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diff --git a/40119-8.txt b/40119-8.txt deleted file mode 100644 index d73d46c..0000000 --- a/40119-8.txt +++ /dev/null @@ -1,3213 +0,0 @@ -Project Gutenberg's Curiosities of Light and Sight, by Shelford Bidwell - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org - - -Title: Curiosities of Light and Sight - -Author: Shelford Bidwell - -Release Date: July 1, 2012 [EBook #40119] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK CURIOSITIES OF LIGHT AND SIGHT *** - - - - -Produced by The Online Distributed Proofreading Team at -http://www.pgdp.net (This file was produced from images -generously made available by The Internet Archive.) - - - - - - - - - -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 -theoretical interest. - -[Illustration: _Fig. 38.--Recurrent Vision with Spectrum._] - -The arrangement adopted is shown in the annexed diagram (Fig. 38). L is a -lantern containing an oxyhydrogen light or an electric arc lamp, S is an -adjustable slit, M a projection lens, P a bisulphide of carbon prism, D a -metal plate in the middle of which is a circular aperture 2 millimetres -(1/12 inch) in diameter. A bright spectrum, 6 or 7 centimetres in length -(about 3 inches), is projected upon this metal plate, and a small -selected portion of it passes through the round hole; thence the coloured -light goes through the lens N to the little mirror Q, which reflects it -upon the white screen R. By properly adjusting the position of the lens N -a sharp monochromatic image of the round hole in the plate D is focussed -upon the screen R. To the back of the mirror Q is attached a horizontal -arm which is not quite perpendicular to the mirror, its inclination being -capable of adjustment. The arm is turned slowly by clock-work, thus -causing the coloured spot on the screen to revolve in a circular orbit -about 30 centimetres (1 foot) in diameter, its recurrent image following -at a short distance behind it. When the mirror turns once in 1-1/2 -seconds, this image appears about 50° behind the coloured spot, the -corresponding time-interval being about one-fifth of a second. - -Using this apparatus, it was found that white light was followed by a -violet recurrent image; after blue and green, when the image was -brightest, its colour was also violet; after yellow and orange it appeared -blue or greenish blue. On the other hand, when a complete spectrum was -caused to revolve upon the screen, the whole of its recurrent image from -end to end appeared violet; there was no suspicion of blue or -greenish-blue at the less refrangible end. For this and other reasons -given in the paper it was concluded that the true colour was in all cases -really violet, the blue and greenish-blue apparently seen in conjunction -with the much brighter yellow and orange of the primary being merely an -illusory effect of contrast. - -It seems likely, then, that the phenomenon which has been spoken of as -recurrent vision, is due principally, if not entirely, to an action of the -violet nerve-fibres. - -Recurrent vision is, no doubt, generally most conspicuous after a very -brief period of retinal illumination, such as was employed in the -experiments which we have been discussing; this is evidently due to the -fact that the effect is most easily perceived when the sensibility of the -retina has not been impaired by fatigue. But by a little effort it may be -detected even after very prolonged illumination, and a practised observer -can hardly avoid noticing a short flash of bluish light which manifests -itself about a quarter of a second after the lights in a room have been -suddenly extinguished; the phenomenon forces itself upon my attention -almost every night when I turn off the electric lights. It need hardly be -pointed out that it represents only a transient phase of the well known -positive after-image, and it had even been observed in a vague and -uncertain sort of way long before the date of Professor Young's -experiment. Helmholtz, for example, mentions the case of a positive -after-image which seemed to disappear and then to brighten up again, but -he goes on to explain--erroneously, as it turns out--that the seeming -disappearance was illusory. - -M. Charpentier, of Nancy, whose work in physiological optics is well -known, was the first to notice and record a remarkable phenomenon which, -in some form or other, must present itself many times daily to every -person who is not blind, but which until about seven years ago had been -absolutely and universally ignored. The law which is associated with -Charpentier's name is this:--When darkness is succeeded by light, the -stimulus which the retina at first receives, and which causes the -sensation of luminosity, is followed by a brief period of insensibility, -resulting in the sensation of momentary darkness. It appears that the dark -period begins about one sixtieth of a second after the light has first -been admitted to the eye, and lasts for about an equal time. The whole -alternation from light to darkness and back again to light is performed so -rapidly, that except under certain conditions, which, however, occur -frequently enough, it cannot be detected. - -[Illustration: _Fig. 39.--Charpentier's Dark Band._] - -The apparatus which Charpentier employed for demonstrating and measuring -the duration of this effect is very simple. It consists of a blackened -disk with a white sector, mounted upon an axis. When the disk is -illuminated by sunlight and turned rather slowly, the direction of the -gaze being fixed upon the centre, there appears upon the white sector, -close behind its leading edge, a narrow but quite conspicuous dark band. -(See Fig. 39.) The portion of the retina which at any moment is apparently -occupied by the dark band, is that upon which the light reflected by the -leading edge of the white sector impinged one sixtieth of a second -previously. - -But no special apparatus is required to show the dark reaction. In Fig. 40 -an attempt has been made to illustrate what any one may see if he simply -moves his hand between his eyes and the sky or any strongly illuminated -white surface. The hand appears to be followed by a dark outline separated -from it by a bright interval. The same kind of thing happens, in a more or -less marked degree, whenever a dark object moves across a bright -background, or a bright object across a dark background. - -[Illustration: _Fig. 40.--Charpentier's Effect shown with the Hand._] - -In order to see the effect distinctly by Charpentier's original method, -the illumination must be strong. If, howover, the arrangement is slightly -varied, so that transmitted instead of reflected light is made use of, -comparatively feeble illumination is sufficient. A very effective way is -to turn a small metal disk, having an open sector of about 60°, in front -of a sheet of ground or opal glass behind which is a lamp. By an -arrangement of this kind upon a larger scale, the effect may easily be -rendered visible to an audience. The eyes should not be allowed to follow -the disk in its rotation, but should be directed steadily upon the centre. - -The acute and educated vision of Charpentier enabled him, even when -working with his black and white disk, to detect the existence, under -favourable conditions, of a second, and sometimes a third, band of greatly -diminished intensity, though he remarks that the observation is a very -difficult one. What is probably the same effect can, however, as pointed -out in my paper of 1894, be shown quite easily in a different manner. If -a disk with a narrow radial slit, about half a millimetre (1/50 inch) -wide, is caused to rotate at the rate of about one turn per second in -front of a bright background, such as a sheet of ground glass with a lamp -behind it, the moving slit assumes the appearance of a fan-shaped luminous -patch, the brightness of which diminishes with the distance from the -leading edge. And if the eyes are steadily fixed upon the centre of the -disk, it will be noticed that this bright image is streaked with a number -of dark radial bands, suggestive of the ribs or sticks of a fan. Near the -circumference as many as four or five such dark streaks can be -distinguished without difficulty; towards the centre they are less -conspicuous, owing to the overlapping of the successive images of the -slit. The effect is roughly indicated in Fig. 41. - -[Illustration: _Fig. 41.--Multiple Dark Bands._] - -The dark reaction known as the Charpentier effect occurs at the beginning -of a period of illumination. There is also a dark reaction of very short -duration at the end of a period of illumination. It should be explained -that, owing to what is called the proper light of the retina, ordinary -darkness does not appear absolutely black: even in a dark room on a dark -night with the eyes carefully covered, there is always some sensation of -luminosity which would be sufficient to show up a really black image if -one could be produced. Now the darkness which is experienced after the -extinction of a light is for a small fraction of a second more intense -than common darkness. - -The first mention of this dark reaction perhaps occurs in an article -contributed to _Nature_ in 1885, in which it was stated that when the -current was cut off from an illuminated vacuum tube "the luminous image -was almost instantly replaced by a corresponding image which seemed to be -intensely black upon a less dark background," and which was estimated to -last from a-quarter to a-half second. "Abnormal darkness," it was added, -"follows as a reaction after luminosity." - -[Illustration: _Fig. 42.--Temporary Insensitiveness of the Eye._] - -In the Royal Society paper before referred to the point is further -discussed, and a method is described by which the stage of reaction may be -easily exhibited and its duration approximately measured. If a translucent -disk, made of stout drawing-paper and having an open sector, is caused to -rotate slowly in front of a luminous background, a narrow radial dark -band, like a streak of black paint, appears upon the paper very near the -edge which follows the open sector. From the space covered by this band -when the disk was rotating at a known speed, the duration of the dark -reaction was calculated to be about one-fiftieth of a second; my original -estimate was therefore an excessive one. The experiment is illustrated in -Fig. 42. - -One more interesting point should be noticed in the train of visual -phenomena which attend a period of illumination. The sensation of -luminosity which is excited when light first strikes the eye is for about -a sixtieth of a second much more intense than it subsequently becomes. -This is shown by the fact, which is obvious enough when once attention has -been directed to it, that the bright band, which in the Charpentier disk -intervenes between the dark band and the leading edge of the white sector, -appears to be much more strongly illuminated than any other portion of the -sector. - -The complete order of visual phenomena observed when the retina is exposed -to the action of light for a limited time may therefore be summed up as -follows:-- - - (1) Immediately upon the impact of the light there is experienced a - sensation of luminosity, the intensity of which increases for about - one-sixtieth of a second: more rapidly towards the end of that period - than at first. - - (2) Then ensues a sudden re-action, lasting also for about - one-sixtieth of a second, in virtue of which the retina becomes - partially insensible to renewed or continued luminous impressions. - -These two effects may be repeated in a diminished degree, as often as -three or four times. - - (3) The stage of fluctuation is succeeded by a sensation of steady - luminosity, the intensity of which is, however, considerably below the - mean of that experienced during the first one-sixtieth of a second. - - (4) After the external light has been shut off, a sensation of - diminishing luminosity continues for a short time, and is succeeded by - a brief interval of darkness. - - (5) Then follows a sudden and clearly-defined sensation of what may be - called abnormal darkness--darker than common darkness--which lasts for - about one-sixtieth of a second, and is followed by another interval of - ordinary darkness. - - (6) Finally, in about a fifth of a second after the extinction of the - external light, there occurs another transient impression of - luminosity, generally violet coloured, after which the uniformity of - the darkness remains undisturbed. - -Fig. 43, which is copied from my paper, gives a rough diagrammatic -representation of the above described chain of sensations. No account is -here taken of the comparatively feeble after-images which succeed the -recurrent image, and may last for several seconds. - -I propose now to say a few words about a curious phenomenon of vision -which a short time ago excited considerable interest. - -[Illustration: _Fig. 43.--Visual Sensations attending a period of -Illumination._] - -[Illustration: _Fig. 44.--Benham's Top._] - -In the year 1895 Mr. C. E. Benham brought out a pretty little toy which he -called the Artificial Spectrum Top. It consists of a cardboard disk, one -half of which is painted black, while on the other half are drawn four -successive groups of curved black lines at different distances from the -centre, as shown in Fig. 44. When the disk rotates rather slowly, each -group of black lines generally appears to assume a different colour, the -nature of which depends upon the speed of the rotation and the intensity -and quality of the light. Under the best conditions the inner and outer -groups of lines become bright red and dark blue; at the same time the -intermediate groups also appear tinted, but the hues which they assume are -rather uncertain and difficult to specify. By far the most striking of the -colours exhibited by the top is the red, and next to that the blue; this -latter is, however, sometimes described as bluish-green. - -Some experiments carried out by myself in 1896 (Proc. Roy. Soc., vol. 60, -p. 370) seem to indicate pretty clearly the cause of the remarkable bright -red colour, and also that of the blue. The more feeble tints of the two -intermediate groups of lines perhaps result from similar causes in a -modified form, but these have not yet been investigated. - -In the red colour we have another striking example of an exceedingly -common phenomenon which is habitually disregarded; indeed I can find no -record of its ever having been noticed at all. The fact is that whenever a -bright image is suddenly formed upon the retina after a period of -comparative darkness, this image appears for a short time to be surrounded -by a narrow coloured border, the colour, under ordinary conditions of -illumination, being red. If the light is very strong, the transient border -is greenish-blue, but this colour, as will be explained later, turned out -to be merely an after-effect of red. Sometimes, when the object is in -motion, both red and blue are seen together. - -The observations were first made in the following manner. A blackened zinc -plate, in which is a small round hole covered with a piece of thin -writing-paper, is fixed over a larger opening in a wooden board; thus we -are furnished with a sharply-defined translucent disk, which is surrounded -by a perfectly opaque substance. An arrangement is provided for covering -the translucent disk with a shutter, which can be opened very rapidly by -releasing a strong spring. If this apparatus is held between the eyes and -a lamp, and the translucent disk is suddenly disclosed by working the -shutter, the disk appears for a short time to be surrounded by a narrow -red border. The width of the border is perhaps a millimetre (1/25 inch), -and the appearance lasts for something like a tenth of a second. Most -people are at first quite unable to recognise this effect, the difficulty -being, not to see it, but to know that one sees it. Those who have been -accustomed to visual observations generally perceive it without any -difficulty when they know what to look for, and no doubt it would be very -evident to a baby which had not advanced very far in the education of its -eyes. - -The observation is made rather less difficult by a further device. If the -disk is divided into two parts by an opaque strip across the middle, it is -clear that each half disk will have its red border, and if the strip is -made sufficiently narrow, the red borders along its edges will meet or -perhaps overlap, and the whole strip will, for a moment after the shutter -is opened, appear red. A disk was thus prepared by gumming across the -paper a very narrow strip of tinfoil. The effect produced when such a disk -is suddenly exposed is indicated in Fig. 45, the red colour being -represented by shading. - -[Illustration: _Fig. 45.--Demonstration of Red Borders._] - -A simpler apparatus is, however, quite sufficient for showing the -phenomenon,[12] and with practice one can even acquire the power of -seeing it without any artificial aid at all. I have many times noticed -flashes of red upon the black letters of a book that I was reading, or -upon the edges of the page: bright metallic, or polished objects often -show it when they pass across the field of vision in consequence of a -movement of the eyes, and it was an accidental observation of this kind -which suggested the following easy way of exhibiting the effect -experimentally. - -An incandescent electric lamp was fixed behind a round hole in a sheet of -metal which was attached to a board. The hole was covered with two or -three thicknesses of writing paper, making a bright disk of nearly uniform -luminosity. When this arrangement was moved rather quickly either -backwards and forwards or round and round in a small circle, the edge of -the streak of light thus formed appeared to be bordered with red. - -If this experiment is performed with a strong light behind the paper, the -streak becomes bordered with greenish-blue instead of red. With an -intermediate degree of illumination, both blue and red may be seen -together. - -Most of the effects that have so far been described were produced by -transmitted light, but reflected light will show them equally well. If you -place a printed book in front of you near a good lamp and interpose a dark -screen before your eyes, then, when the screen is suddenly withdrawn, the -printed letters will for a moment appear red, quickly changing to black. -Some practice is required before this observation can be made -satisfactorily, but by a simple device it is possible to obliterate the -image of the letters before the redness has had time to disappear; the -colour then becomes quite easily perceptible. - -Hold two screens together side by side, a black one and a white one, in -such a manner that an open space is left between them. (See Fig. 46.) In -the first place let the black screen cover the printing; then quickly move -the screens sideways so that the printed letters may be for a moment -exposed to view through the gap, stopping the movement as soon as the page -is covered by the white screen. During the brief glimpse that will be had -of the black letters while the gap is passing over them, they will, if -the illumination is suitable, appear to be bright red. - -[Illustration: _Fig. 46.--Black and White Screens._] - -[Illustration: _Fig. 47.--Disk for Red Borders._] - -We may go a step further. Cut out a disk of white cardboard, divide it -into two equal parts by a straight line through the centre, and paint one -half black.[13] At the junction of the black and white portions cut out a -gap, which may conveniently be of the form of a sector of 45°. (See Fig. -47.) Stick a long pin through the centre and hold the arrangement by the -pointed end of the pin a few inches above a printed page near a good -light. Make the disk spin at the rate of about five or six turns a second -by striking the edge with the finger. As before, the letters when seen -through the gap will appear red, and persistence will render the repeated -impressions almost continuous so long as the rotation is kept up; any one -seeing the printing for the first time through the rotating disk would -believe that it was done with red ink. Care must be taken that the disk -does not cast a shadow upon the page, and that the intensity of the -illumination is properly adjusted. I have devised several rather more -elaborate contrivances for making the disks rotate at a uniform speed; one -of these is shown in Fig. 50. - -In none of these experiments does an extended black surface ever appear -red, but only black dots or lines. And the lines must not be too thick; if -their thickness is much more than a millimetre (1/25 inch), the lines, as -seen by an observer from the usual distance for reading, do not become red -throughout, but only along their edges. The red appearance does not in -fact originate in the black lines themselves: these serve merely as a -background for showing up the red border which fringes externally the -white portions of the paper, and the width of this border does not exceed -about one-fifth of a degree. But by employing a sufficiently large disk -and selecting designs or letters composed of lines of suitable thickness, -the colour effect has been shown to a large audience. - -When the disk is turned in the opposite direction, so that the gap is -preceded by white and followed by black, the lines of the design appear at -first sight to become dark blue instead of red. Attentive observation, -however, shows that the apparently blue tint is not formed upon the lines -themselves, as the red tint was, but upon the white ground just outside -them. This introduces to our notice another border phenomenon, which seems -to present itself when a dark patch is suddenly formed on a bright ground, -for that is essentially what takes place when the disk is turned the -reverse way. I made some attempts to obtain more direct evidence that such -a dark patch appeared for a moment to have a blue border, and after some -trouble succeeded in doing so. - -A circular aperture was cut in a wooden board and covered with white -paper; a lamp was placed behind the board, and thus a bright disk was -obtained, as in the former experiment. An arrangement was prepared by -means of which one half of this bright disk could be suddenly covered by -a metal shutter, and it was found that when this was done a narrow blue -band appeared on the bright ground just beyond and adjoining the edge of -the shutter when it had come to rest. The blue band lasted for about a -tenth of a second, and it seemed to disappear by retreating into the black -edge of the shutter. The phenomenon is illustrated in Fig. 48, where the -shaded band indicates the blue border. - -[Illustration: _Fig. 48.--Demonstration of Blue Border._] - -We have then to account, if possible, for the two facts that, in the -formation of these transient colour-borders, the red sensation occurs in a -portion of the retina which has not itself been exposed to the direct -action of light, while the blue occurs in a portion which is steadily -illuminated, both colour sensations being referred to localities adjacent -to those in which a change of illumination has suddenly taken place. -Accepting the Young-Helmholtz theory of colour vision, the effects must, I -think, be attributed to a sympathetic affection of the red nerve fibres. -When the various nerve fibres occupying a limited portion of the retina -are suddenly stimulated by white light (or by any kind of light which -contains a red constituent) the immediately surrounding red nerve fibres -are for a short period excited sympathetically, while the violet and green -fibres are not so excited, or in a much less degree. And again, when light -is suddenly cut off from a patch in a bright field, there occurs a -sympathetic insensitive reaction in the red fibres just outside the -darkened patch, in virtue of which they cease for a moment to respond to -the luminous stimulus; the green and violet fibres, by continuing to -respond uninterruptedly, give rise to the sensation of a blue border. - -It is perhaps desirable to refer briefly to another proposed explanation -of the phenomenon, which occurred to myself at an early stage of the -investigation, and has since been suggested by many different persons. The -explanation in question is of a purely physical character, and depends -upon the non-achromatism of the eye. - -[Illustration: _Fig. 49.--Disk for experiments on the origin of -Colour-borders._] - -Without going into details, it will suffice to quote a single experiment -which is of itself fatal to any such theory. Prepare a disk like that -shown in Fig. 49, and spin it above a page of printing. The letters -beneath the zone which is partly black and partly white will, under the -usual conditions, turn red, but those beneath the remainder of the disk -will retain their blackness. The demarcation is quite definite, and a -single printed word may be made to appear red in the middle and black at -its two ends. Now it is, of course, impossible that the lenses of the eye -should be perfectly accommodated for the letters which appear black, and -at the same time seriously out of focus for the others. This explanation, -therefore, simple and obvious as it may seem, is altogether untenable. - -Whether or not the hypothesis which I have suggested is correct in all its -details, it is, I think, sufficiently obvious that the red and blue -colours of Benham's top are due to exactly the same causes as the colours -observed in my own experiments, for the essential conditions are the same -in both cases. - -The last curiosity which I will notice is connected with the fact already -mentioned, that when the illumination is strong, the transient -border-colours are nearly reversed, greenish-blue appearing in place of -red, and brick-red in place of blue. - -I was for a long time quite unable to imagine any reasonably probable -explanation of this circumstance, but a clue was finally obtained from -consideration of the fact that greenish-blue is the complementary colour -to red, and in a subsequent memoir (Proc. Roy. Soc., vol. 61, p. 269) some -experiments were described which show, as I believe conclusively, that the -greenish-blue borders seen in a strong light are simply negative -after-images of the usual red one. - -These negative after-images are of the familiar kind that are observed -after one has gazed for some time at a bright coloured object. If a red -"wafer" lying upon a sheet of white or grey paper is looked at steadily -for about half a minute, and the gaze is then suddenly transferred to some -other part of the paper, a greenish-blue ghost of the wafer will be seen. -The portion of the retina upon which the red image at first falls becomes -fatigued and partially insensible to red light; it is therefore unable to -appreciate the red component of the white light afterwards reflected to it -by the paper, and the sensation of the complementary colour consequently -predominates; hence the greenish-blue ghost, which is called the negative -after-image of the wafer. - -The new experiments show that, if a certain condition is fulfilled, the -usual prolonged stare becomes unnecessary, a momentary glance sufficing to -produce a strong but fugitive after-image. The condition is that the part -of the retina where the image is to be formed, shall have been darkened -immediately before excitation by the bright object. The retinal nerves, -when in darkness, rapidly acquire a state of sensitiveness far exceeding -the normal average in the light, but quickly diminishing again under the -influence of illumination. This peculiar sensitiveness may, indeed, be -both gained and lost in a small fraction of a second, and is therefore -very favourable for the rapid generation of negative after-images. - -Once more making use of the black and white screens depicted in Fig. 46, -let the black screen first cover the paper upon which the wafer is lying; -this will darken a portion of the retina, and render it sensitive. Then -let the screens be quickly moved sideways, so that the wafer, after having -been seen for a moment through the opening, may be immediately covered by -the white screen. A bright but evanescent greenish-blue ghost will succeed -the red impression. - -But the most curious thing is that if the illumination is strong, and the -screens are moved at the proper speed, no trace of red will be seen at -all; it will appear exactly as if the actual colour of the wafer seen -through the gap were greenish-blue. I am informed that analogous phenomena -have been observed in other branches of physiology; a well-defined -reaction sometimes occurs when no direct evidence can be detected of the -existence of the excitation to which the reaction must be due. - -As in the former experiments, the effect may be shown continuously by -means of a rotating disk with an open sector. The annexed diagram (Fig. -50) indicates a convenient apparatus for the purpose. The disk is made of -thin metal, and properly balanced; the dark portion of the surface is -covered with black velvet, and the light portion with unglazed grey or -buff paper. It should turn some six or eight times in a second, while its -front is well illuminated either by bright diffused daylight or by a -powerful lamp. A red card placed behind the rotating disk is made to -appear green, a green card pink, and a blue one yellow, while a black -patch painted upon a white ground appears lighter than the ground itself. -I have prepared some designs which demonstrate the phenomenon in a very -striking manner. One of these is a picture of a lady with indigo-blue -hair, an emerald-green face, and a scarlet gown, who is represented as -admiring a violet sunflower with purple leaves. Seen through the disk, the -lady's tresses appear flaxen, her complexion a delicate pink, and her -dress a light peacock-blue; the petals of the sunflower also become -yellow, and its foliage green. Other designs show equally remarkable -transformations of colour. - -[Illustration: _Fig. 50.--Disk for transforming Colours._] - -I have mentioned only a few among many curious phenomena which have -presented themselves in the course of these investigations. It is not -improbable that a careful study of the subjective effects produced by -intermittent illumination would lead to results tending to clear up -several doubtful points in the theory of colour vision. - - -William Byles & Sons, Printers, 129, Fleet Street, London, and Bradford. - - - - -FOOTNOTES: - -[1] It should be clearly understood that the length of each wave of a -series is measured by the distance between the crests of two successive -waves. The length of water-waves which break upon a sea shore is not the -length along the crest of a single wave measured in a direction parallel -to the shore, as the uninitiated are apt to suppose. The true wave-length, -or distance from crest to crest of successive waves, can be well observed -from the top of a cliff. - -[2] In practice, wave-lengths are expressed in ten-millionths of a -millimetre. The wave-lengths of the lines A and H of the solar spectrum, -which approximately coincide with the limits of visibility, are 7594 and -3968 ten-millionths of a millimetre. - -[3] Possibly the human eye is at present in process of transformation from -an inferior type to a different and more perfect one. - -[4] It is sometimes necessary to place the lens I on the other side of K. - -[5] It is easy to find specimens of red and green glass suitable for this -experiment. The proper kind of purple is not so commonly met with. - -[6] Some recent experiments on artificial colour-blindness (Proc. Roy. -Soc., Feb., 1898) have led Mr. Burch to the conclusion that there are -really _four_ fundamental colour-sensations--a red, a green, a blue, and a -violet. His results are, however, thought to be capable of a different -interpretation. - -[7] Or through several pieces superposed. - -[8] A violet-coloured haze may sometimes be actually seen around the opal -globes of the electric lamps in the streets. - -[9] A "focus" electric lamp was used in the lantern. - -[10] Proc. Roy. Soc., Jan., 1899. - -[11] After a few seconds' observation the greenish-blue colour often -becomes much more intense, but this is an effect of fatigue, with which we -are not at present concerned. - -[12] See _Nature_, vol. 55, p. 367 (Feb. 18th, 1897). - -[13] Or, for best results, use a balanced metal disk covered with black -velvet and white paper. - - - - - - -End of Project Gutenberg's Curiosities of Light and Sight, by Shelford Bidwell - -*** END OF THIS PROJECT GUTENBERG EBOOK CURIOSITIES OF LIGHT AND SIGHT *** - -***** This file should be named 40119-8.txt or 40119-8.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/0/1/1/40119/ - -Produced by The Online Distributed Proofreading Team at -http://www.pgdp.net (This file was produced from images -generously made available by The Internet Archive.) - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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