,,curiosities ,,of ,,light ,,and ,,sight4 ,,curiosities ,,of ,,light ,,and ,,sight ,,by ,,shelford ,,bidwell1 ,m4,a41 ,,ll4,b41 ,f4,r4,s4 ,,with ,,fifty ,,illustrations ,,london3 ,,swan ,,sonnenschein ,,co41 ,,limited ,,paternoster ,,square #ahii ,,preface4 ,the following chapters are based upon notes of several unconnected lectures addressed to audiences of very different classes in the theatres of the ,royal ,institution1 the ,london ,institution1 the ,leeds ,philosophical and ,literary ,society1 and ,caius ,house1 ,battersea4 ,in preparing the notes for publication the matter has been re-arranged with the object of presenting it1 as far as might be1 in methodical order2 additions and omissions have been freely made1 and numerous diagrams1 illustrative of the apparatus and experiments described1 have been provided4 ,i do not know that any apology is needed for offering the collection as thus re-modelled to a larger public4 ,though the essays are1 for the most part1 of a popular and informal character1 they touch upon a number of curious matters of which no readily accessible account has yet appeared1 while1 even in the most elementary parts1 an attempt has been made to handle the subject with some degree of freshness4 ,the interesting subjective phenomena which are associated with the sense of vision do not appear to have received in this country the attention they deserve4 ,this little book may perhaps be of some slight service in suggesting to experimentalists1 both professional and amateur1 an attractive field of research which has hitherto been only partially explored4 ,,contents4 ,,page4 ,,chapter ,i4 ,light and the ,eye #a ,,chapter ,,ii4 ,colour and its ,perception #ci ,,chapter ,,iii4 ,some ,optical ,defects of the ,eye #hd ,,chapter ,,iv4 ,some ,optical ,illusions #acj ,,chapter ,v4 ,curiosities of ,vision #afe ,,list ,,of ,,diagrams4 ,,fig4 ,,page4 #a4 ,image of ,slit and ,spectrum #ab #b4 ,diagram of the ,eye #bd #c4 ,abney's ,colour-patch ,apparatus #de #d4 ,partially ,intercepted ,spectrum #di #e4 ,stencil ,cards #eb #f4 ,helmholtz's ,curves of ,colour ,sensations #gb #g4 ,knig's ,curves #gc #h4 ,stencil ,card for ,complementary ,colours #gg #i4 ,another form #gi #aj4 ,slide for ,mixing any two ,spectral ,colours #hj #aa4 ,refraction of ,monochromatic ,light by ,lens #hg #ab4 ,refraction of ,dichromatic ,light #hi #ac4 ,narrow ,spectrum as seen from a ,distance #ig #ad4 ,spectrum formed with ,v-shaped ,slit #ajc #ae4 ,bezold's ,device for ,demonstrating ,non-achromatism of the ,eye #ajh #af4 ,crossed ,lines showing the ,effect of ,astigmatism #aac #ag4 ,another ,design showing the same #aad #ah4 ,star-like ,images of ,luminous ,points #aaf #ai4 ,sutures of the ,crystalline ,lens #aag #bj4 ,multiple ,images of a ,luminous ,point #abj #ba4 ,the same1 showing an increased number of ,images #abb #bb4 ,the same when a ,slit is held before the ,eye #abc #bc4 ,multiple ,images of an ,electric ,lamp ,filament #abe #bd4 ,the same seen through a ,slit #abf-abh #be4 ,illusion of ,length #acb #bf4 ,another form #ace #bg4 ,another form #acf #bh4 ,another form #acg #bi4 ,another form #ach #cj4 ,illusion of ,inclination #adc #ca4 ,zllner's ,lines #add #cb4 ,slide for showing ,illusions of ,motions #adg #cc4 ,illusion of ,motion #adi #cd4 ,illusion of ,luminosity #aeb #ce4 ,illusion of ,colour #aee #cf4 ,recurrent ,vision demonstrated with a ,vacuum ,tube #agf #cg4 ,the same with a ,rotating ,disk #agh #ch4 ,apparatus for showing ,recurrent ,vision with ,spectral ,colours #aha #ci4 ,charpentier's ,dark ,band #ahg #dj4 ,charpentier's ,effect shown with the ,hand #ahi #da4 ,multiple ,dark ,bands #aib #db4 ,temporary ,insensitiveness of the ,eye after ,illumination #aid #dc4 ,visual ,sensations attending a ,period of ,illumination #aii #dd4 ,benham's ,artificial ,spectrum ,top #bjj #de4 ,demonstration of ,red ,colour-borders #bje #df4 ,black and ,white ,screens for the same #bji #dg4 ,rotating ,disk for the same #baj #dh4 ,demonstration of ,blue ,colour-borders #bae #di4 ,disk for ,experiments on the ,origin of the ,colour-borders #bag #ej4 ,disk for the ,subjective ,transformation of ,colours #bbd ,,chapter ,i4 ,,light ,,and ,,the ,,eye4 ,in the present scientific age every one knows that light is transmitted across space through the medium of the luminiferous ether4 ,this ether fills the whole of the known universe1 as far at least as the remotest star visible in the most powerful telescopes1 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 difficulty4 ,the ether is a thing of immeasurable tenuity1 being many millions of times rarer than the most perfect vacuum of which we have any experience3 it offers no sensible obstruction to the movements of the celestial bodies1 and even the flimsiest of material substances can pass through it as if it were nothing4 ,yet we have been taught that this same ether is an elastic solid with a great degree of rigidity1 its resistance to distortion being1 in comparison with the density1 nearly ten thousand million times greater than that of steel3 thus was explained the prodigious speed with which it propagates transverse vibrations4 ,a few years ago1 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 pitch4 ,he showed that the pitch was hard and brittle1 yet1 as he said1 a bullet laid upon the slab would1 in the course of a few months1 sink into and penetrate through it1 the hard brittle mass being really a very viscous fluid4 ,the ether1 it was suggested1 resembled the pitch in having the rigidity of a solid and yet gradually yielding2 it was1 in fact1 a rigid solid for luminiferous vibrations executed in about a hundred-billionth part of a second1 and at the same time highly mobile to bodies like the earth going through it at the rate of twenty miles in a second4 ,this illustration1 felicitous as it is1 would1 however1 scarcely avail to force conviction upon an unwilling mind1 even if it were admitted that the period of an ether wave is necessarily no more than a hundred-billionth of a second or thereabouts1 which is probably very far from the truth4 ,but1 indeed1 the elastic solid theory of the ether has failed to give a consistent explanation of some of the most important points in observational optics2 and1 in spite of the exalted position which it has held1 it can now hardly be regarded as representing a physical reality4 ,the famous researches of ,hertz have established upon a secure experimental basis the hypothesis of ,maxwell that light is an electro-magnetic phenomenon4 ,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 due4 ,they travel through space with the same speed2 they can be reflected1 refracted1 polarised1 and made to exhibit interference effects4 ,no fact in physics can be much more firmly established than that of the essential identity of light and electricity4 ,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 water1 or which occur in the air when sound is transmitted through it4 ,the displacements which the ether undergoes are not mechanical--primarily at all events--but electrical4 ,every one knows what a simple mechanical displacement is4 ,if we push aside the bob of a suspended pendulum1 that is a mechanical displacement4 ,but if we electrify a stick of sealing wax by rubbing it with flannel1 the surrounding ether undergoes electric displacement1 and no one understands what electric displacement really is4 ,ultimately1 no doubt1 it will turn out to be of a mechanical nature1 but it is almost certainly not a simple bodily distortion such as is caused1 for example1 when one presses a jelly with the finger4 ,since1 then1 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 light1 one of the most serious difficulties in the way of its acceptance is removed4 ,it is true that nothing is definitely known concerning the mechanism which takes the place of the simple transverse vibrations formerly postulated1 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 impossible4 ,all scientific men are in fact agreed in recognising the real and genuine existence throughout space of an ether capable1 among other things1 of transmitting at the speed of #ahf1jjj miles per second disturbances which1 whatever their precise nature1 are of the kind which mathematicians are accustomed to call waves4 ,how an ether wave is constituted will probably be known when we have found out exactly what electricity is3 and that may be never4 ,the sensation of light results from the action of ether waves upon the organism of the eye1 but the old belief that the sensation was primarily due to a series of mere mechanical impulses or beats1 just as that of sound results from the mechanical impact of air-waves upon the drum of the ear1 cannot any longer be upheld4 ,the essential nature of the action exerted by ether waves is still undetermined1 though many guesses at the truth have been hazarded4 ,it may be electrical or it may be chemical2 possibly it is both4 ,ether-waves1 we know1 are competent to bring about chemical changes1 as in the familiar instance of the photographic processes2 they can also produce electric phenomena1 as1 for example1 when they fall upon a suitably prepared piece of selenium2 but there is no evidence that they can exert any direct mechanical action of a vibratory character1 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-waves4 ,of the multitude of ether-waves which traverse space it is only comparatively few that have the power of exciting the sensation of light4 ,as regards limited range of sensibility there is a very close analogy between hearing and seeing4 ,no sensation of sound 7at least of continuous sound7 is produced when air-waves beat upon our ears unless the rate of the successive impulses lies within certain definite limits4 ,it is just so with vision4 ,if ether-waves fall upon our eyes at a less rate than about #djj billions per second1 or at a greater rate than #gej billions per second1 no sensation of light is perceived4 ,there is another and more generally convenient way of stating this fact4 ,since all waves found in the ether travel through space at exactly the same speed--#ahf1jjj miles a second--it follows that the length#a of each of a series of homogeneous waves must be inversely proportional to their frequency1 that is1 to the rate at which they strike a fixed object1 such as the eye4 ,instead1 therefore1 of specifying waves by their frequency we may equally well specify them by their length4 ,waves whose frequency is #djj billions per second have a length of about #a_/cdjjj inch1 this being the one four hundred billionth part of #ahf1jjj miles2 and those whose frequency is #gej billions have a wave-length of #a_/fdjjj inch4 ,waves1 then1 of a length greater than #a_/cdjjj inch or less than #a_/fdjjj inch have no effect upon our organs of vision4#b ,in relation to this important fact it will be convenient to refer to a familiar but very beautiful experiment--the formation of a spectrum4 ,an electric lamp is enclosed in an iron lantern1 having in its front an upright slit2 from this slit there issues a narrow beam of white light1 which is made up of rays of many different wave-lengths1 all mixed up together4 ,by causing the light to pass through a prism the mixed rays are sorted out side by side according to their several wave-lengths1 forming a broad1 many-hued band or spectrum upon a white screen placed to receive it4 7,see ,fig4 #a47 ,to the visible rays of the longest wave-length is due the red colour on the extreme left4 ,waves of somewhat shorter length produce the adjoining stripe of orange1 and the succeeding colours--yellow1 green1 and blue--correspond respectively to waves of shorter and shorter lengths4 ,lastly there comes a patch of violet due to those of the visible rays whose wave-length is the shortest of all4 ,the wave-length of the light at the extreme edge of the red is about #a_/cdjjj inch1 and as we pass along the spectrum the wave-length gradually diminishes1 until at the extreme outer edge of the violet it is about #a_/fdjjj inch1 or not much more than half that at the other end4 ,illustration3 ,fig4 #a4--;,image of ,slit and of ,spectrum4 ,the two ends of the spectrum gradually fade away into darkness1 and the point that ,i wish to insist upon and make perfectly clear is this3--,the position of the boundaries terminating the visible spectrum does not depend upon anything whatever in the nature of light regarded as a physical phenomenon4 ,ether waves which are much longer and much shorter than those which illuminate the spectrum certainly exist1 and evidence of their existence is easily obtainable4 ,but we cannot see them2 they fall upon our eyes without exciting the faintest sensation of light4 ,the visible spectrum is limited solely by the physiological constitution of our organs of vision1 and the fact that it begins and ends where it does is1 from a physical point of view1 a mere accident4 ,the spectrum actually projected upon the screen is in truth much longer than that portion of it which any one can see3 it extends for a considerable distance beyond the violet at the one end and beyond the red at the other1 these invisible portions being known as the ultra-violet and infra-red regions4 ,people's eyes differ in regard to range of sensibility just as their ears do4 ,i believe the sensibility of my own eyes to be normal1 but if ,i were to indicate the two points where the spectrum appears to me to begin and to end1 a great many persons would certainly be inclined to disagree with me and place the boundaries somewhere else4 ,some1 indeed1 could see nothing whatever in what appears to most of us to be a brilliant portion of the red4 ,again1 it is by no means probable that in all animals and insects the limits of vision are the same as they are in man4 ,we might naturally expect that larger and perhaps more coarsely constructed eyes than our own would respond to waves of greater average length1 while the visual organs of small insects might on the other hand be more sensitive to shorter waves4 ,the point is not one that can be easily settled1 because we are unable to cross-examine an animal as to what it sees under different conditions4 ,but ,sir ,john ,lubbock1 taking advantage of the dislike which ants when in their nests have for light1 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 all4 ,that region of the spectrum which appears brightest to the eye of an ant is what we should call a perfectly dark one1 lying outside the violet1 where the incident waves have a length of less than #a_/fdjjj inch4 ,as ,lord ,salisbury said at ,oxford1 the function of the ether is to undulate1 and1 in fact1 it transports energy from one place to another by wave-motion4 ,some of its waves1 such as those which proceed from an electric-light dynamo1 may be thousands of miles in length1 others may be shorter than a millionth of an inch1 as is perhaps the case with those associated with ,professor ,rntgen's ,x-rays2 but all1 so far as is known1 are of essentially the same character1 differing from one another only as the billows of the ,atlantic differ from the ripples on the surface of a pond4 ,no matter how the disturbance is first set up1 whether by the sun1 or by a dynamo1 or by a warm flat-iron1 in every case the ether conveys nothing at all but the energy of wave-motion1 and when the waves1 encountering some material obstacle which does not reflect them1 become quenched1 their energy takes another form1 and some kind of work is done1 or heat is generated in the obstacle4 ,the whole1 or at least the greater part1 of the energy given up by the waves is in most cases transformed into heat1 but under special circumstances1 as1 for instance1 when the waves fall upon a green leaf or a living eye1 a few of them may perform work of an electrical or chemical nature4 ,the process of the transmission of energy from one body to another by propagation through an intervening medium has long been spoken of as radiation1 and in recent years the same term has been largely employed to denote the energy itself while in the stage of transmission4 ,radiation in the latter sense--meaning ether wave-energy--includes what is often improperly called light4 ,light1 people say1 takes about eight minutes in travelling from the sun to the earth4 ,but while it is on its journey it is not light in the true sense of the word2 neither does anything of the nature of light ever start from the sun4 ,light has no more existence in nature outside a living body than the flavour of onions has2 both are merely sensations4 ,if a boy throws a stone which hits you in the face1 you feel a pain2 but you do not say that it was a pain which left the boy's hand and travelled through space from him to you4 ,the stone1 instead of causing pain in a sentient being1 might have broken a window1 or knocked down an apple4 ,just so1 the same radiation which1 when it chances to encounter an eye1 produces a certain sensation1 will produce a chemical decomposition if it falls upon a cabbage1 an electrical effect in a selenium cell1 or a heating effect in almost anything4 ,why1 then1 should it be specially identified with the sensation8 ,radiation also includes1 and is nearly synonymous with1 what is often miscalled radiant heat4 ,after what has been already indicated1 ,i need hardly say that there is no such thing as radiant heat4 ,the truth is that the sun or other hot body generates wave-energy in the ether at the expense of some of its own heat1 and any distant substance which absorbs a portion of this energy generally 7but not necessarily7 acquires an equivalent quantity of heat4 ,the result may be exactly the same as if heat left the hot body and travelled across space to the substance2 but the process is different4 ,it is like sending a sovereign to a friend by a postal order4 ,you part with a sovereign and he receives one1 but the piece of paper which goes through the post is not a sovereign4 ,it is strictly correct to say that the sun loses heat by radiation1 just as you lose a sovereign by investing it in the purchase of a postal order4 ,but that is not the same thing as saying that the sun radiates heat4 ,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 else2 but it is1 unfortunately1 impossible in the present condition of things to use it as freely as one could wish without pedantry1 and we must still often speak of light or of heat when radiation would express our meaning with greater accuracy4 ,light1 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 beings1 with the result that1 in some unknown and probably unknowable manner1 a special sensation is called into play--the sensation of luminosity4 ,and in order that the creature may be able not only to perceive light but also to see things1 that is1 to appreciate the forms of external objects1 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 elements4 ,in man and the higher animals the optical apparatus1 or eye1 consists of a stiff globular shell1 having in front an opening provided with a system of lenses1 and1 at the back of the interior1 a delicate perceptive membrane1 upon which the transmitted light is received4 ,so much of the light emitted or reflected from an external object as passes through the lenses1 is distributed by them in such a manner as to form what is called an image upon the membrane1 every elementary point of the image receiving the light which issues from a corresponding point of the object1 and no other4 ,the contrivance evidently bears a close resemblance to a photographic camera1 the sensitive plate or film1 upon which the picture is projected1 being analogous to the perceptive membrane4 ,i am not going to attempt a detailed description of the human eye4 ,it will be sufficient to point out briefly some of its principal features as indicated in the annexed diagrammatic section1 ,fig4 #b4 ,illustration3 ,fig4 #b4--;,diagram of the ,eye4 ,the opening in front of the globe is covered by a slightly protuberant transparent medium ,c1 which is shaped like a small watch-glass1 and on account of its horn-like structure has been named the cornea4 ,the space between the cornea ,c and the body marked ,l is filled with a watery liquid ,a1 known as the aqueous humour3 this liquid with its curved surfaces constitutes a meniscus lens1 convex on the outer side and concave on the inner4 ,then comes the biconvex crystalline lens ,l1 an elastic gelatinous-looking solid1 which is easily distorted by pressure4 ,the convexity of this lens can be varied by the action of a surrounding muscle ,m ,m1 and in this way the focus is adjusted for objects at different distances from the eye4 ,when the muscle is relaxed and the lens in its natural condition1 the curvature of its surfaces is such that a sharp image is formed of objects distant about forty feet and upwards4 ,when by an effort of will1 the muscle is contracted1 the lens becomes more convex1 and distinct pictures can thus be focussed of things which are only a few inches away4 ,this process of adjustment by muscular effort is technically known as accommodation4 ,the remainder of the globe is filled with the so-called vitreous body ,v1 which derives its name from its fancied resemblance to liquid glass3 it might perhaps be more properly likened to a thin colourless jelly4 ,the vitreous body plays a part in the refraction of the light4 ,the perceptive membrane1 or retina ,r ,r1 which lines rather more than half the interior of the eye-ball1 is an exceedingly complex structure4 ,though its average thickness is less than #a_/ajj inch it is known to consist of nine distinct layers1 most of which are marvels of minute intricacy4 ,of these layers ,i shall notice only two1 the so-called bacillary layer1 which is in immediate contact with the inner coating of the eye-ball1 and the fibrous layer1 or layer of optic nerve fibres1 which is only separated from the vitreous body by a thin protective film4 ,the bacillary layer 7from bacillum1 a wand7 consists of a vast assemblage of little elongated bodies called rods and cones1 which are placed side by side and set perpendicularly to the surfaces of the retina1 or in other words1 radially to the eye-ball4 ,let us try to make the arrangement clear by an illustration4 ,imagine a small portion of the inner surface of the eye-ball1 one-tenth of an inch square1 to be magnified #bjjj diameters 7four million times71 and let the enlarged area be represented by the floor of a room #ag feet square4 ,procure a quantity of cedar pencils1 and set them on the floor in an upright position and very close to one another4 ,it will be found that the number of pencils required to fill the space will be about half-a-million4 ,to make the analogy more complete1 let some of the pencils be sharpened to a long tapering point at their lower ends1 the greater number remaining uncut1 just as received from the manufacturers4 ,neglecting details which are immaterial for our present purpose1 we may regard the uncut pencils as representing upon an enormously magnified scale the rods of the retina1 and the pointed ones the cones4 ,the flat upper ends of the pencils may be painted in different uniform colours1 and arranged so as to form a large picture in mosaic1 and if this is looked at from such a distance that its image on the retina is a tenth of an inch square 7which will be the case when the picture is about forty yards away7 all possibility of distinguishing the separate elements which compose it will be lost1 and the picture will seem to be a perfectly continuous one4 ,although the light which enters the eye cannot reach the rods and cones until it has traversed all the other layers of the retina1 yet these intervening layers1 being transparent1 offer little obstruction to its passage1 and it can hardly be doubted that the rods and cones are the special organs upon which light exerts its action1 the picture focussed upon their ends being in truth an exceedingly fine mosaic4 ,from every separate element of the mosaic--from every single rod and cone--there proceeds a slender transparent filament3 all these make their way through the intermediate layers of the retina1 without1 as is believed1 any break of functional continuity1 and emerge near its internal surface2 here they bend over at right angles1 and the thousands of filaments form a tangle which lines the inside of the eye like a fine network1 and constitute the layer of optic nerve-fibres already referred to4 ,the filaments1 or nerve-fibres1 do not however terminate within the eye2 they all pass through the hole marked ,n in the figure1 and thence1 in the form of a many-stranded cable1 constituting the optic nerve1 they are led to the brain1 to which each individual fibre is separately attached4 ,if1 therefore1 what ,i have said is true--and1 though it has not1 ,i believe1 been all rigorously proved1 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 brain4 ,the mind1 which is mysteriously connected with the brain1 is thus afforded the means of localising all the points of luminous excitation relatively to one another1 and furnished with data for estimating the form of the object from which the light proceeds4 ,there are two small regions of the retina which are of special interest4 ,one of them lies just over the opening ,n where the optic nerve enters4 ,here it is evident that there can be no rods and cones1 their place being wholly occupied by strands of nerve-fibre4 ,now it is remarkable that this spot is totally insensitive to light4 ,the other interesting portion is situated opposite the middle of the front opening1 and is marked by a small yellow patch1 in the centre of which is a depression or pit1 which is shown in an exaggerated form at ,f1 and is called the fovea4 ,it has been ascertained that the depression is due partly to the absence of the layer of nerve-fibres1 which are here bent aside out of their natural course1 and partly to a local reduction in the thickness of some of the intermediate retinal layers4 ,this spot1 being at the centre of the field of vision1 occupies a position of great importance1 and the evident purpose of the superficial depression is to allow the light to reach the underlying bacillary layer with as little obstruction as possible4 ,it is noteworthy that the bacillary layer beneath the yellow spot is composed entirely of cones1 the rods1 which elsewhere are in excess1 being altogether wanting4 ,the only other accessory of the visual apparatus to which ,i shall refer is the iris 7,i ,i1 ,fig4 #b71 a coloured disk having a central perforation4 ,this can be seen through the cornea and is consequently a very familiar object4 ,the iris serves the same purpose as the stop1 or diaphragm1 of a photographic lens1 its function being to limit and regulate the quantity of light which is admitted into the eye4 ,the size of the central opening1 or pupil1 varies automatically with the intensity of the illumination3 in a strong light the opening becomes small2 in a feeble light or in darkness it is enlarged4 ,the pupil also contracts when the eye is focussed upon a near object and dilates when the vision is directed to a distance4 ,this brief sketch may serve to give some slight idea of the complexity and delicacy of the visual apparatus4 ,only a few of its more salient features have been touched upon2 when our scrutiny is carried into details the complexity becomes bewildering4 ,even such simple-looking things as the cornea and the vitreous body turn out on close examination to be most elaborately constituted4 ,much1 no doubt1 remains to be discovered1 and of what has already been investigated much is at present only partially understood4 ,and yet1 though it is true that man is fearfully and wonderfully made1 it is equally true that he is far from perfect2 and while there is no structure in the whole human anatomy which exhibits so abundant a profusion of marvels as the eye1 there is perhaps none which is marked with imperfections so striking4 ,many of its defects are the more striking because they are so obvious1 being such as would never be tolerated in optical instruments of human manufacture4 ,in any fairly good camera or telescope or microscope we should expect to find that the lenses were symmetrically figured1 free from stri and properly centred2 also that they were achromatic and efficiently corrected for spherical aberration4 ,in the eye not one of these elementary requirements is fulfilled4 ,the external surface of the lens formed by the aqueous humour and the cornea is not a surface of revolution1 such as would be fashioned by a turning lathe or a lens-grinding machine2 its curvature is greater in a vertical than in a horizontal direction1 and the distinctness of the focussed image is consequently impaired4 ,again1 the crystalline lens is constructed of a number of separate portions which are imperfectly joined together4 ,stri occur along the junctions1 and the light which traverses them1 instead of being uniformly refracted1 is scattered irregularly4 ,moreover the system of lenses is not centred upon a common axis2 neither is it achromatic1 while the means employed for correcting spherical aberration are inadequate4 ,the purchaser of an optical instrument which turned out to have such faults as these would certainly1 as the late ,professor ,helmholtz remarked1 be justified in returning it to the maker and blaming him severely for his carelessness4 ,i would not1 of course1 have it believed that scientific men are conceited enough to imagine themselves capable of designing a better eye than is to be found in nature4 ,that would be an absurdity4 ,they are quite ready to admit that there may exist sufficiently good reasons for the undoubted blemishes which have been indicated1 as well as for others which will be referred to later4 ,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 parts4 ,with all its anomalies the eye fulfils its proper function very perfectly1 and is regarded by those who have studied it most closely with feelings of wonder and humble admiration4#c ,,chapter ,,ii4 ,,colour ,,and ,,its ,,perception4 ,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 eye1 and is suitably distributed over the retina by the action of a system of lenses4 ,now the image thus formed is not generally perceived as a simple monochromatic one1 darker in some parts1 lighter in others1 like a black and white engraving4 ,it is1 in most cases at least1 characterised by a variety of colours1 the light which comes from different objects1 or from different parts of the same object1 having the power of exciting different colour sensations4 ,light which has the property of exciting the sensation of any colour is commonly spoken of as coloured light4 ,the light reflected by a soldier's coat1 for example1 may be called red light1 because when it falls upon the eye it gives rise to a sensation of redness4 ,but it must be understood that this mode of expression is only a convenient abbreviation1 for there can1 of course1 be no objective colour in the light or radiation itself4 ,wherein1 then1 does coloured light differ from white8 ,why do things appear to be variously coloured when illuminated by light which is colourless8 ,and how do coloured lights affect the visual organs so as to evoke appropriate sensations8 ,these are questions--the first two of a physical character1 the last partly physiological and partly psychological--which it is now proposed to discuss4 ,the matter has already been touched upon1 though very slightly1 in connection with the spectrum4 ,let us again turn to the spectrum and consider it a little more fully4 ,it is easily seen that the luminous band contains six principal hues or tones of colour--red1 orange1 yellow1 green1 blue1 and violet4 7,see ,fig4 #a1 page #ab47 ,these however merge into one another so gradually that it is impossible to say exactly where any one colour begins and ends4 ,look1 for instance1 at the somewhat narrow but very conspicuous stripe of yellow4 ,towards the right of this stripe the colour gradually becomes greenish-yellow2 a little further on it is yellowish-green1 and at length1 by insensible gradations1 a full1 pure green is reached4 ,the six most prominent hues of the spectrum are1 in fact1 supplemented by an immense multitude of subordinate ones1 the total number which the eye can recognise as distinct being not less than a thousand4 ,all the colours that we see in nature1 with the exception of the purples 7about which ,i shall say more presently71 are here represented1 and every single variety of tone in the prismatic scale corresponds with one1 and only one1 definite wave-length of light4 ,the source of all these colours is1 as we know1 a beam of white or colourless light1 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-lengths4 ,if1 then1 these coloured constituents were all mixed together again1 it would be reasonable to expect that pure white light would be reproduced4 ,the experiment has been performed in a great many different ways1 several of which were devised by ,newton himself1 and the result admits of no doubt whatever4 ,the method which ,i intend to describe is not quite so simple as some others1 but it has great advantages in the way of convenient manipulation1 and affords the means of demonstrating a number of interesting colour effects in an easily intelligible manner4 ,by the simple operation of moving aside a lens out of the track of the light1 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 patch1 which1 though due to a mixture of a thousand different hues1 is absolutely white4 ,when the lens is replaced1 which is done in an instant1 the mixture is again analysed into its component parts1 and the spectrum reappears4 ,the arrangement of the apparatus1 which is essentially the same as that devised by ,captain ,abney1 and called by him the colour-patch apparatus1 is shown in the annexed diagram 7,fig4 #c74 ,illustration3 ,fig4 #c4--;,abney's ,colour-patch ,apparatus4 ,the light of an electric lamp ,a placed inside the lantern is concentrated by the condensing lenses ,b upon a narrow adjustable slit ,c4 ,the framework of this slit is attached to one end of a telescope tube1 which carries at the other end an achromatic lens ,d of about #aj inches focus4 ,the rays having been rendered parallel by ,d are refracted by the prism ,e2 they then pass through a circular opening in the brass plate ,f to the lens ,g1 the focal length of which is #g inches1 and form a little bright spectrum upon a white card held in a grooved support at ,h4 ,the card being removed1 we place at ,k a lens having a diameter of #e-a_/b inches and a focal length of #ah inches or more1 and adjust it so that a sharply defined image of the hole in the brass plate ,f is formed upon the distant white screen ,l4 ,if all the lenses are correctly placed1 this image1 though formed entirely by the rays which constituted the little spectrum at ,h1 will be perfectly free from colour even around the edge4 ,if we wish to project upon the screen ,l an enlarged image of the little spectrum1 we have only to use another suitable lens ,i in conjunction with ,k3 the diameter of that used by myself is #b-c_/d inches1 and its focal length #f-a_/b inches4 ,when we have once found by trial the position in which this supplementary lens gives the clearest image#d it is easy to arrange a contrivance for removing and replacing it correctly without need of any further adjustment4 ,this apparatus shows then that ordinary white light may be regarded as a mixture of all the variously coloured lights which occur in the spectrum1 the sensation produced when it falls upon the eye being consequently a compound one4 ,from these and similar experiments the scientific neophyte is not unlikely to draw an erroneous conclusion4 ,white light1 he is apt to think1 is always due to the combined action of rays of every possible wave-length1 while coloured light consists of rays of one definite wave-length only4 ,neither of these inferences would be correct4 ,it is not true that white light necessarily contains rays of all possible wave-lengths3 the sensation of whiteness may1 as will be shown by and bye1 be produced quite as effectively by the combination of only two or three different wave-lengths4 ,nor is it true that such colours as we see in nature are always due to light of a single wave-length2 light of this kind is indeed rarely met with outside laboratories and lecture rooms4 ,far more commonly coloured light consists of mixed rays1 and like ordinary white light1 it may1 and generally does1 contain all the colours of the spectrum1 but in different proportions4 ,this last assertion is easily proved4 ,by means of a slip of card we may intercept a portion of the little spectrum formed at ,h 7,fig4 #c74 ,the dark shadow of the card in the enlarged spectrum on the screen is shown in ,fig4 #d4 ,it will be noticed that the shadow cuts off a part only of the red1 orange1 and yellow light1 allowing the remainder to pass through the projection lenses4 ,there are still rays of every possible wave-length from extreme red to extreme violet1 but the proportion of those towards the red end is less than it was before the card was interposed4 ,illustration3 ,fig4 #d4--,partially intercepted ,spectrum4 ,if now we remove the lens ,i 7,fig4 #c7 and so mix the colours of this mutilated spectrum1 the bright round patch where the mixed rays fall upon the screen will no longer appear white but greenish-blue4 ,if we transfer the card to the other end of the little spectrum1 so as to cause a partial eclipse of the violet1 blue1 and green rays1 the colour of the patch will be changed to orange4 ,if we remove the card altogether1 the patch will once more become white4 ,it follows a fortiori that when any portion of the little spectrum is eclipsed totally1 instead of only partially1 the light from the remainder will appear1 when combined1 to be coloured4 ,very beautiful changes of hue are exhibited by the bright patch when a narrow opaque strip1 such as the small blade of a pocket knife1 is slowly moved along the little spectrum at ,h1 eclipsing different portions of it in succession4 ,the patch first becomes green1 then by imperceptible gradations it changes successively to blue1 purple1 scarlet1 orange1 yellow1 and finally1 when the knife has completed its course1 all colour disappears and the patch is again white4 ,we may improve upon this crude experiment1 and1 after ,captain ,abney's plan1 prepare a number of small cardboard stencils1 with openings corresponding to any selected parts of the little spectrum4 ,when a card so prepared is placed at ,h 7,fig4 #c7 the bright patch upon the screen is formed by the combination of the selected rays1 all the others being quenched4 ,we shall find that under these conditions the bright patch is generally1 but not always1 coloured4 ,illustration3 ,fig4 #e4--,stencil ,cards4 ,the first diagram in ,fig4 #e represents a blackened card1 which allows only the red and a little of the orange to pass through4 ,when this is inserted in the grooved holder at ,h1 the bright patch immediately turns red4 ,the second diagram shows another1 which transmits the middle portion of the spectrum1 but blocks the red and the violet at its two ends3 with this card the colour of the patch becomes green4 ,the third card has openings for the violet and the red rays3 this turns the patch a beautiful purple1 a hue which1 as already mentioned1 is not produced by light of any single wave-length4 ,the purples are mixtures of red and violet or of red and blue4 ,now ,i have in my possession three pieces of glass 7or1 to be strictly accurate1 two pieces of glass and one glass-mounted gelatine film7 which1 when placed transversely in the beam of light1 either at ,h 7,fig4 #c7 or anywhere else1 behave exactly like these three cardboard stencils4 ,the first glass cuts off all the spectrum except the red and part of the orange1 just as the first stencil does1 though the line of demarcation is not quite so sharp4 ,this is in fact a piece of red glass1 or in other words the light that it transmits produces the sensation of red4 ,the second glass1 like the second stencil1 allows the whole of the spectral rays to pass freely except the red and the violet1 which disappear as if they were obstructed by an opaque body4 ,this is a green glass4 ,and the third 7which is really a film of gelatine7 cuts out the middle of the spectrum but transmits the red and violet ends4 ,the colour of the gelatine is purple4#e ,the glasses and the gelatine in question act like the cardboard stencils in completely cutting off some of the spectral rays and transmitting others1 and they owe their apparent colours to the combined influence which the transmitted rays exert upon the eye4 ,many other coloured glasses merely weaken some of the rays1 without entirely quenching any4 ,a piece of pale yellow glass1 for example1 when placed in the path of the beam of light from which the spectrum on the screen is formed1 simply diminishes the brightness of the blue region and does not wholly quench any of the rays2 and again1 a common kind of violet-coloured glass enfeebles1 but does not quite obliterate1 the middle portion of the spectrum4 ,from such observations as these we infer that the glasses derive their respective colours from the light which falls upon them4 ,the first glass would not appear red if seen in a light which contained no red rays4 ,this is easily proved by an experiment with the colour-patch apparatus4 ,the spectrum being once more combined into a bright white patch 7which turns red if the glass is for a moment interposed71 let all the red rays and part of the orange be cut off with a suitable stencil4 ,the re-combined light is no longer white but greenish-blue1 as is evidenced by the colour of the patch2 and nothing that is illuminated by this light can possibly appear red4 ,the piece of red glass1 if placed in the beam1 will now cast a perfectly black shadow1 and a square of bright red paper held in the middle of the patch will look as black as ink4 ,it will be shown later how we may obtain light which1 although it appears to the eye to differ in no respect from ordinary white daylight1 yet contains no red component1 and is consequently as powerless as this greenish-blue light to reveal any red colour in the objects which it illuminates4 ,if we substitute a stencil which admits only red rays1 we shall obtain a beam of light in which no colour but red can be seen4 ,green and blue glasses when exposed to this light will cast black shadows1 while pieces of green and blue paper will become either black or dark grey4 ,we see then that the colours of transparent objects1 like the glasses used in these experiments1 are brought out by a process of filtration4 ,certain of the coloured ingredients of white light are filtered out and quenched inside the glass1 and it is to the remaining ingredients which pass through unimpeded that the observed colour is due4 ,the energy of the absorbed rays is not lost of course1 for energy1 like matter1 is indestructible4 ,it is transformed into heat4 ,a coloured glass held in a strong beam of light will in a short time become sensibly warmer than one that is clear and colourless4 ,in studying colour effects as produced by coloured glasses1 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 colours4 ,for the truth is that few things are perfectly opaque4 ,when white light falls upon a coloured body1 it generally penetrates to a small depth below the surface1 and in so doing loses by absorption some of its coloured components1 just as it does in passing through the pieces of glass4 ,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 irregularities1 which turn the light back again and compel it to pass a second time through the same thickness of the substance3 it thus becomes still more effectively sifted1 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 substance4 ,any coloured rays reflected by an object must necessarily be contained in the light by which the object is seen4 ,the following is a curious experiment illustrating this4 ,a large bright spectrum is projected upon a screen and in the green or blue portion of it is held a wall poster4 ,the letters and figures upon the paper are seen to stand out boldly as if printed with the blackest ink4 ,but if the poster is moved into the red part of the spectrum1 the printing at once disappears as if by magic1 and the paper appears perfectly blank4 ,the explanation is that the letters are printed in red ink--they can reflect no light but red4 ,green or blue light falling upon them is absorbed and quenched1 and the letters consequently appear black4 ,on the other hand when the poster is illuminated by the red rays of the spectrum1 the letters reflect just as much light as the paper itself1 and are therefore indistinguishable from it4 ,anything which1 when illuminated by a source of white light1 reflects all its various components equally and without absorbing a larger proportion of some than of others1 appears white or grey4 ,between white and grey there is no essential difference except in luminosity1 or brightness1 that is to say1 in the quantity of light reflected to the eye1 or--to go a step further back--in the amplitude of the ether waves4 ,under different conditions of illumination any substance which reflects all the rays of the spectrum equally may appear either white or grey1 or even black4 ,a snowball can easily be made to look blacker than pitch1 and a block of pitch whiter than snow4 ,it must have struck many of those who have thought about the matter at all as a most remarkable coincidence that sunlight should be white4 ,white light1 as we have seen1 consists of a mixture of variously-coloured rays in very different and apparently arbitrary proportions1 and if these proportions were a little changed the light would no longer be quite colourless4 ,no ordinary artificial light is so exactly white as that of the sun4 ,the light of candles1 gas1 oil1 and electric glow-lamps is yellow2 that of the electric arc 7when unaffected by atmospheric absorption7 is blue1 and that of the incandescent gas burner green4 ,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 colourless4 ,but on a little further reflection it will1 ,i think1 appear that this is not the right way to look at the matter4 ,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 colour4 ,we take sunlight as our standard of neutrality1 and anything that reflects it without altering the proportions of its constituents we consider as being colourless4 ,there can be little doubt that if the sun were purple instead of white1 our sentiments as regards these two hues would be interchanged2 we should talk quite naturally of a pure purple1 entirely free from any trace of colour1 or perhaps describe a lady's costume as being of a gaudy white4 ,even as things are1 the standard of neutrality is not quite a hard and fast one4 ,we have a tendency to regard any artificial light which we may happen to be using1 as more free from colour than it would turn out to be if compared directly with sunlight4 ,if in the middle of the day we go suddenly into a gas-lit room1 we cannot fail to observe how intensely yellow the illumination at first appears2 in a few minutes1 however1 the colour loses its obtrusiveness and we cease to take much notice of it4 ,the effect may be partly a physiological one1 depending upon unequal fatigue of the various perceptive nerves of the retina2 but ,i believe that it is to a large extent due to mental judgment4 ,the standard of whiteness1 or colour-zero1 can apparently be changed within certain limits in a very short time1 and1 as we shall see later1 this is only one of many instances in which our organs of vision seem to be incapable of recognising a constant standard of reference4 ,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 hues4 ,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 perception2 and it is not necessary to suppose anything of the kind4 ,experiment shows that all the various hues of the spectrum1 as well as all 7including white7 that can be formed from their mixture1 may be derived from no more than three distinct colours4 ,there are1 in fact1 an indefinite number of triads of colours which1 in suitable combinations1 are capable of producing the sensation of every tone1 tint1 and shade of colour which the eye of man has ever beheld4 ,old-fashioned books1 such as an early edition of ,ganot's ,physics1 tell us that the three primary colours are red1 yellow1 and blue1 and that all others are produced by mixtures of these4 ,this was the basis of ,sir ,david ,brewster's theory1 which attained a very wide popularity1 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 science4 ,but it is not true4 ,a fatal objection to it is the well-ascertained fact that no combination of red1 yellow1 and blue1 or of any two of them1 such as blue and yellow1 for example1 will produce green4 ,yet every painter knows that if he mixes blue and yellow pigments together he gets green4 ,that is one of the first things that a child learns when he is allowed to play with a box of water-colours1 and no doubt ,brewster was misled by the fact4 ,the truth is1 that the colours of all1 or almost all1 known blue and yellow pigments happen to be composite4 ,an ordinary blue paint reflects not only blue light1 but a large quantity of green as well2 while an ordinary yellow paint reflects a large quantity of green light in addition to yellow4 ,when such paints are mixed together1 the blue and yellow hues neutralise one another1 and only the green1 which is common to both1 remains4 ,the spectrum apparatus will make this clearer4 ,hold a piece of bright blue glass before the slit2 the light passing through the glass will be analysed by the prism1 and you will see that it really contains almost as much green as blue4 ,if a yellow glass is substituted1 not only will yellow light be transmitted1 but1 as before1 a considerable quantity of green4 ,if now both glasses be placed together before the slit1 what will happen8 ,the yellow glass will stop the blue light transmitted by the blue glass1 the blue glass will stop the yellow light transmitted by the yellow glass1 and only the green light which both glasses have the power of transmitting will pass through unimpeded1 forming a band of pure green colour upon the screen4 ,the combination of simple blue and yellow lights of suitable relative luminosities results in the formation of white or neutral light4 ,if the blue is a little in excess1 the combined light will be of a bluish tint2 if the yellow is in excess1 the combination will have a yellowish tint4 ,it will never contain any trace of green4 ,the combination of simple spectral blue and yellow is easily effected by the colour-patch apparatus1 and the result will be found to bear out what has been said4 ,since1 then1 no mixture of red1 yellow1 and blue1 or of any two of them1 will produce green1 we cannot regard these colours as being1 in ,brewster's sense of the term1 primary ones4 ,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 whatever4 ,now this experimental fact is obviously suggestive of a possible converse1 namely1 that almost every colour sensation may in reality be a compound one1 the resultant of not more than three simple sensations4 ,assuming this to be so1 it is evident that if each elementary area of the retina were provided with only three suitable colour organs1 nothing more would be requisite for the perception of an indefinite number of distinct colours4 ,such a hypothesis was first proposed by ,thomas ,young at the beginning of the present century2 but it came before its time and met with no attention until fifty years later1 when it was unearthed by the distinguished physicist and physiologist1 ,helmholtz1 who accorded to it his powerful support and modified it in one or two important details4 ,illustration3 ,fig4 #f4--;,helmholtz's ,curves of ,colour ,perception4 ,according to the ,young-,helmholtz theory1 as it is now called1 there are three different kinds of nerve-fibres distributed over the retina4 ,the first1 when separately stimulated1 produce the sensation of red1 the second that of green1 and the third that of violet4 ,light having the same wave-length as the extreme red rays of the spectrum stimulates the red nerve-fibres only2 that having the same wave-length as the extreme violet rays stimulates the violet nerve-fibres only4 ,light of all intermediate wave-lengths1 corresponding to the orange1 yellow1 green1 and blue of the spectrum1 stimulates all three sets of nerve-fibres at once1 but in different degrees4 ,the proportionate stimulation of the red1 green1 and violet nerves throughout the spectrum is indicated in ,fig4 #f1 which is derived from the rough sketch first given by ,helmholtz4 ,the yellow rays of the spectrum1 it will be seen1 excite the red and green nerves strongly1 and the violet feebly2 green light excites the green nerves strongly1 and the red and violet moderately2 while blue light excites the green and violet nerves strongly1 and the red feebly4 ,illustration3 ,fig4 #g4--,knig's ,curves4 ,fig4 #g shows another set of curves given more recently by ,dr4 ,knig as the result of many thousands of experiments made1 not only upon persons whose vision was normal1 but also upon some who were colour-blind4 ,knig found that the equations he obtained were best satisfied by assuming as the normal fundamental sensations a purplish red 7not to be found in the spectrum71 a green like that of wave-length #ejej1 and a blue like that of wave-length #dgjj approximately1 the two latter1 however1 being purer or more saturated than any actual spectrum colour4 ,but ,knig's curves are not consistent with every class of vision which he examined1 and the question as to what are the true fundamental colour-sensations1 if such really exist at all1 cannot yet be regarded as finally settled4#f ,the ,young-,helmholtz theory of colour-vision1 whether or not it is destined in the future to be superseded by some other1 has at all events proved an invaluable guide in experimental work1 and there are very few colour phenomena of which it is not competent to offer a satisfactory explanation4 ,it has at present only one serious rival--the theory of ,hering1 which1 although it seems to be curiously attractive to many physiologists1 can hardly be said to present less serious difficulties than that which it seeks to displace4 ,neither of these competing theories has yet had its fundamental assumptions confirmed by any direct evidence1 and the advantage must rest with the one which best accords with the facts of colour vision4 ,in my judgment the older of the two is to be greatly preferred as a useful working hypothesis4 ,certain curiosities of vision with which ,i propose to deal in a future chapter depend upon the properties of what are known as complementary colours4 ,two colours are said to be complementary to each other when their combination in proper proportions results in the formation of white4 ,illustration3 ,fig4 #h4--,stencil ,card for ,complementary ,colours4 ,if we produce a compound hue by mixing together the colours of any portion of the spectrum1 and a second compound hue by mixing the remainder of the spectrum1 it must be evident that these two hues are necessarily complementary1 for when they are united they contain together all the elements of the entire spectrum1 and therefore appear as white4 ,this may be illustrated with the aid of the colour-patch apparatus4 ,place at ,h 7,fig4 #c7 a cardboard stencil of the form shown in ,fig4 #h1 and focus upon it a little spectrum1 the principal hues of which are indicated by the letters ,r ,o ,y ,g ,b ,v 7red1 orange1 yellow1 green1 blue1 violet74 ,the two oblong apertures in the card should be of exactly the same height1 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 green1 while the other admits rays from the remainder of the spectrum4 ,if now the lower aperture be covered1 only the red1 orange1 yellow1 and part of the green rays will pass through the stencil1 and these being combined by the lens ,k 7,fig4 #c7 will form upon the screen a bright patch1 the colour of which will be yellow4 ,if the upper aperture be covered1 and the rest of the green1 together with the blue and violet rays1 allowed to pass through the other1 the colour of the patch will become blue2 and if both apertures be uncovered at the same time1 rays from the whole length of the spectrum will pass through the stencil1 and the patch will1 of course1 turn white4 ,the yellow and the blue which were compounded from the two portions of the spectrum are1 therefore1 in accordance with the definition1 complementary colours4 ,in a similar manner by dividing the spectrum into any two portions whatever--as1 for example1 by the complicated stencil shown in ,fig4 #i--we can obtain an indefinite number of pairs of complementary colours4 ,illustration3 ,fig4 #i4--,stencil ,card for ,complementary ,colours4 ,but it is by no means indispensable that both or either of a pair of complementary colours should be compound4 ,to prove this1 two strips of card with narrow vertical openings ,a and ,b are prepared as shown in ,fig4 #aj4 ,the cards are placed one above the other and can be slipped in a horizontal direction1 so that the narrow openings can be brought into any desired part of the spectrum which is indicated in outline by the dotted oblong4 ,illustration3 ,fig4 #aj4--,slide for mixing any two ,spectral ,colours4 ,bring the opening ,a of the upper card into the yellow of the spectrum and the opening ,b of the lower card into the blue4 ,the bright patch formed upon the screen will then be illuminated by simple blue and yellow rays2 yet it will be white--not green1 as it would be if ,brewster's theory were correct4 ,if upon the first trial the white should not be absolutely pure1 it can easily be made so by partially covering either ,a or ,b--the first if the white is yellowish1 the second if it is bluish4 ,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 parts4 ,it is noticeable1 however1 that the white light resulting from the combination of blue and yellow1 though it cannot be distinguished by the eye from ordinary white light1 is yet possessed of very different properties4 ,most coloured objects when illuminated by it have their hues greatly altered2 a piece of ribbon1 for example1 which in common light is bright red1 will appear when held in the blue-yellow light to be of a dark slate colour1 almost black4 ,if the opening ,a is placed in any part whatever of the spectrum except the green1 it will always be possible1 by moving ,b backwards or forwards1 to find some other part where the colour is complementary to that at ,a4 ,to green there is no simple complementary2 a purple is required1 which is not found in the spectrum1 but may be formed by combining small portions of spectral blue and red4 ,for studying mixtures of three simple colours1 a third slide may be added to the two shown in ,fig4 #aj4 ,the following little table gives the principal pairs of complementary colours4 ,,table ,,of ,,complementary ,,colours4 ,red ,greenish-blue ,orange ,sky-blue ,yellow ,blue ,greenish-yellow ,violet ,green ,purple ,,chapter ,,iii4 ,,some ,,optical ,,defects ,,of ,,the ,,eye4 ,more than one reference has been made to the fact that the sense of sight1 even in its best normal condition1 is characterised by certain defects and anomalies4 ,some of these arise directly from causes inherent in the design or structure of the eye itself1 and may be broadly classified as physical2 others are of psychological origin1 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 brain4 ,among the numerous physical defects of the eye none is more remarkable than the absence of means for properly correcting chromatic aberration4 ,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 avoided4 ,so far as a mere theorist can judge1 an achromatic arrangement of lenses would have been just as simple and just as cheap 7if ,i may use the term7 as the arrangement with which we find ourselves provided4 ,it is true that we manage to go through life very well with our uncorrected lenses1 and indeed it is hardly possible by ordinary observation to detect any evidence of the imperfection4 ,yet its existence in a glaring degree is undoubted1 and can be readily demonstrated by a great variety of methods4 ,the conclusion is inevitable that with achromatic eyes our vision would be improved1 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 answered4 ,without going into matters which are dealt with in every elementary text book of optics or general physics1 it may be desirable to explain shortly what is meant by the terms chromatic aberration1 and achromatism4 ,illustration3 ,fig4 #aa4--,refraction of monochromatic ,light by a lens4 ,let ,l ,l1 ,fig4 #aa1 represent in section a circular convex lens1 and ,p a luminous point1 which is most conveniently supposed to be situated on the axis of the lens4 ,imagine ,p to be surrounded in the first instance by a glass shade which transmits only monochromatic red light4 ,so much of the light from ,p as falls upon the lens will be refracted to a point at the conjugate focus ,f1 and after passing this point will diverge again2 the refracted light rays will1 in fact1 form a double cone1 of which ,f is the apex4 ,if a white screen be held at ,f1 there will be focussed upon it a small clearly-defined image of the luminous point4 ,if1 however1 the screen be moved nearer to or further from the lens1 it will cut the cone of light1 and the image will then no longer appear as a point1 but as a circular red disk1 which will be larger the greater the distance of the screen from ,f4 ,such a disk is known as a diffusion circle4 ,suppose now that we substitute for the red glass1 surrounding the source of light1 a purple one capable of transmitting not only red rays but violet as well4 ,the lens will cause both the red and the violet rays which pass through it to converge2 but since the violet rays are more refrangible--more easily refracted or bent aside out of their straight course--than the red1 there will now be two double cones1 as shown in ,fig4 #ab1 where the contours of the red cones are represented by solid lines and those of the violet by dots4 ,illustration3 ,fig4 #ab4--,refraction of dichromatic ,light4 ,the focus of the red rays will as before be at ,f1 but that of the violet will be nearer to the lens1 as at ,h1 and this being so1 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 lens4 ,held in the position indicated by the line ,c ,c1 where it passes through the focus of the red rays1 the screen cuts one of the cones of violet light1 and the image at ,f will appear to be surrounded by a violet halo4 ,held at ,a ,a1 the screen evidently receives an image with a red halo round it4 ,only at ,b ,b1 in the plane where the surfaces of the red and violet cones cut one another1 will it be possible to obtain an image without a coloured border2 but here good definition is unattainable1 for neither the red nor the violet rays are in focus1 and the luminous point is represented by a purple disk or diffusion circle of sensible diameter4 ,if rays of every possible refrangibility are allowed to fall upon the lens1 as is the case when the source of light is not shielded by any coloured glass1 there will be formed an indefinite number of pairs of cones1 the apices of which will lie along the straight line joining ,h and ,f4 ,it is clear that all these cones cannot possibly intersect in a single plane1 and consequently no position can be found where the edge of the projected image is perfectly free from colour1 though at a certain distance from the lens1 where the brightest constituents of the light--namely1 the yellow and green--are approximately focussed1 the coloured border is least conspicuous1 and is of a purple tint1 due to the mixture of the red and violet rays4 ,for these reasons a single glass lens cannot1 except with homogeneous light1 be made to give a perfectly distinct image of a luminous point1 nor of an illuminated object1 the surface of which may be regarded as an assemblage of points4 ,such a lens1 therefore1 is never employed when good definition is required4 ,the confusion resulting from the unequal refrangibility of the differently coloured rays is said to be due to the chromatic aberration of the lens4 ,in connection with this matter1 the history of physical optics contains an interesting little episode4 ,it occurred to ,sir ,isaac ,newton that although a single lens could never be free from chromatic aberration1 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 point1 whatever their refrangibility1 to one focus4 ,experiments which he undertook for the purpose of testing the matter led him to form the conclusion that such a result could never be attained1 the amount of colour dispersion in all substances being1 as he stated1 always exactly proportional to that of refraction4 ,for this reason he confidently announced that it was useless to attempt the construction of a really good refracting telescope1 and so great was the authority attaching to his name that for many years all efforts in that direction were abandoned4 ,nevertheless from time to time certain philosophers ventured to surmise that ,newton might perhaps have been mistaken1 and the curious thing is that they all based their scepticism upon what they considered the self-evident fact of the achromatism of the eye4 ,the system of lenses in the eye1 they argued1 being unquestionably achromatic1 why should not an equally effective combination be constructed artificially8 ,at length1 more than eighty years after ,newton had made and published his fundamental experiments1 it occurred to a working optician1 ,john ,dollond1 that it might be worth while to repeat them1 and upon doing so he at once found that ,newton was wrong in his facts1 the results as recorded by him being in direct opposition to the truth4 ,with proper respect for the memory of a great man it is usual to speak of ,newton's observation as a hasty one1 but if in these days a junior science student were to be guilty of a similar lapse1 his conduct would not impossibly be stigmatised as grossly careless4 ,having established ,newton's error1 ,dollond found little difficulty in constructing achromatic lenses of very satisfactory quality2 telescopes of his manufacture long enjoyed the highest reputation1 and the best optical instruments of the present day are the direct offspring of his invention4 ,those who entertained the opinion that ,newton's conclusion was erroneous were therefore in the right1 but it is remarkable that the reason upon which that opinion rested was altogether invalid1 for1 as ,i have said1 the lenses of the eye are by no means achromatic4 ,of the many ways in which this can be demonstrated1 the following is one of the most impressive4 ,let a long and narrow spectrum of the electric light be projected upon a white screen1 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 parallel4 ,to an observer standing close to the screen1 the spectrum will present the appearance of a bright parti-coloured rectangle4 ,but viewed from a distance of a few feet the spectrum will not seem to be rectangular1 its upper and lower edges no longer appearing to be parallel1 but to diverge1 fan-like1 towards the blue and violet1 as shown in ,fig4 #ac4 ,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 retina4 ,they are too much refracted1 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 image4 ,every point is expanded into a luminous circle1 which is the larger the more refrangible the rays1 and it is the extension of these diffusion circles beyond the proper boundaries of the image that gives the appearance of increased breadth4 ,it is a simple matter to counteract the effects of undue convexity by means of a concave lens4 ,if a normal-eyed person1 to whom the violet end of the spectrum when seen from a distance appears blurred and widened1 will look at it through suitable glasses adapted for short sight1 he will at once see it clearly defined and of its proper width4 ,illustration3 ,fig4 #ac4--,narrow ,spectrum as seen from a distance4 ,let a rectangular patch of white light having about the same dimensions as the rectangular spectrum be now thrown upon the screen4 ,the light reflected from the patch will contain1 as before1 all the various spectral colours1 but they will be mixed or superposed1 instead of being spread out side by side4 ,the patch will send forth1 among others1 can yellow and green rays1 which the eye easily focus2 it will also send out violet rays1 which1 as we have shown1 cannot be focussed by the unassisted eye4 ,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 colours4 ,viewed from a distance therefore the white patch might be expected to exhibit a violet border4 ,yet it may be confidently asserted that the observer will not be conscious of seeing any such border1 for though one actually exists1 it is possessed of such comparatively feeble luminosity that it is lost in the glare produced by the brighter rays4 ,it is1 however1 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 light4 ,the rectangle will then be of a blue-violet colour1 and when looked at closely1 will still be quite clear and sharply defined1 but viewed from a little distance it will appear blurred and of an exaggerated size4 ,another and perhaps even better way of demonstrating this last effect is to enclose the source of light 7which should be a powerful one1 such as an arc lamp or limelight7 inside a box having a ground-glass window in one side4 ,when the window is covered by the coloured glasses its outline cannot be clearly distinguished unless the observer is near1 but if he uses suitable concave spectacles1 he will be able to see it quite distinctly1 even from a considerable distance4 ,it is well known that ideas of distance are associated with certain colours4 ,a room gives one the impression of being larger when it is papered or painted a blue-violet colour than when its colouring is red4 ,in the former case the walls seem to retire from the spectator1 in the latter to approach him4 ,so too a red spot upon a violet ground appears to be distinctly raised above the surface1 while a violet spot upon a red ground appears to be depressed4 ,these phenomena are fully explained by the imperfect achromatism of the eye4 ,when we look at a red object1 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 object2 in both cases it is necessary to increase the convexity of the lens1 and so diminish its focal length1 in order to obtain a clear image upon the retina4 ,and again1 when we wish to see a blue or violet thing distinctly1 the ciliary muscle must be relaxed and the convexity of the lens as far as possible diminished1 just as if the gaze were directed to the horizon4 ,we are accustomed to estimate the distances of things largely by the muscular effort required to focus their images1 and thus it happens that the colour red comes to be associated in our minds with nearness1 and violet with remoteness4 ,these psychological effects are perfectly well marked even with the impure colours met with in ordinary life1 but they are naturally more evident when the colours observed are pure1 like those of the spectrum4 ,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 ,v4 ,the gorgeously coloured ,v seems to stand out in strong relief like a pair of inclined boards1 the nearer edges being red1 the farther ones violet4 7,see ,fig4 #ad47 ,illustration3 ,fig4 #ad4--,spectrum formed with ,v-shaped ,slit4 ,in many other ways1 and with little or no apparatus1 any one may easily convince himself that the different constituents of white light are not equally refracted by the lenses of the eye4 ,look1 for instance1 at the incandescent filament of an electric lamp through a piece#g of common dark blue cobalt glass1 which has the property of obstructing the coloured rays corresponding to the middle of the spectrum1 while transmitting the red and the blue4 ,seen from a distance of only a few inches1 the filament appears to be pale blue with a bright red border1 the blue rays being perfectly focussed1 while the red form diffusion circles4 ,move some six or eight feet away and look again2 the colours will now be reversed1 the filament appearing red and the border blue-violet4 ,from a still greater distance--about fifteen or twenty feet--the whole lamp-bulb will seem to be filled with a blue-violet glow1 due to large diffusion circles1 while the red image of the filament may be even more clearly defined than before4 ,no doubt it is partly owing to the non-achromatism of the eye that distant arc lights always appear to have a yellowish hue1 even when the air is quite clear2 a considerable proportion of their blue and violet components must necessarily be lost by extensive diffusion4#h ,again1 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 spectrum4 ,you will find yourself for the time terribly short-sighted1 everything appearing blurred and indistinct4 ,but if you resort to the usual corrective for myopia1 and put on a pair of concave spectacles1 your normal vision will be restored2 trees and houses will be seen as clearly as the feebleness of the light transmitted by the coloured glasses will permit1 and the letters of the poster will become easily legible4 ,now1 of course1 the interposition of coloured glasses does not actually give rise to these blurred images2 it merely enables one to detect their existence4 ,under ordinary conditions they always accompany the clearer images produced by the more luminous rays1 and their presence cannot fail to exert a detrimental effect upon the general definition4 ,such blurs must at least tend to fog the darker portions of the focussed picture1 and though we are not distinctly conscious of their existence1 it is certain that if they were annulled the acuteness of our vision would be improved4 ,the diffusion circles produced by the red rays1 when the eye is accommodated 7as it commonly is7 for the yellow and green1 are less conspicuous than those due to the most refrangible rays4 ,yet ,i find it impossible to focus a red object1 such as the filament of an electric lamp screened by a properly selected deep red glass1 when placed at the ordinary distance of distinct vision--some nine or ten inches from the eye--without the aid of a convex lens4 ,in this case one is not too short-sighted but too long-sighted to see the object distinctly2 in other words1 the lenses of the eye cannot refract the red rays sufficiently to produce well-defined images upon the retina1 and the refraction has to be increased by artificial means4 ,though1 as ,i have said1 it is difficult1 or even impossible to detect any trace of a coloured border when looking at a bright object for which the eye is accommodated1 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 vision4 ,a very remarkable device for the purpose is one due to von ,bezold4 ,this may be illustrated by using a non-achromatic glass lens1 such as a common magnifying glass1 to project a transparency or lantern-slide upon which is painted a target-like design1 consisting of a series of circular black bands surrounding a circular black spot4#i 7,see ,fig4 #ae47 ,illustration3 ,fig4 #ae4--;,bezold's ,diagram4 ,suppose the glass lens to represent the lenses of a gigantic eye 7in a definite condition of accommodation7 and the screen the retina4 ,the imaginary eye is looking at the design on the lantern-slide1 and when this is at the distance of most distinct vision a fairly well defined image of the target is formed upon the retinal screen4 ,now gradually move the lantern slide towards the lens 7or the lens towards the slide71 thus bringing it too near for distinct vision4 ,this has the effect of enlarging the diffusion circles formed by the less refrangible rays corresponding to the red end of the spectrum1 and at the same time of diminishing those formed by the more refrangible rays corresponding to the violet end4 ,the first result is that the circular dark bands become reddish brown1 and the spaces between them bluish4 ,as the distance between the lens and the slide is still further diminished1 the tints become more varied and brilliant1 until at last there appears a beautiful series of coloured rings around a bright red central spot4 ,these effects are not produced when the lens employed is an achromatic one2 with such a lens the diffusion circles are all enlarged or diminished together1 and a to-and-fro movement of the lantern slide 7or of the lens7 merely affects the definition of the image without causing any perceptible dispersion of colour4 ,now it is noteworthy that the chromatic phenomena exhibited with the uncorrected glass lens are quite well shown by the lenses of the eye4 ,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 distinctly4 ,the black bands will then appear to turn brown1 the white ones blue1 and the central spot bright red4 ,the printed diagram 7,fig4 #ae7 will itself show the colours if it is held at a distance of four to five inches from one eye in a good light4 ,one more experiment may be referred to4 ,look with one eye at a well-lighted page of print1 and with a strip of brown paper1 held quite near the eye1 cover about half the pupil4 ,the black letters will now appear to be bordered with colour--blue towards the apparent edge of the brown paper1 orange on the opposite side4 ,if the letters are white on a black ground1 as sometimes happens in the case of advertisements1 the colours will be interchanged4 ,the cause of the coloured borders will be readily understood from an inspection of the diagram ,fig4 #ab2 but it must be remembered that the images on the retina are inverted4 ,thus it is proved beyond all question that the lenses of the eye do not form an achromatic combination4 ,another peculiarity by which the eye is affected1 and which does not occur in optical instruments1 is that known as astigmatism4 ,the surface of the cornea1 which1 with the aqueous humour1 forms the outer lens1 is not often perfectly spherical2 generally it is shaped something like the bowl of a spoon1 the curvature being greater vertically than horizontally4 ,rays issuing from a luminous point do not1 after refraction by such a lens1 cross at a single focus1 but along two short straight lines1 the one horizontal the other vertical1 which are at different distances from the lens2 thus a distinct image of a small point cannot anywhere be produced4 ,illustration3 ,fig4 #af4--;,effect of ,astigmatism4 ,a very curious result follows from this deformity4 ,if two straight lines are drawn at right angles to each other1 as in ,fig4 #af1 it is impossible to see both of them quite clearly at the same time4 ,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 defined1 while the other is rather grey and indistinct2 at a greater distance the upright line seems to be the blacker4 ,the effect is very well shown by the diagram1 ,fig4 #ag4 ,to most persons the lines occupying the middle portion will appear either much blacker or much lighter than those at the two ends1 though in fact they are exactly alike4 ,when this form of astigmatism is excessive1 it may be corrected by the use of spectacles fitted with cylindrical lenses4 ,illustration3 ,fig4 #ag4--;,effect of ,astigmatism4 ,but there is a different kind of astigmatism--irregular astigmatism it is called--to which every one is more or less a victim1 and which cannot be relieved by any artificial appliances4 ,fortunately it does not often cause much practical inconvenience4 ,irregular astigmatism is commonly demonstrated in the following manner4 ,with the point of a fine needle1 prick a very small hole in a sheet of tinfoil4 ,hold up the tinfoil to the light and look at the hole with one eye1 the other being closed4 ,even at the distance of most distinct vision--ten inches or thereabouts1--there will probably be a ragged appearance about the hole1 as if it were not perfectly round4 ,but if you bring the tinfoil an inch or two nearer to the eye1 the hole will not seem to be even approximately circular2 it will assume the form of a little star with five or more distinct rays4 ,the configuration of the star is not generally the same for the right eye as for the left2 the rays may differ in number and in relative magnitude1 and may be inclined at different angles to the vertical4 ,fig4 #ah shows the stars as they appear to my two eyes1 when the illumination is rather strong4 ,illustration3 ,fig4 #ah4--,star-like ,images of luminous ,point4 ,if several holes are pricked in the tinfoil1 each will of course originate a separate star1 and all the stars as seen by the same eye will appear to be figured upon the same model1 though some may be larger or brighter than others4 ,illustration3 ,fig4 #ai4--,sutures of crystalline ,lens4 ,there can be no doubt that the stellate form observed in these experiments1 as well as that of the stars of heaven themselves 7which with perfect vision would be seen simply as luminous points71 is a consequence of the singular structure of the crystalline lens of the eye4 ,this does not consist of one uniform homogeneous mass like a glass lens1 but of a number of separate portions pieced together radially1 as indicated diagrammatically in ,fig4 #ai4 ,in the eye of a newly-born child there are three such portions1 and the radial junctions on one side of the lens are not opposite to those on the other1 but are intermediate4 ,in the figure the junctions at the front of the lens are represented by continuous lines and those at the back by dots4 ,the number of sutures found in the adult lens is generally greater than six4 ,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 point1 it must be confessed that no adequate explanation has yet been given of the precise manner in which the phenomenon is brought about4 ,ophthalmologists seem to have been contented with vague statements about irregular refraction1 but what kind of irregularity would sufficiently account for all the facts of observation has never1 so far as ,i know1 been exactly determined4 ,the problem can hardly be very difficult of solution1 and would1 no doubt1 readily yield to the joint efforts of a physicist and a physiologist4 ,the phenomena of irregular astigmatism as exhibited by a normal eye are exceedingly curious1 and perhaps ,i may be allowed to refer briefly to one or two experiments which ,i have myself made on the subject4#aj ,illustration3 ,fig4 #bj4--,multiple ,images of a luminous ,point4 ,light from an enclosed electric lamp of twenty-five candle power was admitted through a circular aperture about #a_/ab-;inch 7#bmm47 in diameter perforated in a brass plate2 a sheet of ground glass and another of ruby-red glass were placed behind the aperture4 ,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 ground4 ,the appearance is represented in a somewhat idealised form in ,fig4 #bj2 but the spots were not quite so distinct nor so regularly disposed as there shown1 neither was their configuration exactly the same for the right eye as for the left4 ,on gradually increasing the distance each circumferential spot became at first elongated radially and afterwards split up into two circular ones2 at the same time new spots were developed upon the luminous ground1 the approximate symmetry of the figure being still retained4 ,fig4 #ba represents a certain stage in this process of expansion4 ,the appearance was happily likened by an observer who repeated the experiment to that of a large unripe blackberry4 ,as the distance was still further increased1 the spots continued to multiply1 ultimately becoming very numerous2 their arrangement however soon became much less regular1 and the definition of most of them less distinct4 ,at about twenty feet there was seen a luminous patch1 roughly circular in outline1 and covered with irregular speckles2 superposed upon this were strings of bright1 partially overlapping spots1 corresponding apparently to the sutures of the crystalline lens4 ,illustration3 ,fig4 #ba4--;,increased number of ,images4 ,when the hole was looked at from a moderate distance through a narrow slit 7about #a_/cj inch wide7 interposed between the eye and the lens1 there was seen only a single row of circular spots1 which were arranged sinuously1 as shown in ,fig4 #bb4 ,a slight movement of the slit in the direction perpendicular to its length produced a wave-like motion of the circles1 suggestive1 as pointed out by the excellent observer before referred to of the wriggling of a caterpillar4 ,illustration3 ,fig4 #bb4--,multiple ,images seen through a ,slit4 ,by sufficiently increasing the distance between the source of light and the eye1 as many as twenty-four or twenty-five bright spots might be made to appear in the row1 but they could not be counted with any great certainty4 ,at a still longer distance or with a lens of shorter focus 7convex or concave7 they became less distinct1 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 lines4 ,illustration3 ,fig4 #bc4--;,images of an electric lamp ,filament4 ,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 circle4 ,some experiments were therefore made with semi-circular and triangular holes1 and these were in some respects preferable2 but far better results were afterwards obtained by using as a source of light the horse-shoe shaped filament of an electric lamp1 screened by a coloured glass4 ,when such a lamp was looked at through a lens1 concave or convex1 of about six inches focus1 from a distance of a few feet1 the roughly oval patch of luminosity formed upon the retina1 instead of being a mere ill-defined blur1 such as would be produced if the transparent media of the eye were composed of homogeneous substances like glass or water1 appeared to be made up of a crowd of separate images of the filament1 some being brighter than others1 as is shown in the diagram ,fig4 #bc4 ,illustration3 ,fig4 #bd;,a4--,images with horizontal ,slit4 ,illustration3 ,fig4 #bd;,b4--,images with vertical ,slit4 ,if a spectroscope slit was interposed between the eye and the lens1 and its width suitably adjusted1 only a single row of filaments was observed1 the appearances with the slit in horizontal1 vertical1 and intermediate positions being as represented in ,fig4 #bd1 ,a1 ,b1 ,c4 ,as before1 it was found possible by gradually retiring from the lamp to bring the number of images up to about twenty-five1 but attentive examination showed that most of these really consisted of clusters1 each composed of perhaps fifteen or twenty confused images of the filament4 ,a stronger lens still further separated the constituents of the clusters1 exhibiting a total number of indistinctly seen images which was estimated to amount to nearly five hundred4 ,assuming the diameter of the pupil of the eye to be one-fifth of an inch1 these observations seem to indicate as a cause of the phenomenon some fairly regular anatomical structure1 situated in or near the crystalline lens and composed of elements measuring about #a_/bjjj inch in length or breadth4 ,whether the structure which gives rise to these multiple images is to be found in the fibres of the crystalline lens itself1 or in the membranes which cover it1 is a question upon which ,i will not venture an opinion4 ,illustration3 ,fig4 #bd;,c4--,images with oblique ,slit4 ,it is indeed wonderful that an organ affected by peculiarities of which those that have been referred to are merely specimens1 should give such well-defined pictures as it does when accommodated for the objects looked at4 ,,chapter ,,iv4 ,,some ,,optical ,,illusions4 ,optical illusions generally result from the mind's faulty interpretation of phenomena presented to it through the medium of the visual organs4 ,they are of many different kinds1 but a large class1 which at first sight may seem to have little or nothing in common1 arise1 ,i believe1 from a single cause1 namely1 the inability of the mind to form and adhere to a definite scale or standard of measurement4 ,in specifying quantities and qualities by physical methods1 the standards of reference that we employ are invariable4 ,we may1 for example1 measure a length by reference to a rule1 an interval of time by a clock1 a mass or weight by comparison with standardised lumps of metal1 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 results4 ,but two lengths1 which when tested with the same foot rule are found to be exactly equal1 are not necessarily equal in the estimate formed of them by the mind4 ,look1 for instance1 at the two lines in ,fig4 #be4 ,according to the foot rule each of them is just one inch in length1 but the mind unhesitatingly pronounces the upright one to be considerably longer than the other2 the standard which it applies is not1 like a physical one1 identical in the two cases4 ,many other examples might be cited illustrative of the general uncertainty of mental estimates4 ,illustration3 ,fig4 #be4--;,illusion of ,length4 ,the variation of the vague mental standard which we unconsciously employ seems to be governed by a law of very wide if not universal application4 ,though this law is in itself simple and intelligible enough1 it cannot easily be formulated in terms of adequate generality4 ,the best result of my efforts is the following unwieldy statement3--,the mental standard which is applied in the estimation of a quality or a condition tends to assimilate itself1 as regards the quality or condition in question1 to the object or other entity under comparison of which the same 7quality or condition7 is an attribute4 ,in plainer but less precise language1 there is a disposition to minimise extremes of whatever kind2 to underestimate any deviation from a mean or average state of things1 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 large4 ,thus1 when we look at a thing which impresses us as being long or tall1 the mental standard of length is at once increased4 ,it is as if1 in making a physical measurement1 our foot rule were automatically to add some inches to its length1 while still supposed to represent a standard foot3 clearly anything measured by means of the augmented rule would seem to contain a fewer number of feet1 and1 therefore1 to be shorter than if the rule had not undergone a change4 ,it is not an uncommon thing for people visiting ,switzerland for the first time to express disappointment at the apparently small height of the mountains4 ,a mountain of #aj1jjj feet certainly does not seem to be twenty times as lofty as a hill of #ejj4 ,the fact is that a different scale of measurement is applied in the two cases2 though the observer is unaware of it1 the mountain is estimated in terms of a larger unit than the hill4 ,illustration3 ,fig4 #bf4--;,illusion of ,length4 ,if we mentally compare two adjacent things of unequal length1 such as the two straight lines in ,fig4 #bf1 there is a tendency to regard the shorter one as longer than it would appear if seen alone1 and the longer one as shorter4 ,the lower of the two lines in the figure is just twice as long as the other1 but it does not look so2 each is regarded as differing less than it really does from an imaginary line of intermediate length4 ,illustration3 ,fig4 #bg4--;,illusion of ,length4 ,two divergently oblique lines attached to the ends of a straight line as at ,a1 ,fig4 #bg1 suggest to the mind the idea of lengths greater than that of the straight line itself2 the latter1 being thought of as comparatively small1 is therefore estimated in terms of a smaller unit than would be employed if the attachments were absent1 and consequently appears longer4 ,if1 on the other hand1 the attachments are made convergent1 as at ,b1 shorter lengths are suggested2 the length of the given line is regarded as exceeding an average or mean2 the standard applied in estimating it is accordingly increased1 and the line is made to seem unduly short4 ,in spite of appearances to the contrary1 the two lines ,a and ,b are actually of the same length4 ,by duplicating the attached lines1 as shown in ,fig4 #bh1 their misleading effect becomes intensified4 ,here we have a well-known illusion of which several explanations have been proposed4 ,the fallacy is1 ,i think1 sufficiently accounted for by variation of the mental standard1 in accordance with the law to which ,i have called attention4 ,illustration3 ,fig4 #bh4--;,illusion of ,length4 ,a number of other paradoxical effects may be referred to the operation of the same law4 ,fig4 #bi shows a curious specimen4 ,at each end of the diagram is a short upright line2 exactly in the middle is another2 between the middle and the left hand end are inserted several more lines1 the space to the right of the middle being left blank4 ,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 line1 the left hand portion appearing sensibly longer than the other4 ,illustration3 ,fig4 #bi4--;,illusion of ,distance4 ,it is not difficult to indicate the source of the illusion4 ,when we look at the left hand portion we attend to the small subdivisions1 and the mental unit becomes correspondingly small2 while in the estimation of the portion which is not subdivided a larger unit is applied4 ,as one more example ,i may refer to a familiar trap for the unwary4 ,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 hat4 ,unless he has been beguiled on a former occasion1 he will certainly place the mark several inches too high4 ,obviously the height of a hat is unconsciously estimated in terms of a smaller standard than that of a room4 ,the illusion presented by the horizontal and vertical lines in ,fig4 #be 7p4 #acb7 depends1 though a little less directly1 upon a similar cause4 ,we habitually apply a larger standard in the estimation of horizontal than of vertical distances1 because the horizontal magnitudes to which we are accustomed are upon the whole very much greater than the vertical ones4 ,the heights of houses1 towers1 spires1 trees1 or even mountains are insignificant in comparison with the horizontal extension of the earth's surface1 and of many things upon it1 to which our notice is constantly directed4 ,for this reason1 we have come to associate horizontality with greater extension and verticality with less1 and1 in conformity with our law1 a given distance appears longer when reckoned vertically than when reckoned horizontally4 ,hence the illusion in ,fig4 #be4 ,but it is not only in regard to lengths and distances that the law in question holds good2 in most1 if not all cases in which a psycho-optical estimate is possible1 the mental standard is unstable and tends to assimilate itself1 as regards the quality or condition to be estimated1 to the entity in which the same is manifested4 ,this is true1 for example1 in judging of an angle of inclination or slope2 of a motion in space2 of luminous intensity1 or of the purity of a colour4 ,every cyclist knows how difficult it is to form a correct judgment of the steepness of a hill by merely looking at it4 ,not only may a slope seem to be greater or less than it really is1 but under certain circumstances a dead level sometimes appears as an upward or downward inclination1 while a gentle ascent may even be mistaken for a descent1 and vice versa4 ,we usually specify a slope by its inclination to a level plane which is parallel to the plane of the horizon1 or at right angles to the direction of gravity4 ,at any given spot the level is1 physically considered1 definite and unalterable4 ,in forming a mental judgment of an inclination1 we employ as our standard of reference an imaginary plane which is intended to be identical with the physical level4 ,but our mental plane is not absolutely stable2 when we refer a slope to it1 we unconsciously give the mental plane a slight tilt1 tending to make it parallel with the slope4 ,hence the inclination of a simple slope1 when misleading complications are absent1 is always underestimated4 ,illustration3 ,fig4 #cj4--;,illusion of ,inclination4 ,this may be illustrated by the diagram ,fig4 #cj4 ,if ,a ,b represents a truly horizontal line1 the slope of the oblique line ,c ,d is correctly specified by the angle ,c ,o ,a4 ,but if we have no instrument at hand to fix the level for us1 we shall infallibly imagine it to be in some such position as that indicated 7in an exaggerated degree7 by the dotted line ,e ,f1 while the true level ,a ,b will appear to slope oppositely to ,c ,d4 ,this class of illusion is remarkably well demonstrated by ,zllner's lines1 ,fig4 #ca2 the two thick lines which appear to diverge from left to right1 are in truth strictly parallel4 ,illustration3 ,fig4 #ca4--,zllner's ,lines4 ,i need not discuss in further detail the various illusions to which a cyclist is subjected when slopes of different inclinations succeed one another3 they all follow simply from the same general principle4 ,a thing is said to be in motion when it is changing its position relatively to the earth1 which for all practical purposes may be regarded as motionless4 ,the state1 as regards motion1 of the earth and anything rigidly attached to it1 therefore constitutes the physical zero or standard to which the motion of everything terrestrial is referred4 ,but the corresponding mental standard1 especially when it cannot easily be checked by comparison with some stationary object1 is liable to deviate from the physical one2 it tends in fact to move in the same direction as the moving body which is under observation1 and the apparent speed of the body is consequently rather less than it should be4 ,the influence exerted upon the judgment sometimes even persists for an appreciable period after the exciting cause has ceased to be operative1 as when the moving body is lost sight of or has suddenly come to rest2 in such cases fixed objects1 being compared with the delusive mental standard1 appear for a few seconds to be moving in the opposite direction4 ,i have devised a lantern slide 7,fig4 #cb7 by the aid of which this phenomenon may be rendered very evident4 ,in a square plate of metal is cut a vertical slot1 which is shaded in the figure2 behind the plate is an opaque disk1 which1 by means of suitable mechanism1 can be made to rotate about its centre4 ,the disk has a spiral opening cut in it of the same width as the slot1 as indicated by the dotted line4 ,the slide is placed in an optical lantern1 and the light passing through the aperture formed where the slot is crossed by the spiral opening1 produces a small bright patch upon a white screen hung at a suitable distance from the lantern4 ,illustration3 ,fig4 #cb4--,slide for showing ,illusions of ,motion4 ,when the disk is turned in the direction indicated by the arrow1 the bright patch moves upwards and ultimately disappears2 but at the moment of its disappearance a fresh patch starts from below1 which also moves in the upward direction2 thus there is formed upon the screen a continuous succession of ascending bright patches4 ,after these have been observed for about a quarter of a minute1 the disk is suddenly stopped1 and the persistence of the fallacious mental standard is at once demonstrated4 ,for the bright patch does not appear to be at rest1 as it actually is1 but to creep steadily downwards1 continuing to do so more and more slowly for perhaps as long as ten seconds4 ,the upward motion of the bright patches had led the observer to assume a slower upward motion as the zero1 or standard of no motion1 and reference of the really stationary patch to this physically false standard induces the illusion that the patch is descending4 ,this experiment is most successful when the bright patches are projected upon the middle of a large screen4 ,the disk should turn about three times in a second1 and the room should be feebly illuminated1 but not quite dark4 ,illustration3 ,fig4 #cc4--;,illusions of ,motion4 ,a very remarkable illusion which no doubt depends upon the same principle as the last1 though its form is entirely different1 is that to which the diagram ,fig4 #cc relates4 ,so far as ,i am aware1 it has not before been noticed4 ,two intersecting straight lines1 the one upright and the other sloping1 as shown in the figure1 are drawn upon a card4 ,the card is to be held vertically before the eyes at the distance of most distinct vision1 and waved up and down through a distance of a few inches4 ,the oblique line will then appear to oscillate transversely1 as if it were not rigidly attached to the card4 ,this is the result of underestimating the speed at which the card is moved4 ,rather than recognise the true state of things1 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 card4 ,when the card is descending the vertical line is supposed to slide a little to the right and the oblique line to the left1 which would have the effect of lowering their point of intersection independently of the downward movement of the card itself4 ,when the card ascends1 these horizontal movements are supposed to be reversed1 and the point of intersection consequently raised4 ,the assumption is exactly analogous to that made when an angle of slope is unwittingly minimised4 ,another example of the instability of a mental standard occurs in the estimation of luminosity4 ,the luminosity of a bright object1 if reckoned in terms of the same unit as that applied in judging of a less bright one1 would appear to be greater than it actually does appear1 and this quite independently of any effects of fatigue4 ,illustration3 ,fig4 #cd4--;,illusion of ,luminosity4 ,the fact is well illustrated by a familiar experiment4 ,fig4 #cd is photographed from a transparency made by superposing several different lengths of gelatine film so as to form a series of steps4 ,at the right-hand end of the image the light has passed through only one layer of the film2 in the next division it has traversed two layers1 in the next1 three1 and in the last1 four4 ,the luminosity of each of the four squares into which the oblong is divided is1 in a physical sense1 quite uniform1 but the mental standard of luminosity varies for different parts of the image1 increasing or decreasing1 as the case may be1 not per saltum1 but smoothly and continuously1 with the result that each square looks brighter towards the left than towards the right4 ,the appearance1 which is often likened to that presented by a fragment of a fluted column1 is equally well shown when the diagram is illuminated instantaneously by an electric spark1 and cannot1 therefore1 be accounted for by retinal fatigue4 ,if the squares are separated from one another by distinct lines of demarcation1 however fine1 the standard of luminosity becomes uniform for each square1 and the illusion vanishes4 ,this fact sufficiently disposes of the hypothesis which has been advanced to the effect that the phenomenon is due to physiological causes4 ,i now propose to discuss a curious consequence of the fluctuation of unaided judgment as regards the purity of a colour4 ,when any colour occupies a predominant place in the field of vision1 we are apt to consider it as being less pure1 or paler1 than we should if it were less conspicuous1 our standard of whiteness tending to approximate itself to the colour in question4 ,for the sake of clearness let us first confine our attention to a definite colour--say red4 ,an absolutely pure red is one that is entirely free from any admixture of white2 in proportion as it contains more and more white1 the more impure1 or in other words1 the more pale does it become1 until at last all trace of perceptible redness is lost and the colour is indistinguishable from white4 ,illustration3 ,fig4 #ce4--;,illusion of ,colour4 ,a convenient way of picturing the scale of purity is shown in ,fig #ce4 ,the shaded oblong may be supposed to represent a painted strip of cardboard or paper4 ,at the extreme right hand end the colour is supposed to be absolutely pure red2 towards the left the red gradually becomes paler or more dilute1 and at the middle of the diagram it has merged into perfect whiteness4 ,the figures #j to #ajj from left to right denote the percentage of free red contained in the mixture at different parts of the scale2 the luminosity is supposed to be uniform throughout4 ,now the white light with which the red is diluted may be regarded as consisting of two parts1 one of which is of exactly the same hue as the pure red itself1 and the other an equivalent proportion of the complementary colour1 which in the present case will be greenish-blue4 ,the fact therefore really is that1 as we pass along the scale from #ajj to #j1 the total quantity of red in the mixture is not reduced to nothing1 but only to one half1 while at the same time greenish-blue is added in proportions increasing from nought at the extreme right to #ej per cent4 of the whole at the middle of the card4 ,the ordinates of the quadrilateral figure ,e ,d ,b ,f show the proportion of red1 and those of the triangle ,e ,f ,b the proportion of greenish-blue1 at different parts of the scale4 ,regarding the portion of the strip which lies above the point marked #j1 as representing the zero of colour--that is1 whiteness or greyness1 which is essentially the same as whiteness--let us continue the diagram in the negative direction1 gradually reducing the quantity of red until it falls from #ej per cent4 of the whole at ,f to nothing at ,a1 and at the same time increasing that of the greenish-blue from #ej per cent4 at ,f to #ajj per cent4 at ,a4 ,the resultant hue in the portion of the card between ,f and ,a will be greenish-blue1 which begins to be perceptible as a very pale tint just to the left of ,f1 and increases in purity as ,a is approached1 at which point the colour will be entirely free from any admixture with white4 ,we have in the scale thus presented to our imagination a pair of colours1 each occupying one-half of the scale1 and gradually diminishing in purity towards the middle line2 here only1 just at the stage where one colour merges into the other1 is there no colour at all1 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 scale4 ,the completed scale1 it will be observed1 though originally intended only for the case of red1 turns out to be equally serviceable for greenish-blue3 if we consider greenish-blue as positive1 then the red1 being on the other side of zero1 must be regarded as negative4 ,any other possible pairs of complementary colours may be similarly treated4 ,this device enables us at once to understand the consequence of mentally displacing the zero1 while physically the scale remains unchanged4 ,when red is the prevailing colour in the field of vision1 we are inclined to consider it unduly pale2 in other words we imagine it to be nearer the zero of the scale than is actually the case1 and so are led to shift our standard of whiteness from the middle slightly towards the red end of the scale4 ,the new position assigned to white1 being a little to the right of the point marked #j in ,fig4 #ce1 is one where1 under customary circumstances1 the colour would be called pale red4 ,at the same time1 an object which is normally white1 and is exactly matched at the middle of the scale1 would be a little to the left of the imaginary zero1 and would consequently appear to be of a greenish-blue tint4 ,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 luminosity4 ,a small fragment of neutral grey paper1 placed upon a much larger piece of a bright red hue1 generally appears at the first glance#aa to be greenish-blue1 but if the light is at all strong1 only slightly so4 ,if1 however1 a sheet of white tissue paper is laid over the whole1 the greenish-blue tint immediately becomes startlingly distinct1 and may even appear more decided than the red itself as seen through the tissue4 ,the same piece of grey paper1 when placed upon a green ground1 appears rose-coloured1 and upon a blue ground1 yellow1 the effect being always greatly increased by the diluent action of superposed tissue paper4 ,there seem to be several reasons1 partly physical and partly psychological1 why these contrast colours1 as they are called1 are more pronounced when the colour that calls them into existence either has a somewhat pale tint or is feebly illuminated4 ,probably the most important is of a purely physical character4 ,the refracting media of the eye are much less perfectly transparent than a good glass lens is2 they are sensibly turbid or opalescent1 and in consequence of this defect some of the light which falls upon them is irregularly scattered over the retina4 ,if we look at a bright red object with a small white patch upon it1 the image of the patch as formed upon the retina is not1 physically speaking1 perfectly white1 but slightly coloured by diffused red light2 owing however to the psychological influence to which our attention has been directed1 the faint red coloration is not consciously perceived2 the same mental displacement of the zero which1 when the exciting colour was feeble1 led us to regard white 7or grey7 as bluish-green1 now causes what is actually pale red to appear white4 ,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 falls4 ,on the contrary1 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 judgment4 ,of the operation of this law ,i have quoted several very diverse instances1 and the number might easily have been increased4 ,nor is it only in relation to optical phenomena that the law holds good2 in its most general form1 supplemented it may be in some instances by obvious corollaries1 it is applicable to almost every case in which physical attributes of whatever kind are the subject of unassisted mental judgment4 ,,chapter ,v4 ,,curiosities ,,of ,,vision4 ,the function of the eye1 regarded as an optical instrument1 is limited to the formation of luminous images upon the retina4 ,from a purely physical point of view it is a simple enough piece of apparatus1 and1 as was forcibly pointed out by ,helmholtz1 it is subject to a number of defects which can be demonstrated by the simplest tests1 and which1 if they occurred in a shop-bought instrument1 would be considered intolerable4 ,what takes place in the retina itself under luminous excitation1 and how the sensation of sight is produced1 are questions which belong to the sciences of physiology and psychology2 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 free4 ,yet in spite of all these drawbacks our eyes do us excellent service1 and provided that they are free from actual malformation and have not suffered from injury or disease1 we do not often find fault with them4 ,this1 however1 is not because they are as good as they might be1 but because with incessant practice we have acquired a very high degree of skill in their use4 ,if anything is more remarkable than the ease and certainty with which we have learnt to interpret ocular indications1 when they are in some sort of conformity with external objects1 it is the pertinacity with which we refuse to be misled when our eyes are doing their best to deceive us4 ,in our earliest years we began to find out that we must not believe all we saw2 experience gradually taught us that on certain points and under certain circumstances the indications of our organs of vision were uniformly meaningless or fallacious1 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 value4 ,in this most of us have been remarkably successful2 so much so1 that if1 from motives of curiosity1 or for the sake of scientific experiment1 we wish to direct our attention to the sensations in question1 and to see things as they actually appear1 we can only do so with the greatest difficulty2 sometimes1 indeed1 not at all1 unless with the assistance of some specially contrived artifice4 ,in the present chapter it is proposed to discuss a few of the less familiar vagaries of the visual organs1 and to show how they may be demonstrated4 ,some of the experiments may1 it is to be feared1 be found rather difficult2 success will depend mainly upon the experimentalist's ability to lay aside habit and prejudice1 and give close attention to his visual sensations2 but it is hardly to be expected that an unskilled person will at the first attempt observe all the phenomena which will be referred to4 ,among the most annoying of the eccentricities which characterise the sense of vision is that known as the persistence of impressions4 ,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 position2 it continues for a period which is generally said to be about a tenth of a second1 but may sometimes be much more or less4 ,it is for this reason that we cannot see the details of anything which is in rapid motion1 but only an indistinct blur1 resulting from the confusion of successive impressions4 ,if a cardboard disk1 which is painted in conspicuous black and white sectors is caused to rotate at a sufficiently high speed1 the divisions are completely lost sight of1 and the whole surface appears to be of a uniformly grey hue4 ,but if the rapidly rotating disk is illuminated by a properly timed series of electric flashes1 it looks as if it were at rest1 and in spite of the intermittent nature of the light1 the black and white sectors can be seen quite continuously1 though as a matter of fact the intervals of darkness are very much longer than those of illumination4 ,persistent impressions of this kind are often spoken of as positive after-images4 ,there is a very remarkable phenomenon accompanying the formation of positive after-images1 especially those following brief illumination1 which seems1 until comparatively recent times1 to have entirely escaped the notice of the most acute observers4 ,it was first observed accidentally by ,professor ,c4 ,a4 ,young1 when he was experimenting with a large electrical machine which had been newly acquired for his laboratory4 ,he noticed that when a powerful ,leyden jar discharge took place in a darkened room1 any conspicuous object was seen twice at least1 with an interval of a trifle less than a quarter of a second1 the first time vividly1 the second time faintly4 ,often it was seen a third time1 and sometimes1 but only with great difficulty1 even a fourth time4 ,he gave to this phenomenon the name of recurrent vision2 it may perhaps be more appropriately denominated the ,young effect4 ,by means of the powerful machine presented to the ,royal ,institution by ,mr4 ,wimshurst1 used in conjunction with a battery of ,leyden jars1 the ,young effect has been successfully shown to a large assembly4 ,but it is quite easy to demonstrate it on a small scale with any influence machine which will give a spark about an inch long4 ,one of the terminals of the machine should be connected by a wire with the inner coating of a half-pint ,leyden jar1 the other with the outer coating1 and the discharging balls should be set a quarter of an inch apart4 ,the observer's eyes must be shielded from the direct light of the spark by any convenient screen1 such as a large book set on end4 ,the best object for the experiment is a sheet of white paper1 placed in an upright position a few inches away from the terminals of the machine and exposed to the full light of the discharge4 ,the room being darkened1 let the machine be worked slowly1 while the eyes are turned towards the white paper4 ,this will be seen for a moment when the spark passes1 and1 after a dark interval of about one-fifth of a second1 it will make another brief appearance4 ,after a further short interval of darkness1 a second recurrent image will often be seen4 ,it may be remarked that the effect is most striking when the eyes are not directed exactly upon the white paper1 but above or on one side of it2 the proper distance of the paper from the spark-gap should be found by trial4 ,under favourable conditions ,i have observed as many as six or seven reappearances of an object which was illuminated by a single discharge4 ,these followed one another at the usual rate--about five in a second--and produced a twinkling or quivering effect1 closely resembling that attending a flash of lightning which is not directly seen4 ,there can indeed be little doubt that the proverbial quiver of the lightning-flash is in many cases merely an effect of recurrent vision1 though sometimes1 of course1 as has been shown by photographs1 the discharge is really multiple4 ,some years ago ,i called attention to a very different method of exhibiting a recurrent image4 ,the apparatus used for the purpose consists of a vacuum tube mounted in the usual way upon a horizontal axis capable of rotation4 ,when the tube is illuminated by a rapid succession of discharges from an induction coil1 and is made to rotate very slowly by clockwork 7turning once in every two or three seconds71 a very curious phenomenon may be noticed4 ,at a distance of a few degrees behind the tube and separated from it by an interval of perfect darkness1 comes a ghost4 ,this ghost is in form an exact reproduction of the tube2 it is very clearly defined1 and though its apparent luminosity is somewhat feeble1 it can in most cases be seen without difficulty4 ,the varied colours of the original are1 however1 absent1 the whole of the phantom tube being of a uniform bluish or violet tint4 ,if the rotation is suddenly stopped the ghost still moves steadily on until it reaches the luminous tube1 with which it coalesces and so disappears4 7,see ,fig4 #cf1 where the recurrent image is represented by dotted lines47 ,illustration3 ,fig4 #cf4--,recurrent ,vision demonstrated with a ,vacuum ,tube4 ,more recently a fresh series of experiments were undertaken in connection with the ,young effect and certain allied matters1 the results being embodied in a communication to the ,royal ,society 7,proc4 ,roy4 ,soc41 #ahid1 vol4 #ef1 p4 #acb74 ,among other things an attempt was made to ascertain how far a recurrent image was affected by the colour of the exciting light4 ,with this object two methods of experimenting were employed4 ,in the first1 coloured light was obtained by passing white light through coloured glasses2 in the second and more perfect series of experiments1 the pure coloured light of the spectrum was used4 ,among other results it was found that1 cteris paribus1 the recurrent image was much stronger with green light than with any other1 and that when the excitation was produced by pure red light1 however intense1 there was no recurrent image at all4 ,illustration3 ,fig4 #cg4--,recurrent ,vision with ,rotating ,disk4 ,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 centre4 ,near the edge of the disk is a small circular aperture4 ,the slide is placed in a limelight lantern1 and a bright image of the hole is focussed upon a distant screen1 all other light being carefully shut off4 ,when the disk is turned slowly1 the spot of light upon the screen goes round and round1 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 colour1 which is the recurrent image of the first4 7,see ,fig4 #cg47 ,it is essential to keep the direction of the eyes perfectly steady1 which is not a very easy thing to do without practice4 ,if a green glass is placed before the lens1 the ghost will be at its best1 and should be seen quite clearly and easily1 provided that no attempt is made to follow it with the eyes4 ,with an orange glass the ghost becomes less distinctly visible1 and its colour generally appears to be greenish-blue1 instead of violet as before4 ,when a red glass is substituted1 the ghost completely disappears4 ,if the speed of rotation is sufficiently high1 the red spot is considerably elongated during its revolution1 and its colour ceases to be uniform1 the tail assuming a light bluish-pink tint4 ,but however great the speed1 no complete separation of the spot into red and pink portions can be effected1 and no recurrent image is ever found4 ,the spectrum method of observation can only be carried out on a small scale1 and is not suited for exhibition to an audience4 ,it1 however1 affords the best means of ascertaining how far the apparent colour of the recurrent image depends upon that of the primary1 a matter of some theoretical interest4 ,illustration3 ,fig4 #ch4--,recurrent ,vision with ,spectrum4 ,the arrangement adopted is shown in the annexed diagram 7,fig4 #ch74 ,l is a lantern containing an oxyhydrogen light or an electric arc lamp1 ,s is an adjustable slit1 ,m a projection lens1 ,p a bisulphide of carbon prism1 ,d a metal plate in the middle of which is a circular aperture #b millimetres 7#a_/ab inch7 in diameter4 ,a bright spectrum1 #f or #g centimetres in length 7about #c inches71 is projected upon this metal plate1 and a small selected portion of it passes through the round hole2 thence the coloured light goes through the lens ,n to the little mirror ,q1 which reflects it upon the white screen ,r4 ,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 ,r4 ,to the back of the mirror ,q is attached a horizontal arm which is not quite perpendicular to the mirror1 its inclination being capable of adjustment4 ,the arm is turned slowly by clock-work1 thus causing the coloured spot on the screen to revolve in a circular orbit about #cj centimetres 7#a foot7 in diameter1 its recurrent image following at a short distance behind it4 ,when the mirror turns once in #a-a_/b seconds1 this image appears about #ej behind the coloured spot1 the corresponding time-interval being about one-fifth of a second4 ,using this apparatus1 it was found that white light was followed by a violet recurrent image2 after blue and green1 when the image was brightest1 its colour was also violet2 after yellow and orange it appeared blue or greenish blue4 ,on the other hand1 when a complete spectrum was caused to revolve upon the screen1 the whole of its recurrent image from end to end appeared violet2 there was no suspicion of blue or greenish-blue at the less refrangible end4 ,for this and other reasons given in the paper it was concluded that the true colour was in all cases really violet1 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 contrast4 ,it seems likely1 then1 that the phenomenon which has been spoken of as recurrent vision1 is due principally1 if not entirely1 to an action of the violet nerve-fibres4 ,recurrent vision is1 no doubt1 generally most conspicuous after a very brief period of retinal illumination1 such as was employed in the experiments which we have been discussing2 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 fatigue4 ,but by a little effort it may be detected even after very prolonged illumination1 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 extinguished2 the phenomenon forces itself upon my attention almost every night when ,i turn off the electric lights4 ,it need hardly be pointed out that it represents only a transient phase of the well known positive after-image1 and it had even been observed in a vague and uncertain sort of way long before the date of ,professor ,young's experiment4 ,helmholtz1 for example1 mentions the case of a positive after-image which seemed to disappear and then to brighten up again1 but he goes on to explain--erroneously1 as it turns out--that the seeming disappearance was illusory4 ,m4 ,charpentier1 of ,nancy1 whose work in physiological optics is well known1 was the first to notice and record a remarkable phenomenon which1 in some form or other1 must present itself many times daily to every person who is not blind1 but which until about seven years ago had been absolutely and universally ignored4 ,the law which is associated with ,charpentier's name is this3--,when darkness is succeeded by light1 the stimulus which the retina at first receives1 and which causes the sensation of luminosity1 is followed by a brief period of insensibility1 resulting in the sensation of momentary darkness4 ,it appears that the dark period begins about one sixtieth of a second after the light has first been admitted to the eye1 and lasts for about an equal time4 ,the whole alternation from light to darkness and back again to light is performed so rapidly1 that except under certain conditions1 which1 however1 occur frequently enough1 it cannot be detected4 ,illustration3 ,fig4 #ci4--;,charpentier's ,dark ,band4 ,the apparatus which ,charpentier employed for demonstrating and measuring the duration of this effect is very simple4 ,it consists of a blackened disk with a white sector1 mounted upon an axis4 ,when the disk is illuminated by sunlight and turned rather slowly1 the direction of the gaze being fixed upon the centre1 there appears upon the white sector1 close behind its leading edge1 a narrow but quite conspicuous dark band4 7,see ,fig4 #ci47 ,the portion of the retina which at any moment is apparently occupied by the dark band1 is that upon which the light reflected by the leading edge of the white sector impinged one sixtieth of a second previously4 ,but no special apparatus is required to show the dark reaction4 ,in ,fig4 #dj 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 surface4 ,the hand appears to be followed by a dark outline separated from it by a bright interval4 ,the same kind of thing happens1 in a more or less marked degree1 whenever a dark object moves across a bright background1 or a bright object across a dark background4 ,illustration3 ,fig4 #dj4--;,charpentier's ,effect shown with the ,hand4 ,in order to see the effect distinctly by ,charpentier's original method1 the illumination must be strong4 ,if1 howover1 the arrangement is slightly varied1 so that transmitted instead of reflected light is made use of1 comparatively feeble illumination is sufficient4 ,a very effective way is to turn a small metal disk1 having an open sector of about #fj1 in front of a sheet of ground or opal glass behind which is a lamp4 ,by an arrangement of this kind upon a larger scale1 the effect may easily be rendered visible to an audience4 ,the eyes should not be allowed to follow the disk in its rotation1 but should be directed steadily upon the centre4 ,the acute and educated vision of ,charpentier enabled him1 even when working with his black and white disk1 to detect the existence1 under favourable conditions1 of a second1 and sometimes a third1 band of greatly diminished intensity1 though he remarks that the observation is a very difficult one4 ,what is probably the same effect can1 however1 as pointed out in my paper of #ahid1 be shown quite easily in a different manner4 ,if a disk with a narrow radial slit1 about half a millimetre 7#a_/ej inch7 wide1 is caused to rotate at the rate of about one turn per second in front of a bright background1 such as a sheet of ground glass with a lamp behind it1 the moving slit assumes the appearance of a fan-shaped luminous patch1 the brightness of which diminishes with the distance from the leading edge4 ,and if the eyes are steadily fixed upon the centre of the disk1 it will be noticed that this bright image is streaked with a number of dark radial bands1 suggestive of the ribs or sticks of a fan4 ,near the circumference as many as four or five such dark streaks can be distinguished without difficulty2 towards the centre they are less conspicuous1 owing to the overlapping of the successive images of the slit4 ,the effect is roughly indicated in ,fig4 #da4 ,illustration3 ,fig4 #da4--,multiple ,dark ,bands4 ,the dark reaction known as the ,charpentier effect occurs at the beginning of a period of illumination4 ,there is also a dark reaction of very short duration at the end of a period of illumination4 ,it should be explained that1 owing to what is called the proper light of the retina1 ordinary darkness does not appear absolutely black3 even in a dark room on a dark night with the eyes carefully covered1 there is always some sensation of luminosity which would be sufficient to show up a really black image if one could be produced4 ,now the darkness which is experienced after the extinction of a light is for a small fraction of a second more intense than common darkness4 ,the first mention of this dark reaction perhaps occurs in an article contributed to ,nature in #ahhe1 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 background1 and which was estimated to last from a-quarter to a-half second4 ,abnormal darkness1 it was added1 follows as a reaction after luminosity4 ,illustration3 ,fig4 #db4--,temporary ,insensitiveness of the ,eye4 ,in the ,royal ,society paper before referred to the point is further discussed1 and a method is described by which the stage of reaction may be easily exhibited and its duration approximately measured4 ,if a translucent disk1 made of stout drawing-paper and having an open sector1 is caused to rotate slowly in front of a luminous background1 a narrow radial dark band1 like a streak of black paint1 appears upon the paper very near the edge which follows the open sector4 ,from the space covered by this band when the disk was rotating at a known speed1 the duration of the dark reaction was calculated to be about one-fiftieth of a second2 my original estimate was therefore an excessive one4 ,the experiment is illustrated in ,fig4 #db4 ,one more interesting point should be noticed in the train of visual phenomena which attend a period of illumination4 ,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 becomes4 ,this is shown by the fact1 which is obvious enough when once attention has been directed to it1 that the bright band1 which in the ,charpentier disk intervenes between the dark band and the leading edge of the white sector1 appears to be much more strongly illuminated than any other portion of the sector4 ,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 follows3-- 7#a7 ,immediately upon the impact of the light there is experienced a sensation of luminosity1 the intensity of which increases for about one-sixtieth of a second3 more rapidly towards the end of that period than at first4 7#b7 ,then ensues a sudden re-action1 lasting also for about one-sixtieth of a second1 in virtue of which the retina becomes partially insensible to renewed or continued luminous impressions4 ,these two effects may be repeated in a diminished degree1 as often as three or four times4 7#c7 ,the stage of fluctuation is succeeded by a sensation of steady luminosity1 the intensity of which is1 however1 considerably below the mean of that experienced during the first one-sixtieth of a second4 7#d7 ,after the external light has been shut off1 a sensation of diminishing luminosity continues for a short time1 and is succeeded by a brief interval of darkness4 7#e7 ,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 second1 and is followed by another interval of ordinary darkness4 7#f7 ,finally1 in about a fifth of a second after the extinction of the external light1 there occurs another transient impression of luminosity1 generally violet coloured1 after which the uniformity of the darkness remains undisturbed4 ,fig4 #dc1 which is copied from my paper1 gives a rough diagrammatic representation of the above described chain of sensations4 ,no account is here taken of the comparatively feeble after-images which succeed the recurrent image1 and may last for several seconds4 ,i propose now to say a few words about a curious phenomenon of vision which a short time ago excited considerable interest4 ,illustration3 ,fig4 #dc4--,visual ,sensations attending a period of ,illumination4 ,illustration3 ,fig4 #dd4--;,benham's ,top4 ,in the year #ahie ,mr4 ,c4 ,e4 ,benham brought out a pretty little toy which he called the ,artificial ,spectrum ,top4 ,it consists of a cardboard disk1 one half of which is painted black1 while on the other half are drawn four successive groups of curved black lines at different distances from the centre1 as shown in ,fig4 #dd4 ,when the disk rotates rather slowly1 each group of black lines generally appears to assume a different colour1 the nature of which depends upon the speed of the rotation and the intensity and quality of the light4 ,under the best conditions the inner and outer groups of lines become bright red and dark blue2 at the same time the intermediate groups also appear tinted1 but the hues which they assume are rather uncertain and difficult to specify4 ,by far the most striking of the colours exhibited by the top is the red1 and next to that the blue2 this latter is1 however1 sometimes described as bluish-green4 ,some experiments carried out by myself in #ahif 7,proc4 ,roy4 ,soc41 vol4 #fj1 p4 #cgj7 seem to indicate pretty clearly the cause of the remarkable bright red colour1 and also that of the blue4 ,the more feeble tints of the two intermediate groups of lines perhaps result from similar causes in a modified form1 but these have not yet been investigated4 ,in the red colour we have another striking example of an exceedingly common phenomenon which is habitually disregarded2 indeed ,i can find no record of its ever having been noticed at all4 ,the fact is that whenever a bright image is suddenly formed upon the retina after a period of comparative darkness1 this image appears for a short time to be surrounded by a narrow coloured border1 the colour1 under ordinary conditions of illumination1 being red4 ,if the light is very strong1 the transient border is greenish-blue1 but this colour1 as will be explained later1 turned out to be merely an after-effect of red4 ,sometimes1 when the object is in motion1 both red and blue are seen together4 ,the observations were first made in the following manner4 ,a blackened zinc plate1 in which is a small round hole covered with a piece of thin writing-paper1 is fixed over a larger opening in a wooden board2 thus we are furnished with a sharply-defined translucent disk1 which is surrounded by a perfectly opaque substance4 ,an arrangement is provided for covering the translucent disk with a shutter1 which can be opened very rapidly by releasing a strong spring4 ,if this apparatus is held between the eyes and a lamp1 and the translucent disk is suddenly disclosed by working the shutter1 the disk appears for a short time to be surrounded by a narrow red border4 ,the width of the border is perhaps a millimetre 7#a_/be inch71 and the appearance lasts for something like a tenth of a second4 ,most people are at first quite unable to recognise this effect1 the difficulty being1 not to see it1 but to know that one sees it4 ,those who have been accustomed to visual observations generally perceive it without any difficulty when they know what to look for1 and no doubt it would be very evident to a baby which had not advanced very far in the education of its eyes4 ,the observation is made rather less difficult by a further device4 ,if the disk is divided into two parts by an opaque strip across the middle1 it is clear that each half disk will have its red border1 and if the strip is made sufficiently narrow1 the red borders along its edges will meet or perhaps overlap1 and the whole strip will1 for a moment after the shutter is opened1 appear red4 ,a disk was thus prepared by gumming across the paper a very narrow strip of tinfoil4 ,the effect produced when such a disk is suddenly exposed is indicated in ,fig4 #de1 the red colour being represented by shading4 ,illustration3 ,fig4 #de4--;,demonstration of ,red ,borders4 ,a simpler apparatus is1 however1 quite sufficient for showing the phenomenon1#ab and with practice one can even acquire the power of seeing it without any artificial aid at all4 ,i have many times noticed flashes of red upon the black letters of a book that ,i was reading1 or upon the edges of the page3 bright metallic1 or polished objects often show it when they pass across the field of vision in consequence of a movement of the eyes1 and it was an accidental observation of this kind which suggested the following easy way of exhibiting the effect experimentally4 ,an incandescent electric lamp was fixed behind a round hole in a sheet of metal which was attached to a board4 ,the hole was covered with two or three thicknesses of writing paper1 making a bright disk of nearly uniform luminosity4 ,when this arrangement was moved rather quickly either backwards and forwards or round and round in a small circle1 the edge of the streak of light thus formed appeared to be bordered with red4 ,if this experiment is performed with a strong light behind the paper1 the streak becomes bordered with greenish-blue instead of red4 ,with an intermediate degree of illumination1 both blue and red may be seen together4 ,most of the effects that have so far been described were produced by transmitted light1 but reflected light will show them equally well4 ,if you place a printed book in front of you near a good lamp and interpose a dark screen before your eyes1 then1 when the screen is suddenly withdrawn1 the printed letters will for a moment appear red1 quickly changing to black4 ,some practice is required before this observation can be made satisfactorily1 but by a simple device it is possible to obliterate the image of the letters before the redness has had time to disappear2 the colour then becomes quite easily perceptible4 ,hold two screens together side by side1 a black one and a white one1 in such a manner that an open space is left between them4 7,see ,fig4 #df47 ,in the first place let the black screen cover the printing2 then quickly move the screens sideways so that the printed letters may be for a moment exposed to view through the gap1 stopping the movement as soon as the page is covered by the white screen4 ,during the brief glimpse that will be had of the black letters while the gap is passing over them1 they will1 if the illumination is suitable1 appear to be bright red4 ,illustration3 ,fig4 #df4--;,black and ,white ,screens4 ,illustration3 ,fig4 #dg4--;,disk for ,red ,borders4 ,we may go a step further4 ,cut out a disk of white cardboard1 divide it into two equal parts by a straight line through the centre1 and paint one half black4#ac ,at the junction of the black and white portions cut out a gap1 which may conveniently be of the form of a sector of #de4 7,see ,fig4 #dg47 ,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 light4 ,make the disk spin at the rate of about five or six turns a second by striking the edge with the finger4 ,as before1 the letters when seen through the gap will appear red1 and persistence will render the repeated impressions almost continuous so long as the rotation is kept up2 any one seeing the printing for the first time through the rotating disk would believe that it was done with red ink4 ,care must be taken that the disk does not cast a shadow upon the page1 and that the intensity of the illumination is properly adjusted4 ,i have devised several rather more elaborate contrivances for making the disks rotate at a uniform speed2 one of these is shown in ,fig4 #ej4 ,in none of these experiments does an extended black surface ever appear red1 but only black dots or lines4 ,and the lines must not be too thick2 if their thickness is much more than a millimetre 7#a_/be inch71 the lines1 as seen by an observer from the usual distance for reading1 do not become red throughout1 but only along their edges4 ,the red appearance does not in fact originate in the black lines themselves3 these serve merely as a background for showing up the red border which fringes externally the white portions of the paper1 and the width of this border does not exceed about one-fifth of a degree4 ,but by employing a sufficiently large disk and selecting designs or letters composed of lines of suitable thickness1 the colour effect has been shown to a large audience4 ,when the disk is turned in the opposite direction1 so that the gap is preceded by white and followed by black1 the lines of the design appear at first sight to become dark blue instead of red4 ,attentive observation1 however1 shows that the apparently blue tint is not formed upon the lines themselves1 as the red tint was1 but upon the white ground just outside them4 ,this introduces to our notice another border phenomenon1 which seems to present itself when a dark patch is suddenly formed on a bright ground1 for that is essentially what takes place when the disk is turned the reverse way4 ,i made some attempts to obtain more direct evidence that such a dark patch appeared for a moment to have a blue border1 and after some trouble succeeded in doing so4 ,a circular aperture was cut in a wooden board and covered with white paper2 a lamp was placed behind the board1 and thus a bright disk was obtained1 as in the former experiment4 ,an arrangement was prepared by means of which one half of this bright disk could be suddenly covered by a metal shutter1 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 rest4 ,the blue band lasted for about a tenth of a second1 and it seemed to disappear by retreating into the black edge of the shutter4 ,the phenomenon is illustrated in ,fig4 #dh1 where the shaded band indicates the blue border4 ,illustration3 ,fig4 #dh4--;,demonstration of ,blue ,border4 ,we have then to account1 if possible1 for the two facts that1 in the formation of these transient colour-borders1 the red sensation occurs in a portion of the retina which has not itself been exposed to the direct action of light1 while the blue occurs in a portion which is steadily illuminated1 both colour sensations being referred to localities adjacent to those in which a change of illumination has suddenly taken place4 ,accepting the ,young-,helmholtz theory of colour vision1 the effects must1 ,i think1 be attributed to a sympathetic affection of the red nerve fibres4 ,when the various nerve fibres occupying a limited portion of the retina are suddenly stimulated by white light 7or by any kind of light which contains a red constituent7 the immediately surrounding red nerve fibres are for a short period excited sympathetically1 while the violet and green fibres are not so excited1 or in a much less degree4 ,and again1 when light is suddenly cut off from a patch in a bright field1 there occurs a sympathetic insensitive reaction in the red fibres just outside the darkened patch1 in virtue of which they cease for a moment to respond to the luminous stimulus2 the green and violet fibres1 by continuing to respond uninterruptedly1 give rise to the sensation of a blue border4 ,it is perhaps desirable to refer briefly to another proposed explanation of the phenomenon1 which occurred to myself at an early stage of the investigation1 and has since been suggested by many different persons4 ,the explanation in question is of a purely physical character1 and depends upon the non-achromatism of the eye4 ,illustration3 ,fig4 #di4--;,disk for experiments on the origin of ,colour-borders4 ,without going into details1 it will suffice to quote a single experiment which is of itself fatal to any such theory4 ,prepare a disk like that shown in ,fig4 #di1 and spin it above a page of printing4 ,the letters beneath the zone which is partly black and partly white will1 under the usual conditions1 turn red1 but those beneath the remainder of the disk will retain their blackness4 ,the demarcation is quite definite1 and a single printed word may be made to appear red in the middle and black at its two ends4 ,now it is1 of course1 impossible that the lenses of the eye should be perfectly accommodated for the letters which appear black1 and at the same time seriously out of focus for the others4 ,this explanation1 therefore1 simple and obvious as it may seem1 is altogether untenable4 ,whether or not the hypothesis which ,i have suggested is correct in all its details1 it is1 ,i think1 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 experiments1 for the essential conditions are the same in both cases4 ,the last curiosity which ,i will notice is connected with the fact already mentioned1 that when the illumination is strong1 the transient border-colours are nearly reversed1 greenish-blue appearing in place of red1 and brick-red in place of blue4 ,i was for a long time quite unable to imagine any reasonably probable explanation of this circumstance1 but a clue was finally obtained from consideration of the fact that greenish-blue is the complementary colour to red1 and in a subsequent memoir 7,proc4 ,roy4 ,soc41 vol4 #fa1 p4 #bfi7 some experiments were described which show1 as ,i believe conclusively1 that the greenish-blue borders seen in a strong light are simply negative after-images of the usual red one4 ,these negative after-images are of the familiar kind that are observed after one has gazed for some time at a bright coloured object4 ,if a red wafer lying upon a sheet of white or grey paper is looked at steadily for about half a minute1 and the gaze is then suddenly transferred to some other part of the paper1 a greenish-blue ghost of the wafer will be seen4 ,the portion of the retina upon which the red image at first falls becomes fatigued and partially insensible to red light2 it is therefore unable to appreciate the red component of the white light afterwards reflected to it by the paper1 and the sensation of the complementary colour consequently predominates2 hence the greenish-blue ghost1 which is called the negative after-image of the wafer4 ,the new experiments show that1 if a certain condition is fulfilled1 the usual prolonged stare becomes unnecessary1 a momentary glance sufficing to produce a strong but fugitive after-image4 ,the condition is that the part of the retina where the image is to be formed1 shall have been darkened immediately before excitation by the bright object4 ,the retinal nerves1 when in darkness1 rapidly acquire a state of sensitiveness far exceeding the normal average in the light1 but quickly diminishing again under the influence of illumination4 ,this peculiar sensitiveness may1 indeed1 be both gained and lost in a small fraction of a second1 and is therefore very favourable for the rapid generation of negative after-images4 ,once more making use of the black and white screens depicted in ,fig4 #df1 let the black screen first cover the paper upon which the wafer is lying2 this will darken a portion of the retina1 and render it sensitive4 ,then let the screens be quickly moved sideways1 so that the wafer1 after having been seen for a moment through the opening1 may be immediately covered by the white screen4 ,a bright but evanescent greenish-blue ghost will succeed the red impression4 ,but the most curious thing is that if the illumination is strong1 and the screens are moved at the proper speed1 no trace of red will be seen at all2 it will appear exactly as if the actual colour of the wafer seen through the gap were greenish-blue4 ,i am informed that analogous phenomena have been observed in other branches of physiology2 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 due4 ,as in the former experiments1 the effect may be shown continuously by means of a rotating disk with an open sector4 ,the annexed diagram 7,fig4 #ej7 indicates a convenient apparatus for the purpose4 ,the disk is made of thin metal1 and properly balanced2 the dark portion of the surface is covered with black velvet1 and the light portion with unglazed grey or buff paper4 ,it should turn some six or eight times in a second1 while its front is well illuminated either by bright diffused daylight or by a powerful lamp4 ,a red card placed behind the rotating disk is made to appear green1 a green card pink1 and a blue one yellow1 while a black patch painted upon a white ground appears lighter than the ground itself4 ,i have prepared some designs which demonstrate the phenomenon in a very striking manner4 ,one of these is a picture of a lady with indigo-blue hair1 an emerald-green face1 and a scarlet gown1 who is represented as admiring a violet sunflower with purple leaves4 ,seen through the disk1 the lady's tresses appear flaxen1 her complexion a delicate pink1 and her dress a light peacock-blue2 the petals of the sunflower also become yellow1 and its foliage green4 ,other designs show equally remarkable transformations of colour4 ,illustration3 ,fig4 #ej4--;,disk for transforming ,colours4 ,i have mentioned only a few among many curious phenomena which have presented themselves in the course of these investigations4 ,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 vision4 ,william ,byles ,sons1 ,printers1 #abi1 ,fleet ,street1 ,london1 and ,bradford4 ,,footnotes3 #a ,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 waves4 ,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 shore1 as the uninitiated are apt to suppose4 ,the true wave-length1 or distance from crest to crest of successive waves1 can be well observed from the top of a cliff4 #b ,in practice1 wave-lengths are expressed in ten-millionths of a millimetre4 ,the wave-lengths of the lines ,a and ,h of the solar spectrum1 which approximately coincide with the limits of visibility1 are #geid and #cifh ten-millionths of a millimetre4 #c ,possibly the human eye is at present in process of transformation from an inferior type to a different and more perfect one4 #d ,it is sometimes necessary to place the lens ,i on the other side of ,k4 #e ,it is easy to find specimens of red and green glass suitable for this experiment4 ,the proper kind of purple is not so commonly met with4 #f ,some recent experiments on artificial colour-blindness 7,proc4 ,roy4 ,soc41 ,feb41 #ahih7 have led ,mr4 ,burch to the conclusion that there are really four fundamental colour-sensations--a red1 a green1 a blue1 and a violet4 ,his results are1 however1 thought to be capable of a different interpretation4 #g ,or through several pieces superposed4 #h ,a violet-coloured haze may sometimes be actually seen around the opal globes of the electric lamps in the streets4 #i ,a focus electric lamp was used in the lantern4 #aj ,proc4 ,roy4 ,soc41 ,jan41 #ahii4 #aa ,after a few seconds' observation the greenish-blue colour often becomes much more intense1 but this is an effect of fatigue1 with which we are not at present concerned4 #ab ,see ,nature1 vol4 #ee1 p4 #cfg 7,feb4 #ahth1 #ahig74 #ac ,or1 for best results1 use a balanced metal disk covered with black velvet and white paper4