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]