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diff --git a/40119-0.txt b/40119-0.txt new file mode 100644 index 0000000..d148e03 --- /dev/null +++ b/40119-0.txt @@ -0,0 +1,2823 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 40119 *** + +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 THE PROJECT GUTENBERG EBOOK 40119 *** |