the earth and the
trees glisten with its reflexions. If the wind blows, the partially
obliterated foliage will display the extent of its agitation. The
objects of still life, too, give reality and animation to the scene.
The streets display their stationary chariots, the esplanade its
military array, and the market-place its colloquial groups, while
the fields are studded with the forms and attitudes of animal life.
The incidents of time and the forms of space are thus simultaneously
recorded, and every picture from the sober palette of the sun becomes
an authentic chapter in the history of the world.[62]

[62] These views are well illustrated by the remarkable photographs of
the Crimean war.

But, however valuable photography has become to the artist, science
has recently given him another important auxiliary. In order to make
this available, he must employ a small pocket binocular camera, to
take double pictures to be united in the stereoscope. His trees will
thus exhibit the roundness of their trunks and stems, the leaves and
branches will place themselves at their proper distance, and he will
discover the reason of peculiar effects which in the plane photograph
he has been unable to understand. Seeing that his own picture is to be
upon a plane surface, I can hardly expect to convince the artist that
he will obtain more information by reproducing the original in relief.
It is a fact, however, beyond dispute, that effects are produced by
the stereoscopic union of two plane photographs which are invisible in
the single picture. These effects, which are chiefly those of lustre
and shade, are peculiarly remarkable in Daguerreotype, and it is by
no means easy to explain the cause. In a Daguerreotype, for example,
of two figures in black bronze, with a high metallic lustre, it is
impossible, by looking at the single picture, to tell the material of
which they are made; but the moment they are united into stereoscopic
relief their true character is instantly seen. In a Daguerreotype of
Alexander and Bucephalus, portions of the figure seem as if shaded
with China ink of a nearly uniform tint, but when seen in relief the
peculiar shade entirely disappears. The stereoscopic combination of
two surfaces of different intensities, though of the same colour,
produces effects which have not yet been sufficiently studied. But,
independently of these peculiarities, the artist will certainly derive
more aid from his landscape in relief, and from the study of its
individual parts, in their roundness and relative distances, than when
he examines them in their plane representations. The shadows which the
branches of leaves cast upon the trunks and stems of his trees he will
be able to trace to the causes which produce them. Effects in outline,
as well as in light and shadow, which may perplex him, will find an
explanation in the relative distances and differences of apparent
magnitude of individual parts; and, after becoming familiar with his
landscape in relief, as it exists in Nature, he cannot fail to acquire
new principles and methods of manipulation. Nature flattened upon paper
or metal, and Nature round and plump, as if fresh from the chisel of
the Divine sculptor, must teach very different lessons to the aspiring
artist.

The historical painter, or the more humble artist who delineates the
scenes of common or domestic life, will derive from the photographic
camera and the stereoscope advantages of equal importance. The
hero, the sage, and the martyr, drawn from living originals, may
be placed in the scenes where they suffered, or in the localities
which they hallowed. The lawgiver of Egypt, though he exists only
in the painter’s eye, may take his place beside the giant flanks of
Horeb or the awe-inspiring summit of Mount Sinai; and He whom we may
not name may challenge our love and admiration amid the sun-painted
scenes of his youth, of his miracles, and of his humiliation. The
fragments of ancient grandeur which time and war have spared, the
relics of bygone ages which have resisted the destructive elements,
will, as the materials of art, give reality and truth to the pictorial
history of times past, while the painter of modern events can command
the most accurate representations not only of the costume, but of
the very persons of the great men whose deeds he is called upon to
immortalize. The heroes of the Crimean war, whether friends or foes,
will be descried in the trenches in which they fought, amid the ranks
which they led to victory, or among the wrecks of the fatal encounter
in which they fell. The sun will thus become the historiographer of
the future, and in the fidelity of his pencil and the accuracy of
his chronicle, truth itself will be embalmed and history cease to be
fabulous.

But even in the narrower, though not less hallowed sphere of domestic
life, where the magic names of kindred and home are inscribed, the
realities of stereoscopic photography will excite the most thrilling
interest. In the transition forms of his offspring, which link infancy
with manhood, the parent will recognise the progress of his mortal
career, and in the successive phases which mark the sunset of life,
the stripling in his turn will read the lesson that his pilgrimage too
has a term which must close. Nor are such delineations interesting
only as works of art, or as incentives to virtue; they are instinct
with associations vivid and endearing. The picture is connected with
its original by sensibilities peculiarly tender. It was the very light
which radiated from her brow,—the identical gleam which lighted up her
eye,—the hectic flush or the pallid hue that hung upon her cheek, which
pencilled the cherished image, and fixed themselves for ever there.




CHAPTER XI.

APPLICATION OF THE STEREOSCOPE TO SCULPTURE,

ARCHITECTURE, AND ENGINEERING.


To the arts of sculpture and architecture, the processes of binocular
photography and stereoscopic combination are particularly applicable.
The landscape painter has every day within his reach examples of the
picturesque, the wild and the sublime in nature. In the fields which
surround him, in the river, or even in the “brook that bubbles by,” on
the shore, on the heath, or on the mountain side, he has the choice of
materials for every department of his art. The sculptor has no such
advantage. Swathed in impenetrable drapery the human figure mocks his
eager eye, and it is only by stolen glances, or during angel visits,
few and far between, that he can see those divine forms which it is his
business to portray. He must therefore quit his home and seek for the
models of ancient and modern art. In the British Museum, in the Louvre,
in the Vatican, and in the repositories of art in Berlin, Munich, and
other European cities, he must spend months and years in the study of
his profession. He must copy, day after day, those master triumphs of
genius which the taste of ages has consecrated, and gather from their
study the true principles of his art. Transferred to his own studio,
these copies will be his instructor and his guide. They will exhibit
to him forms more than human, though human still, embodying all that
is true and beautiful in what might be man. The value of these copies,
however, depends on the skill and care with which they have been taken;
but no labour however great, and no power of drawing however masterly,
can give even an approximate idea either of the outline or round of
solid figures, whether single or in groups. Light and shade can alone
evolve those muscular prominences, or those soft and sphere-like
relievos which give such power and beauty to forms, male and female;
but how can an artist catch and fix those lights and shades which give
relief to the parts which they illuminate or obscure? The light of
the sun, even in a cloudless sky, is ever varying in intensity, and
the breadth and direction of the shadows which he casts are varying
from hour to hour. In a cloudy day, the motion of the clouds, and the
varying reflexions within his apartment, subject the lights and shadows
to constant change. The portions of the drawing executed in the morning
will not harmonize with what is drawn at noon, or during the decline
of day. We consider it, therefore, impossible to execute a drawing of
a statue, or of a group of statues, from which the artist can have
anything like an accurate idea of the forms which compose them.

From all these difficulties the sculptor has been relieved by the
invention of the photographic process. He may thus take copies of
statues in a few minutes, and take them in all their aspects, and as
seen at various distances, and in this manner he will obtain drawings
with the shadows as they existed at a particular instant, so that the
lights and shades, upon every individual part of the statue, will be
correctly related to each other. But valuable as these drawings are,
compared with those executed by the pencil, their value becomes tenfold
greater when they are taken with the binocular camera, and with small
lenses, as already described. When combined in the stereoscope, he may
reproduce the statue in relief, in all its aspects, and of different
sizes, and derive from its study the same advantages which the statue
itself would have furnished. In one respect the creations of the
stereoscope surpass the original. While the artist is surveying and
drawing instruction from the marble prototype, its lights and shadows,
and consequently the delicate forms, convex and concave, by which they
are produced, are constantly changing, whereas, in the stereoscopic
statue, everything is fixed and invariable.[63] In taking busts and
statues from the living subject, the sculptor will derive great
advantage from the stereoscope. Double pictures of the whole, or of any
portion of the subject, may be taken and raised into relief, and from
such binocular pictures, executed on one side of the globe, an artist,
on the other side, may complete an admirable statue. The dying and the
dead may thus be modelled without the rude contact of a mask, and those
noble forms perpetuated which affection or gratitude has endeared.

[63] A French sculptor has actually modelled a statue from the
stereoscopic relief of binocular pictures.

We must warn the sculptor, however, against the employment of binocular
pictures taken with large lenses. Not only will the individual picture
be deformed, but a double deformity will be induced by their union; and
whether he copies from a statue or from a living figure, his work must
be defective, even to an ordinary eye.

In architecture, and all those arts in which ornamental forms are
given to solid materials, the binocular camera and the stereoscope
will be found indispensable. The carvings of ancient, or mediæval,
or modern art may be copied and reproduced in relief, whatever be
the material from which they have been cut. The rich forms of Gothic
architecture, and the more classical productions of Greek and Roman
genius, will swell the artist’s portfolio, and possess all the value
of casts. With the aid of the Kaleidoscope the modern artist may
surpass all his predecessors. He may create an infinite variety of
those forms of symmetry which enter so largely into the decorative
arts; and if the individual forms, which constitute the symmetrical
picture, are themselves solid, the binocular-kaleidoscopic pictures,
taken photographically, will be raised into the original relief of
their component parts, or they may be represented directly to the eye
in relief, by semi-lenses placed at the ocular extremities of the
reflecting plates.[64] If the symmetrical forms are taken from lines
in the same plane, no relief will be obtained from the kaleidoscopic
pictures.

[64] See my Treatise on the Kaleidoscope, second edition, just
published.

But it is not merely to the decorative parts of architecture that the
stereoscope is applicable. The noblest edifices, whether of a civil, a
religious, or a military character, which he could otherwise study only
as a traveller, and represent in hurried and imperfect sketches, will,
when taken binocularly, stand before him in their full relief and
grandeur, reflecting to his eye the very lights and shadows which at a
given hour the sun cast upon their walls.

In the erection of public buildings, hourly or daily photographs have
been taken of them, to shew to the absent superintendent the progress
of his work; but these pictures will be still more expressive if
binocular ones are combined in the stereoscope.

To the engineer and the mechanist, and the makers of instruments of all
kinds, the stereoscope will be of inestimable value. The difficulty of
representing machinery is so great that it is not easy to understand
its construction or its mode of operation from plans and perspective
views of it. The union of one or two binocular pictures of it, when
thrown into relief, will, in many cases, remove the difficulty both
of drawing and understanding it. Photographs of machinery, however,
consisting of a number of minute parts at different distances from
the eye, have, when taken by large lenses, all the defects which we
explained in reference to trees and their branches and leaves. Supports
and axles will be transparent, and the teeth of the wheels, and the
small and distant parts of the mechanism, will be seen through all the
nearer parts whose width is less than the diameter of the lens.

In taking a binocular picture of a machine or instrument consisting
of various parts, that minute accuracy which is necessary to give
the true form and expression of the human face is not required;
but if it should happen that, in a correct binocular view of the
object, parts are concealed which it would be useful to see, we must
discover the binocular angle which will shew these parts in the two
pictures, or, generally speaking, which will give the best view of
the mechanism, and then adjust the lenses of the camera to give the
desired representations of it. These observations will be found useful
in obtaining stereoscopic views of the structures in carpentry and
ship-building.




CHAPTER XII.

APPLICATION OF THE STEREOSCOPE TO NATURAL HISTORY.


In treating of those objects of natural history which enter into the
composition of landscape scenery, such as trees, plants, and rocks, we
have pointed out the method of having them accurately drawn for the
stereoscope; but it is to the importance of stereoscopic photography
in natural history as a science that we propose to devote the present
Chapter.

When we reflect upon the vast number of species which have been
described by zoologists, the noble forms of animated nature, whether
wild or domesticated, and the valuable services which many of them
perform as the slaves of man, we can hardly attach too much importance
to the advantage of having them accurately delineated and raised into
stereoscopic relief. The animal painters of the present day,—the
Landseers, the Cowpers, and the Ansdells, have brought this branch of
their art to a high degree of perfection, but the subjects of their
pencil have been principally dogs, horses, deer, and cattle, and a few
other animals, with which they are well acquainted, and specimens of
which were within their reach. To give accurate representations of
giraffes, hyænas, and the rarer animals which are found alive only in
zoological gardens and travelling caravans, is a more difficult task,
and one which has been necessarily intrusted to inferior hands. In this
branch of his art the photographer is perplexed with the difficulty of
arresting his subject in a position of repose and in the attitude which
he requires. But this difficulty will diminish as his materials become
more sensitive to light; and means may be found for fixing, without
constraint, certain animals in the desired position. We have seen the
portrait of a dog taken with such minute accuracy that the slightest
trace of any motion could not be perceived. Its master directed his
attention to a piece of bread, and he stood firmly waiting for his
reward. Considering truth as an essential element in all photographs,
we are unwilling to counsel the artist to have recourse to a large lens
for the purpose of accelerating his process by seizing his restless
object in a single instant of time; but what cannot be tolerated in the
human form may be permitted in animal portraiture as a necessary evil.
The divine lineaments and delicate forms which in man the intellect
and the affections conspire to mould, are concealed under the shaggy
drapery of the world of instinct; and even if they existed and were
perceived, could hardly be appreciated by those who have not studied
its manners and submitted to its laws. But even in the present state
of photography such a celerity of process has been attained that a
distinguished amateur in Edinburgh has constructed a portable camera,
which, by pulling a trigger, instantaneously records upon its sensitive
retina the surf which is hurrying to the shore, or the stranger who
is passing in the street. With such an instrument, in such hands, the
denizens of the jungle or of the plains may be taken captive in their
finest attitudes and in their most restless moods. Photographs thus
obtained will possess a value of no ordinary kind, and when taken in
the binocular camera and raised into relief by the stereoscope, will be
valuable auxiliaries to the naturalist, and even to the painters and
the poets whose works or whose lyrics may require an introduction to
the brutes that perish.

In representing with accuracy the osteology and integuments of the
zoological world—the framework which protects life, and to which life
gives activity and power, the aid of the stereoscope is indispensable.
The repose of death, and the sharp pencil which resides in the small
lens, will place before the student’s eye the skeleton, clothed
or unclothed, in accurate perspective and true relief, while he
contemplates with wonder, in their true apparent magnitude, the
gigantic Mastodon, the colossal Megatherion, and the huge Dinornis, or
examines the crushed remains of the lengthened Saurian, or the hollow
footsteps which ancient life has impressed on the massive sandstone or
the indurated clay.

In the other branches of natural history, ichthyology, ornithology,
conchology, &c., the stereoscope will be found equally useful. In
entomology, where insects are to be represented, the microscopic
binocular camera must be used; and in order to prevent the legs, the
antennæ, and other small parts of the object from being transparent,
and therefore spotted, with the images of objects or parts beyond them,
as explained in a preceding chapter, the smallest lenses should be
employed.

The roots and bulbs which are raised by the agriculturist and the
horticulturist, the turnip, the beet, the carrot, and the onion; and
the fruits raised in the orchard, on the wall, or in the hothouse, may
be exhibited in all their roundness and solidity in the stereoscope;
and as articles of commerce they might be purchased on the authority
of their pictures in relief. The microscopic stereoscope will, in like
manner, give accurate magnified representations in relief of grains and
seeds of all kinds, and by comparing these with the representations of
those of a standard form and quality, the purchaser may be enabled to
form a better idea of their excellence than if he saw them with his own
eyes, or had them in his own hands.




CHAPTER XIII.

APPLICATION OF THE STEREOSCOPE TO EDUCATIONAL PURPOSES.


The observations contained in the preceding chapters prepare us for
appreciating the value of the stereoscope as an indispensable auxiliary
in elementary as well as in professional education. When the scholar
has learned to read, to write, and to count, he has obtained only the
tools of instruction. To acquire a general knowledge of the works of
God and of man—of things common and uncommon—of the miracles of nature
and of art, is the first step in the education of the people. Without
such knowledge, the humblest of our race is unfit for any place in the
social scale. He may have learned to read his Bible, and he may have
read it after he had learned to read;—he may have committed to memory
every sentence in the Decalogue;—he may have packed into the storehouse
of his brain all the wisdom of Solomon, and all the divine precepts
of a greater than Solomon, while he is utterly ignorant of everything
above him, around him, and within him,—ignorant, too, of the form, the
magnitude, and the motions of his terrestrial home,—ignorant of the
gigantic structures which constitute the material universe,—ignorant of
the fabrics which industry prepares for his use, and of the luxuries
which commerce brings from the ends of the earth and places at his
door,—ignorant even of the wonderful operations of that beneficent
commissariat, which is every moment, while he sleeps and dreams,
elaborating the materials by which he is fed and clothed.

Were we to say, though we do not say it, that in our own country the
teachers, so penuriously endowed by the State, are not much in advance
of their pupils, we should err only in stating what is not universally
true; and yet there are men of influence and character insisting upon
the imposition of sectarian tests, and thus barricading our schools
against the admission of the wisest and the fittest masters! And while
every civilized community in the world is eagerly teaching their
people, irrespective of religious creeds, the same bigots, civil and
ecclesiastical, in our own country, have combined to resist the only
system of education which can stem the tide of vice and crime which is
desolating the land.

Missionary labour and reformatory institutions, valuable as they are,
presuppose an educated community. To instruct and reform a race that
can neither read their Bible nor derive knowledge from books, is a
task beyond human achievement. The dearest interests of society,
therefore, call loudly for _Secular Education_,—the greatest boon which
philanthropy ever demanded from the State. The minister who, in the
face of sectarian factions, dares not identify himself with a large
legislative measure for the education of the people, and resigns office
when he fails to carry it, prefers power to duty, and, if he ever
possessed it, divests himself of the character of a statesman and a
patriot. He may be justified in punishing the law-breaker who cannot
read his statutes, but he is himself the breaker of laws of a higher
order, and sanctioned by a higher tribunal.

If the education of the people is to be attempted either by partial or
comprehensive legislation, the existing system is utterly inefficient.
The teacher, however wisely chosen and well qualified, has not at his
command the means of imparting knowledge. He may pour it in by the
ear, or extract it from the printed page, or exhibit it in caricature
in the miserable embellishments of the school-book, but unless he
teaches through the eye, the great instrument of knowledge, by means
of truthful pictures, or instruments, or models, or by the direct
exhibition of the products of nature and of art, which can be submitted
to the scrutiny of the senses, no satisfactory instruction can be
conveyed.[65] Every school, indeed, should have a museum, however
limited and humble. Even from within its narrow sphere objects of
natural history and antiquities might be collected, and duplicates
exchanged; and we are sure that many a chimney-piece in the district
would surrender a tithe of its curiosities for the public use. Were
the British Museum, and other overflowing collections, to distribute
among provincial museums the numerous duplicates which they possess,
they would gradually pass into the schools, and before a quarter of a
century elapsed, museums would be found in every proper locality.

[65] “The importance of establishing a _permanent Museum of Education_
in this country, with the view of _introducing improvements in the
existing methods of instruction_, and specially directing public
attention in a practical manner to the question of National Education,
has been of late generally recognised.”—_Third Report of the
Commissioners for the Exhibition of 1851_, presented to both Houses of
Parliament, p. 37. Lond., 1856.

As we cannot indulge in the hope that any such boon will be conferred
on our educational institutions, it becomes an important question how
far it is possible to supply the defect by the means within our reach.
The photographic process may be advantageously employed in producing
accurate representations of those objects, both of nature and of art,
which it would be desirable to describe and explain in the instruction
of youth; but as experience has not yet taught us that such pictures
will be permanent, and capable of resisting the action of time and the
elements, it would be hazardous to employ them in the illustration
of popular works. It is fortunate, however, that the new art of
galvanography enables us, by a cheap process, to give to photographs
the permanence of engravings, and to employ them in the illustration of
educational works.[66]

[66] This fine invention we owe to Mr. Paul Pretsch, late director of
the Imperial Printing Office at Vienna. It is secured by patent, and is
now in practical operation in Holloway Place, Islington.

But however much we may value such an auxiliary, representations or
drawings, on a plane, of solids or combinations of solids at different
distances from the eye, are in many cases unintelligible even to
persons well informed; so that, on this ground alone, we cannot but
appreciate the advantages to be derived from binocular pictures and
their stereoscopic relievo, not only in the instruction of youth, but
in the diffusion of knowledge among all ranks of society.

One of the most palpable advantages to be derived from the illustration
of school-books by pictures in relief, is the communication of correct
knowledge of the various objects of natural history. If, as we have
already shewn, the naturalist derives important assistance in his
studies from correct representations of animated nature, how much more
valuable must they be to the scholar who never saw, and may never see
the objects themselves. In the department of zoology, the picture
might frequently be taken from the living animal, standing before the
camera in vigorous life and transcendent beauty; or when this cannot
be done, from the fine specimens of zoological forms which adorn our
metropolitan and provincial museums. The trees and plants, too, of
distant zones, whether naked in their osteology, or luxurious in their
foliage, would shew themselves in full relief;—the banyan, clinging
with its hundred roots to the ground,—the bread-fruit tree, with its
beneficent burden,—the cow tree, with its wholesome beverage,—the
caoutchouc tree, yielding its valuable juice,—or the deadly upas,
preparing its poison for the arrow of the savage or the poniard of the
assassin.

With no less interest will the schoolboy gaze on the forms of insect
life, which will almost flutter before him, and on the tenants of
the air and of the ocean, defective only in the colours which adorn
them. The structures of the inorganic world will equally command
his admiration. The minerals which have grown in the earth beneath
his feet, and the crystals which chemistry has conjured into being,
will display to him their geometric forms, infinite in variety, and
interesting from their rarity and value. Painted by the very light
which streamed from them, he will see, in their retiring and advancing
facets, the Kohinoor and other diamonds, and the huge rubies, and
sapphires, and emeralds, which have adorned the chaplet of beauty, or
sparkled in the diadem of kings. The gigantic productions of the earth
will appeal to him with equal power,—the colossal granites, which have
travelled in chariots of ice, and the rounded boulders, which have
been transported in torrents of mud; and while he admires, in their
strong relief, the precipices of ancient lava—the Doric colonnades
of basalt—the upheaved and contorted strata beside them, and the
undisturbed beds which no internal convulsions have shaken, he will
stand appalled before the fossil giants of the primeval world that trod
the earth during its preparation for man, and have been embalmed in
stone to instruct and to humble him.

In acquiring a knowledge of physical geography, in which the
grander aspects of nature arrest our attention, their stereoscopic
representations will be particularly instructive. The mountain range,
whether abrupt in its elevation, or retiring from our view,—whether
scarred with peaks or undulating in outline,—the insulated mountain
tipped with snow or glowing with fire,—the volcano ejecting its burning
missiles,[67]—the iceberg fixed in the shore, or floating on the
deep,—the deafening cataract,—the glacier and its moraines, sinking
gently to the plains,—and even the colossal wave with its foaming
crest, will be portrayed in the binocular camera, and exhibited in all
the grandeur and life of nature.

[67] An accomplished traveller, the Rev. Mr. Bridges, who ascended
Mount Etna for the purpose of taking Talbotype drawings of its scenery,
placed his camera on the edge of the crater to obtain a representation
of it. No sooner was the camera fixed and the sensitive paper
introduced, than an eruption took place, which forced Mr. Bridges to
quit his camera in order to save his life. When the eruption closed, he
returned to collect the fragments of his instrument, when, to his great
surprise and delight, he found that his camera was not only uninjured,
but contained a picture of the crater and its eruption.

The works of human hands,—the structures of civilisation, will stand
before the historian and the antiquary, as well as the student, in
their pristine solidity, or in their ruined grandeur,—the monuments by
which sovereigns and nations have sought to perpetuate their names,—the
gorgeous palaces of kings,—the garish temples of superstition,—the
humbler edifices of Christian faith,—the bastions and strongholds of
war, will display themselves in the stereoscope as if the observer were
placed at their base, and warmed by the very sun which shone upon their
walls.

Although few of our village youth may become sculptors, yet the
exhibition of ancient statues in their actual relief, and real apparent
magnitude, cannot fail to give them salutary instruction and rational
pleasure. To gaze upon the Apollo Belvidere,—the Venus de Medici,—the
Laocoon, and the other masterpieces of ancient art, standing in the
very halls which they now occupy; or to see the _chef d’œuvres_ of
Canova, Thorvaldsen, and Chantrey, or the productions of living artists
in their own studio, with the sculptor himself standing by their side,
will excite an interest of no ordinary kind.

From the works of the architect, the engineer, and the mechanist,
as exhibited in full relief, the student, whether at our schools or
colleges, will derive the most valuable instruction. The gigantic
aqueducts of ancient and modern times,—the viaducts and bridges which
span our valleys and our rivers, and the machinery in our arsenals,
factories, and workshops, will be objects of deep interest to the
general as well as the professional inquirer.

There is yet another application of the stereoscope to educational
purposes, not less important than those which have been mentioned.
In the production of diagram representing instruments and apparatus,
which cannot be understood from drawings of them on a plane, it will
be of incalculable use to the teacher to have stereoscopic pictures
of them. In every branch of physical science, diagrams of this kind
are required. When they are intended to represent apparatus and
instruments, either for illustrating known truths, or carrying on
physical researches, binocular pictures can be easily obtained; but
when the diagrams have not been taken from apparatus, but are merely
combinations of lines, we can obtain binocular photographs of them only
from models constructed on purpose. These models will give binocular
representations in various azimuths, so that the true position of
planes at different inclinations, and lines at various angles with
each other, and at different distances from the eye, will be readily
apprehended. Astronomical diagrams, in which orbits, &c., may be
represented by wires, and optical figures, in which the rays may be
formed by threads or wires, would be thus easily executed.

Among the binocular diagrams, consisting of white lines upon a black
ground, which have been executed in Paris, there is one representing
the apparatus in which a ray of light, polarized by reflexion from a
glass plate, passes through a crystallized film perpendicular to the
plane of the paper, and is subsequently analysed by reflexion from
another plate at right angle to the following plate. This diagram, when
placed in relief by the stereoscope, gives as correct an idea of the
process as the apparatus itself.

As an auxiliary in the investigation of questions of difficulty and
importance, both in physics and metaphysics, the stereoscope is
peculiarly valuable. It enables us to place in its true light the
celebrated theory of vision on which Bishop Berkeley reared the ideal
philosophy, of which he was the founder, and it gives us powerful aid
in explaining many physical phenomena which have long baffled the
ingenuity of philosophers. It would be out of place to give any account
of these in a work like this, but there is one so remarkable, and at
the same time so instructive, as to merit special notice. In order to
exhibit, by means of _three_ diagrams, a solid in relief and hollow at
the same time, which had not been previously done, I executed three
drawings of the frustum of a cone, resembling those in Fig. 31, so
that the _left_-hand one and the middle one gave the _hollow_ cone,
while the _middle_ one and the _right_-hand one gave the _raised_
cone. Having their summits truncated, as in the figure, the cones
exhibit, in the one case, a circle at the bottom of the hollow cone,
and in the other, a circle on the summit of the raised cone. When these
three diagrams[68] are placed in an open lenticular stereoscope, or
are united by the convergency of the optical axes, so that we can not
only see the _hollow_ and the _raised_ cones, but the flat drawing on
each side of them, we are enabled to give an ocular and experimental
proof of the cause of the large size of the horizontal moon, of her
small size when in the meridian or at a great altitude, and of her
intermediate apparent magnitude at intermediate altitudes,—phenomena
which had long perplexed astronomers, and which Dr. Berkeley, rejecting
previous and well-founded explanations, ascribed to the different
degrees of brightness of the moon in these different positions.

[68] A binocular slide, copied from the one originally designed by
myself, forms No. 27 of the Series of white-lined diagrams upon a black
ground executed in Paris. The drawings, however, are too large for the
common stereoscope.

As the circular summit of the _raised_ cone _appears_ to be _nearest_
the eye of the observer, the summit of the _hollow_ cone _farthest_
off, and the similar central circle in the flat drawing on each side,
at an intermediate distance, the apparent distances from the eye of
different and equal circles will represent the apparent distance of
the moon in the _zenith_, or very high in the elliptical celestial
vault,—the same distance when she is in the _horizon_, and the same
when at an intermediate altitude. Being in reality of exactly the same
size, and at the same distance from the eye, these circular summits, or
sections of the cone, are precisely in the same circumstances as the
moon in the three positions already mentioned. If we now contemplate
them in the lenticular stereoscope, we shall see the circular summit of
the _hollow_ cone the _largest_, like the _horizontal_ moon, because
it _seems_ to be at the _greatest_ distance from the eye,—the circular
summit of the _raised_ cone the _smallest_, because it appears at
the _least_ distance, like the _zenith_ or culminating moon,—and the
circular summits of the flat cones on each side, of an _intermediate_
size, like the moon at an _intermediate_ altitude, because their
distance from the eye is intermediate. The same effect will be equally
well seen by placing three small wafers of the same size and colour on
the square summits of the drawings of the quadrangular pyramids, or
more simply, by observing the larger size of the square summit of the
hollow pyramid.

This explanation of the cause of the increased size of the horizontal
moon is rigorously correct. If any person should suspect that the
circles which represent the moon are unequal in size, or are at
different distances from the eye, they have only to cut the diagram
into three parts, and make each drawing of the frustum of the cone
occupy a different place in the binocular slide, and they will obtain
the very same results. Hence we place beyond a doubt the incorrectness
of Dr. Berkeley’s theory of the size of the horizontal moon,—a theory
to which the stereoscope enables us to apply another test, for if we
make one or more of these circles less bright than the rest, no change
whatever will be produced in their apparent magnitude.




CHAPTER XIV.

APPLICATION OF THE STEREOSCOPE TO PURPOSES OF AMUSEMENT.


Every experiment in science, and every instrument depending on
scientific principles, when employed for the purpose of amusement, must
necessarily be instructive. “Philosophy in sport” never fails to become
“Science in earnest.” The toy which amuses the child will instruct
the sage, and many an eminent discoverer and inventor can trace the
pursuits which immortalize them to some experiment or instrument which
amused them at school. The soap bubble, the kite, the balloon, the
water wheel, the sun-dial, the burning-glass, the magnet, &c., have all
been valuable incentives to the study of the sciences.

In a list of about 150 binocular pictures issued by the London
Stereoscopic Company, under the title of “Miscellaneous Subjects of the
‘Wilkie’ character,” there are many of an amusing kind, in which scenes
in common life are admirably represented. Following out the same idea,
the most interesting scenes in our best comedies and tragedies might
be represented with the same distinctness and relief as if the actors
were on the stage. Events and scenes in ancient and modern history
might be similarly exhibited, and in our day, binocular pictures of
trials, congresses, political, legislative, and religious assemblies,
in which the leading actors were represented, might be provided for the
stereoscope.

For the purpose of amusement, the photographer might carry us even
into the regions of the supernatural. His art, as I have elsewhere
shewn, enables him to give a spiritual appearance to one or more of his
figures, and to exhibit them as “thin air” amid the solid realities of
the stereoscopic picture. While a party is engaged with their whist or
their gossip, a female figure appears in the midst of them with all the
attributes of the supernatural. Her form is transparent, every object
or person beyond her being seen in shadowy but distinct outline. She
may occupy more than one place in the scene, and different portions
of the group might be made to gaze upon one or other of the visions
before them. In order to produce such a scene, the parties which are
to compose the group must have their portraits nearly finished in the
binocular camera, in the attitude which they may be supposed to take,
and with the expression which they may be supposed to assume, if the
vision were real. When the party have nearly sat the proper length
of time, the female figure, suitably attired, walks quickly into the
place assigned her, and after standing a few seconds in the proper
attitude, retires quickly, or takes as quickly, a second or even a
third place in the picture if it is required, in each of which she
remains a few seconds, so that her picture in these different positions
may be taken with sufficient distinctness in the negative photograph.
If this operation has been well performed, all the objects immediately
behind the female figure, having been, previous to her introduction,
impressed upon the negative surface, will be seen through her, and
she will have the appearance of an aerial personage, unlike the other
figures in the picture. This experiment may be varied in many ways.
One body may be placed within another, a chicken, for example, within
an egg, and singular effects produced by combining plane pictures
with solid bodies in the arrangement of the persons and things placed
before the binocular camera. Any individual in a group may appear more
than once in the same picture, either in two or more characters, and
no difficulty will be experienced by the ingenious photographer in
giving to these double or triple portraits, when it is required, the
same appearance as that of the other parties who have not changed their
place. In groups of this kind curious effects might be produced by
placing a second binocular slide between the principal slide and the
eye, and giving it a motion within the stereoscope. The figures upon
it must be delineated photographically upon a plate of glass, through
which the figures on the principal slide are seen, and the secondary
slide must be so close to the other that the figures on both may be
distinctly visible, if distinct vision is required for those which are
to move.

Another method of making solid figures transparent in a photograph
has been referred to in the preceding chapter, and may be employed in
producing amusing combinations. The transparency is, in this case,
produced by using a large lens, the margin of which receives the rays
which issue from bodies, or parts of bodies, situated _behind_ other
bodies, or parts of bodies, whose images are given in the photograph.
The body thus rendered transparent must be less in superficial extent
than the lens, and the body seen through it must be so far behind it
that rays emanating from it would fall upon some part of the lens, the
luminosity of this body on the photograph being proportional to the
part of the surface of the lens upon which the rays fall. This will be
readily understood from Figs. 48 and 49, and their description, and
the ingenious photographer will have no difficulty in producing very
curious effects from this property of large object-glasses.

One of the most interesting applications of the stereoscope is in
combining binocular pictures, constructed like the plane picture, used
in what has been called the _cosmorama_ for exhibiting dissolving
views. These plane pictures are so constructed, that when we view
them by reflected light, as pictures are generally viewed, we see a
particular scene, such as the Chamber of Deputies in its external
aspect; but when we allow no light to fall upon it, but view it by
transmitted light, we see the interior of the building brilliantly
lighted up, and the deputies listening to the debate. In like
manner, the one picture may represent two armies in battle array,
while the other may represent them in action. A cathedral in all its
architectural beauty may be combined with the same building in the act
of being burned to the ground; or a winter scene covered with snow
may be conjoined with a landscape glowing with the warmth and verdure
of summer. In the cosmorama, the reflected light which falls upon
the front of the one picture is obtained by opening a lid similar to
that of the stereoscope, as shewn at CD, Fig. 14, while another lid
opening behind the picture stops any light which might pass through
it, and prevents the second picture from being seen. If, when the
first picture is visible, we gradually open the lid behind it, and
close the lid CD before it, it gradually disappears, or _dissolves_,
and the second picture gradually appears till the first vanishes and
the second occupies its place. A great deal of ingenuity is displayed
by the Parisian artists in the composition of these pictures, and the
exhibition of them, either in small portable instruments held in the
hand, or placed on the table, or on a great scale, to an audience,
by means of the oxygen and hydrogen light, never fails to excite
admiration.

The pictures thus exhibited, though finely executed, have only that
degree of relief which I have called _monocular_, and which depends
on correct shading and perspective; but when the dissolving views are
obtained from binocular pictures, and have all the high relief given
them by their stereoscopic combination, the effect must be singularly
fine.

Very interesting and amusing effects are produced by interchanging
the right and the left eye pictures in the stereoscope. In general,
what was formerly convex is now concave, what was round is hollow, and
what was near is distant. The effect of this interchange is finely
seen in the symmetrical diagrams, consisting of white lines upon black
ground, such as Nos. 1, 5, 9, 12, 18 and 27 of the Parisian set; but
when the diagrams are not symmetrical, that is, when the one half is
not the reflected image of the other, such as Nos. 26, &c., which are
transparent polygonal solids, formed as it were by white threads or
wires, no effect, beyond a slight fluttering, is perceived. As the
right and left eye pictures are inseparable when on glass or silver
plate, the experiments must be made by cutting in two the slides on
Bristol board. This, however, is unnecessary when we have the power
of uniting the two pictures by the convergency of the optic axes to
a nearer point, as we obtain, in this case, the same effect as if we
had interchanged the pictures. The following are some of the results
obtained in this manner from well-known slides:—

In single portraits no effect is produced by the interchange of the
right and left eye pictures. If any loose part of the dress is in the
foreground it may be carried into the distance, and _vice versa_. In
one portrait, the end of the hat-band, which hung down loosely behind
the party, was made to hang in front of it.

In pictures of streets or valleys, and other objects in which the
foreground is connected with the middle-ground, and the middle-ground
with the distance, without any break, no effect is produced by the
interchange. Sometimes there is a little bulging out of the middle
distance, injurious to the monocular effect.

In the binocular picture of the Bridge of Handeck, the Chalet in the
foreground retires, and the middle distance above it advances.

In the picture of the sacristy of Notre Dame, the sacristy retires
within the cathedral.

In the Maison des Chapiteaux at Pompeii, the picture is completely
inverted, the objects in the distance coming into the foreground.

In the Daguerreotype of the Crystal Palace, the water in the
foreground, with the floating plants, retires and takes an inclined
position below a horizontal plane.

In the binocular picture of the lower glacier of Rosenlaui, the roof of
the ice-cave becomes hollow, and the whole foreground is thrown into a
disordered perspective.

In Copeland’s Venus, the arm holding the bunch of grapes is curiously
bent and thrown behind the head, while the left arm advances before the
child.

In the picture of the Greek Court in the Crystal Palace, the wall
behind the statues and columns advances in front of them.

The singular fallacy in vision which thus takes place is best seen in
a picture where a number of separate articles are placed upon a table,
and in other cases where the judgment of the spectator is not called
upon to resist the optical effect. Although the nose of the human face
should retire behind the ears yet no such effect is produced, as all
the features of the face are connected with each other, but if the nose
and ears had been represented separately in the position which they
occupy in the human head, the nearer features would have retired behind
the more remote ones, like the separate articles on a table.

We shall have occasion to resume this subject in our concluding chapter
on the fallacies which take place in viewing solids, whether raised or
hollow, and whether seen by direct or inverted vision.




CHAPTER XV.

ON THE PRODUCTION OF STEREOSCOPIC PICTURES FROM A SINGLE PICTURE.


Those who are desirous of having stereoscopic _relievos_ of absent or
deceased friends, and who possess single photographic portraits of
them, or even oil paintings or miniatures, will be anxious to know
whether or not it is possible to obtain from one plane picture another
which could be combined with it in the stereoscope; that is, if we
consider the picture as one seen by either eye alone, can we by any
process obtain a second picture as seen by the other eye? We have no
hesitation in saying that it is impossible to do this by any direct
process.

Every picture, whether taken photographically or by the eye, is
necessarily a picture seen by one eye, or from one point of sight; and,
therefore, a skilful artist, who fully understands the principle of
the stereoscope, might make a copy of any picture as seen by the other
eye, so approximately correct as to appear in relief when united with
the original in the stereoscope; but the task would be a very difficult
one, and if well executed, so as to give a relievo without distortion,
the fortune of the painter would be made.

When the artist executes a portrait, he does it from one point of
sight, which we may suppose fixed, and corresponding with that which
is seen with his _left_ eye. If he takes another portrait of the same
person, occupying exactly the same position, from another point of
sight, two and a half inches to the right of himself, as seen with
his _right_ eye, the two pictures will differ only in this, that
each point in the head, and bust, and drapery, will, in the second
picture, _be carried farther to the left of the artist_ on the plane
of representation. The points which project most, or are most distant
from that plane, will be carried farther to the left than those which
project less, the extent to which they are carried being proportional
to the amount of their projection, or their distance from the plane.
But since the painter cannot discover from the original or left-eye
plane picture the degree of prominence of the leading points of the
head, the bust, and the drapery, he must work by guess, and submit his
empirical touches, step by step, to the judgment of the stereoscope. In
devoting himself to this branch of the art he will doubtless acquire
much knowledge and dexterity from experience, and may succeed to a very
considerable extent in obtaining pictures in relief, if he follows
certain rules, which we shall endeavour to explain.

If the given portrait, or picture of any kind, is not of the proper
size for the stereoscope, it must be reduced to that size, by taking
a photographic copy of it, from which the right-eye picture is to be
drawn.

[Illustration: FIG. 50.]

In order to diminish the size of the diagram, let us suppose that the
plane on which the portrait is taken touches the back of the head,
and is represented in section by AB, Fig. 50. We must now assume,
under the guidance of the original, a certain form of the head, whose
breadth from ear to ear is EE″, N being the point of the nose in the
horizontal section of the head, E″NEN′, passing through the nose N, and
the lobes EE″ of the two ears. Let L, R be the left and right eyes of
the person viewing them, and LN the distance at which they are viewed,
and let lines be drawn from L and R, through L, N, E and E″, meeting
the plane AB on which the portrait is taken in _e′_, E‴, _n_, N′, _e_,
and E′. The breadth, E‴_e′_, and the distances of the nose from the
ears N′E′, N′E‴, being given by measurement of the photograph suited
to the stereoscope, the distances NN′, EE′, E″E‴ may be approximately
obtained from the known form of the human head, either by projection
or calculation. With these data, procured as correctly as we can, we
shall, from the position of the nose _n_, as seen by the right eye R,
have the formula

            LR × NN′
    N′_n_ = ————————
               NL.


The distance of the _right_ ear _e′_, from the right-eye picture, will
be,

    _ne′_ = _e′_N - N′_n_;

                   LR × EE′
    and as E′_e_ = —————————
                      EL.


The distance of the _left_ ear _e_, in the right-eye picture, from the
nose _n_, will be

    _ne_ = N′_n_ + N′E′ - E′_e_.

In order to simplify the diagram we have made the original, or left-eye
picture, a front view, in which the nose is in the middle of the face,
and the line joining the ears parallel to the plane of the picture.

When the position of the nose and the ears has been thus approximately
obtained, the artist may, in like manner, determine the place of the
pupils of the two eyes, the point of the chin, the summit of the
eyebrows, the prominence of the lips, and the junction of the nose with
the teeth, by assuming, under the guidance of the original picture,
the distance of these different parts from the plane of projection.
In the same way other leading points in the figure and drapery may be
found, and if these points are determined with tolerable accuracy the
artist will be able to draw the features in their new place with such
correctness as to give a good result in the stereoscope.

In drawing the right-eye picture the artist will, of course, employ as
the groundwork of it a faint photographic impression of the original,
or left-eye picture, and he may, perhaps, derive some advantage from
placing the original, when before the camera, at such an inclination
to the axis of the lens as will produce the same diminution in the
horizontal distance between any two points in the head, at a mean
distance between N and N′, as projected upon the plane AB. The line
N′E‴, for example, which in the left-eye photograph is a representation
of the cheek NE″, is reduced, in the right-eye photograph, to _ne′_,
and, therefore, if the photograph on AB, as seen by the right eye, were
placed so obliquely to the axis of the lens that N′_e_ was reduced
to _ne′_, the copy obtained in the camera would have an approximate
resemblance to the right-eye picture required, and might be a better
groundwork for the right-eye picture than an accurate copy of the
photograph on AB, taken when it is perpendicular to the axis of the
lens.

In preparing the right-eye picture, the artist, in place of using
paint, might use very dilute solutions of aceto-nitrate of silver,
beginning with the faintest tint, and darkening these with light till
he obtained the desired effect, and, when necessary, diminishing the
shades with solutions of the hypo-sulphite of soda. When the picture
is finished, and found satisfactory, after examining its relief in the
stereoscope, a negative picture of it should be obtained in the camera,
and positive copies taken, to form, with the original photographs, the
pair of binocular portraits required.




CHAPTER XVI.

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.




CHAPTER XVII.

ON CERTAIN DIFFICULTIES EXPERIENCED IN THE USE OF THE STEREOSCOPE.


There are many persons who experience great difficulty in uniting the
two pictures in the stereoscope, and consequently in seeing the relief
produced by their union. If the eyes are not equal in focal length,
that is, in the distance at which they see objects most distinctly;
or if, from some defect in structure, they are not equally good, they
will still see the stereoscopic relief, though the picture will be
less vivid and distinct than if the eyes were in every respect equal
and good. There are many persons, however, whose eyes are equal and
perfect, but who are not able to unite the pictures in the stereoscope.
This is the more remarkable, as children of four or five years of age
see the stereoscopic effect when the eye-tubes are accommodated to the
distance between their eyes. The difficulty experienced in uniting the
binocular pictures is sometimes only temporary. On first looking into
the instrument, _two_ pictures are seen in place of _one_; but by a
little perseverance, and by drawing the eyes away from the eye-tubes,
and still looking through them, the object is seen single and in
perfect relief. After having ceased to use the instrument for some
time, the difficulty of uniting the pictures recurs, but, generally
speaking, it will gradually disappear.

[Illustration: FIG. 52.]

In those cases where it cannot be overcome by repeated trials, it
must arise either from the distance between the lenses being greater
or less than the distance between the eyes, or from some peculiarity
in the power of converging the optical axes, which it is not easy to
explain.

If the distance between the pupils of the two eyes, E, E′, Fig. 52,
which has been already explained on Fig. 18, is _less_ than the
distance between the semi-lenses L, L′, then, instead of looking
through the middle portions _no, n′o′_, of the lenses, the observer
will look through portions between _o_ and L, and _o′_ and L′, which
have a _greater_ power of refracting or displacing the pictures than
the portions _no, n′o′_, and therefore the pictures will be _too much_
displaced, and will have so far _overpassed_ one another that the
observer is not able to _bring them back_ to their place of union,
half-way between the two pictures in the slide.

If, on the other hand, the distance between the pupils of the
observer’s eyes is _greater_ than the distance between the semi-lenses
L, L′, then, instead of looking through the portions _no, n′o′_ of the
lenses, the observer will look through portions between _n_ and L, and
_n′_ and L′, which have a _less_ power of refracting or displacing the
pictures than the portions _no, n′o′_, and therefore the pictures will
be so _little_ displaced as not to reach their place of union, and will
stand at such a distance that the observer is not able to _bring them
up_ to their proper place, half-way between the two pictures in the
slide.

Now, in both these cases of _over_ and _under displacement_, many
persons have such a power over their optical axes, that by converging
them to a point _nearer_ than the picture, they would, in the first
case, _bring them back_ to their place of union, and by converging them
to a point _more remote_ than the picture, would, in the second case,
_bring them up_ to their place of union; but others are very defective
in this power of convergence, some having a facility of converging them
beyond the pictures, and others between the pictures and the eye. This
last, however, namely, that of near convergence, is by far the most
common, especially among men; but it is of no avail, and the exercise
of it is injurious when the under refracted pictures have not come up
to their place of union. The power of remote convergence, which is
very rare, and which would assist in bringing back the over refracted
pictures to their place of union, is of no avail, and the exercise of
it is injurious when the pictures have been too much displaced, and
made to pass beyond their place of union.

When the stereoscope is perfectly adapted to the eyes of the observer,
and the _general_ union of the pictures effected, the remote parts
of the picture, that is, the objects seen in the distance, may be
under refracted, while those in the foreground are over refracted,
so that while eyes which have the power of convergence beyond the
picture, unite the more distant objects which are under refracted, they
experience much difficulty in uniting those in the foreground which
are over refracted. In like manner, eyes which have the power of near
convergence will readily unite objects in the foreground which are over
refracted, while they experience much difficulty in uniting objects in
the distance which are under refracted. If the requisite power over the
optical axes is not acquired by experience and perseverance, when the
stereoscope is suited to the eyes of the observer, the only suggestion
which we can make is to open the eyes wide, and expand the eyebrows,
which we do in staring at an object, or in looking at a distant one,
when we wish to converge the axes, as in Fig. 22, to a point _beyond_
the pictures, and to contract the eyes and the eyebrows, which we do in
too much light, in looking at a _near_ object, when we wish to converge
the optic axes, as in Fig. 21, to a point _between_ the pictures and
the eye.

When the binocular pictures are taken at too great an angle, so as to
produce a startling amount of relief, the distance between similar
points in each picture, both in the distance and in the foreground, is
much greater than it ought to be, and hence the difficulty of uniting
the pictures is greatly increased, so that persons who would have
experienced no difficulty in uniting them, had they been taken at the
proper angle, will fail altogether in bringing them into stereoscopic
relief.

In these observations, it is understood that the observer obtains
distinct vision of the pictures in the stereoscope, either by the
adjustment of the moveable eye-tubes, if they are moveable, as they
ought to be, or by the aid of convex or concave glasses for both eyes,
either in the form of spectacles, or separate lenses placed immediately
above, or immediately below the semi-lenses in the eye-tubes. If the
eyes have different focal lengths, which is not unfrequently the case,
lenses differing in convexity or concavity should be employed to
equalize them.

EDINBURGH: T. CONSTABLE, PRINTER TO HER MAJESTY.