N FIG. 7. - Spherical Aberration.
FIG. 9. - Diagram illustrating the Dispersion of Light by a Lens.
b If the light ente a the cornea, as in the figure to the right, and if the B A.
movement b if does not eytheond ex the ,© middle of the - cornea, but in the FIG. to. - Purkinje's Figures. opposite direction the eye to the right the illumination is to the light through the sclerotic, and in the one to the when the latter left through the cornea. is moved up and down. Thus, if a be moved to a', d will be moved to d', the shadow on the retina from c to c', and the image b to b'. If, on the other hand, a be moved above the plane of the paper, d will move below, consequently c will move above, and b' will appear to sink. (2) The retinal vessels may also be seen by looking at a strong light through a minute aperture, in front of which a rapid to-and-fro movement is made. Such experiments prove that the sensitive part of the retina is its deepest and most external layer (Jacob's membrane).
4. Accommodation, or the Mechanism of Adjustment for Di f ferent Distances. - When a camera is placed in front of an object, it is necessary to focus accurately in order to obtain a clear and distinct image on the sensitive plate. This may be done by moving either the lens or the sensitive plate backwards or forwards so as to have the posterior focal point of the lens corresponding with the sensitive plate. For similar reasons, a mechanism of adjustment, or accommodation for different distances, is necessary in the human eye. In the normal eye, any number of parallel rays, coming from a great distance, are focused on the retina. Such an eye is termed emmetropic (fig. 11, A). Another form of eye (B) may be such that parallel rays are brought to a focus in front of the retina. This form of eye is myopic or shortsighted, inasmuch as, for distinct vision, the object must be brought near the eye, so as to catch the divergent rays, which are then focused on the retina. A third form is seen in C, where the focal point, for ordinary distances, is behind the retina, and consequently the object must be held far off, so as to allow only the less divergent or parallel rays to reach the eye. This kind of eye is called hypermetro pic, or far-sighted. For ordinary distances, at which objects must be seen distinctly in everyday life, the fault of the myopic eye maybe corrected by the use of concave and of the hypermetropic by convex glasses. In the first case, the concave glass will move the posterior focal point a little farther back, and in the second the convex glass will bring it farther forwards; in both cases, however, the glasses may be so adjusted, both as regards refractive index and radius of curvature, as to bring the rays to a focus on the retina, and consequently secure distinct vision.
From any point 65 metres distant, rays may be regarded as almost parallel, and the point will be seen without any effort of accommodation. This point, either at this distance or in infinity, is called the punctum remotum, or the most distant point seen without accommodation. In the myopic eye it is much nearer, and for the hypermetropic there is really no such point, and accommodation is always necessary. If an object were brought too close to the eye for the refractive media to focus it on the retina, circles of diffusion would be formed, with the result of causing indistinctness of vision, unless the eye possessed some power of adapting itself to different distances. That the eye has some such power of accommodation is proved by the fact that, if we attempt to look through the meshes of a net at a distant object, we cannot see both the meshes and the object with equal distinctness at the same time. Again, if we look continuously at very near objects, the eye speedily becomes fatigued. Beyond a distance of 65 metres, no accommodation is necessary; but within it, the condition of the eye must be adapted to the diminished distance until we reach a point near the eye which may be regarded as the limit of visibility for near objects. This point, called the punctum proximum, is usually 12 centimetres (or 4.8 inches) from the eye. The range of accommodation is thus from the punctum remotum to the punctum proximum.
The mechanism of accommodation has been much disputed, but there can be no doubt it is chiefly effected by a change in the curvature of the anterior surface of the crystalline lens. If we hold a lighted candle in front and a little to the side of an eye to be examined, three reflections may be seen in the eye, as represented in fig. 12. The first, a, is erect, large and bright, from the anterior surface of the cornea; the second, b, also erect, but dim, from the anterior surface of the crystalline lens; and a 4 the third, c, inverted, and very dim, from the posterior surface of the lens, or perhaps the concave surface of the vitreous humour to which the convex surface of the lens is adapted. Suppose the three images to be in the position shown in the figure for FIG. 12. - Reflected distant vision, it will be found that the middle Images in the Eye. image b moves towards a, on looking at a near object. The change is due to an alteration of the curvature of the lens, as shown in fig. 13. The changes occurring during accommodation are: FIG. 13. - Mechanism of Accommodation.
A, The lens during accommodation, showing its anterior surface advanced; B, The lens as for distant vision; C, Position of the ciliary muscle.
(I) the curvature of the anterior surface of the crystalline lens increases, and may pass from Io to 6 mm.; (2) the pupil contracts; and (3) the intraocular pressure increases in the posterior part of the eye. An explanation of the increased curvature of the anterior surface of the lens during accommodation has been thus given by H. von Helmholtz. In the normal condition, that is, for the emmetropic eye, the crystalline lens is flattened anteriorly by the pressure of the anterior layer of the capsule; during accommodation, the radiating fibres of the ciliary muscles pull the ciliary processes forward, thus relieving the tension of the anterior layer of the capsule, and the lens at once bulges forward by its elasticity.
By this mechanism the radius of curvature of the anterior A A A, Emmetropic or normal eye; B, Myopic or short-sighted eye; C, Hypermetropic or long-sighted eye.
surface of the lens, as the eye accommodates from the far to the near point, may shorten from 10 mm. to 6 mm. The ciliary muscle, however, contains two sets of fibres, the longitudinal or meridional, which run from before backwards, and the circular or equatorial (Miller's muscle), which run, as their name indicates, around the band of longitudinal fibres forming the muscle. Direct observation on the eye of an animal immediately after death shows that stimulation of the ciliary nerves actually causes a forward movement of the ciliary processes, and there can be little doubt that the explanation above given applies to man, probably most mammals, and to birds and most reptiles. In birds, which are remarkable for acuteness of vision, the mechanism is somewhat peculiar. In them the fibres of the ciliary muscle have a strong attachment posteriorly, and when these contract they pull back the inner posterior layers of the cornea, and thus relax that part of the ciliary zone called the ligamentum pectinatum. In a state of rest this structure in the bird's eye is tense, but in accommodation it becomes relaxed. Thus by a somewhat different mechanism in the bird, accommodation consists in allowing the anterior surface of the lens to become more and more convex. In reptiles generally the mechanism resembles that of the bird; but it is said that in snakes and amphibia there is a movement forwards of the lens as a whole, so as to catch rays at a less divergent angle. When the eye is directed to a distant object, such as a star, the mechanism of accommodation is at rest in mammals, birds, reptiles and amphibia, but in fishes and cephalopods the eye at rest is normally adjusted for near vision. Consequently accommodation in the latter is brought about by a mechanism that carries the lens as a whole backwards. There is still some difficulty in explaining the action of the equatorial (circular) fibres. Some have found that the increased convexity of the anterior surface of the lens takes place only in the central portions of the lens, and that the circumferential part of the lens is actually flattened, presumably by the contraction of the equatorial fibres. Seeing, however, that the central part of the lens is the portion used in vision, as the pupil contracts during accommodation, a flattening of the margins of the lens can have no optical effect. Further, another explanation can be offered of the flattening. As just stated, during accommodation the pupil contracts, and the pupillary edge of the iris, thinned out, spreads over the anterior surface of the capsule of the lens, which it actually touches, and this part of the iris, along with the more convex central part of the lens, bulges into the anterior chamber, and must thus displace some of the aqueous humour. To make room for this, however, the circumferential part of the iris, related to the ligamentum pectinatum, moves backwards very slightly, while the flattening of the circumferential part of the lens facilitates this movement.
Helmholtz succeeded in measuring with accuracy the sizes of these reflected images by means of an instrument termed an ophthalmometer, the construction of which is based on the following optical principles: When a luminous ray traverses a plate of glass having parallel sides, if it fall perpendicular to the plane of the plate, it will pass through without deviation; but if it fall obliquely on the plate (as shown in the left-hand diagram in fig. 14) it undergoes a lateral deviation, but in a direction parallel to that of the incident ray, so that to an eye placed behind the glass plate, at the lower A, the luminous point, upper A, would be in the direction of the prolonged emergent ray, and thus there would be an apparent lateral displacement of the point, the amount of which would increase with the obliquity of the incident ray. If, instead of one plate, we take two plates of equal thickness, one placed above the other, two images will be seen, and by turning the one plate with reference to the other, each image may be displaced a little to one side. The instrument consists of a small telescope (fig. 14) T, the axis of which coincides with the plane separating the two glass plates C C and B B. When we look at an object X Y, and turn the plates till we see two objects touching each other, the size of the image X Y will be equal to the distance the one object is displaced to the one side and the other object to the other side. Having thus measured the size of the reflection, it is not difficult, if we know the size of the object reflecting the light and its distance from the eye, to calculate the radius of the curved surface (Appendix to M`Kendricks's Outlines of Physiology, 1878). The general result is that, in accommodation for near objects, the middle reflected image becomes smaller, and the radius of curvature of the anterior surface of the lens becomes shorter.
(b) By Method of Reflection
Place a red wafer on b, in fig. 9 and a blue wafer on d, and so angle a small glass plate a as to transmit to the eye a reflection of the blue wafer on d in the same line as the rays transmitted from the red wafer on b. The sensation will be that of purple; and by using wafers of different colours, many experiments may thus be performed.
(c) By Rotating Disks which quickly superpose on the same Area of Retina the Impres- sions of Dif f erent Wave-lengths. 'b' - Such disks may be constructed of cardboard, on which coloured sectors are painted, as shown in fig. 20, representing diagrammatically the arrangement of Sir Isaac Newton. The angles of the sectors were thus given by him: - With sectors of such a size, white will be produced on rotating the disk rapidly. This method has been carried cut with great efficiency by the colour-top of J. Clerk-Maxwell. It is a flat top, on the surface of which disks of various colours may be placed. Dancer has added to it a method by which, even while the top is rotating rapidly and the sensation of a mixed colour is strongly perceived, the eye may be able to see the simple colours of which it is composed. This is done by placing on the handle of the top, a short distance above the coloured surface, a thin black FIG. 20. - Diagram of the Colour d i sk, perforated by holes of Disk of Sir Isaac Newton.
various size and pattern, and weighted a little on one side. This disk vibrates to and fro rapidly, and breaks the continuity of the colour impression; and thus the constituent colours are readily seen.
3. The Geometric Representation of Colours. - Colours may be arranged in a linear series, as in the solar spectrum. Each point of the line corresponds to a determinate impression of colour; the line is not a straight line, as regards luminous effect, but is better represented by a curve, passing from the red to the violet. This curve might be represented as a circle in the circumference of which the various colours might be placed, in which case the complementary colours would be at the extremities of the same diameter. Sir Isaac Newton arranged the colours in the form of a triangle, as shown in fig. 21. If we place three of the spectral colours at three angles, thus - green, violet and red - the sides of the triangle include the intermediate colours of the spectrum, except purple.
The point S corresponds to white, consequently, from the intersection of the lines which join the complementary colours, the straight lines from green to S, RS and VS represent the amount of green, red and violet necessary to form white; the same holds good for the complementary colours; for example, for blue and red, the line SB=the amount of blue, and the line SR=the amount of red required to form white.
Again, any point, say M; on the surface of the triangle, will represent a mixed colour, the composition of which may be obtained by mixing the,three fundamental colours in the proportions represented by the length of the lines M to green, MV and MR. But the line VM passes on to the yellow Y; we may then FIG. 2 i. - Geometrical Representation replace the red and green of the Relations of Colours as shown by the yellow, in the proby Newton.
portion of the length of the line MY, and mix it with violet in the proportion of SV. The same colour would also be formed by mixing the amount MY of yellow with MS of white, or by the amount RM of red with the amount MD of greenish blue.
The following list shows characteristic complementary colours, with their wave-lengths (X) in millionths of a millimetre: Red, X 656. Blue-green, X 492.
Orange, A 608. Blue, A 490.
Gold-yellow, X 574. Blue, A 482.
Yellow, X 567. Indigo-blue, A 464.
Greenish yellow, A 564. Violet, A 433 By combining colours at opposite ends of the spectrum, the effect of the intermediate colours may be produced; but the lowest and the highest, red and violet, cannot thus be formed. These are therefore fundamental or primary colours, colours that cannot be produced by the fusion of other colours. If now to red and violet we add green, which has a rate of vibration about midway between red and violet, we obtain a sensation of white. Red, green and violet are therefore the three fundamental colours.
4. Physiological Characters of Colours. - Colour physiologically is a sensation, and it therefore does not depend only on the physical stimulus of light, but also on the part of the retina affected. The power of distinguishing colours is greatest when they fall on, or immediately around, the yellow spot, where the number of cones is greatest. In these regions more than two hundred different tints of colour may be distinguished. Outside of this area lies a middle zone, where fewer tints are perceived, mostly confined to shades of yellow and blue. If intense coloured stimuli are employed, colours may be perceived even to the margin of the periphery of the retina, but with weak stimuli coloured objects may seem to be black, or dark like shadows. In passing a colour from the periphery to the centre of the yellow spot, remarkable changes in hue may be observed. Orange is first grey, then yellow, and it only appears as orange when it enters the zone sensitive to red. Purple and bluish green are blue at the periphery, and only show the true tint in the central region. Four tints have been found which do not thus change: a red obtained by adding to the red of the spectrum a little blue (a purple), a yellow of 574.5 A, a green of 495 A and a blue of 471 A.
The question now arises, How can we perceive differences in colour ? We might suppose a molecular vibration to be set up in the nerve-endings synchronous with the undulations of the luminiferous aether, without any change in the chemical constitution of the sensory surface, and we might suppose that where various series of waves in the aether corresponding to different colours act together, these may be fused together, or to interfere so as to give rise to a vibration of modified form or rate that corresponded in some way to the sensation. Or, to adopt another line of thought, we might suppose that the effect of different rays (rays differing in frequency of vibration and in physiological effect) is to promote or retard chemical changes in the sensory surface, " which again so affect the sensory nerves as to give rise to differing states in the nerves and the nerve centres, with differing concomitant sensations." The former of these thoughts is the foundation of the Young-Helmholtz theory, while the latter is applicable to the theory of E. Hering.
e f FIG. 18. - Diagram of Double Spectrum partially superposed.
d FIG. 19. - Diagram showing Lambert's Method of mixing Sensations of Colour.
Green 5. Theories of Colour-Perception. - A theory widely accepted by physicists was first proposed by Thomas Young and BOY G B Y afterwards revived by FIG. 22. - Diagram showing the Irritability of the Three Kinds of Retinal Elements.
r, red; 2, green; 3, violet. R, O, Y, G, B, V, initial letters of colours.
sets of fibres. Helmholtz thus applies the theory: " r. Red excites strongly the fibres sensitive to red and feebly the other two - sensation: Red. 2. Yellow excites moderately the fibres sensitive to red and green, feebly the violet - sensation: Yellow. 3. Green excites strongly the green, feebly the other two - sensation: Green. 4. Blue excites moderately the fibres sensitive to green and violet, and feebly the red - sensation: Blue. 5. Violet excites strongly the fibres sensitive to violet, and feebly the other two - sensation: Violet. 6. When the excitation is nearly equal for the three kinds of fibres, then the sensation is White." The Young-Helmholtz theory explains the appearance of the consecutive coloured images. Suppose, for example, that we look at a red object for a considerable time; the retinal elements sensitive to red become fatigued. Then (I) if the eye be kept in darkness, the fibres affected by red being fatigued do not act so as to give a sensation of red; those of green and of violet have been less excited, and this excitation is sufficient to give the sensation of pale greenish blue; (2) if the eye be fixed on a white surface, the red fibres, being fatigued, are not excited by the red rays contained in the white light; on the contrary, the green and violet fibres are strongly excited, and the consequence is that we have an intense complementary image; (3) if we look at a bluish green surface, the complementary of red, the effect will be to excite still more strongly the green and violet fibres, and consequently to have a still more intense complementary image; (4) if we regard a red surface, the primitive colour, the red fibres are little affected in consequence of being fatigued, the green and violet fibres will be only feebly excited, and therefore only a very feeble complementary image will be seen; and (5) if we look at a surface of a different colour altogether, this colour may combine with that of the consecutive image, and produce a mixed colour; thus, on a yellow surface, we will see an image of an orange colour.
Every colour has three qualities: (i) hue, or tint, such as red, green, violet; (2) degree of saturation, or purity, according to the amount of white mixed with the tint, as when we recognize a red or green as pale or deep; and (3) intensity, or luminosity, or brightness as when we designate the tint of a red rose as dark or bright. Two colours are identical when they agree as to these three qualities. Observation shows, however, that out of one hundred men ninety-six agree in identifying or in discriminating colours, while the remaining four show defective appreciation. These latter are called colour-blind. This defect is about ten times less frequent in women. Colour-blindness is congenital and incurable, and it is due to an unknown condition of the retina or nerve centres, or both, and must be distinguished from transient colour-blindness, sometimes caused by the excessive use of tobacco and by disease. When caused by tobacco, the sensation of blue is the last to disappear. Absolute inability to distinguish colour is rare, if it really exists; in some rare cases there is only one colour sensation; and in a few cases the colour-blind fails to distinguish blue from green, or there is insensibility to violet. Daltonism, or red-green blindness, of which there are two varieties, the red-blind and the green-blind, is the more common defect. Red appears to a redblind person as a dark green or greenish yellow, yellow and orange as dirty green, and green is green and brighter than the green of the yellow and orange. To a green-blind person red appears as dark yellow, yellow is yellow, except a little lighter in shade than the red he calls dark yellow, and green is pale yellow.
According to the Young-Helmholtz theory, there are three fundamental colour sensations, red, green and violet, by the combination of which all other colours may be formed, and it is assumed that there exist in the retina three kinds of nerve elements, each of which is specially responsive to the stimulus of waves of a certain frequency corresponding to one colour, and much less so to waves of other frequencies and other colours. If waves corresponding to pure red alone act on the retina, only the corresponding nerve element for red would be excited, and so with green and violet. But if waves of different frequencies are mixed (corresponding to a mixture of colours), then the nerve elements will be set in action in proportion to the amount and intensity of the constituent excitant rays in the colour. Thus if all the nerve elements were simultaneously set in action, the sensation is that of white light; if that corresponding to red and green, the resultant sensation will be orange or yellow; if mainly the green and violet, the sensation will be blue and indigo. Then red-blindness may be explained by supposing that the elements corresponding to the sensation of red are absent; and green-blindness, to the absence of the elements sensitive to green. If to a red-blind person the green and violet are equal, and when to a green-blind person the red and violet are equal, they may have sensations which to them constitute white, while to the normal eye the sensation is not white, but bluish green in the one case and green in the other. In each case, to the normal eye, the sensation of green has been added to the sensations of red and blue. It will be evident, also, that whiteness to the colour-blind eye cannot be the same as whiteness to the normal eye. No doubt this theory explains certain phenomena of colour-blindness, of after-coloured images, and of contrast of colour, but it is open to various objections. It has no anatomical basis, as it has been found to be impossible to demonstrate the existence of three kinds of nerve elements, or retinal elements, corresponding to the three fundamental colour sensations. Why should red to a colour-blind person give rise to a sensation of something like green, or why should it give rise to a sensation at all ? Again, and as already stated, in cases of colourblindness due to tobacco or to disease, only blue may be seen, while it is said that the rest of the spectrum seems to be white. It is difficult to understand how white can be the sensation if the sensations of red and green are lost. On the other hand, it may be argued that such colour-blind eyes do not really see white as seen by a normal person, and that they only have a sensation which they have been accustomed to call white. According to this theory, we never actually experience the primary sensations. Thus we never see primary red, as the sensation is more or less mixed with primary green, and even with primary blue (violet). So with regard to primary green and primary violet. Helmholtz, in his last work on the subject, adopted as the three primary colours a red bluer than spectral red, (a) a green lying between 540 X and 560 X (b, like the green of vegetation), and a blue at about 470 X (c, like ultramarine), all, however, much more highly saturated than any colours existing in the spectrum.
In Handbuch der Physiologischen Optik (Hamburg and Leipzig, 1896) Helmholtz pointed out that luminosity or brightness plays a more important part in colour perception than has been supposed. Each spectral colour is composed of certain proportions of these fundamental colours, or, to put it in another way, a combination of two of them added to a certain amount of white.
Hering's theory proceeds on the assumption of chemical changes in the retina under the influence of light. It also assumes that certain fundamental sensations are excited by light or occur during the absence of light. These fundamental sensations are white, black, red, yellow, green and blue. They are arranged in pairs, the one colour in each pair being, in a sense, complementary to the other, as white to black, red to green, and yellow to blue. Hering also supposes that when rays of a certain wave-length fall on visual substances assumed to exist in the retina, destructive or, as it is termed, katabolic changes occur, while rays having other wavelengths cause constructive or anabolic changes. Suppose that in a red-green substance katabolic and anabolic changes occur in equal amount, there may be no sensation, but when waves of a certain wave-length or frequency cause katabolic changes in excess, there will be a sensation of red, while shorter waves and of greater frequency, by exciting anabolic changes, will cause a sensation of green. In like manner, katabolism of a yellow-blue visual substance gives rise to a sensation we call yellow, while anabolism, by shorter waves acting on the same substance, causes the sensation of blue. Again, katabolism of a white-black visual substance Helmholtz. It is based on the assumption that three kinds of nervous elements exist in the retina, the excitation of which give respectively sensations of red, green and violet. These may be regarded as fundamental sensations. Homogeneous light excites all three, but with different intensities according to the length of the wave. Thus long waves will excite most strongly fibres sensitive to red, medium waves those sensitive to green, and short waves those sensitive to violet. Fig. 22 shows graphically the irritability of the three gives white, while anabolism, in the dark, gives rise to the sensation of blackness. Thus blackness is a sensation as well as whiteness, and the members of each pair are antagonistic as well as complementary. In the red end of the spectrum the rays cause katabolism of the red-green substance, while they have no effect on the yellowblue substance. Here the sensation is red. The shorter .waves of the spectral yellow cause katabolism of the yellow-blue material, while katabolism and anabolism of the red-green substance are here equal. Here the sensation is yellow. Still shorter waves, corresponding to green, now cause anabolism of the red-green substance, while their influence on the yellow-blue substance, being equal in amount as regards katabolism and anabolism, is neutral. Here the sensation is green. Short waves of the blue of the spectrum cause anabolism of the yellow-blue material, and as their action on the red-green matter is neutral, the sensation is blue. The very short waves at the blue end of the spectrum excite katabolism of the red-green substance, and thus give violet by adding red to blue. The sensation orange is experienced when there is excess of katabolism, and greenish blue when there is excess of anabolism in both substances. Again, when all the rays of the spectrum fall on the retina, katabolism and anabolism in the red-green and yellow-blue matters are equal and neutralize each other, but katabolism is great in the white-black substance, and we call the sensation white. Lastly, when no light falls on the retina, anabolic changes are going on and there is the sensation of black.
Hering's theory accounts satisfactorily for the formation of coloured after-images. Thus, if we suppose the retina to be stimulated by red light, katabolism takes place, and if the effect continues after withdrawal of the red stimulus, we have a positive after-image. Then anabolic changes occur under the influence of nutrition, and the effect is assisted by the anabolic effect of shorter wave-lengths, with the result that the negative after-image, green, is perceived. Perhaps the distinctive feature of Hering's theory is that white is an independent sensation, and not the secondary result of a mixture of primary sensations, as held by the Young-Helmholtz view. The greatest difficulty in the way of the acceptance of Hering's theory is with reference to the sensation of black. Black is held to be due to anabolic changes occurring in the white-black substance. Suppose that anabolism and katabolism of the white-black substance are in equilibrium, unaccompanied by stimulation of either the red-green or the yellow-blue substances, we find that we have a sensation of darkness, but not one of intense blackness. This " darkness " has still a certain amount of luminosity, and it has been termed the " intrinsic light " of the retina. Sensations of black differing from this darkness may be readily experienced, as when we expose the retina to bright sunshine for a few moments and then close the eye. We then have a sensation of intense blackness, which soon, however, is succeeded by the darkness of the " intrinsic light." The various degrees of blackness, if it is truly a sensation, are small compared with the degrees in the intensity of whiteness. In the consideration of both theories changes in the cerebral centres have not been taken into account, and of these we know next to nothing.
6. The Contrast of Colours. - If we look at a small white, grey or black object on a coloured ground, the object appears to have the colour complementary to the ground. Thus a circle of grey paper on a red ground appears to be of a greenish-blue colour, whilst on a blue ground it will appear pink. This effect is heightened if we place over the paper a thin sheet of tissue paper; but it disappears at once if we place a black ring or border round the grey paper. Again, if we place two complementary colours side by side, both appear to be increased in intensity. Various theories have been advanced to explain these facts. Helmholtz was of opinion that the phenomena consist rather in modifications of judgment than in different sensory impressions; J. A. F. Plateau, on the other hand, attempted to explain them by the theory of consecutive images.
5. ' THE Movements Of The Eye I. General Statement. - The globe of the eye has a centre of rotation, which is not exactly in the centre of the optic axis, but a little behind it. On this centre it may move round axes of rotation, of which there are three - an antero-posterior, a vertical and a transverse. In normal vision, the two eyes are always placed in such a manner as to be fixed on one point, called the fixed point or the point of regard. A line passing from the centre of rotation to the point of regard is called the line of regard. The two lines of regard form an angle at the point of regard, and the base is formed by a line passing from the one centre of rotation to the other. A plane passing through both lines of regard is called the plane of regard. With these definitions, we can now describe the movements of the eyeball, which are of three kinds: (r) First position. The head is erect, and the line of regard is directed towards the distant horizon. (2) Second position. This indicates all the movements round the transverse and horizontal axes. When the eye rotates round the first, the line of regard is displaced above or below, and makes with a line indicating its former position an angle termed by Helmholtz the angle of vertical displacement, or the ascensional angle; and when it rotates round the vertical axis, the line of regard is displaced from side to side, forming with the median plane of the eye an angle called the angle of lateral displacement. (3) Third order of positions. This includes all those which the globe may assume in performing a rotatory movement along with lateral or vertical displacements. This movement of rotation is measured by the angle which the plane of regard makes with the transverse plane, an angle termed the angle of rotation or of torsion. The two eyes move together as a system, so that we direct the two lines of regard to the;11* same point in space.
The eyeball is moved by six muscles, which are described in the article EYE (Anatomy). The relative attachments and the axes of rotation are shown in fig. 23.
The term visual field is given to the area intercepted by the extreme visual lines which pass through the centre of the pupil, the amount of dilatation of which determines its size. It follows the movements of the eye, and is dis placed with it. Each point in the visual field has a corresponding point on the retina, but the portion, as already explained, which secures our attention is that falling on the yellow spot.
2. Simple Vision with Two Eyes. - When we look at an object with both eyes, having the optic axes parallel, its image falls upon the two yellow spots, and it is seen as one object. If, however, we displace one eyeball by pressing it with the finger, then the image in the displaced eye does not fall on the yellow spot, and we see two objects, one of them being less distinct than the other. It is not necessary, however, in order to see a single object with two eyes that the two images fall on the two yellow spots; an object is always single if its image fall on corresponding points in the two eyes.
The eye may rotate round three possible axes, a vertical, horizontal and antero-posterior. These movements are effected by four straight muscles and two oblique. The four straight muscles arise from the back of the orbit, and pass forward to be inserted into the front part of the eyeball, or its equator, if we regard the anterior and posterior ends of the globe as the poles. The two obliques (one originating at the back of the orbit) come, as it were, from the nasal side - the one goes above the eyeball, the other below, while both are inserted into the eyeball on the temporal side, the superior oblique above and the inferior oblique below. The six muscles work in pairs. The internal and external recti turn the eye round the vertical axis, s10, T law FIG. 23. - Diagram of the Attachments of the Muscles of the Eye and of their Axes of Rotation, the latter being shown by dotted lines. (Fick.) The axis of rotation of the rectus internus and rectus externus being vertical, that is, perpendicular to the plane of the paper, cannot be shown.
a, FIG. 24. - Diagram to illustrate the Physiological Relations of the two Retinae.
so that the line of vision is directed to the right or left. The superior and inferior recti rotate the eye round the horizontal axis, and thus the line of vision is raised or lowered. The oblique muscles turn the eye round an axis passing through the centre of the eye to the back of the head, so that the superior oblique muscle lowers, while the inferior oblique raises, the visual line. It was also shown by Helmholtz that the oblique muscles sometimes cause a slight rotation of the eyeball round the visual axis itself. These movements are under the control of the will up to a certain point, but there are slighter movements that are altogether involuntary. Helmholtz studied these slighter movements by a method first suggested by F. C. Donders. By this method the apparent position of afterimages produced by exhausting the retina, say with a red or green object, was compared with that of a line or fixed point gazed at with a new position of the eyeball. The ocular spectra soon vanish, but a quick observer can determine the coincidence of lines with the spectra. After producing an after-image with the head in the erect position, the head may be placed into any inclined position, and if the attention is then fixed on a diagram having vertical lines ruled upon it, it can easily be seen whether the after-image coincides with these lines. As the after-image must remain in the same position on the retina, it will be evident that if it coincides with the vertical lines there must have been a slight rotation of the eyeball. Such a coincidence always takes place, and thus it is proved that there is an involuntary rotation. This minute rotation enables us to judge more accurately of the position of external objects.
3. The horopter is the locus of those points of space which are projected on retinal points. While geometrically it may be conceived as simple, as a matter of fact it is generally a line of double curvature produced by the intersection of two hyperboloids, or, in other words, it is a twisted cubic curve formed by the intersection of two hyperboloids which have a common generator. The curves pass through the nodal point of both eyes. An infinite number of lines may be drawn from any point of the horopter, so that the point may be seen as a single point, and these lines lie on a cone of the second order, whose vertex is the point. When we gaze at the horizon, the horopter is really a horizontal plane passing through our feet. The horopter in this instance is the ground on which we stand. Experiments show " that the forms and the distances of these objects which are situated in, or very nearly in, the horopter, are perceived with a greater degree of accuracy than the same forms and distances would be when not situated in the horopter " (M`Kendrick, Life of Helmholtz, 1899, p. 172 et seq.). An object which is not found in the horopter, or, in other words, does not form an image on corresponding points of the retinae, is seen double. When the eyeballs are so acted upon by their muscles as to secure images on non-corresponding points, and consequently double vision, the condition is termed strabismus, or squinting, of which there are several varieties treated of in works on ophthalmic surgery. It is important to observe that in the fusion of double images we must assume, not only the correctness of the theory of corresponding points of the retina, but also that there are corresponding points in the brain, at the central ends of the optic fibres. Such fusion of images may occur without consciousness - at all events, it is possible to imagine that the cerebral effect (except as regards consciousness) would be the same when a single object was placed before the two eyes, in the proper position, whether the individual were conscious or not. On the other hand, as we are habitually conscious of a single image, there is a psychical tendency to fuse double images when they are not too dissimilar.
(c) Apparent Distance
We judge of distance, as regards large objects at a great distance from the eye - (i) from their apparent size, which depends on the dimensions of the visual angle, and (2) from the interposition of other objects between the eye and the distant object. Thus, at sea, we cannot form, FIG.
FIG. 28. - Illustrating Stereoscopic Vision.
the defect is revealed. In the normal eye distant objects are focused on the retina without the use of the ciliary muscle, FIG. 29. - Showing Parallel Rays focused on the Retina of a Hyperopic Eye by means of a Convex Lens.
which is only employed when looking at near objects; but the hyperope has to use this muscle all his waking hours for both near and distant vision, so that his eyes are never at rest. Fortunately he has some compensation for this extra work, for in most hyperopes the ciliary muscle becomes more or less hypertrophied; but even so, if near work is at all excessive, or if the defect is associated with astigmatism or anisometropia, symptoms of eye-strain will sooner or later show themselves (see Eye-strain, below).
In older people a very common symptom is blurring of the type while reading; the book has to be put down and the eyes rested for some minutes before reading can be resumed. This is due to the fatigued ciliary muscle giving way and becoming unable to focus.
As we advance in years we lose accommodation power (see Presbyopia, below), so that the time comes to every hyperope, if he live long enough, when he not only has to use glasses for reading (at an earlier period than the normal person), but he also finds that he is gradually losing his distant vision. This is very alarming to many, until it is explained that all that has happened is the loss of power to correct the defect, which defect, of course, has always existed, and which in future will have to be corrected by suitable glasses. The higher the hyperopia the sooner will these symptoms manifest themselves.
In quite young children, sometimes the earliest sign of the presence of hyperopia is a convergent strabismus (internal squint). As a rule, this squint is nothing more than an overconvergence brought about by over-accommodation in those who cannot dissociate their convergence and accommodation; if we remove the necessity for over-accommodation by correcting the defect with suitable glasses, the over-convergence disappears and the squint is cured.
The total hyperopia of the eye is divided into manifest hyperopia and latent hyperopia. Manifest hyperopia is expressed in amount by the strongest convex glass that allows clear distant vision when the eye is not under atropine. Latent hyperopia is the additional hyperopia which is revealed under atropine. With advancing years the latent hyperopia becomes more and more manifest, and between the ages of 45 and 50 the total hyperopia is entirely manifest.
In addition to the symptoms already described, a very common one among young hyperopes is spasm of the ciliary muscle. This cramp of the muscle causes distant objects to be very indistinct, improvement only taking place with a concave glass, and near work has to be approached very close to the eyes, thus giving a wrong idea that the child is suffering from myopia; by paralysing the ciliary muscle with atropine the spasm disappears and the true nature of the defect is revealed.
The treatment essentially consists in ascertaining the total hyperopia of the eye, and this can only be done satisfactorily, when latent hyperopia is present, by paralysing the accommodation, using atropine for those under 25, and homatropine for those between the ages of 25 and 35 or 40. Over 40 (and when the hyperopia is high, even at an earlier age) no cyclo plegic is necessary - in fact it is in many cases dangerous, as an attack of glaucoma may be induced. (See EYE: diseases.) Having found the total hyperopia, we learn the amount of the latent hyperopia, and, roughly speaking, the convex glass required is equal to the whole of the manifest hyperopia added to, from one-third to a half, of the latent; but the treatment varies with the age of the individual and the amount of the hyperopia, and is too complicated to be detailed here.
Myopia (M.) (Short-sight). - Typical myopia is due to an elongation of the antero-posterior diameter of the eye, so that the retina is situated behind the principal focus, and only diver FIG. 30.
gent rays of light from a near point (fig. 30), or parallel rays made divergent by a concave glass (fig. 31), can come to a FIG. 31 focus on the retina. In other words, the far point of a myope is at a short distance in front of the eye, the distance being the measure of the myopia.
A myope can see distinctly at a distance when the eye is at rest (i.e. when accommodation is not being used), with that concave glass whose focal length is equal to the distance of the far point from the eye, and the converse is true; the measurement of myopia is that concave glass with which the myopic eye sees distinctly objects at a distance, and its focal length is equal to the distance of the myope's far point from the eye.
The Causes of Myopia. - Although myopia is hereditary, it is, with few exceptions, not congenital. We have seen that almost all eyes are hyperopic at birth. The savage is rarely myopic: it is civilization that is responsible for it; the necessity for constantly adapting the eye for near objects means undue convergence. We find that myopia generally first shows itself at the age of 8 to io, when school work begins in earnest - that is, when convergence is first used in excess - and there is no doubt that it is excessive convergence that is mostly responsible for the development of myopia. The over-used internal recti constantly pulling at the sclerotic tend to lengthen the antero-posterior diameter of the eye, and as this lengthening of the anteroposterior axis necessitates greater convergence still, a vicious circle is produced, and the myopia gradually increases. The hereditary character of myopia is explained by the existence in such eyes of an " anatomical predisposition " to myopia. The sclera is unusually thin, and consequently less able to resist the pull of the internal recti, and the relative position of the recti and the position of the optic nerve, both of which may be hereditary, may be factors in the production of this defect. Anything which causes young subjects to approach their work too near the eyes may be the starting-point. Bad illumination, or the light coming from the wrong direction (for instance, in front), or defective vision produced by corneal nebulae, or lamellar cataract, &c., all necessitate over-convergence in order to obtain clearer images, and myopia may be produced.
It is interesting to note that when the work is approached very near the eye, but convergence is not used, as in the case of watchmakers, who habitually use a strong convex glass in one eye, there is no special tendency to myopia.
Some of the more common symptoms of myopia are: - (r) Distant objects are seen indistinctly. (2) Near objects are seen distinctly, and the near point is much nearer than in the normal eye. (3) Acuteness of vision is often lowered, and especially is this the case in high myopia. (4) Eye-strain is often present, due to overuse of the muscles of convergence, and this may lead to (5) an external or divergent squint.
(6) Floating black specks are often complained of, these are generally muscae volitantes, but often, especially in high myopia, may be actual opacities floating in the vitreous.
(7) Myopes often stoop and become " round shouldered " from their habit of poring over their work.
A small amount of myopia, if it is stationary, is in no sense a serious defect of the eye, the possessors of it are often quite unconscious of any deficiency in vision, and in fact brag that they have better vision than their fellows. The reason of this is that they learn in early life to recognize indistinct distant objects by the aid of other senses in a way that the ordinary individual can hardly understand, and in later life they can postpone the wearing of glasses for near work for many years, and sometimes until extreme old age. Unfortunately myopia is, as a rule, not stationary; it almost always tends to increase, and if this increase leads to very high myopia such serious changes may occur in the eyes as to lower the visual acuity enormously and sometimes lead to total loss of vision.
The treatment of myopia is general and local.