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CURIOSITIES OF LIGHT AND SIGHT.

  CURIOSITIES OF LIGHT AND SIGHT

  BY SHELFORD BIDWELL, M.A., LL.B., F.R.S.

  _WITH FIFTY ILLUSTRATIONS_

  LONDON:
  SWAN SONNENSCHEIN & CO., LIMITED
  PATERNOSTER SQUARE
  1899

PREFACE.

The following chapters are based upon notes of several unconnected
lectures addressed to audiences of very different classes in the theatres
of the Royal Institution, the London Institution, the Leeds Philosophical
and Literary Society, and Caius House, Battersea.

In preparing the notes for publication the matter has been re-arranged
with the object of presenting it, as far as might be, in methodical order;
additions and omissions have been freely made, and numerous diagrams,
illustrative of the apparatus and experiments described, have been
provided.

I do not know that any apology is needed for offering the collection as
thus re-modelled to a larger public. Though the essays are, for the most
part, of a popular and informal character, they touch upon a number of
curious matters of which no readily accessible account has yet appeared,
while, even in the most elementary parts, an attempt has been made to
handle the subject with some degree of freshness.

The interesting subjective phenomena which are associated with the sense
of vision do not appear to have received in this country the attention
they deserve. This little book may perhaps be of some slight service in
suggesting to experimentalists, both professional and amateur, an
attractive field of research which has hitherto been only partially
explored.

CONTENTS.

                                        PAGE.

  CHAPTER I.
    Light and the Eye                       1

  CHAPTER II.
    Colour and its Perception              39

  CHAPTER III.
    Some Optical Defects of the Eye        84

  CHAPTER IV.
    Some Optical Illusions                130

  CHAPTER V.
    Curiosities of Vision                 165

LIST OF DIAGRAMS.

  FIG.                                                 PAGE.

   1. Image of Slit and Spectrum                          12

   2. Diagram of the Eye                                  24

   3. Abney's Colour-patch Apparatus                      45

   4. Partially Intercepted Spectrum                      49

   5. Stencil Cards                                       52

   6. Helmholtz's Curves of Colour Sensations             72

   7. König's Curves                                      73

   8. Stencil Card for Complementary Colours              77

   9. Another form                                        79

  10. Slide for Mixing any two Spectral Colours           80

  11. Refraction of Monochromatic Light by Lens           87

  12. Refraction of Dichromatic Light                     89

  13. Narrow Spectrum as seen from a Distance             97

  14. Spectrum formed with V-shaped Slit                 103

  15. Bezold's Device for Demonstrating
      Non-achromatism of the Eye                         108

  16. Crossed Lines showing the Effect of Astigmatism    113

  17. Another Design showing the same                    114

  18. Star-like Images of Luminous Points                116

  19. Sutures of the Crystalline Lens                    117

  20. Multiple Images of a Luminous Point                120

  21. The same, showing an increased number of Images    122

  22. The same when a Slit is held before the Eye        123

  23. Multiple Images of an Electric Lamp Filament       125

  24. The same seen through a Slit                   126-128

  25. Illusion of Length                                 132

  26. Another form                                       135

  27. Another form                                       136

  28. Another form                                       137

  29. Another form                                       138

  30. Illusion of Inclination                            143

  31. Zöllner's Lines                                    144

  32. Slide for showing Illusions of Motions             147

  33. Illusion of Motion                                 149

  34. Illusion of Luminosity                             152

  35. Illusion of Colour                                 155

  36. Recurrent Vision demonstrated with a Vacuum
      Tube                                               176

  37. The same with a Rotating Disk                      178

  38. Apparatus for showing Recurrent Vision with
      Spectral Colours                                   181

  39. Charpentier's "Dark Band"                          187

  40. Charpentier's Effect shown with the Hand           189

  41. Multiple Dark Bands                                192

  42. Temporary Insensitiveness of the Eye after
      Illumination                                       194

  43. Visual Sensations attending a Period of
      Illumination                                       199

  44. Benham's Artificial Spectrum Top                   200

  45. Demonstration of Red Colour-borders                205

  46. Black and White Screens for the same               209

  47. Rotating Disk for the same                         210

  48. Demonstration of Blue Colour-borders               215

  49. Disk for Experiments on the Origin of the
      Colour-borders                                     217

  50. Disk for the Subjective Transformation of
      Colours                                            224

CHAPTER I.

LIGHT AND THE EYE.

In the present scientific age every one knows that light is transmitted
across space through the medium of the luminiferous ether. This ether
fills the whole of the known universe, as far at least as the remotest
star visible in the most powerful telescopes, and is often said to be
possessed of properties of so paradoxical a character that their
unreserved acceptance has always been a matter of considerable difficulty.

The ether is a thing of immeasurable tenuity, being many millions of
times rarer than the most perfect vacuum of which we have any experience:
it offers no sensible obstruction to the movements of the celestial
bodies, and even the flimsiest of material substances can pass through it
as if it were nothing. Yet we have been taught that this same ether is an
elastic solid with a great degree of rigidity, its resistance to
distortion being, in comparison with the density, nearly ten thousand
million times greater than that of steel: thus was explained the
prodigious speed with which it propagates transverse vibrations.

A few years ago, a distinguished leader in science endeavoured in the
course of a lecture to illustrate these apparently incompatible properties
with the aid of a large slab of Burgundy pitch. He showed that the pitch
was hard and brittle, yet, as he said, a bullet laid upon the slab would,
in the course of a few months, sink into and penetrate through it, the
hard brittle mass being really a very viscous fluid. The ether, it was
suggested, resembled the pitch in having the rigidity of a solid and yet
gradually yielding; it was, in fact, a rigid solid for luminiferous
vibrations executed in about a hundred-billionth part of a second, and at
the same time highly mobile to bodies like the earth going through it at
the rate of twenty miles in a second.

This illustration, felicitous as it is, would, however, scarcely avail to
force conviction upon an unwilling mind, even if it were admitted that the
period of an ether wave is necessarily no more than a hundred-billionth of
a second or thereabouts, which is probably very far from the truth.

But, indeed, the elastic solid theory of the ether has failed to give a
consistent explanation of some of the most important points in
observational optics; and, in spite of the exalted position which it has
held, it can now hardly be regarded as representing a physical reality.
The famous researches of Hertz have established upon a secure experimental
basis the hypothesis of Maxwell that light is an electro-magnetic
phenomenon. Such electrical radiations as can be produced by suitable
instruments are found to behave in exactly the same manner as those to
which light is due. They travel through space with the same speed; they
can be reflected, refracted, polarised, and made to exhibit interference
effects. No fact in physics can be much more firmly established than that
of the essential identity of light and electricity. It follows then that
the displacements of the ether which constitute light-waves are not
necessarily of the same gross mechanical nature as those which we see on
the surface of water, or which occur in the air when sound is transmitted
through it. The displacements which the ether undergoes are not
mechanical--primarily at all events--but electrical. Every one knows what
a simple mechanical displacement is. If we push aside the bob of a
suspended pendulum, that is a mechanical displacement. But if we electrify
a stick of sealing wax by rubbing it with flannel, the surrounding ether
undergoes electric displacement, and no one understands what electric
displacement really is. Ultimately, no doubt, it will turn out to be of a
mechanical nature, but it is almost certainly not a simple bodily
distortion such as is caused, for example, when one presses a jelly with
the finger.

Since, then, it is no longer necessary to assume that the exceedingly rare
and subtile ether is a jelly-like solid in order to account for the manner
in which it transmits light, one of the most serious difficulties in the
way of its acceptance is removed. It is true that nothing is definitely
known concerning the mechanism which takes the place of the simple
transverse vibrations formerly postulated, but every one will admit that
it is far easier to believe in what we know nothing about than in what we
know to be impossible.

All scientific men are in fact agreed in recognising the real and genuine
existence throughout space of an ether capable, among other things, of
transmitting at the speed of 186,000 miles per second disturbances which,
whatever their precise nature, are of the kind which mathematicians are
accustomed to call waves. How an ether wave is constituted will probably
be known when we have found out exactly what electricity is: and that may
be never.

The sensation of light results from the action of ether waves upon the
organism of the eye, but the old belief that the sensation was primarily
due to a series of mere mechanical impulses or beats, just as that of
sound results from the mechanical impact of air-waves upon the drum of
the ear, cannot any longer be upheld. The essential nature of the action
exerted by ether waves is still undetermined, though many guesses at the
truth have been hazarded. It may be electrical or it may be chemical;
possibly it is both. Ether-waves, we know, are competent to bring about
chemical changes, as in the familiar instance of the photographic
processes; they can also produce electric phenomena, as, for example, when
they fall upon a suitably prepared piece of selenium; but there is no
evidence that they can exert any direct mechanical action of a vibratory
character, and indeed it is barely conceivable that any portion of our
organism should be adapted to take up vibrations of such enormous rapidity
as those which characterise light-waves.

Of the multitude of ether-waves which traverse space it is only
comparatively few that have the power of exciting the sensation of light.
As regards limited range of sensibility there is a very close analogy
between hearing and seeing. No sensation of sound (at least of continuous
sound) is produced when air-waves beat upon our ears unless the rate of
the successive impulses lies within certain definite limits. It is just so
with vision. If ether-waves fall upon our eyes at a less rate than about
400 billions per second, or at a greater rate than 750 billions per
second, no sensation of light is perceived. There is another and more
generally convenient way of stating this fact. Since all waves found in
the ether travel through space at exactly the same speed--186,000 miles a
second--it follows that the length[1] of each of a series of homogeneous
waves must be inversely proportional to their frequency, that is, to the
rate at which they strike a fixed object, such as the eye. Instead,
therefore, of specifying waves by their frequency we may equally well
specify them by their length. Waves whose frequency is 400 billions per
second have a length of about 1/34000 inch, this being the one four
hundred billionth part of 186,000 miles; and those whose frequency is 750
billions have a wave-length of 1/64000 inch. Waves, then, of a length
greater than 1/34000 inch or less than 1/64000 inch have no effect upon
our organs of vision.[2]

In relation to this important fact it will be convenient to refer to a
familiar but very beautiful experiment--the formation of a spectrum. An
electric lamp is enclosed in an iron lantern, having in its front an
upright slit; from this slit there issues a narrow beam of white light,
which is made up of rays of many different wave-lengths, all mixed up
together. By causing the light to pass through a prism the mixed rays are
sorted out side by side according to their several wave-lengths, forming
a broad, many-hued band or "spectrum" upon a white screen placed to
receive it. (See Fig. 1.) To the visible rays of the longest wave-length
is due the red colour on the extreme left. Waves of somewhat shorter
length produce the adjoining stripe of orange, and the succeeding
colours--yellow, green, and blue--correspond respectively to waves of
shorter and shorter lengths. Lastly there comes a patch of violet due to
those of the visible rays whose wave-length is the shortest of all. The
wave-length of the light at the extreme edge of the red is about 1/34000
inch, and as we pass along the spectrum the wave-length gradually
diminishes, until at the extreme outer edge of the violet it is about
1/64000 inch, or not much more than half that at the other end.

[Illustration: _Fig. 1.--Image of Slit and of Spectrum._]

The two ends of the spectrum gradually fade away into darkness, and the
point that I wish to insist upon and make perfectly clear is this:--The
position of the boundaries terminating the visible spectrum does not
depend upon anything whatever in the nature of light regarded as a
physical phenomenon. Ether waves which are much longer and much shorter
than those which illuminate the spectrum certainly exist, and evidence of
their existence is easily obtainable. But we cannot see them; they fall
upon our eyes without exciting the faintest sensation of light. The
visible spectrum is limited solely by the physiological constitution of
our organs of vision, and the fact that it begins and ends where it does
is, from a physical point of view, a mere accident. The spectrum actually
projected upon the screen is in truth much longer than that portion of it
which any one can see: it extends for a considerable distance beyond the
violet at the one end and beyond the red at the other, these invisible
portions being known as the ultra-violet and infra-red regions. People's
eyes differ in regard to range of sensibility just as their ears do. I
believe the sensibility of my own eyes to be normal, but if I were to
indicate the two points where the spectrum appears to me to begin and to
end, a great many persons would certainly be inclined to disagree with me
and place the boundaries somewhere else. Some, indeed, could see nothing
whatever in what appears to most of us to be a brilliant portion of the
red.

Again, it is by no means probable that in all animals and insects the
limits of vision are the same as they are in man. We might naturally
expect that larger and perhaps more coarsely constructed eyes than our own
would respond to waves of greater average length, while the visual organs
of small insects might on the other hand be more sensitive to shorter
waves. The point is not one that can be easily settled, because we are
unable to cross-examine an animal as to what it sees under different
conditions. But Sir John Lubbock, taking advantage of the dislike which
ants when in their nests have for light, has proved by a series of very
exhaustive and conclusive experiments that these insects are most
sensitive to rays which our own eyes cannot perceive at all. That region
of the spectrum which appears brightest to the eye of an ant is what we
should call a perfectly dark one, lying outside the violet, where the
incident waves have a length of less than 1/64000 inch.

As Lord Salisbury said at Oxford, the function of the ether is to
undulate, and, in fact, it transports energy from one place to another by
wave-motion. Some of its waves, such as those which proceed from an
electric-light dynamo, may be thousands of miles in length, others may be
shorter than a millionth of an inch, as is perhaps the case with those
associated with Professor Röntgen's X-rays; but all, so far as is known,
are of essentially the same character, differing from one another only as
the billows of the Atlantic differ from the ripples on the surface of a
pond. No matter how the disturbance is first set up, whether by the sun,
or by a dynamo, or by a warm flat-iron, in every case the ether conveys
nothing at all but the energy of wave-motion, and when the waves,
encountering some material obstacle which does not reflect them, become
quenched, their energy takes another form, and some kind of work is done,
or heat is generated in the obstacle.

The whole, or at least the greater part, of the energy given up by the
waves is in most cases transformed into heat, but under special
circumstances, as, for instance, when the waves fall upon a green leaf or
a living eye, a few of them may perform work of an electrical or chemical
nature.

The process of the transmission of energy from one body to another by
propagation through an intervening medium has long been spoken of as
"radiation," and in recent years the same term has been largely employed
to denote the energy itself while in the stage of transmission.
"Radiation" in the latter sense--meaning ether wave-energy--includes what
is often improperly called light. Light, people say, takes about eight
minutes in travelling from the sun to the earth. But while it is on its
journey it is not light in the true sense of the word; neither does
anything of the nature of light ever start from the sun. Light has no
more existence in nature outside a living body than the flavour of onions
has; both are merely sensations.

If a boy throws a stone which hits you in the face, you feel a pain; but
you do not say that it was a pain which left the boy's hand and travelled
through space from him to you. The stone, instead of causing pain in a
sentient being, might have broken a window, or knocked down an apple. Just
so, the same radiation which, when it chances to encounter an eye,
produces a certain sensation, will produce a chemical decomposition if it
falls upon a cabbage, an electrical effect in a selenium cell, or a
heating effect in almost anything. Why, then, should it be specially
identified with the sensation?

"Radiation" also includes, and is nearly synonymous with, what is often
miscalled radiant heat. After what has been already indicated, I need
hardly say that there is no such thing as radiant heat. The truth is that
the sun or other hot body generates wave-energy in the ether at the
expense of some of its own heat, and any distant substance which absorbs a
portion of this energy generally (but not necessarily) acquires an
equivalent quantity of heat. The _result_ may be exactly the same as if
heat left the hot body and travelled across space to the substance; but
the _process_ is different. It is like sending a sovereign to a friend by
a postal order. You part with a sovereign and he receives one, but the
piece of paper which goes through the post is not a sovereign. It is
strictly correct to say that the sun loses heat by radiation, just as you
lose a sovereign by investing it in the purchase of a postal order. But
that is not the same thing as saying that the sun radiates heat.

The term "radiation" has the advantage of avoiding any suggestion of the
fallacy that there is some essential difference in the nature of the
ether-waves which may happen to terminate their respective careers in the
production of light or heat or chemical action or something else; but it
is, unfortunately, impossible in the present condition of things to use it
as freely as one could wish without pedantry, and we must still often
speak of light or of heat when radiation would express our meaning with
greater accuracy.

Light, then--to use the term unblushingly in its objectionable but well
understood sense--has the property of stimulating certain nerves which
exist in many living beings, with the result that, in some unknown and
probably unknowable manner, a special sensation is called into play--the
sensation of luminosity. And in order that the creature may be able not
only to perceive light but also to see things, that is, to appreciate the
forms of external objects, it is generally provided with an optical
apparatus by means of which the incident light is suitably distributed
over a large number of independent sensitive elements.

In man and the higher animals the optical apparatus, or eye, consists of a
stiff globular shell, having in front an opening provided with a system
of lenses, and, at the back of the interior, a delicate perceptive
membrane, upon which the transmitted light is received. So much of the
light emitted or reflected from an external object as passes through the
lenses, is distributed by them in such a manner as to form what is called
an "image" upon the membrane, every elementary point of the image
receiving the light which issues from a corresponding point of the object,
and no other. The contrivance evidently bears a close resemblance to a
photographic camera, the sensitive plate or film, upon which the picture
is projected, being analogous to the perceptive membrane.

I am not going to attempt a detailed description of the human eye. It will
be sufficient to point out briefly some of its principal features as
indicated in the annexed diagrammatic section, Fig. 2.

[Illustration: _Fig. 2.--Diagram of the Eye._]

The opening in front of the globe is covered by a slightly protuberant
transparent medium C, which is shaped like a small watch-glass, and on
account of its horn-like structure has been named the _cornea_. The space
between the cornea C and the body marked L is filled with a watery liquid
A, known as the aqueous humour: this liquid with its curved surfaces
constitutes a meniscus lens, convex on the outer side and concave on the
inner. Then comes the biconvex _crystalline lens_ L, an elastic
gelatinous-looking solid, which is easily distorted by pressure. The
convexity of this lens can be varied by the action of a surrounding muscle
M M, and in this way the focus is adjusted for objects at different
distances from the eye. When the muscle is relaxed and the lens in its
natural condition, the curvature of its surfaces is such that a sharp
image is formed of objects distant about forty feet and upwards. When by
an effort of will, the muscle is contracted, the lens becomes more convex,
and distinct pictures can thus be focussed of things which are only a few
inches away. This process of adjustment by muscular effort is technically
known as "accommodation."

The remainder of the globe is filled with the so-called _vitreous body_ V,
which derives its name from its fancied resemblance to liquid glass: it
might perhaps be more properly likened to a thin colourless jelly. The
vitreous body plays a part in the refraction of the light.

The perceptive membrane, or _retina_ R R, which lines rather more than
half the interior of the eye-ball, is an exceedingly complex structure.
Though its average thickness is less than 1/100 inch it is known to
consist of nine distinct layers, most of which are marvels of minute
intricacy. Of these layers I shall notice only two, the so-called
_bacillary layer_, which is in immediate contact with the inner coating
of the eye-ball, and the _fibrous layer_, or layer of optic nerve fibres,
which is only separated from the vitreous body by a thin protective film.

The bacillary layer (from _bacillum_, a wand) consists of a vast
assemblage of little elongated bodies called _rods_ and _cones_, which are
placed side by side and set perpendicularly to the surfaces of the retina,
or in other words, radially to the eye-ball. Let us try to make the
arrangement clear by an illustration.

Imagine a small portion of the inner surface of the eye-ball, one-tenth of
an inch square, to be magnified 2000 diameters (four million times), and
let the enlarged area be represented by the floor of a room 17 feet
square. Procure a quantity of cedar pencils, and set them on the floor in
an upright position and very close to one another. It will be found that
the number of pencils required to fill the space will be about
half-a-million. To make the analogy more complete, let some of the pencils
be sharpened to a long tapering point at their lower ends, the greater
number remaining uncut, just as received from the manufacturers.
Neglecting details which are immaterial for our present purpose, we may
regard the uncut pencils as representing upon an enormously magnified
scale the rods of the retina, and the pointed ones the cones.

The flat upper ends of the pencils may be painted in different uniform
colours, and arranged so as to form a large picture in mosaic, and if this
is looked at from such a distance that its image on the retina is a tenth
of an inch square (which will be the case when the picture is about forty
yards away) all possibility of distinguishing the separate elements which
compose it will be lost, and the picture will seem to be a perfectly
continuous one.

Although the light which enters the eye cannot reach the rods and cones
until it has traversed all the other layers of the retina, yet these
intervening layers, being transparent, offer little obstruction to its
passage, and it can hardly be doubted that the rods and cones are the
special organs upon which light exerts its action, the picture focussed
upon their ends being in truth an exceedingly fine mosaic.

From every separate element of the mosaic--from every single rod and
cone--there proceeds a slender transparent filament: all these make their
way through the intermediate layers of the retina, without, as is
believed, any break of functional continuity, and emerge near its internal
surface; here they bend over at right angles, and the thousands of
filaments form a tangle which lines the inside of the eye like a fine
network, and constitute the layer of optic nerve-fibres already referred
to.

The filaments, or nerve-fibres, do not however terminate within the eye;
they all pass through the hole marked N in the figure, and thence, in the
form of a many-stranded cable, constituting the _optic nerve_, they are
led to the brain, to which each individual fibre is separately attached.
If, therefore, what I have said is true--and, though it has not, I
believe, been all rigorously proved, yet the evidence in its support is
exceedingly cogent--it follows that every one of the multitude of rods and
cones has its own independent line of communication with the brain. The
mind, which is mysteriously connected with the brain, is thus afforded the
means of localising all the points of luminous excitation relatively to
one another, and furnished with data for estimating the form of the object
from which the light proceeds.

There are two small regions of the retina which are of special interest.
One of them lies just over the opening N where the optic nerve enters.
Here it is evident that there can be no rods and cones, their place being
wholly occupied by strands of nerve-fibre. Now it is remarkable that this
spot is totally insensitive to light.

The other interesting portion is situated opposite the middle of the front
opening, and is marked by a small yellow patch, in the centre of which is
a depression or pit, which is shown in an exaggerated form at F, and is
called the _fovea_. It has been ascertained that the depression is due
partly to the absence of the layer of nerve-fibres, which are here bent
aside out of their natural course, and partly to a local reduction in the
thickness of some of the intermediate retinal layers. This spot, being at
the centre of the field of vision, occupies a position of great
importance, and the evident purpose of the superficial depression is to
allow the light to reach the underlying bacillary layer with as little
obstruction as possible. It is noteworthy that the bacillary layer
beneath the yellow spot is composed entirely of cones, the rods, which
elsewhere are in excess, being altogether wanting.

The only other accessory of the visual apparatus to which I shall refer is
the _iris_ (I I, Fig. 2), a coloured disk having a central perforation.
This can be seen through the cornea and is consequently a very familiar
object. The iris serves the same purpose as the stop, or diaphragm, of a
photographic lens, its function being to limit and regulate the quantity
of light which is admitted into the eye. The size of the central opening,
or _pupil_, varies automatically with the intensity of the illumination:
in a strong light the opening becomes small; in a feeble light or in
darkness it is enlarged. The pupil also contracts when the eye is
focussed upon a near object and dilates when the vision is directed to a
distance.

This brief sketch may serve to give some slight idea of the complexity and
delicacy of the visual apparatus. Only a few of its more salient features
have been touched upon; when our scrutiny is carried into details the
complexity becomes bewildering. Even such simple-looking things as the
cornea and the vitreous body turn out on close examination to be most
elaborately constituted. Much, no doubt, remains to be discovered, and of
what has already been investigated much is at present only partially
understood.

And yet, though it is true that man is "fearfully and wonderfully made,"
it is equally true that he is far from perfect; and while there is no
structure in the whole human anatomy which exhibits so abundant a
profusion of marvels as the eye, there is perhaps none which is marked
with imperfections so striking.

Many of its defects are the more striking because they are so obvious,
being such as would never be tolerated in optical instruments of human
manufacture. In any fairly good camera or telescope or microscope we
should expect to find that the lenses were symmetrically figured, free
from striæ and properly centred; also that they were achromatic and
efficiently corrected for spherical aberration. In the eye not one of
these elementary requirements is fulfilled.

The external surface of the lens formed by the aqueous humour and the
cornea is not a surface of revolution, such as would be fashioned by a
turning lathe or a lens-grinding machine; its curvature is greater in a
vertical than in a horizontal direction, and the distinctness of the
focussed image is consequently impaired. Again, the crystalline lens is
constructed of a number of separate portions which are imperfectly joined
together. Striæ occur along the junctions, and the light which traverses
them, instead of being uniformly refracted, is scattered irregularly.
Moreover the system of lenses is not centred upon a common axis; neither
is it achromatic, while the means employed for correcting spherical
aberration are inadequate. The purchaser of an optical instrument which
turned out to have such faults as these would certainly, as the late
Professor Helmholtz remarked, be justified in returning it to the maker
and blaming him severely for his carelessness.

I would not, of course, have it believed that scientific men are conceited
enough to imagine themselves capable of designing a better eye than is to
be found in nature. That would be an absurdity. They are quite ready to
admit that there may exist sufficiently good reasons for the undoubted
blemishes which have been indicated, as well as for others which will be
referred to later. It is indeed well known that the general efficiency of
a machine as a whole may often be best secured by the sacrifice of ideal
perfection in some of its parts.

With all its anomalies the eye fulfils its proper function very perfectly,
and is regarded by those who have studied it most closely with feelings of
wonder and humble admiration.[3]

CHAPTER II.

COLOUR AND ITS PERCEPTION.

It was explained in the last chapter that we see things through the agency
of the light--emitted or reflected--which proceeds from them to the eye,
and is suitably distributed over the retina by the action of a system of
lenses.

Now the "image" thus formed is not generally perceived as a simple
monochromatic one, darker in some parts, lighter in others, like a black
and white engraving. It is, in most cases at least, characterised by a
variety of colours, the light which comes from different objects, or from
different parts of the same object, having the power of exciting different
colour sensations. Light which has the property of exciting the sensation
of any colour is commonly spoken of as coloured light. The light reflected
by a soldier's coat, for example, may be called red light, because when it
falls upon the eye it gives rise to a sensation of redness. But it must be
understood that this mode of expression is only a convenient abbreviation,
for there can, of course, be no objective colour in the light or
"radiation" itself.

Wherein, then, does coloured light differ from white? Why do things appear
to be variously coloured when illuminated by light which is colourless?
And how do coloured lights affect the visual organs so as to evoke
appropriate sensations? These are questions--the first two of a physical
character, the last partly physiological and partly psychological--which
it is now proposed to discuss.

The matter has already been touched upon, though very slightly, in
connection with the spectrum. Let us again turn to the spectrum and
consider it a little more fully.

It is easily seen that the luminous band contains six principal hues or
tones of colour--red, orange, yellow, green, blue, and violet. (See Fig.
1, page 12.) These however merge into one another so gradually that it is
impossible to say exactly where any one colour begins and ends. Look, for
instance, at the somewhat narrow but very conspicuous stripe of yellow.
Towards the right of this stripe the colour gradually becomes
greenish-yellow; a little further on it is yellowish-green, and at
length, by insensible gradations, a full, pure green is reached.

The six most prominent hues of the spectrum are, in fact, supplemented by
an immense multitude of subordinate ones, the total number which the eye
can recognise as distinct being not less than a thousand. All the colours
that we see in nature, with the exception of the purples (about which I
shall say more presently), are here represented, and every single variety
of tone in the prismatic scale corresponds with one, and only one,
definite wave-length of light.

The source of all these colours is, as we know, a beam of white or
colourless light, the constituents of which have been sorted out and
arranged so that they fall side by side upon the screen in the order of
their several wave-lengths. If, then, these coloured constituents were
all mixed together again, it would be reasonable to expect that pure white
light would be reproduced.

The experiment has been performed in a great many different ways, several
of which were devised by Newton himself, and the result admits of no doubt
whatever. The method which I intend to describe is not quite so simple as
some others, but it has great advantages in the way of convenient
manipulation, and affords the means of demonstrating a number of
interesting colour effects in an easily intelligible manner. By the simple
operation of moving aside a lens out of the track of the light, we can
gather up and thoroughly mix together all the variously coloured rays of
the spectrum and cause them to form upon the screen a bright circular
patch, which, though due to a mixture of a thousand different hues, is
absolutely white. When the lens is replaced, which is done in an instant,
the mixture is again analysed into its component parts, and the spectrum
reappears.

The arrangement of the apparatus, which is essentially the same as that
devised by Captain Abney, and called by him the "colour-patch apparatus,"
is shown in the annexed diagram (Fig. 3).

[Illustration: _Fig. 3.--Abney's Colour-patch Apparatus._]

The light of an electric lamp A placed inside the lantern is concentrated
by the condensing lenses B upon a narrow adjustable slit C. The framework
of this slit is attached to one end of a telescope tube, which carries at
the other end an achromatic lens D of about 10 inches focus. The rays
having been rendered parallel by D are refracted by the prism E; they
then pass through a circular opening in the brass plate F to the lens G,
the focal length of which is 7 inches, and form a little bright spectrum
upon a white card held in a grooved support at H. The card being removed,
we place at K a lens having a diameter of 5-1/2 inches and a focal length
of 18 inches or more, and adjust it so that a sharply defined image of the
hole in the brass plate F is formed upon the distant white screen L. If
all the lenses are correctly placed, this image, though formed entirely by
the rays which constituted the little spectrum at H, will be perfectly
free from colour even around the edge.

If we wish to project upon the screen L an enlarged image of the little
spectrum, we have only to use another suitable lens I in conjunction with
K: the diameter of that used by myself is 2-3/4 inches, and its focal
length 6-1/2 inches. When we have once found by trial the position in
which this supplementary lens gives the clearest image[4] it is easy to
arrange a contrivance for removing and replacing it correctly without need
of any further adjustment.

This apparatus shows then that ordinary white light may be regarded as a
mixture of all the variously coloured lights which occur in the spectrum,
the sensation produced when it falls upon the eye being consequently a
compound one.

From these and similar experiments the scientific neophyte is not unlikely
to draw an erroneous conclusion. White light, he is apt to think, is
_always_ due to the combined action of rays of every possible wave-length,
while coloured light consists of rays of one definite wave-length only.
Neither of these inferences would be correct. It is not true that white
light necessarily contains rays of all possible wave-lengths: the
sensation of whiteness may, as will be shown by and bye, be produced quite
as effectively by the combination of only two or three different
wave-lengths. Nor is it true that such colours as we see in nature are
always due to light of a single wave-length; light of this kind is indeed
rarely met with outside laboratories and lecture rooms. Far more commonly
coloured light consists of mixed rays, and like ordinary white light, it
may, and generally does, contain all the colours of the spectrum, but in
different proportions.

This last assertion is easily proved. By means of a slip of card we may
intercept a portion of the little spectrum formed at H (Fig. 3). The dark
shadow of the card in the enlarged spectrum on the screen is shown in Fig.
4. It will be noticed that the shadow cuts off a part only of the red,
orange, and yellow light, allowing the remainder to pass through the
projection lenses. There are still rays of every possible wave-length from
extreme red to extreme violet, but the proportion of those towards the red
end is less than it was before the card was interposed.

[Illustration: _Fig. 4.--Partially intercepted Spectrum._]

If now we remove the lens I (Fig. 3) and so mix the colours of this
mutilated spectrum, the bright round patch where the mixed rays fall upon
the screen will no longer appear white but greenish-blue. If we transfer
the card to the other end of the little spectrum, so as to cause a partial
eclipse of the violet, blue, and green rays, the colour of the patch will
be changed to orange. If we remove the card altogether, the patch will
once more become white.

It follows _a fortiori_ that when any portion of the little spectrum is
eclipsed totally, instead of only partially, the light from the remainder
will appear, when combined, to be coloured. Very beautiful changes of hue
are exhibited by the bright patch when a narrow opaque strip, such as the
small blade of a pocket knife, is slowly moved along the little spectrum
at H, eclipsing different portions of it in succession. The patch first
becomes green, then by imperceptible gradations it changes successively to
blue, purple, scarlet, orange, yellow, and finally, when the knife has
completed its course, all colour disappears and the patch is again white.

We may improve upon this crude experiment, and, after Captain Abney's
plan, prepare a number of small cardboard stencils, with openings
corresponding to any selected parts of the little spectrum. When a card so
prepared is placed at H (Fig. 3) the bright patch upon the screen is
formed by the combination of the selected rays, all the others being
quenched. We shall find that under these conditions the bright patch is
generally, but not always, coloured.

[Illustration: _Fig. 5.--Stencil Cards._]

The first diagram in Fig. 5 represents a blackened card, which allows
only the red and a little of the orange to pass through. When this is
inserted in the grooved holder at H, the bright patch immediately turns
red. The second diagram shows another, which transmits the middle portion
of the spectrum, but blocks the red and the violet at its two ends: with
this card the colour of the patch becomes green. The third card has
openings for the violet and the red rays: this turns the patch a beautiful
purple, a hue which, as already mentioned, is not produced by light of any
single wave-length. The purples are mixtures of red and violet or of red
and blue.

Now I have in my possession three pieces of glass (or, to be strictly
accurate, two pieces of glass and one glass-mounted gelatine film) which,
when placed transversely in the beam of light, either at H (Fig. 3) or
anywhere else, behave exactly like these three cardboard stencils. The
first glass cuts off all the spectrum except the red and part of the
orange, just as the first stencil does, though the line of demarcation is
not quite so sharp. This is in fact a piece of red glass, or in other
words the light that it transmits produces the sensation of red. The
second glass, like the second stencil, allows the whole of the spectral
rays to pass freely except the red and the violet, which disappear as if
they were obstructed by an opaque body. This is a green glass. And the
third (which is really a film of gelatine) cuts out the middle of the
spectrum but transmits the red and violet ends. The colour of the gelatine
is purple.[5]

The glasses and the gelatine in question act like the cardboard stencils
in completely cutting off some of the spectral rays and transmitting
others, and they owe their apparent colours to the combined influence
which the transmitted rays exert upon the eye. Many other coloured glasses
merely weaken some of the rays, without entirely quenching any. A piece of
pale yellow glass, for example, when placed in the path of the beam of
light from which the spectrum on the screen is formed, simply diminishes
the brightness of the blue region and does not wholly quench any of the
rays; and again, a common kind of violet-coloured glass enfeebles, but
does not quite obliterate, the middle portion of the spectrum.

From such observations as these we infer that the glasses derive their
respective colours from the light which falls upon them. The first glass
would not appear red if seen in a light which contained no red rays. This
is easily proved by an experiment with the colour-patch apparatus. The
spectrum being once more combined into a bright white patch (which turns
red if the glass is for a moment interposed), let all the red rays and
part of the orange be cut off with a suitable stencil. The re-combined
light is no longer white but greenish-blue, as is evidenced by the colour
of the patch; and nothing that is illuminated by this light can possibly
appear red. The piece of red glass, if placed in the beam, will now cast a
perfectly black shadow, and a square of bright red paper held in the
middle of the patch will look as black as ink. It will be shown later how
we may obtain light which, although it appears to the eye to differ in no
respect from ordinary white daylight, yet contains no red component, and
is consequently as powerless as this greenish-blue light to reveal any red
colour in the objects which it illuminates.

If we substitute a stencil which admits only red rays, we shall obtain a
beam of light in which no colour but red can be seen. Green and blue
glasses when exposed to this light will cast black shadows, while pieces
of green and blue paper will become either black or dark grey.

We see then that the colours of transparent objects, like the glasses used
in these experiments, are brought out by a process of filtration. Certain
of the coloured ingredients of white light are filtered out and quenched
inside the glass, and it is to the remaining ingredients which pass
through unimpeded that the observed colour is due. The energy of the
absorbed rays is not lost of course, for energy, like matter, is
indestructible. It is transformed into heat. A coloured glass held in a
strong beam of light will in a short time become sensibly warmer than one
that is clear and colourless.

In studying colour effects as produced by coloured glasses, we have at the
same time been learning how the great majority of natural objects--not
only those which are transparent but also those called opaque--become
possessed of their colours. For the truth is that few things are perfectly
opaque. When white light falls upon a coloured body, it generally
penetrates to a small depth below the surface, and in so doing loses by
absorption some of its coloured components, just as it does in passing
through the pieces of glass. But before it has gone very far--generally
much less than a thousandth part of an inch--it has encountered a number
of little reflecting surfaces due to optical irregularities, which turn
the light back again and compel it to pass a second time through the same
thickness of the substance: it thus becomes still more effectively sifted,
and on emerging is imbued with a colour due to such of the components as
have not been quenched in the course of their double journey through a
superficial layer of the substance.

Any coloured rays reflected by an object must necessarily be contained in
the light by which the object is seen. The following is a curious
experiment illustrating this.

A large bright spectrum is projected upon a screen and in the green or
blue portion of it is held a wall poster. The letters and figures upon the
paper are seen to stand out boldly as if printed with the blackest ink.
But if the poster is moved into the red part of the spectrum, the printing
at once disappears as if by magic, and the paper appears perfectly blank.
The explanation is that the letters are printed in red ink--they can
reflect no light but red. Green or blue light falling upon them is
absorbed and quenched, and the letters consequently appear black. On the
other hand when the poster is illuminated by the red rays of the
spectrum, the letters reflect just as much light as the paper itself, and
are therefore indistinguishable from it.

Anything which, when illuminated by a source of white light, reflects all
its various components equally and without absorbing a larger proportion
of some than of others, appears white or grey. Between white and grey
there is no essential difference except in luminosity, or brightness, that
is to say, in the quantity of light reflected to the eye, or--to go a step
further back--in the amplitude of the ether waves. Under different
conditions of illumination any substance which reflects all the rays of
the spectrum equally may appear either white or grey, or even black. A
snowball can easily be made to look blacker than pitch, and a block of
pitch whiter than snow.

It must have struck many of those who have thought about the matter at all
as a most remarkable coincidence that sunlight should be white. White
light, as we have seen, consists of a mixture of variously-coloured rays
in very different and apparently arbitrary proportions, and if these
proportions were a little changed the light would no longer be quite
colourless. No ordinary artificial light is so exactly white as that of
the sun. The light of candles, gas, oil, and electric glow-lamps is
yellow; that of the electric arc (when unaffected by atmospheric
absorption) is blue, and that of the incandescent gas burner green. It is
exceedingly convenient that the light which serves us for the greater
part of our waking lives should happen to be just so constituted that it
is colourless.

But on a little further reflection it will, I think, appear that this is
not the right way to look at the matter. It is precisely because the hue
called white is the one which is associated with the light of our sun that
we regard whiteness as synonymous with absence of colour. We take sunlight
as our standard of neutrality, and anything that reflects it without
altering the proportions of its constituents we consider as being
colourless.

There can be little doubt that if the sun were purple instead of white,
our sentiments as regards these two hues would be interchanged; we should
talk quite naturally of "a pure purple, entirely free from any trace of
colour," or perhaps describe a lady's costume as being of a "gaudy white."

Even as things are, the standard of neutrality is not quite a hard and
fast one. We have a tendency to regard any artificial light which we may
happen to be using, as more free from colour than it would turn out to be
if compared directly with sunlight. If in the middle of the day we go
suddenly into a gas-lit room, we cannot fail to observe how intensely
yellow the illumination at first appears; in a few minutes, however, the
colour loses its obtrusiveness and we cease to take much notice of it.

The effect may be partly a physiological one, depending upon unequal
fatigue of the various perceptive nerves of the retina; but I believe that
it is to a large extent due to mental judgment. The standard of
whiteness, or colour-zero, can apparently be changed within certain limits
in a very short time, and, as we shall see later, this is only one of many
instances in which our organs of vision seem to be incapable of
recognising a constant standard of reference.

And now let us consider how it comes about that each elementary portion of
the retina--at least in its central region--has the power of
distinguishing so many hundreds of different hues. It is incredible that
every little area of microscopic dimensions should be furnished with such
a multitude of independent organs as would be necessary if each of the
many colours met with in nature required a separate organ for its
perception; and it is not necessary to suppose anything of the kind.

Experiment shows that all the various hues of the spectrum, as well as all
(including white) that can be formed from their mixture, may be derived
from no more than three distinct colours. There are, in fact, an
indefinite number of triads of colours which, in suitable combinations,
are capable of producing the sensation of every tone, tint, and shade of
colour which the eye of man has ever beheld.

Old-fashioned books, such as an early edition of Ganot's "Physics," tell
us that the three "primary" colours are red, yellow, and blue, and that
all others are produced by mixtures of these. This was the basis of Sir
David Brewster's theory, which attained a very wide popularity, and even
at the present time is held as an article of faith among the great
majority of intelligent persons who have not paid any special attention to
science. But it is not true. A fatal objection to it is the
well-ascertained fact that no combination of red, yellow, and blue, or of
any two of them, such as blue and yellow, for example, will produce green.

Yet every painter knows that if he mixes blue and yellow pigments together
he gets green. That is one of the first things that a child learns when he
is allowed to play with a box of water-colours, and no doubt Brewster was
misled by the fact.

The truth is, that the colours of all, or almost all, known blue and
yellow pigments happen to be composite. An ordinary blue paint reflects
not only blue light, but a large quantity of green as well; while an
ordinary yellow paint reflects a large quantity of green light in addition
to yellow. When such paints are mixed together, the blue and yellow hues
neutralise one another, and only the green, which is common to both,
remains.

The spectrum apparatus will make this clearer. Hold a piece of bright blue
glass before the slit; the light passing through the glass will be
analysed by the prism, and you will see that it really contains almost as
much green as blue. If a yellow glass is substituted, not only will yellow
light be transmitted, but, as before, a considerable quantity of green. If
now both glasses be placed together before the slit, what will happen? The
yellow glass will stop the blue light transmitted by the blue glass, the
blue glass will stop the yellow light transmitted by the yellow glass, and
only the green light which both glasses have the power of transmitting
will pass through unimpeded, forming a band of pure green colour upon the
screen.

The combination of simple blue and yellow lights of suitable relative
luminosities results in the formation of white or neutral light. If the
blue is a little in excess, the combined light will be of a bluish tint;
if the yellow is in excess, the combination will have a yellowish tint. It
will never contain any trace of green. The combination of simple spectral
blue and yellow is easily effected by the colour-patch apparatus, and the
result will be found to bear out what has been said.

Since, then, no mixture of red, yellow, and blue, or of any two of them,
will produce green, we cannot regard these colours as being, in
Brewster's sense of the term, primary ones.

But it is quite possible to find a group of three different hues--and
indeed many such groups--which when made to act upon the eye
simultaneously and in the right proportions can give rise to the sensation
of any colour whatever. Now this experimental fact is obviously suggestive
of a possible converse, namely, that almost every colour sensation may in
reality be a compound one, the resultant of not more than three simple
sensations. Assuming this to be so, it is evident that if each elementary
area of the retina were provided with only three suitable colour organs,
nothing more would be requisite for the perception of an indefinite number
of distinct colours.

Such a hypothesis was first proposed by Thomas Young at the beginning of
the present century; but it came before its time and met with no attention
until fifty years later, when it was unearthed by the distinguished
physicist and physiologist, Helmholtz, who accorded to it his powerful
support and modified it in one or two important details.

[Illustration: _Fig. 6.--Helmholtz's Curves of Colour Perception._]

According to the Young-Helmholtz theory, as it is now called, there are
three different kinds of nerve-fibres distributed over the retina. The
first, when separately stimulated, produce the sensation of red, the
second that of green, and the third that of violet. Light having the same
wave-length as the extreme red rays of the spectrum stimulates the red
nerve-fibres only; that having the same wave-length as the extreme violet
rays stimulates the violet nerve-fibres only. Light of all intermediate
wave-lengths, corresponding to the orange, yellow, green, and blue of the
spectrum, stimulates all three sets of nerve-fibres at once, but in
different degrees. The proportionate stimulation of the red, green, and
violet nerves throughout the spectrum is indicated in Fig. 6, which is
derived from the rough sketch first given by Helmholtz. The yellow rays of
the spectrum, it will be seen, excite the red and green nerves strongly,
and the violet feebly; green light excites the green nerves strongly, and
the red and violet moderately; while blue light excites the green and
violet nerves strongly, and the red feebly.

[Illustration: _Fig. 7.--König's Curves._]

Fig. 7 shows another set of curves given more recently by Dr. König as the
result of many thousands of experiments made, not only upon persons whose
vision was normal, but also upon some who were colour-blind. König found
that the equations he obtained were best satisfied by assuming as the
normal fundamental sensations a purplish red (not to be found in the
spectrum), a green like that of wave-length 5050, and a blue like that of
wave-length 4700 approximately, the two latter, however, being purer or
more saturated than any actual spectrum colour. But König's curves are not
consistent with every class of vision which he examined, and the question
as to what are the true fundamental colour-sensations, if such really
exist at all, cannot yet be regarded as finally settled.[6]

The Young-Helmholtz theory of colour-vision, whether or not it is destined
in the future to be superseded by some other, has at all events proved an
invaluable guide in experimental work, and there are very few colour
phenomena of which it is not competent to offer a satisfactory
explanation. It has at present only one serious rival--the theory of
Hering, which, although it seems to be curiously attractive to many
physiologists, can hardly be said to present less serious difficulties
than that which it seeks to displace. Neither of these competing theories
has yet had its fundamental assumptions confirmed by any direct evidence,
and the advantage must rest with the one which best accords with the facts
of colour vision. In my judgment the older of the two is to be greatly
preferred as a useful working hypothesis.

Certain curiosities of vision with which I propose to deal in a future
chapter depend upon the properties of what are known as complementary
colours. Two colours are said to be complementary to each other when their
combination in proper proportions results in the formation of white.

[Illustration: _Fig. 8.--Stencil Card for Complementary Colours._]

If we produce a compound hue by mixing together the colours of any portion
of the spectrum, and a second compound hue by mixing the remainder of the
spectrum, it must be evident that these two hues are necessarily
complementary, for when they are united they contain together all the
elements of the entire spectrum, and therefore appear as white. This may
be illustrated with the aid of the colour-patch apparatus. Place at H
(Fig. 3) a cardboard stencil of the form shown in Fig. 8, and focus upon
it a little spectrum, the principal hues of which are indicated by the
letters R O Y G B V (red, orange, yellow, green, blue, violet). The two
oblong apertures in the card should be of exactly the same height, and the
card so placed that one aperture may admit rays extending from the red end
of the spectrum to about the middle of the green, while the other admits
rays from the remainder of the spectrum. If now the lower aperture be
covered, only the red, orange, yellow, and part of the green rays will
pass through the stencil, and these being combined by the lens K (Fig. 3)
will form upon the screen a bright patch, the colour of which will be
yellow. If the upper aperture be covered, and the rest of the green,
together with the blue and violet rays, allowed to pass through the other,
the colour of the patch will become blue; and if both apertures be
uncovered at the same time, rays from the whole length of the spectrum
will pass through the stencil, and the patch will, of course, turn white.
The yellow and the blue which were compounded from the two portions of the
spectrum are, therefore, in accordance with the definition, complementary
colours.

In a similar manner by dividing the spectrum into any two portions
whatever--as, for example, by the complicated stencil shown in Fig. 9--we
can obtain an indefinite number of pairs of complementary colours.

[Illustration: _Fig. 9.--Stencil Card for Complementary Colours._]

But it is by no means indispensable that both or either of a pair of
complementary colours should be compound. To prove this, two strips of
card with narrow vertical openings A and B are prepared as shown in Fig.
10. The cards are placed one above the other and can be slipped in a
horizontal direction, so that the narrow openings can be brought into any
desired part of the spectrum which is indicated in outline by the dotted
oblong.

[Illustration: _Fig. 10.--Slide for mixing any two Spectral Colours._]

Bring the opening A of the upper card into the yellow of the spectrum and
the opening B of the lower card into the blue. The bright patch formed
upon the screen will then be illuminated by simple blue and yellow rays;
yet it will be white--not green, as it would be if Brewster's theory were
correct. If upon the first trial the white should not be absolutely pure,
it can easily be made so by partially covering either A or B--the first if
the white is yellowish, the second if it is bluish. Simple spectral blue
and yellow are therefore no less truly complementary colours than are the
compound hues formed when the spectrum is divided into two parts.

It is noticeable, however, that the white light resulting from the
combination of blue and yellow, though it cannot be distinguished by the
eye from ordinary white light, is yet possessed of very different
properties. Most coloured objects when illuminated by it have their hues
greatly altered; a piece of ribbon, for example, which in common light is
bright red, will appear when held in the blue-yellow light to be of a dark
slate colour, almost black.

If the opening A is placed in any part whatever of the spectrum except the
green, it will always be possible, by moving B backwards or forwards, to
find some other part where the colour is complementary to that at A. To
green there is no simple complementary; a purple is required, which is
not found in the spectrum, but may be formed by combining small portions
of spectral blue and red. For studying mixtures of three simple colours, a
third slide may be added to the two shown in Fig. 10.

The following little table gives the principal pairs of complementary
colours.

TABLE OF COMPLEMENTARY COLOURS.

  Red                  Greenish-blue
  Orange               Sky-blue
  Yellow               Blue
  Greenish-yellow      Violet
  Green                Purple

CHAPTER III.

SOME OPTICAL DEFECTS OF THE EYE.

More than one reference has been made to the fact that the sense of sight,
even in its best normal condition, is characterised by certain defects and
anomalies. Some of these arise directly from causes inherent in the design
or structure of the eye itself, and may be broadly classified as physical;
others are of psychological origin, and result from the erroneous
interpretations placed by the mind upon the phenomena presented to it
through the medium of the optic nerve and the brain.

Among the numerous physical defects of the eye none is more remarkable
than the absence of means for properly correcting chromatic aberration.
This defect is remarkable because it appears--at least to those who are
without actual experience in the manufacture of eyes--to be one which
might very easily have been avoided. So far as a mere theorist can judge,
an achromatic arrangement of lenses would have been just as simple and
just as cheap (if I may use the term) as the arrangement with which we
find ourselves provided. It is true that we manage to go through life very
well with our uncorrected lenses, and indeed it is hardly possible by
ordinary observation to detect any evidence of the imperfection. Yet its
existence in a glaring degree is undoubted, and can be readily
demonstrated by a great variety of methods. The conclusion is inevitable
that with achromatic eyes our vision would be improved, but whether there
may not possibly exist reasons why such an improvement could only be
achieved at a disproportionately high cost is a question which cannot at
present be answered.

Without going into matters which are dealt with in every elementary text
book of optics or general physics, it may be desirable to explain shortly
what is meant by the terms chromatic aberration, and achromatism.

[Illustration: _Fig. 11.--Refraction of monochromatic Light by a lens._]

Let L L, Fig. 11, represent in section a circular convex lens, and P a
luminous point, which is most conveniently supposed to be situated on the
axis of the lens. Imagine P to be surrounded in the first instance by a
glass shade which transmits only monochromatic red light. So much of the
light from P as falls upon the lens will be refracted to a point at the
conjugate focus F, and after passing this point will diverge again; the
refracted light rays will, in fact, form a double cone, of which F is the
apex. If a white screen be held at F, there will be focussed upon it a
small clearly-defined image of the luminous point. If, however, the screen
be moved nearer to or further from the lens, it will cut the cone of
light, and the image will then no longer appear as a point, but as a
circular red disk, which will be larger the greater the distance of the
screen from F. Such a disk is known as a "diffusion circle."

Suppose now that we substitute for the red glass, surrounding the source
of light, a purple one capable of transmitting not only red rays but
violet as well. The lens will cause both the red and the violet rays which
pass through it to converge; but since the violet rays are more
refrangible--more easily refracted or bent aside out of their straight
course--than the red, there will now be two double cones, as shown in Fig.
12, where the contours of the red cones are represented by solid lines and
those of the violet by dots.

[Illustration: _Fig. 12.--Refraction of dichromatic Light._]

The focus of the red rays will as before be at F, but that of the violet
will be nearer to the lens, as at H, and this being so, it is evident that
a well defined image of the purple source of light cannot possibly be
formed upon a screen placed anywhere behind the lens. Held in the position
indicated by the line C C, where it passes through the focus of the red
rays, the screen cuts one of the cones of violet light, and the image at F
will appear to be surrounded by a violet halo. Held at A A, the screen
evidently receives an image with a red halo round it. Only at B B, in the
plane where the surfaces of the red and violet cones cut one another, will
it be possible to obtain an image without a coloured border; but here good
definition is unattainable, for neither the red nor the violet rays are in
focus, and the luminous point is represented by a purple disk or diffusion
circle of sensible diameter.

If rays of every possible refrangibility are allowed to fall upon the
lens, as is the case when the source of light is not shielded by any
coloured glass, there will be formed an indefinite number of pairs of
cones, the apices of which will lie along the straight line joining H and
F. It is clear that all these cones cannot possibly intersect in a single
plane, and consequently no position can be found where the edge of the
projected image is perfectly free from colour, though at a certain
distance from the lens, where the brightest constituents of the
light--namely, the yellow and green--are approximately focussed, the
coloured border is least conspicuous, and is of a purple tint, due to the
mixture of the red and violet rays.

For these reasons a single glass lens cannot, except with homogeneous
light, be made to give a perfectly distinct image of a luminous point, nor
of an illuminated object, the surface of which may be regarded as an
assemblage of points. Such a lens, therefore, is never employed when good
definition is required. The confusion resulting from the unequal
refrangibility of the differently coloured rays is said to be due to the
chromatic aberration of the lens.

In connection with this matter, the history of physical optics contains an
interesting little episode. It occurred to Sir Isaac Newton that although
a single lens could never be free from chromatic aberration, yet it might
be possible to arrange a so-called achromatic combination of lenses in
such a manner as to overcome the defect and bring all the rays issuing
from a point, whatever their refrangibility, to one focus. Experiments
which he undertook for the purpose of testing the matter led him to form
the conclusion that such a result could never be attained, the amount of
colour dispersion in all substances being, as he stated, always exactly
proportional to that of refraction. For this reason he confidently
announced that it was useless to attempt the construction of a really good
refracting telescope, and so great was the authority attaching to his name
that for many years all efforts in that direction were abandoned.

Nevertheless from time to time certain philosophers ventured to surmise
that Newton might perhaps have been mistaken, and the curious thing is
that they all based their scepticism upon what they considered the
self-evident fact of the achromatism of the eye. The system of lenses in
the eye, they argued, being unquestionably achromatic, why should not an
equally effective combination be constructed artificially?

At length, more than eighty years after Newton had made and published his
fundamental experiments, it occurred to a working optician, John Dollond,
that it might be worth while to repeat them, and upon doing so he at once
found that Newton was wrong in his facts, the results as recorded by him
being in direct opposition to the truth. With proper respect for the
memory of a great man it is usual to speak of Newton's observation as a
"hasty" one, but if in these days a junior science student were to be
guilty of a similar lapse, his conduct would not impossibly be stigmatised
as grossly careless.

Having established Newton's error, Dollond found little difficulty in
constructing achromatic lenses of very satisfactory quality; telescopes of
his manufacture long enjoyed the highest reputation, and the best optical
instruments of the present day are the direct offspring of his invention.

Those who entertained the opinion that Newton's conclusion was erroneous
were therefore in the right, but it is remarkable that the reason upon
which that opinion rested was altogether invalid, for, as I have said, the
lenses of the eye are by no means achromatic. Of the many ways in which
this can be demonstrated, the following is one of the most impressive.

Let a long and narrow spectrum of the electric light be projected upon a
white screen, the prisms and lenses being carefully arranged in such a
manner as to ensure that the upper and lower edges of the spectrum are
clearly defined and strictly parallel. To an observer standing close to
the screen, the spectrum will present the appearance of a bright
parti-coloured rectangle. But viewed from a distance of a few feet the
spectrum will not seem to be rectangular, its upper and lower edges no
longer appearing to be parallel, but to diverge, fan-like, towards the
blue and violet, as shown in Fig. 13. This is because the violet and some
of the blue rays proceeding from an object at a little distance cannot by
any effort be focussed upon the retina. They are too much refracted, and
the mechanism by which the eye is adjusted is incompetent to diminish the
convexity of the lenses sufficiently to enable them to project a clear
image. Every point is expanded into a luminous circle, which is the larger
the more refrangible the rays, and it is the extension of these diffusion
circles beyond the proper boundaries of the image that gives the
appearance of increased breadth.

It is a simple matter to counteract the effects of undue convexity by
means of a concave lens. If a normal-eyed person, to whom the violet end
of the spectrum when seen from a distance appears blurred and widened,
will look at it through suitable glasses adapted for short sight, he will
at once see it clearly defined and of its proper width.

[Illustration: _Fig. 13.--Narrow Spectrum as seen from a distance._]

Let a rectangular patch of white light having about the same dimensions
as the rectangular spectrum be now thrown upon the screen. The light
reflected from the patch will contain, as before, all the various spectral
colours, but they will be mixed or superposed, instead of being spread out
side by side. The patch will send forth, among others, can yellow and
green rays, which the eye easily focus; it will also send out violet rays,
which, as we have shown, cannot be focussed by the unassisted eye. Owing
to the existence of diffusion circles there must necessarily be formed
upon the retina a violet image larger than the approximately superposed
images due to rays of brighter colours. Viewed from a distance therefore
the white patch might be expected to exhibit a violet border. Yet it may
be confidently asserted that the observer will not be conscious of seeing
any such border, for though one actually exists, it is possessed of such
comparatively feeble luminosity that it is lost in the glare produced by
the brighter rays.

It is, however, possible to cut off these brighter rays by interposing
between the projection lantern and the screen a combination of glasses
which has been found by trial with a spectroscope to transmit only dark
blue and violet light. The rectangle will then be of a blue-violet colour,
and when looked at closely, will still be quite clear and sharply defined,
but viewed from a little distance it will appear blurred and of an
exaggerated size.

Another and perhaps even better way of demonstrating this last effect is
to enclose the source of light (which should be a powerful one, such as
an arc lamp or limelight) inside a box having a ground-glass window in one
side. When the window is covered by the coloured glasses its outline
cannot be clearly distinguished unless the observer is near, but if he
uses suitable concave spectacles, he will be able to see it quite
distinctly, even from a considerable distance.

It is well known that ideas of distance are associated with certain
colours. A room gives one the impression of being larger when it is
papered or painted a blue-violet colour than when its colouring is red. In
the former case the walls seem to retire from the spectator, in the latter
to approach him. So too a red spot upon a violet ground appears to be
distinctly raised above the surface, while a violet spot upon a red
ground appears to be depressed. These phenomena are fully explained by the
imperfect achromatism of the eye. When we look at a red object, we have to
adjust the crystalline lens by means of the ciliary muscle in exactly the
same way as when we look at a near object; in both cases it is necessary
to increase the convexity of the lens, and so diminish its focal length,
in order to obtain a clear image upon the retina. And again, when we wish
to see a blue or violet thing distinctly, the ciliary muscle must be
relaxed and the convexity of the lens as far as possible diminished, just
as if the gaze were directed to the horizon. We are accustomed to estimate
the distances of things largely by the muscular effort required to focus
their images, and thus it happens that the colour red comes to be
associated in our minds with nearness, and violet with remoteness.

These psychological effects are perfectly well marked even with the impure
colours met with in ordinary life, but they are naturally more evident
when the colours observed are pure, like those of the spectrum.

A beautiful example is that presented by the pair of short bright spectra
formed upon the screen when a double slit is used shaped like the letter
V. The gorgeously coloured V seems to stand out in strong relief like a
pair of inclined boards, the nearer edges being red, the farther ones
violet. (See Fig. 14.)

[Illustration: _Fig. 14.--Spectrum formed with V-shaped Slit._]

In many other ways, and with little or no apparatus, any one may easily
convince himself that the different constituents of white light are not
equally refracted by the lenses of the eye. Look, for instance, at the
incandescent filament of an electric lamp through a piece[7] of common
dark blue cobalt glass, which has the property of obstructing the coloured
rays corresponding to the middle of the spectrum, while transmitting the
red and the blue. Seen from a distance of only a few inches, the filament
appears to be pale blue with a bright red border, the blue rays being
perfectly focussed, while the red form diffusion circles. Move some six or
eight feet away and look again; the colours will now be reversed, the
filament appearing red and the border blue-violet. From a still greater
distance--about fifteen or twenty feet--the whole lamp-bulb will seem to
be filled with a blue-violet glow, due to large diffusion circles, while
the red image of the filament may be even more clearly defined than
before. No doubt it is partly owing to the non-achromatism of the eye that
distant arc lights always appear to have a yellowish hue, even when the
air is quite clear; a considerable proportion of their blue and violet
components must necessarily be lost by extensive diffusion.[8]

Again, look at a sunlit landscape or a printed wall poster through a
combination of coloured glasses which will transmit only the violet end of
the spectrum. You will find yourself for the time terribly short-sighted,
everything appearing blurred and indistinct. But if you resort to the
usual corrective for myopia, and put on a pair of concave spectacles, your
normal vision will be restored; trees and houses will be seen as clearly
as the feebleness of the light transmitted by the coloured glasses will
permit, and the letters of the poster will become easily legible.

Now, of course, the interposition of coloured glasses does not actually
give rise to these blurred images; it merely enables one to detect their
existence. Under ordinary conditions they always accompany the clearer
images produced by the more luminous rays, and their presence cannot fail
to exert a detrimental effect upon the general definition. Such blurs must
at least tend to fog the darker portions of the focussed picture, and
though we are not distinctly conscious of their existence, it is certain
that if they were annulled the acuteness of our vision would be improved.

The diffusion circles produced by the red rays, when the eye is
accommodated (as it commonly is) for the yellow and green, are less
conspicuous than those due to the most refrangible rays. Yet I find it
impossible to focus a red object, such as the filament of an electric lamp
screened by a properly selected deep red glass, when placed at the
ordinary distance of distinct vision--some nine or ten inches from the
eye--without the aid of a convex lens. In this case one is not too
short-sighted but too long-sighted to see the object distinctly; in other
words, the lenses of the eye cannot refract the red rays sufficiently to
produce well-defined images upon the retina, and the refraction has to be
increased by artificial means.

Though, as I have said, it is difficult, or even impossible to detect any
trace of a coloured border when looking at a bright object for which the
eye is accommodated, it is quite easy to bring such borders into
prominence if the object is at a distance a little too great or too small
for distinct vision. A very remarkable device for the purpose is one due
to von Bezold. This may be illustrated by using a non-achromatic glass
lens, such as a common magnifying glass, to project a transparency or
lantern-slide upon which is painted a target-like design, consisting of a
series of circular black bands surrounding a circular black spot.[9] (See
Fig. 15.)

[Illustration: _Fig. 15.--Bezold's Diagram._]

Suppose the glass lens to represent the lenses of a gigantic eye (in a
definite condition of accommodation) and the screen the retina. The
imaginary eye is looking at the design on the lantern-slide, and when this
is at the distance of most distinct vision a fairly well defined image of
the target is formed upon the retinal screen.

Now gradually move the lantern slide towards the lens (or the lens towards
the slide), thus bringing it too near for distinct vision. This has the
effect of enlarging the diffusion circles formed by the less refrangible
rays corresponding to the red end of the spectrum, and at the same time of
diminishing those formed by the more refrangible rays corresponding to the
violet end. The first result is that the circular dark bands become
reddish brown, and the spaces between them bluish. As the distance between
the lens and the slide is still further diminished, the tints become more
varied and brilliant, until at last there appears a beautiful series of
coloured rings around a bright red central spot.

These effects are not produced when the lens employed is an achromatic
one; with such a lens the diffusion circles are all enlarged or diminished
together, and a to-and-fro movement of the lantern slide (or of the lens)
merely affects the definition of the image without causing any perceptible
dispersion of colour.

Now it is noteworthy that the chromatic phenomena exhibited with the
uncorrected glass lens are quite well shown by the lenses of the eye. It
is only necessary to hold the lantern-slide before a bright background and
gradually bring it so close to the eye that the design cannot be seen
distinctly. The black bands will then appear to turn brown, the white ones
blue, and the central spot bright red. The printed diagram (Fig. 15) will
itself show the colours if it is held at a distance of four to five inches
from one eye in a good light.

One more experiment may be referred to. Look with one eye at a
well-lighted page of print, and with a strip of brown paper, held quite
near the eye, cover about half the pupil. The black letters will now
appear to be bordered with colour--blue towards the apparent edge of the
brown paper, orange on the opposite side. If the letters are white on a
black ground, as sometimes happens in the case of advertisements, the
colours will be interchanged. The cause of the coloured borders will be
readily understood from an inspection of the diagram Fig. 12; but it must
be remembered that the images on the retina are inverted.

Thus it is proved beyond all question that the lenses of the eye do not
form an achromatic combination.

Another peculiarity by which the eye is affected, and which does not occur
in optical instruments, is that known as _astigmatism_. The surface of the
cornea, which, with the aqueous humour, forms the outer lens, is not often
perfectly spherical; generally it is shaped something like the bowl of a
spoon, the curvature being greater vertically than horizontally. Rays
issuing from a luminous point do not, after refraction by such a lens,
cross at a single focus, but along two short straight lines, the one
horizontal the other vertical, which are at different distances from the
lens; thus a distinct image of a small point cannot anywhere be produced.

[Illustration: _Fig. 16.--Effect of Astigmatism._]

A very curious result follows from this deformity. If two straight lines
are drawn at right angles to each other, as in Fig. 16, it is impossible
to see both of them quite clearly at the same time. When the paper is held
at a certain short distance from the eye--about eight or nine inches--the
horizontal line appears black and well defined, while the other is rather
grey and indistinct; at a greater distance the upright line seems to be
the blacker. The effect is very well shown by the diagram, Fig. 17. To
most persons the lines occupying the middle portion will appear either
much blacker or much lighter than those at the two ends, though in fact
they are exactly alike. When this form of astigmatism is excessive, it may
be corrected by the use of spectacles fitted with cylindrical lenses.

[Illustration: _Fig. 17.--Effect of Astigmatism._]

But there is a different kind of astigmatism--irregular astigmatism it is
called--to which every one is more or less a victim, and which cannot be
relieved by any artificial appliances. Fortunately it does not often cause
much practical inconvenience.

Irregular astigmatism is commonly demonstrated in the following manner.
With the point of a fine needle, prick a very small hole in a sheet of
tinfoil. Hold up the tinfoil to the light and look at the hole with one
eye, the other being closed. Even at the distance of most distinct
vision--ten inches or thereabouts,--there will probably be a ragged
appearance about the hole, as if it were not perfectly round. But if you
bring the tinfoil an inch or two nearer to the eye, the hole will not seem
to be even approximately circular; it will assume the form of a little
star with five or more distinct rays. The configuration of the star is not
generally the same for the right eye as for the left; the rays may differ
in number and in relative magnitude, and may be inclined at different
angles to the vertical. Fig. 18 shows the stars as they appear to my two
eyes, when the illumination is rather strong.

[Illustration: _Fig. 18.--Star-like Images of luminous Point._]

If several holes are pricked in the tinfoil, each will of course originate
a separate star, and all the stars as seen by the same eye will appear to
be figured upon the same model, though some may be larger or brighter
than others.

[Illustration: _Fig. 19.--Sutures of crystalline Lens._]

There can be no doubt that the stellate form observed in these
experiments, as well as that of the stars of heaven themselves (which with
perfect vision would be seen simply as luminous points), is a consequence
of the singular structure of the crystalline lens of the eye. This does
not consist of one uniform homogeneous mass like a glass lens, but of a
number of separate portions pieced together radially, as indicated
diagrammatically in Fig. 19. In the eye of a newly-born child there are
three such portions, and the radial junctions on one side of the lens are
not opposite to those on the other, but are intermediate. In the figure
the junctions at the front of the lens are represented by continuous lines
and those at the back by dots. The number of sutures found in the adult
lens is generally greater than six.

But while it is certain that these radial sutures are in some way closely
connected with the luminous rays which appear to proceed from a bright
point, it must be confessed that no adequate explanation has yet been
given of the precise manner in which the phenomenon is brought about.
Ophthalmologists seem to have been contented with vague statements about
irregular refraction, but what kind of irregularity would sufficiently
account for all the facts of observation has never, so far as I know, been
exactly determined. The problem can hardly be very difficult of solution,
and would, no doubt, readily yield to the joint efforts of a physicist and
a physiologist.

The phenomena of irregular astigmatism as exhibited by a normal eye are
exceedingly curious, and perhaps I may be allowed to refer briefly to one
or two experiments which I have myself made on the subject.[10]

[Illustration: _Fig. 20.--Multiple Images of a luminous Point._]

Light from an enclosed electric lamp of twenty-five candle power was
admitted through a circular aperture about 1/12-inch (2mm.) in diameter
perforated in a brass plate; a sheet of ground glass and another of
ruby-red glass were placed behind the aperture. When the little disk of
monochromatic light thus formed was looked at through a concave lens of
eleven inches focal length from a suitable distance--nearly two feet in my
own case--it appeared as seven bright round spots upon a less luminous
ground. The appearance is represented in a somewhat idealised form in Fig.
20; but the spots were not quite so distinct nor so regularly disposed as
there shown, neither was their configuration exactly the same for the
right eye as for the left.

On gradually increasing the distance each circumferential spot became at
first elongated radially and afterwards split up into two circular ones;
at the same time new spots were developed upon the luminous ground, the
approximate symmetry of the figure being still retained. Fig. 21
represents a certain stage in this process of expansion. The appearance
was happily likened by an observer who repeated the experiment to that of
a large unripe blackberry.

As the distance was still further increased, the spots continued to
multiply, ultimately becoming very numerous; their arrangement however
soon became much less regular, and the definition of most of them less
distinct. At about twenty feet there was seen a luminous patch, roughly
circular in outline, and covered with irregular speckles; superposed upon
this were strings of bright, partially overlapping spots, corresponding
apparently to the sutures of the crystalline lens.

[Illustration: _Fig. 21.--Increased number of Images._]

When the hole was looked at from a moderate distance through a narrow
slit (about 1/30 inch wide) interposed between the eye and the lens,
there was seen only a single row of circular spots, which were arranged
sinuously, as shown in Fig. 22. A slight movement of the slit in the
direction perpendicular to its length produced a wave-like motion of the
circles, suggestive, as pointed out by the excellent observer before
referred to of the wriggling of a caterpillar.

[Illustration: _Fig. 22.--Multiple Images seen through a Slit._]

By sufficiently increasing the distance between the source of light and
the eye, as many as twenty-four or twenty-five bright spots might be made
to appear in the row, but they could not be counted with any great
certainty. At a still longer distance or with a lens of shorter focus
(convex or concave) they became less distinct, and finally seemed to be
resolved into a multitude of small blurred images--probably several
hundreds--which were separated from one another by hazy dark lines.

[Illustration: _Fig. 23.--Images of an electric lamp Filament._]

I thought that the observations might be rendered easier if the source of
light had a more distinctive and conspicuous form than that of a simple
circle. Some experiments were therefore made with semi-circular and
triangular holes, and these were in some respects preferable; but far
better results were afterwards obtained by using as a source of light the
horse-shoe shaped filament of an electric lamp, screened by a coloured
glass. When such a lamp was looked at through a lens, concave or convex,
of about six inches focus, from a distance of a few feet, the roughly oval
patch of luminosity formed upon the retina, instead of being a mere
ill-defined blur, such as would be produced if the transparent media of
the eye were composed of homogeneous substances like glass or water,
appeared to be made up of a crowd of separate images of the filament, some
being brighter than others, as is shown in the diagram Fig. 23.

[Illustration: _Fig. 24A.--Images with horizontal Slit._]

[Illustration: _Fig. 24B.--Images with vertical Slit._]

If a spectroscope slit was interposed between the eye and the lens, and
its width suitably adjusted, only a single row of filaments was observed,
the appearances with the slit in horizontal, vertical, and intermediate
positions being as represented in Fig. 24, A, B, C. As before, it was
found possible by gradually retiring from the lamp to bring the number of
images up to about twenty-five, but attentive examination showed that
most of these really consisted of clusters, each composed of perhaps
fifteen or twenty confused images of the filament. A stronger lens still
further separated the constituents of the clusters, exhibiting a total
number of indistinctly seen images which was estimated to amount to nearly
five hundred. Assuming the diameter of the pupil of the eye to be
one-fifth of an inch, these observations seem to indicate as a cause of
the phenomenon some fairly regular anatomical structure, situated in or
near the crystalline lens and composed of elements measuring about 1/2000
inch in length or breadth. Whether the structure which gives rise to these
multiple images is to be found in the fibres of the crystalline lens
itself, or in the membranes which cover it, is a question upon which I
will not venture an opinion.

[Illustration: _Fig. 24C.--Images with oblique Slit._]

It is indeed wonderful that an organ affected by peculiarities of which
those that have been referred to are merely specimens, should give such
well-defined pictures as it does when accommodated for the objects looked
at.

CHAPTER IV.

SOME OPTICAL ILLUSIONS.

Optical illusions generally result from the mind's faulty interpretation
of phenomena presented to it through the medium of the visual organs. They
are of many different kinds, but a large class, which at first sight may
seem to have little or nothing in common, arise, I believe, from a single
cause, namely, the inability of the mind to form and adhere to a definite
scale or standard of measurement.

In specifying quantities and qualities by physical methods, the standards
of reference that we employ are invariable. We may, for example, measure
a length by reference to a rule, an interval of time by a clock, a mass or
weight by comparison with standardised lumps of metal, and in all such
cases--provided that our instruments are good ones and skilfully used--we
have every confidence in the constancy and uniformity of our results.

But two lengths, which when tested with the same foot rule are found to be
exactly equal, are not necessarily equal in the estimate formed of them by
the mind. Look, for instance, at the two lines in Fig. 25. According to
the foot rule each of them is just one inch in length, but the mind
unhesitatingly pronounces the upright one to be considerably longer than
the other; the standard which it applies is not, like a physical one,
identical in the two cases. Many other examples might be cited
illustrative of the general uncertainty of mental estimates.

[Illustration: _Fig. 25.--Illusion of Length._]

The variation of the vague mental standard which we unconsciously employ
seems to be governed by a law of very wide if not universal application.
Though this law is in itself simple and intelligible enough, it cannot
easily be formulated in terms of adequate generality. The best result of
my efforts is the following unwieldy statement:--The mental standard which
is applied in the estimation of a quality or a condition tends to
assimilate itself, as regards the quality or condition in question, to the
object or other entity under comparison of which the same (quality or
condition) is an attribute.

In plainer but less precise language, there is a disposition to minimise
extremes of whatever kind; to underestimate any deviation from a mean or
average state of things, and consequently to vary our conception of the
mean or standard condition in such a manner that the deviation from it
which is presented to our notice in any particular instance may seem to be
small rather than large.

Thus, when we look at a thing which impresses us as being long or tall,
the mental standard of length is at once increased. It is as if, in
making a physical measurement, our foot rule were automatically to add
some inches to its length, while still supposed to represent a standard
foot: clearly anything measured by means of the augmented rule would seem
to contain a fewer number of feet, and, therefore, to be shorter than if
the rule had not undergone a change.

It is not an uncommon thing for people visiting Switzerland for the first
time to express disappointment at the apparently small height of the
mountains. A mountain of 10,000 feet certainly does not seem to be twenty
times as lofty as a hill of 500. The fact is that a different scale of
measurement is applied in the two cases; though the observer is unaware of
it, the mountain is estimated in terms of a larger unit than the hill.

[Illustration: _Fig. 26.--Illusion of Length._]

If we mentally compare two adjacent things of unequal length, such as the
two straight lines in Fig. 26, there is a tendency to regard the shorter
one as longer than it would appear if seen alone, and the longer one as
shorter. The lower of the two lines in the figure is just twice as long as
the other, but it does not look so; each is regarded as differing less
than it really does from an imaginary line of intermediate length.

[Illustration: _Fig. 27.--Illusion of Length._]

Two divergently oblique lines attached to the ends of a straight line as
at A, Fig. 27, suggest to the mind the idea of lengths greater than that
of the straight line itself; the latter, being thought of as comparatively
small, is therefore estimated in terms of a smaller unit than would be
employed if the attachments were absent, and consequently appears longer.
If, on the other hand, the attachments are made convergent, as at B,
shorter lengths are suggested; the length of the given line is regarded as
exceeding an average or mean; the standard applied in estimating it is
accordingly increased, and the line is made to seem unduly short. In spite
of appearances to the contrary, the two lines A and B are actually of the
same length.

By duplicating the attached lines, as shown in Fig. 28, their misleading
effect becomes intensified. Here we have a well-known illusion of which
several explanations have been proposed. The fallacy is, I think,
sufficiently accounted for by variation of the mental standard, in
accordance with the law to which I have called attention.

[Illustration: _Fig. 28.--Illusion of Length._]

A number of other paradoxical effects may be referred to the operation of
the same law. Fig. 29 shows a curious specimen. At each end of the diagram
is a short upright line; exactly in the middle is another; between the
middle and the left hand end are inserted several more lines, the space to
the right of the middle being left blank. Any one looking casually at the
diagram would be inclined to suppose that it was not equally divided by
what purports to be the middle line, the left hand portion appearing
sensibly longer than the other.

[Illustration: _Fig. 29.--Illusion of Distance._]

It is not difficult to indicate the source of the illusion. When we look
at the left hand portion we attend to the small subdivisions, and the
mental unit becomes correspondingly small; while in the estimation of the
portion which is not subdivided a larger unit is applied.

As one more example I may refer to a familiar trap for the unwary. Ask a
person to mark upon the wall of a room the height above the floor which he
thinks will correspond to that of a gentleman's tall hat. Unless he has
been beguiled on a former occasion, he will certainly place the mark
several inches too high. Obviously the height of a hat is unconsciously
estimated in terms of a smaller standard than that of a room.

The illusion presented by the horizontal and vertical lines in Fig. 25
(p. 132) depends, though a little less directly, upon a similar cause. We
habitually apply a larger standard in the estimation of horizontal than of
vertical distances, because the horizontal magnitudes to which we are
accustomed are upon the whole very much greater than the vertical ones.
The heights of houses, towers, spires, trees, or even mountains are
insignificant in comparison with the horizontal extension of the earth's
surface, and of many things upon it, to which our notice is constantly
directed. For this reason, we have come to associate horizontality with
greater extension and verticality with less, and, in conformity with our
law, a given distance appears longer when reckoned vertically than when
reckoned horizontally. Hence the illusion in Fig. 25.

But it is not only in regard to lengths and distances that the law in
question holds good; in most, if not all cases in which a psycho-optical
estimate is possible, the mental standard is unstable and tends to
assimilate itself, as regards the quality or condition to be estimated, to
the entity in which the same is manifested. This is true, for example, in
judging of an angle of inclination or slope; of a motion in space; of
luminous intensity, or of the purity of a colour.

Every cyclist knows how difficult it is to form a correct judgment of the
steepness of a hill by merely looking at it. Not only may a slope seem to
be greater or less than it really is, but under certain circumstances a
dead level sometimes appears as an upward or downward inclination, while
a gentle ascent may even be mistaken for a descent, and _vice versa_.

We usually specify a slope by its inclination to a level plane which is
parallel to the plane of the horizon, or at right angles to the direction
of gravity. At any given spot the level is, physically considered,
definite and unalterable. In forming a mental judgment of an inclination,
we employ as our standard of reference an imaginary plane which is
intended to be identical with the physical level. But our mental plane is
not absolutely stable; when we refer a slope to it, we unconsciously give
the mental plane a slight tilt, tending to make it parallel with the
slope. Hence the inclination of a simple slope, when misleading
complications are absent, is always underestimated.

[Illustration: _Fig. 30.--Illusion of Inclination._]

This may be illustrated by the diagram Fig. 30. If A B represents a truly
horizontal line, the slope of the oblique line C D is correctly specified
by the angle C O A. But if we have no instrument at hand to fix the level
for us, we shall infallibly imagine it to be in some such position as that
indicated (in an exaggerated degree) by the dotted line E F, while the
true level A B will appear to slope oppositely to C D.

This class of illusion is remarkably well demonstrated by Zöllner's lines,
Fig. 31; the two thick lines which appear to diverge from left to right,
are in truth strictly parallel.

[Illustration: _Fig. 31.--Zöllner's Lines._]

I need not discuss in further detail the various illusions to which a
cyclist is subjected when slopes of different inclinations succeed one
another: they all follow simply from the same general principle.

A thing is said to be in motion when it is changing its position
relatively to the earth, which for all practical purposes may be regarded
as motionless. The state, as regards motion, of the earth and anything
rigidly attached to it, therefore constitutes the physical zero or
standard to which the motion of everything terrestrial is referred. But
the corresponding mental standard, especially when it cannot easily be
checked by comparison with some stationary object, is liable to deviate
from the physical one; it tends in fact to move in the same direction as
the moving body which is under observation, and the apparent speed of the
body is consequently rather less than it should be.

The influence exerted upon the judgment sometimes even persists for an
appreciable period after the exciting cause has ceased to be operative, as
when the moving body is lost sight of or has suddenly come to rest; in
such cases fixed objects, being compared with the delusive mental
standard, appear for a few seconds to be moving in the opposite direction.

I have devised a lantern slide (Fig. 32) by the aid of which this
phenomenon may be rendered very evident. In a square plate of metal is cut
a vertical slot, which is shaded in the figure; behind the plate is an
opaque disk, which, by means of suitable mechanism, can be made to rotate
about its centre. The disk has a spiral opening cut in it of the same
width as the slot, as indicated by the dotted line. The slide is placed in
an optical lantern, and the light passing through the aperture formed
where the slot is crossed by the spiral opening, produces a small bright
patch upon a white screen hung at a suitable distance from the lantern.

[Illustration: _Fig. 32.--Slide for showing Illusions of Motion._]

When the disk is turned in the direction indicated by the arrow, the
bright patch moves upwards and ultimately disappears; but at the moment
of its disappearance a fresh patch starts from below, which also moves in
the upward direction; thus there is formed upon the screen a continuous
succession of ascending bright patches. After these have been observed for
about a quarter of a minute, the disk is suddenly stopped, and the
persistence of the fallacious mental standard is at once demonstrated. For
the bright patch does not appear to be at rest, as it actually is, but to
creep steadily downwards, continuing to do so more and more slowly for
perhaps as long as ten seconds. The upward motion of the bright patches
had led the observer to assume a slower upward motion as the zero, or
standard of no motion, and reference of the really stationary patch to
this physically false standard induces the illusion that the patch is
descending.

This experiment is most successful when the bright patches are projected
upon the middle of a large screen. The disk should turn about three times
in a second, and the room should be feebly illuminated, but not quite
dark.

[Illustration: _Fig. 33.--Illusions of Motion._]

A very remarkable illusion which no doubt depends upon the same principle
as the last, though its form is entirely different, is that to which the
diagram Fig. 33 relates. So far as I am aware, it has not before been
noticed.

Two intersecting straight lines, the one upright and the other sloping, as
shown in the figure, are drawn upon a card. The card is to be held
vertically before the eyes at the distance of most distinct vision, and
waved up and down through a distance of a few inches. The oblique line
will then appear to oscillate transversely, as if it were not rigidly
attached to the card.

This is the result of underestimating the speed at which the card is
moved. Rather than recognise the true state of things, the mind prefers to
accept the suggestion that the upward or downward movement of the point of
intersection is in part due to oppositely directed horizontal movements of
the lines themselves upon the surface of the card. When the card is
descending the vertical line is supposed to slide a little to the right
and the oblique line to the left, which would have the effect of lowering
their point of intersection independently of the downward movement of the
card itself. When the card ascends, these horizontal movements are
supposed to be reversed, and the point of intersection consequently
raised. The assumption is exactly analogous to that made when an angle of
slope is unwittingly minimised.

Another example of the instability of a mental standard occurs in the
estimation of luminosity. The luminosity of a bright object, if reckoned
in terms of the same unit as that applied in judging of a less bright one,
would appear to be greater than it actually does appear, and this quite
independently of any effects of fatigue.

[Illustration: _Fig. 34.--Illusion of Luminosity._]

The fact is well illustrated by a familiar experiment. Fig. 34 is
photographed from a transparency made by superposing several different
lengths of gelatine film so as to form a series of steps. At the
right-hand end of the image the light has passed through only one layer of
the film; in the next division it has traversed two layers, in the next,
three, and in the last, four. The luminosity of each of the four squares
into which the oblong is divided is, in a physical sense, quite uniform,
but the mental standard of luminosity varies for different parts of the
image, increasing or decreasing, as the case may be, not _per saltum_, but
smoothly and continuously, with the result that each square looks brighter
towards the left than towards the right. The appearance, which is often
likened to that presented by a fragment of a fluted column, is equally
well shown when the diagram is illuminated instantaneously by an electric
spark, and cannot, therefore, be accounted for by retinal fatigue.

If the squares are separated from one another by distinct lines of
demarcation, however fine, the standard of luminosity becomes uniform for
each square, and the illusion vanishes. This fact sufficiently disposes
of the hypothesis which has been advanced to the effect that the
phenomenon is due to physiological causes.

I now propose to discuss a curious consequence of the fluctuation of
unaided judgment as regards the purity of a colour.

When any colour occupies a predominant place in the field of vision, we
are apt to consider it as being less pure, or paler, than we should if it
were less conspicuous, our standard of whiteness tending to approximate
itself to the colour in question.

For the sake of clearness let us first confine our attention to a definite
colour--say red. An absolutely pure red is one that is entirely free from
any admixture of white; in proportion as it contains more and more white,
the more impure, or in other words, the more pale does it become, until at
last all trace of perceptible redness is lost and the colour is
indistinguishable from white.

[Illustration: _Fig. 35.--Illusion of Colour._]

A convenient way of picturing the scale of purity is shown in Fig 35. The
shaded oblong may be supposed to represent a painted strip of cardboard
or paper. At the extreme right hand end the colour is supposed to be
absolutely pure red; towards the left the red gradually becomes paler or
more dilute, and at the middle of the diagram it has merged into perfect
whiteness. The figures 0 to 100 from left to right denote the percentage
of free red contained in the mixture at different parts of the scale; the
luminosity is supposed to be uniform throughout.

Now the white light with which the red is diluted may be regarded as
consisting of two parts, one of which is of exactly the same hue as the
pure red itself, and the other an equivalent proportion of the
complementary colour, which in the present case will be greenish-blue. The
fact therefore really is that, as we pass along the scale from 100 to 0,
the _total_ quantity of red in the mixture is not reduced to nothing, but
only to one half, while at the same time greenish-blue is added in
proportions increasing from nought at the extreme right to 50 per cent. of
the whole at the middle of the card. The ordinates of the quadrilateral
figure E D B F show the proportion of red, and those of the triangle E F B
the proportion of greenish-blue, at different parts of the scale.

Regarding the portion of the strip which lies above the point marked 0, as
representing the zero of colour--that is, whiteness or greyness, which is
essentially the same as whiteness--let us continue the diagram in the
negative direction, gradually reducing the quantity of red until it falls
from 50 per cent. of the whole at F to nothing at A, and at the same time
increasing that of the greenish-blue from 50 per cent. at F to 100 per
cent. at A. The resultant hue in the portion of the card between F and A
will be greenish-blue, which begins to be perceptible as a very pale tint
just to the left of F, and increases in purity as A is approached, at
which point the colour will be entirely free from any admixture with
white.

We have in the scale thus presented to our imagination a pair of colours,
each occupying one-half of the scale, and gradually diminishing in purity
towards the middle line; here only, just at the stage where one colour
merges into the other, is there no colour at all, and this region
represents the fixed physical zero or standard from which is reckoned the
purity of a colour corresponding to any other portion of the scale. The
completed scale, it will be observed, though originally intended only for
the case of red, turns out to be equally serviceable for greenish-blue: if
we consider greenish-blue as positive, then the red, being on the other
side of zero, must be regarded as negative. Any other possible pairs of
complementary colours may be similarly treated.

This device enables us at once to understand the consequence of mentally
displacing the zero, while physically the scale remains unchanged. When
red is the prevailing colour in the field of vision, we are inclined to
consider it unduly pale; in other words we imagine it to be nearer the
zero of the scale than is actually the case, and so are led to shift our
standard of whiteness from the middle slightly towards the red end of the
scale. The new position assigned to white, being a little to the right of
the point marked 0 in Fig. 35, is one where, under customary
circumstances, the colour would be called pale red. At the same time, an
object which is normally white, and is exactly matched at the middle of
the scale, would be a little to the left of the imaginary zero, and would
consequently appear to be of a greenish-blue tint.

This apparent transformation of white or grey into a decided colour is
most striking when the inducing colour is considerably diluted with white
or is of feeble luminosity. A small fragment of neutral grey paper, placed
upon a much larger piece of a bright red hue, generally appears at the
first glance[11] to be greenish-blue, but if the light is at all strong,
only slightly so. If, however, a sheet of white tissue paper is laid over
the whole, the greenish-blue tint immediately becomes startlingly
distinct, and may even appear more decided than the red itself as seen
through the tissue. The same piece of grey paper, when placed upon a green
ground, appears rose-coloured, and upon a blue ground, yellow, the effect
being always greatly increased by the diluent action of superposed tissue
paper.

There seem to be several reasons, partly physical and partly
psychological, why these contrast colours, as they are called, are more
pronounced when the colour that calls them into existence either has a
somewhat pale tint or is feebly illuminated. Probably the most important
is of a purely physical character. The refracting media of the eye are
much less perfectly transparent than a good glass lens is; they are
sensibly turbid or opalescent, and in consequence of this defect some of
the light which falls upon them is irregularly scattered over the retina.
If we look at a bright red object with a small white patch upon it, the
image of the patch as formed upon the retina is not, physically speaking,
perfectly white, but slightly coloured by diffused red light; owing
however to the psychological influence to which our attention has been
directed, the faint red coloration is not consciously perceived; the same
mental displacement of the zero which, when the exciting colour was
feeble, led us to regard white (or grey) as bluish-green, now causes what
is actually pale red to appear white.

There is no need whatever to assume that the contrast colours with which
we have been dealing are of physiological origin and due to an inductive
action excited in portions of the retina adjacent to those upon which
coloured light falls. On the contrary, it would be a matter for surprise
if the case in question presented an exception to the comprehensive law
which governs the fluctuation of the mental judgment.

Of the operation of this law I have quoted several very diverse instances,
and the number might easily have been increased. Nor is it only in
relation to optical phenomena that the law holds good; in its most general
form, supplemented it may be in some instances by obvious corollaries, it
is applicable to almost every case in which physical attributes of
whatever kind are the subject of unassisted mental judgment.

CHAPTER V.

CURIOSITIES OF VISION.

The function of the eye, regarded as an optical instrument, is limited to
the formation of luminous images upon the retina. From a purely physical
point of view it is a simple enough piece of apparatus, and, as was
forcibly pointed out by Helmholtz, it is subject to a number of defects
which can be demonstrated by the simplest tests, and which, if they
occurred in a shop-bought instrument, would be considered intolerable.

What takes place in the retina itself under luminous excitation, and how
the sensation of sight is produced, are questions which belong to the
sciences of physiology and psychology; and in the physiological and
psychological departments of the visual machinery we meet with an
additional host of objectionable peculiarities from which any
humanly-constructed apparatus is by the nature of the case free.

Yet in spite of all these drawbacks our eyes do us excellent service, and
provided that they are free from actual malformation and have not suffered
from injury or disease, we do not often find fault with them. This,
however, is not because they are as good as they might be, but because
with incessant practice we have acquired a very high degree of skill in
their use. If anything is more remarkable than the ease and certainty
with which we have learnt to interpret ocular indications, when they are
in some sort of conformity with external objects, it is the pertinacity
with which we refuse to be misled when our eyes are doing their best to
deceive us. In our earliest years we began to find out that we must not
believe all we saw; experience gradually taught us that on certain points
and under certain circumstances the indications of our organs of vision
were uniformly meaningless or fallacious, and we soon discovered that it
would save us trouble and add to the comfort of life if we cultivated a
habit of completely ignoring all such visual sensations as were of no
practical value. In this most of us have been remarkably successful; so
much so, that if, from motives of curiosity, or for the sake of
scientific experiment, we wish to direct our attention to the sensations
in question, and to see things as they actually appear, we can only do so
with the greatest difficulty; sometimes, indeed, not at all, unless with
the assistance of some specially contrived artifice.

In the present chapter it is proposed to discuss a few of the less
familiar vagaries of the visual organs, and to show how they may be
demonstrated. Some of the experiments may, it is to be feared, be found
rather difficult; success will depend mainly upon the experimentalist's
ability to lay aside habit and prejudice, and give close attention to his
visual sensations; but it is hardly to be expected that an unskilled
person will at the first attempt observe all the phenomena which will be
referred to.

Among the most annoying of the eccentricities which characterise the sense
of vision is that known as the persistence of impressions. The sensation
of sight which is produced by an illuminated object does not cease at the
moment when the exciting cause is removed or changed in position; it
continues for a period which is generally said to be about a tenth of a
second, but may sometimes be much more or less. It is for this reason that
we cannot see the details of anything which is in rapid motion, but only
an indistinct blur, resulting from the confusion of successive
impressions. If a cardboard disk, which is painted in conspicuous black
and white sectors is caused to rotate at a sufficiently high speed, the
divisions are completely lost sight of, and the whole surface appears to
be of a uniformly grey hue. But if the rapidly rotating disk is
illuminated by a properly timed series of electric flashes, it looks as if
it were at rest, and in spite of the intermittent nature of the light, the
black and white sectors can be seen quite continuously, though as a matter
of fact the intervals of darkness are very much longer than those of
illumination. Persistent impressions of this kind are often spoken of as
positive after-images.

There is a very remarkable phenomenon accompanying the formation of
positive after-images, especially those following brief illumination,
which seems, until comparatively recent times, to have entirely escaped
the notice of the most acute observers. It was first observed
accidentally by Professor C. A. Young, when he was experimenting with a
large electrical machine which had been newly acquired for his laboratory.
He noticed that when a powerful Leyden jar discharge took place in a
darkened room, any conspicuous object was seen twice at least, with an
interval of a trifle less than a quarter of a second, the first time
vividly, the second time faintly. Often it was seen a third time, and
sometimes, but only with great difficulty, even a fourth time. He gave to
this phenomenon the name of recurrent vision; it may perhaps be more
appropriately denominated the Young effect.

By means of the powerful machine presented to the Royal Institution by Mr.
Wimshurst, used in conjunction with a battery of Leyden jars, the Young
effect has been successfully shown to a large assembly. But it is quite
easy to demonstrate it on a small scale with any influence machine which
will give a spark about an inch long. One of the terminals of the machine
should be connected by a wire with the inner coating of a half-pint Leyden
jar, the other with the outer coating, and the discharging balls should be
set a quarter of an inch apart. The observer's eyes must be shielded from
the direct light of the spark by any convenient screen, such as a large
book set on end. The best object for the experiment is a sheet of white
paper, placed in an upright position a few inches away from the terminals
of the machine and exposed to the full light of the discharge.

The room being darkened, let the machine be worked slowly, while the eyes
are turned towards the white paper. This will be seen for a moment when
the spark passes, and, after a dark interval of about one-fifth of a
second, it will make another brief appearance. After a further short
interval of darkness, a second recurrent image will often be seen. It may
be remarked that the effect is most striking when the eyes are not
directed exactly upon the white paper, but above or on one side of it; the
proper distance of the paper from the spark-gap should be found by trial.

Under favourable conditions I have observed as many as six or seven
reappearances of an object which was illuminated by a single discharge.
These followed one another at the usual rate--about five in a second--and
produced a twinkling or quivering effect, closely resembling that
attending a flash of lightning which is not directly seen. There can
indeed be little doubt that the proverbial quiver of the lightning-flash
is in many cases merely an effect of recurrent vision, though sometimes,
of course, as has been shown by photographs, the discharge is really
multiple.

Some years ago I called attention to a very different method of exhibiting
a recurrent image. The apparatus used for the purpose consists of a vacuum
tube mounted in the usual way upon a horizontal axis capable of rotation.
When the tube is illuminated by a rapid succession of discharges from an
induction coil, and is made to rotate very slowly by clockwork (turning
once in every two or three seconds), a very curious phenomenon may be
noticed. At a distance of a few degrees behind the tube and separated from
it by an interval of perfect darkness, comes a ghost. This ghost is in
form an exact reproduction of the tube; it is very clearly defined, and
though its apparent luminosity is somewhat feeble, it can in most cases be
seen without difficulty. The varied colours of the original are, however,
absent, the whole of the phantom tube being of a uniform bluish or violet
tint. If the rotation is suddenly stopped the ghost still moves steadily
on until it reaches the luminous tube, with which it coalesces and so
disappears. (See Fig. 36, where the recurrent image is represented by
dotted lines.)

[Illustration: _Fig. 36.--Recurrent Vision demonstrated with a Vacuum
Tube._]

More recently a fresh series of experiments were undertaken in connection
with the Young effect and certain allied matters, the results being
embodied in a communication to the Royal Society (Proc. Roy. Soc., 1894,
vol. 56, p. 132). Among other things an attempt was made to ascertain how
far a recurrent image was affected by the colour of the exciting light.
With this object two methods of experimenting were employed. In the first,
coloured light was obtained by passing white light through coloured
glasses; in the second and more perfect series of experiments, the pure
coloured light of the spectrum was used. Among other results it was found
that, _cæteris paribus_, the recurrent image was much stronger with green
light than with any other, and that when the excitation was produced by
pure red light, however intense, there was no recurrent image at all.

[Illustration: _Fig. 37.--Recurrent Vision with Rotating Disk._]

For a repetition of my first experiment a mechanical lantern slide is
required containing a metal disk about three inches in diameter which can
be caused to rotate slowly and steadily about its centre. Near the edge of
the disk is a small circular aperture. The slide is placed in a limelight
lantern, and a bright image of the hole is focussed upon a distant screen,
all other light being carefully shut off. When the disk is turned slowly,
the spot of light upon the screen goes round and round, and it is
generally possible to see at once that the bright primary spot appears to
be followed at a short distance by a much feebler spot of a violet colour,
which is the recurrent image of the first. (See Fig. 37.) It is essential
to keep the direction of the eyes perfectly steady, which is not a very
easy thing to do without practice.

If a green glass is placed before the lens, the ghost will be at its best,
and should be seen quite clearly and easily, provided that no attempt is
made to follow it with the eyes. With an orange glass the ghost becomes
less distinctly visible, and its colour generally appears to be
greenish-blue, instead of violet as before. When a red glass is
substituted, the ghost completely disappears. If the speed of rotation is
sufficiently high, the red spot is considerably elongated during its
revolution, and its colour ceases to be uniform, the tail assuming a light
bluish-pink tint. But however great the speed, no complete separation of
the spot into red and pink portions can be effected, and no recurrent
image is ever found.

The spectrum method of observation can only be carried out on a small
scale, and is not suited for exhibition to an audience. It, however,
affords the best means of ascertaining how far the apparent colour of the
recurrent image depends upon that of the primary, a matter of some