Fig. 14.—Spectrum formed with V-shaped Slit.
In many other ways, and with little or no apparatus, any one may easily convince himself that the different constituents of white light are not equally refracted by the lenses of the eye. Look, for instance, at the incandescent filament of an electric lamp through a piece[7]of common dark blue cobalt glass, which has the property of obstructing the coloured rays corresponding to the middle of the spectrum, while transmitting the red andthe blue. Seen from a distance of only a few inches, the filament appears to be pale blue with a bright red border, the blue rays being perfectly focussed, while the red form diffusion circles. Move some six or eight feet away and look again; the colours will now be reversed, the filament appearing red and the border blue-violet. From a still greater distance—about fifteen or twenty feet—the whole lamp-bulb will seem to be filled with a blue-violet glow, due to large diffusion circles, while the red image of the filament may be even more clearly defined than before. No doubt it is partly owing to the non-achromatism of the eye that distant arc lights always appear to have a yellowish hue, even when the air is quite clear; a considerable proportion of their blue and violet componentsmust necessarily be lost by extensive diffusion.[8]
Again, look at a sunlit landscape or a printed wall poster through a combination of coloured glasses which will transmit only the violet end of the spectrum. You will find yourself for the time terribly short-sighted, everything appearing blurred and indistinct. But if you resort to the usual corrective for myopia, and put on a pair of concave spectacles, your normal vision will be restored; trees and houses will be seen as clearly as the feebleness of the light transmitted by the coloured glasses will permit, and the letters of the poster will become easily legible.
Now, of course, the interposition of coloured glasses does not actually give rise to these blurred images; it merely enables one to detect their existence. Under ordinary conditions they always accompany the clearer images produced by the more luminous rays, and their presence cannot fail to exert a detrimental effect upon the general definition. Such blurs must at least tend to fog the darker portions of the focussed picture, and though we are not distinctly conscious of their existence, it is certain that if they were annulled the acuteness of our vision would be improved.
The diffusion circles produced by the red rays, when the eye is accommodated (as it commonly is) for the yellow and green, are less conspicuous than those due to the most refrangible rays. YetI find it impossible to focus a red object, such as the filament of an electric lamp screened by a properly selected deep red glass, when placed at the ordinary distance of distinct vision—some nine or ten inches from the eye—without the aid of a convex lens. In this case one is not too short-sighted but too long-sighted to see the object distinctly; in other words, the lenses of the eye cannot refract the red rays sufficiently to produce well-defined images upon the retina, and the refraction has to be increased by artificial means.
Though, as I have said, it is difficult, or even impossible to detect any trace of a coloured border when looking at a bright object for which the eye is accommodated, it is quite easy to bring such borders into prominence if theobject is at a distance a little too great or too small for distinct vision. A very remarkable device for the purpose is one due to von Bezold. This may be illustrated by using a non-achromatic glass lens, such as a common magnifying glass, to project a transparency or lantern-slide upon which is painted a target-like design, consisting of a series of circular black bands surrounding a circular black spot.[9](SeeFig. 15.)
Fig. 15.—Bezold’s Diagram.
Suppose the glass lens to represent the lenses of a gigantic eye (in a definite condition of accommodation) and the screenthe retina. The imaginary eye is looking at the design on the lantern-slide, and when this is at the distance of most distinct vision a fairly well defined image of the target is formed upon the retinal screen.
Now gradually move the lantern slide towards the lens (or the lens towards the slide), thus bringing it too near for distinct vision. This has the effect of enlarging the diffusion circles formed by the less refrangible rays corresponding to the red end of the spectrum, and at the same time of diminishing those formed by the more refrangible rays corresponding to the violet end. The first result is that the circular dark bands become reddish brown, and the spaces between them bluish. As the distance between the lens and the slideis still further diminished, the tints become more varied and brilliant, until at last there appears a beautiful series of coloured rings around a bright red central spot.
These effects are not produced when the lens employed is an achromatic one; with such a lens the diffusion circles are all enlarged or diminished together, and a to-and-fro movement of the lantern slide (or of the lens) merely affects the definition of the image without causing any perceptible dispersion of colour.
Now it is noteworthy that the chromatic phenomena exhibited with the uncorrected glass lens are quite well shown by the lenses of the eye. It is only necessary to hold the lantern-slide before a bright background and gradually bring it so close to the eye that thedesign cannot be seen distinctly. The black bands will then appear to turn brown, the white ones blue, and the central spot bright red. The printed diagram (Fig. 15) will itself show the colours if it is held at a distance of four to five inches from one eye in a good light.
One more experiment may be referred to. Look with one eye at a well-lighted page of print, and with a strip of brown paper, held quite near the eye, cover about half the pupil. The black letters will now appear to be bordered with colour—blue towards the apparent edge of the brown paper, orange on the opposite side. If the letters are white on a black ground, as sometimes happens in the case of advertisements, the colours will be interchanged. The cause of thecoloured borders will be readily understood from an inspection of the diagramFig. 12; but it must be remembered that the images on the retina are inverted.
Thus it is proved beyond all question that the lenses of the eye do not form an achromatic combination.
Another peculiarity by which the eye is affected, and which does not occur in optical instruments, is that known asastigmatism. The surface of the cornea, which, with the aqueous humour, forms the outer lens, is not often perfectly spherical; generally it is shaped something like the bowl of a spoon, the curvature being greater vertically than horizontally. Rays issuing from a luminous point do not, after refraction by such a lens, cross at a single focus, butalong two short straight lines, the one horizontal the other vertical, which are at different distances from the lens; thus a distinct image of a small point cannot anywhere be produced.
Fig. 16.—Effect of Astigmatism.
A very curious result follows from this deformity. If two straight lines are drawn at right angles to each other, as inFig. 16, it is impossible to see both of them quite clearly at the same time. When the paper is held at a certain short distance from the eye—about eightor nine inches—the horizontal line appears black and well defined, while the other is rather grey and indistinct; at a greater distance the upright line seems to be the blacker. The effect is very well shown by the diagram,Fig. 17. To most persons the lines occupying the middle portion will appear either much blacker or much lighter than those at the two ends, though in fact they are exactly alike. When this form of astigmatism is excessive, it may be corrected by the use of spectacles fitted with cylindrical lenses.
Fig. 17.—Effect of Astigmatism.
But there is a different kind ofastigmatism—irregular astigmatism it is called—to which every one is more or less a victim, and which cannot be relieved by any artificial appliances. Fortunately it does not often cause much practical inconvenience.
Irregular astigmatism is commonly demonstrated in the following manner. With the point of a fine needle, prick a very small hole in a sheet of tinfoil. Hold up the tinfoil to the light and look at the hole with one eye, the other being closed. Even at the distance of most distinct vision—ten inches or thereabouts,—there will probably be a ragged appearance about the hole, as if it were not perfectly round. But if you bring the tinfoil an inch or two nearer to the eye, the hole will not seem to be even approximately circular; it will assumethe form of a little star with five or more distinct rays. The configuration of the star is not generally the same for the right eye as for the left; the rays may differ in number and in relative magnitude, and may be inclined at different angles to the vertical.Fig. 18shows the stars as they appear to my two eyes, when the illumination is rather strong.
Fig. 18.—Star-like Images of luminous Point.
If several holes are pricked in the tinfoil, each will of course originate a separate star, and all the stars as seen by the same eye will appear to be figured upon the same model, thoughsome may be larger or brighter than others.
Fig. 19.—Sutures of crystalline Lens.
There can be no doubt that the stellate form observed in these experiments, as well as that of the stars of heaven themselves (which with perfect vision would be seen simply as luminous points), is a consequence of the singular structure of the crystalline lens of the eye. This does not consist of one uniform homogeneous mass like a glass lens, but of a number of separate portions pieced together radially, as indicateddiagrammatically inFig. 19. In the eye of a newly-born child there are three such portions, and the radial junctions on one side of the lens are not opposite to those on the other, but are intermediate. In the figure the junctions at the front of the lens are represented by continuous lines and those at the back by dots. The number of sutures found in the adult lens is generally greater than six.
But while it is certain that these radial sutures are in some way closely connected with the luminous rays which appear to proceed from a bright point, it must be confessed that no adequate explanation has yet been given of the precise manner in which the phenomenon is brought about. Ophthalmologists seem to have been contented with vague statements about irregular refraction,but what kind of irregularity would sufficiently account for all the facts of observation has never, so far as I know, been exactly determined. The problem can hardly be very difficult of solution, and would, no doubt, readily yield to the joint efforts of a physicist and a physiologist.
The phenomena of irregular astigmatism as exhibited by a normal eye are exceedingly curious, and perhaps I may be allowed to refer briefly to one or two experiments which I have myself made on the subject.[10]
Fig. 20.—Multiple Images of a luminous Point.
Light from an enclosed electric lamp of twenty-five candle power was admitted through a circular aperture about1⁄12inch (2mm.) in diameter perforated in a brass plate; a sheet of ground glass and another of ruby-red glass were placed behind the aperture. When the little disk of monochromatic light thus formed was looked at through a concave lens of eleven inches focal length from a suitable distance—nearly two feet in my own case—it appeared as seven bright round spots upon a less luminous ground. The appearance is represented in a somewhat idealised form inFig. 20; but the spots were not quite sodistinct nor so regularly disposed as there shown, neither was their configuration exactly the same for the right eye as for the left.
On gradually increasing the distance each circumferential spot became at first elongated radially and afterwards split up into two circular ones; at the same time new spots were developed upon the luminous ground, the approximate symmetry of the figure being still retained.Fig. 21represents a certain stage in this process of expansion. The appearance was happily likened by an observer who repeated the experiment to that of a large unripe blackberry.
As the distance was still further increased, the spots continued to multiply, ultimately becoming very numerous; their arrangement however soon becamemuch less regular, and the definition of most of them less distinct. At about twenty feet there was seen a luminous patch, roughly circular in outline, and covered with irregular speckles; superposed upon this were strings of bright, partially overlapping spots, corresponding apparently to the sutures of the crystalline lens.
Fig. 21.—Increased number of Images.
When the hole was looked at from a moderate distance through a narrow slit(about1⁄30inch wide) interposed between the eye and the lens, there was seen only a single row of circular spots, which were arranged sinuously, as shown inFig. 22. A slight movement of the slit in the direction perpendicular to its length produced a wave-like motion of the circles, suggestive, as pointed out by the excellent observer before referred to of the wriggling of a caterpillar.
Fig. 22.—Multiple Images seen through a Slit.
By sufficiently increasing the distancebetween the source of light and the eye, as many as twenty-four or twenty-five bright spots might be made to appear in the row, but they could not be counted with any great certainty. At a still longer distance or with a lens of shorter focus (convex or concave) they became less distinct, and finally seemed to be resolved into a multitude of small blurred images—probably several hundreds—which were separated from one another by hazy dark lines.
Fig. 23.—Images of an electric lamp Filament.
I thought that the observations might be rendered easier if the source of light had a more distinctive and conspicuous form than that of a simple circle. Some experiments were therefore made with semi-circular and triangular holes, and these were in some respects preferable; but far better results were afterwardsobtained by using as a source of light the horse-shoe shaped filament of an electric lamp, screened by a coloured glass. When such a lamp was looked at through a lens, concave or convex, of about six inches focus, from a distance of a few feet, the roughly oval patch of luminosity formed upon the retina, instead of being a mere ill-defined blur, such as would be produced if the transparent media of the eye were composed of homogeneous substances like glass or water, appeared to be made up of a crowd of separate images of the filament, some being brighter than others, as is shown in the diagramFig. 23.
Fig. 24A.—Images with horizontal Slit.
Fig. 24B.—Images with vertical Slit.
If a spectroscope slit was interposed between the eye and the lens, and its width suitably adjusted, only a single row of filaments was observed, the appearances with the slit in horizontal, vertical, and intermediate positions being as represented inFig. 24, A,B,C. As before, it was found possible by gradually retiring from the lamp to bring the number of images up to about twenty-five, but attentive examinationshowed that most of these really consisted of clusters, each composed of perhaps fifteen or twenty confused images of the filament. A stronger lens still further separated the constituents of the clusters, exhibiting a total number of indistinctly seen images which was estimated to amount to nearly five hundred. Assuming the diameter ofthe pupil of the eye to be one-fifth of an inch, these observations seem to indicate as a cause of the phenomenon some fairly regular anatomical structure, situated in or near the crystalline lens and composed of elements measuring about1⁄2000inch in length or breadth. Whether the structure which gives rise to these multiple images is to be found in the fibres of the crystalline lens itself, or in the membranes which cover it, is a question upon which I will not venture an opinion.
Fig. 24C.—Images with oblique Slit.
It is indeed wonderful that an organ affected by peculiarities of which those that have been referred to are merely specimens, should give such well-defined pictures as it does when accommodated for the objects looked at.
SOME OPTICAL ILLUSIONS.
Optical illusions generally result from the mind’s faulty interpretation of phenomena presented to it through the medium of the visual organs. They are of many different kinds, but a large class, which at first sight may seem to have little or nothing in common, arise, I believe, from a single cause, namely, the inability of the mind to form and adhere to a definite scale or standard of measurement.
In specifying quantities and qualities by physical methods, the standards of reference that we employ are invariable.We may, for example, measure a length by reference to a rule, an interval of time by a clock, a mass or weight by comparison with standardised lumps of metal, and in all such cases—provided that our instruments are good ones and skilfully used—we have every confidence in the constancy and uniformity of our results.
But two lengths, which when tested with the same foot rule are found to be exactly equal, are not necessarily equal in the estimate formed of them by the mind. Look, for instance, at the two lines inFig. 25. According to the foot rule each of them is just one inch in length, but the mind unhesitatingly pronounces the upright one to be considerably longer than the other; the standard which it applies is not, like aphysical one, identical in the two cases. Many other examples might be cited illustrative of the general uncertainty of mental estimates.
Fig. 25.—Illusion of Length.
The variation of the vague mental standard which we unconsciously employ seems to be governed by a law of very wide if not universal application. Though this law is in itself simple and intelligible enough, it cannot easily be formulated in terms of adequate generality. The best result of my efforts is the following unwieldy statement:—The mental standard which is applied in theestimation of a quality or a condition tends to assimilate itself, as regards the quality or condition in question, to the object or other entity under comparison of which the same (quality or condition) is an attribute.
In plainer but less precise language, there is a disposition to minimise extremes of whatever kind; to underestimate any deviation from a mean or average state of things, and consequently to vary our conception of the mean or standard condition in such a manner that the deviation from it which is presented to our notice in any particular instance may seem to be small rather than large.
Thus, when we look at a thing which impresses us as being long or tall, the mental standard of length is at onceincreased. It is as if, in making a physical measurement, our foot rule were automatically to add some inches to its length, while still supposed to represent a standard foot: clearly anything measured by means of the augmented rule would seem to contain a fewer number of feet, and, therefore, to be shorter than if the rule had not undergone a change.
It is not an uncommon thing for people visiting Switzerland for the first time to express disappointment at the apparently small height of the mountains. A mountain of 10,000 feet certainly does not seem to be twenty times as lofty as a hill of 500. The fact is that a different scale of measurement is applied in the two cases; though the observer is unaware of it, the mountainis estimated in terms of a larger unit than the hill.
Fig. 26.—Illusion of Length.
If we mentally compare two adjacent things of unequal length, such as the two straight lines inFig. 26, there is a tendency to regard the shorter one as longer than it would appear if seen alone, and the longer one as shorter. The lower of the two lines in the figure is just twice as long as the other, but it does not look so; each is regarded as differing less than it really does from an imaginary line of intermediate length.
Fig. 27.—Illusion of Length.
Two divergently oblique lines attached to the ends of a straight line as at A,Fig. 27, suggest to the mind the idea of lengths greater than that of the straight line itself; the latter, being thought of as comparatively small, is therefore estimated in terms of a smaller unit than would be employed if the attachments were absent, and consequently appears longer. If, on the other hand, the attachments are made convergent, as at B, shorter lengths are suggested; the length of the given line is regarded as exceeding an average or mean; the standardapplied in estimating it is accordingly increased, and the line is made to seem unduly short. In spite of appearances to the contrary, the two lines A and B are actually of the same length.
By duplicating the attached lines, as shown inFig. 28, their misleading effect becomes intensified. Here we have a well-known illusion of which several explanations have been proposed. The fallacy is, I think, sufficiently accounted for by variation of the mental standard, in accordance with the law to which I have called attention.
Fig. 28.—Illusion of Length.
A number of other paradoxical effects may be referred to the operation of the same law.Fig. 29shows a curious specimen. At each end of the diagram is a short upright line; exactly in the middle is another; between the middle and the left hand end are inserted several more lines, the space to the right of the middle being left blank. Any one looking casually at the diagram would be inclined to suppose that it was not equally divided by what purports to be the middle line, the left hand portion appearing sensibly longer than the other.
Fig. 29.—Illusion of Distance.
It is not difficult to indicate thesource of the illusion. When we look at the left hand portion we attend to the small subdivisions, and the mental unit becomes correspondingly small; while in the estimation of the portion which is not subdivided a larger unit is applied.
As one more example I may refer to a familiar trap for the unwary. Ask a person to mark upon the wall of a room the height above the floor which he thinks will correspond to that of a gentleman’s tall hat. Unless he has been beguiled on a former occasion, he will certainly place the mark several inches too high. Obviously the height of a hat is unconsciously estimated in terms of a smaller standard than that of a room.
The illusion presented by thehorizontal and vertical lines inFig. 25(p. 132) depends, though a little less directly, upon a similar cause. We habitually apply a larger standard in the estimation of horizontal than of vertical distances, because the horizontal magnitudes to which we are accustomed are upon the whole very much greater than the vertical ones. The heights of houses, towers, spires, trees, or even mountains are insignificant in comparison with the horizontal extension of the earth’s surface, and of many things upon it, to which our notice is constantly directed. For this reason, we have come to associate horizontality with greater extension and verticality with less, and, in conformity with our law, a given distance appears longer when reckoned vertically than when reckonedhorizontally. Hence the illusion inFig. 25.
But it is not only in regard to lengths and distances that the law in question holds good; in most, if not all cases in which a psycho-optical estimate is possible, the mental standard is unstable and tends to assimilate itself, as regards the quality or condition to be estimated, to the entity in which the same is manifested. This is true, for example, in judging of an angle of inclination or slope; of a motion in space; of luminous intensity, or of the purity of a colour.
Every cyclist knows how difficult it is to form a correct judgment of the steepness of a hill by merely looking at it. Not only may a slope seem to be greater or less than it really is, but under certain circumstances a dead levelsometimes appears as an upward or downward inclination, while a gentle ascent may even be mistaken for a descent, andvice versa.
We usually specify a slope by its inclination to a level plane which is parallel to the plane of the horizon, or at right angles to the direction of gravity. At any given spot the level is, physically considered, definite and unalterable. In forming a mental judgment of an inclination, we employ as our standard of reference an imaginary plane which is intended to be identical with the physical level. But our mental plane is not absolutely stable; when we refer a slope to it, we unconsciously give the mental plane a slight tilt, tending to make it parallel with the slope. Hence the inclination of a simple slope, whenmisleading complications are absent, is always underestimated.
Fig. 30.—Illusion of Inclination.
This may be illustrated by the diagramFig. 30. If A B represents a truly horizontal line, the slope of the oblique line C D is correctly specified by the angle C O A. But if we have no instrument at hand to fix the level for us, we shall infallibly imagine it to be in some such position as that indicated (in an exaggerated degree) by the dotted lineE F, while the true level A B will appear to slope oppositely to C D.
This class of illusion is remarkably well demonstrated by Zöllner’s lines,Fig. 31; the two thick lines which appear to diverge from left to right, are in truth strictly parallel.
Fig. 31.—Zöllner’s Lines.
I need not discuss in further detail the various illusions to which a cyclist is subjected when slopes of different inclinations succeed one another: they all follow simply from the same general principle.
A thing is said to be in motion when it is changing its position relatively tothe earth, which for all practical purposes may be regarded as motionless. The state, as regards motion, of the earth and anything rigidly attached to it, therefore constitutes the physical zero or standard to which the motion of everything terrestrial is referred. But the corresponding mental standard, especially when it cannot easily be checked by comparison with some stationary object, is liable to deviate from the physical one; it tends in fact to move in the same direction as the moving body which is under observation, and the apparent speed of the body is consequently rather less than it should be.
The influence exerted upon the judgment sometimes even persists for an appreciable period after the exciting cause has ceased to be operative, as whenthe moving body is lost sight of or has suddenly come to rest; in such cases fixed objects, being compared with the delusive mental standard, appear for a few seconds to be moving in the opposite direction.
I have devised a lantern slide (Fig. 32) by the aid of which this phenomenon may be rendered very evident. In a square plate of metal is cut a vertical slot, which is shaded in the figure; behind the plate is an opaque disk, which, by means of suitable mechanism, can be made to rotate about its centre. The disk has a spiral opening cut in it of the same width as the slot, as indicated by the dotted line. The slide is placed in an optical lantern, and the light passing through the aperture formed where the slot is crossed by the spiral opening, produces a small brightpatch upon a white screen hung at a suitable distance from the lantern.
Fig. 32.—Slide for showing Illusions of Motion.
When the disk is turned in the direction indicated by the arrow, the bright patch moves upwards andultimately disappears; but at the moment of its disappearance a fresh patch starts from below, which also moves in the upward direction; thus there is formed upon the screen a continuous succession of ascending bright patches. After these have been observed for about a quarter of a minute, the disk is suddenly stopped, and the persistence of the fallacious mental standard is at once demonstrated. For the bright patch does not appear to be at rest, as it actually is, but to creep steadily downwards, continuing to do so more and more slowly for perhaps as long as ten seconds. The upward motion of the bright patches had led the observer to assume a slower upward motion as the zero, or standard of no motion, and reference of the really stationary patch to this physically falsestandard induces the illusion that the patch is descending.
This experiment is most successful when the bright patches are projected upon the middle of a large screen. The disk should turn about three times in a second, and the room should be feebly illuminated, but not quite dark.
Fig. 33.—Illusions of Motion.
A very remarkable illusion which no doubt depends upon the same principle as the last, though its form is entirely different, is that to which the diagramFig. 33relates. So far as I am aware, it has not before been noticed.
Two intersecting straight lines, the one upright and the other sloping, as shown in the figure, are drawn upon a card. The card is to be held vertically before the eyes at the distance of most distinct vision, and waved up and down through a distance of a few inches. The oblique line will then appear to oscillate transversely, as if it were not rigidly attached to the card.
This is the result of underestimating the speed at which the card is moved. Rather than recognise the true state of things, the mind prefers to accept the suggestion that the upward or downward movement of the point of intersection is in part due to oppositely directed horizontal movements of the lines themselves upon the surface of the card. When the card is descending the verticalline is supposed to slide a little to the right and the oblique line to the left, which would have the effect of lowering their point of intersection independently of the downward movement of the card itself. When the card ascends, these horizontal movements are supposed to be reversed, and the point of intersection consequently raised. The assumption is exactly analogous to that made when an angle of slope is unwittingly minimised.
Another example of the instability of a mental standard occurs in the estimation of luminosity. The luminosity of a bright object, if reckoned in terms of the same unit as that applied in judging of a less bright one, would appear to be greater than it actually does appear, and this quite independently of any effects of fatigue.
Fig. 34.—Illusion of Luminosity.
The fact is well illustrated by a familiar experiment.Fig. 34is photographed from a transparency made by superposing several different lengths of gelatine film so as to form a series of steps. At the right-hand end of the image the light has passed through only one layer of the film; in the next division it has traversed two layers, in the next, three, and in the last, four. The luminosity of each of the foursquares into which the oblong is divided is, in a physical sense, quite uniform, but the mental standard of luminosity varies for different parts of the image, increasing or decreasing, as the case may be, notper saltum, but smoothly and continuously, with the result that each square looks brighter towards the left than towards the right. The appearance, which is often likened to that presented by a fragment of a fluted column, is equally well shown when the diagram is illuminated instantaneously by an electric spark, and cannot, therefore, be accounted for by retinal fatigue.
If the squares are separated from one another by distinct lines of demarcation, however fine, the standard of luminosity becomes uniform for each square, andthe illusion vanishes. This fact sufficiently disposes of the hypothesis which has been advanced to the effect that the phenomenon is due to physiological causes.
I now propose to discuss a curious consequence of the fluctuation of unaided judgment as regards the purity of a colour.
When any colour occupies a predominant place in the field of vision, we are apt to consider it as being less pure, or paler, than we should if it were less conspicuous, our standard of whiteness tending to approximate itself to the colour in question.
For the sake of clearness let us first confine our attention to a definite colour—say red. An absolutely pure red is one that is entirely free from anyadmixture of white; in proportion as it contains more and more white, the more impure, or in other words, the more pale does it become, until at last all trace of perceptible redness is lost and the colour is indistinguishable from white.