ERRORS Ol ACCOMMODATION AND REFRACTION CLARKE r\ i: BttKEllY LIBRARY UHivERSfTY or CALIFOftNIA nu>M 1 THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA THE ERRORS OF ACCOMMODATION AND REFRACTION OF THE EYE THE ERRORS OF ACCOMMODATION AND REFRACTION OF THE EYE AND THEIR TREATMENT A HANDBOOK FOR STUDENTS BY ERNEST CLARKE, M.D., F.R C.S. OPHTHALMIC SURGEON TO THE KING GEORGE HOSPITAL, QUEBN ALEXANDRA HOSPITAL FOR OFFICERS, ETC. CONSULTING SURGEON TO THE CENTRAL LONDON OPHTHALMIC HOSPITAL CONSULTING OPHTHALMIC SURGEON TO THE MILLER GENERAL HOSPITAL FOURTH EDITION NEW YORK WILLIAM WOOD & COMPANY MDCCCCXVIII OPTOMETRY Printed in Great Britain Sb--# V**" orro PREFACE TO THE FOURTH EDITION The first edition of this work was published fifteen years ago based on lectures delivered at the Central London Ophthalmic Hospital and the Medical Graduates' College . I have not altered its character, which is essentially practical, all matter unnecessary for the busy practi- tioner or overburdened student being omitted. The whole work has been thoroughly revised and brought up to date, many chapters having been re- written. The subject of Eyestrain still occupies the prominent place that is its due. ERNEST CLARKE. Chandos Street, Cavendish Square, W. February, 191 8. CONTENTS CHAPTER PAGE I. REFRACTION PRISMS LENSES - - - I II. OPTICAL PROPERTIES OF THE NORMAL EYE - "19 III. ACCOMMODATION - - - - - 29 IV. CONVERGENCE - - - - "39 V. THE OPHTHALMOSCOPE - - - "57 VI. HYPEROPIA - - - - - - 85 VII. MYOPIA - - - - - - 99 VIII. ASTIGMATISM - - - - - "115 IX. PRESBYOPIA - - - - - -142 X. ANISOMETROPIA _ - - - - 152 XI. APHAKIA _----- 159 XII. EYESTRAIN - - - - - -1 62 XIII. HETEROPHORIA - - - " "I?! XrV. STRABISMUS ------ 184 XV. CYCLOPLEGIA, CYCLOPLEGICS, AND CILIARY SPASM - I98 XVI. METHODS OF EXAMINATION NOTE-TAKING - - 202 XVII. SPECTACLES ------ 208 XVIII. ILLUSTRATIVE CASES - - - - -2I3 XIX. VISION TESTS FOR THE SERVICES _ - - 221 BIBLIOGRAPHY - - - - - 23O INDEX ------ 232 VU ERRORS OF ACCOMMODATION AND REFRACTION OF THE EYE CHAPTER I REFRACTION— PRISMS— LENSES Light is propagated in straight lines which diverge from any luminous point in all directions, and these lines of direction are called " luminous rays." The propaga- tion is produced by ether waves which are across the path of light. The velocity of light is, in round numbers, 186,000 miles per second, and is appreciably retarded in passing through a denser medium. Rays of light entering the eye coming from any luminous point at a greater distance than 6 metres may be assumed, for all practical purposes, to be parallel. Light is absorbed, refracted, or reflected. Refraction of Light. — A ray of light passing from a rarer into a denser transparent medium, if it be perpen- dicular to the surface, and the boundaries of the medium be parallel, will pass out of the denser medium in the same straight line (Fig. i, l), the only effect upon it being a retardation. If the ray enter the denser medium other than perpendicularly, or if the boundaries of the medium be not parallel, the ray is bent or refracted. A simple illustration will explain this. Explanation of Refraction. — i\s ether waves are at right angles to the path of light, if a beam of light enter 2 TH£ RtFRACTION OF TH£ EYE a denser medium obliquely, one end of the wave will enter the denser meditim before the other, and conse- quently be retarded earlier. Let A, B, c, d (Fig. i), be a denser medium, with parallel boundaries, and n, o, p, q, the beam of light. The wave front will reach Q before it reaches R, and it will at once be retarded ; and as it thus travels more slowly from Q to s than from p to R (which is outside the denser medium), the beam must be swung round so that it is bent or refracted on entering the denser medium. Fig. I Across the denser medium the whole wave front is equally affected, so that the beam passes across in a straight line ; and if the sides of the medium be parallel the converse happens, and it is again bent on passing out, the incident and the emergent rays being parallel. Let this be applied to the case of, for example, a prism where the sides of the denser medium are not parallel. Suppose A, B, c (Fig. 2), to be a triangular strip of velvet pasted on a smooth board, and suppose d to be two small wheels connected by an axle in such a way that each wheel can turn independently of the other. Roll REFRACTION 3 the wheels up to the velvet triangle; the lower or right wheel will pass on to the velvet at e before the left wheel reaches it, and as the velvet will retard its progress, it will turn now more slowly than the left wheel, so that the pair of wheels will be slewed round towards the base of the triangle. When the left wheel enters on the velvet at /, its progress will be the same as that of the other wheel, and the pair of wheels will cross the velvet now in a straight line ; when it reaches w, the left or upper wheel will leave the velvet earlier, and will consequently travel more rapidly, and will again swing the pair round, so *^ '/ T----:::7 Fig. 2. that in the transit across the triangle the pair of wheels have been bent towards the base. It is in this manner that light behaves; in passing through a prism, it is bent or refracted towards the base. *W| A ray of light passing obliquely from a less dense into a denser transparent medium is refracted or bent towards the perpendicular, and when passing from a dense to a less dense medium is refracted away from the perpendicular. Index of Refraction. — The index of refraction of a transparent substance is the number that denotes the 4 THE REFRACTION OF THE EYE refractive power of such substance compared with air, which is taken as the unit i. In Fig. 3, let A c be the incident ray meeting the horizontal surface of water at c, and forming with p p', the perpendicular, an angle A c P ; and let c b be the refracted ray in water bent towards the perpendicular, and forming the angle B c p'. v^ /O ~~""'^*^^ c W ^ k Fig. 3. The sine l m is to the sine n o as 4 to 3, expressed as I, or 1*33, and this is the index of refraction of water. The following are a few of the indices of refraction useful to the ophthalmologist : Air . . I'O Water 1*33 Cornea 1*33 Aqueous humour 1-3379 Vitreous humour 1-3379 Crystalline lens 1-4 Crown glass 1-5 PRISMS 5 Prisms. — An ophthalmic prism is a wedge-shaped piece of glass having two of its sides, or plane surfaces, inter- secting each other at the apex, and separated at the base, which is the thickest part of the prism. We have already seen that a ray of light entering one of the sides of a prism is refracted or bent towards the base, and the amount of this refraction depends upon — I. The strength of the prism. |2. The refractive index of the prism substance. 3. The position at which the light enters the prism. The Strength of the Prism — The Numbering of Prisms. — ^The power of a prism to deflect or refract light depends on the size of the angle at the apex formed by Fig. the two plane surfaces. This is called the refracting angle, and is written with the sign of a degree after the numeral — thus : 4° — which is scratched on the surface of the glass. This is the old, and even up to the present very general, method of numbering prisms. Maddox has suggested the word " prismetry " to denote the numbering by the deviating angle. IThe Deviating Angle of a Prism. — In Fig. 4, if a ray, p, enter the prism, instead of passing out at p', it is refracted towards O THE REFRACTION OF THE EYE the base b c, and away from the angle b a c, and is again bent towards the base on passing out, and emerges in the direction / (see page 3). The angle p' o f, made by the backward prolonga- tion of / and the forward prolongation of p, is the angle of devia- tion, and it is equal to about half the angle of refraction. To indicate that the angle of deviation is implied, a small d is added; thus, prism 4° is approximately equal to prism 2° d. Angle of Refraction. Angl* of Deviation. 1° 32' 5° 2° 42' 10° 5° 26' As the metrical system is now universally adopted in ophthal- mology. Prentice has suggested the numbering of prisms on the metrical plan, and the prism dioptre is the unit, designated by the sign A after the numeral. A prism of the strength of i P.D. (i A) is a prism that, at a distance of i metre, apparently displaces an object i centi- metre. In Fig. 5, E, being the observer, sees o at o' apparently displaced* i centimetre, the distance between o and the prism Fig. b?ing I metre, and the prism i A ; that is, the apparent displace- ment of an object looked at through a prism is i per cent, of the distance of the prism from the object, multiplied by the prism dioptre. A prism i A apparently displaces an object 3 metres off, 3 centi- metres, and a prism 3 A displaces an object 2 metres off, 6 centi- metres, and so on. Dennett has suggested the centrad as the unit for numbering prisms. The centrad is the hundredth part of a radian, a radian being the angle subtended at the centre of a circle by an arc, which is equal in length to the radius. A prism i centrad, designated i v. deviates a ray of light one-hundredth part of the arc of the radian. It is interesting to note that the centrad has a relative value to the metre angle, in that half the number of centimetres between the pupils indicates the number of centrads in the metre angle. This method is not much used, although probably the most scientific. * Note that the apparent displacement of an object viewed through a prism is always towards the apex. PRISMS 7 All three methods of numbering prisms are practically iden- tical for weak prisms, and, as it is only weak prisms that an oph- thalmologist can use, it matters little what method he adopts. Table showing the Equivalence of Centrads, Prism Dioptres, and Refracting Angle, of the Six Weakest Prisms. (Index of Refraction, 1*54.) Centrad. Prism Dioptre. Refracting Angle. 1 I I* 2 2'OOOI 2*12° 3 3*0013 3*i8° 4 4*0028 4*23° 5 5-0045 5-28° 6 6*0063 6*32° The minimum of deviation occurs when the incident ray crosses the prism parallel to its base; but in thin prisms — and it is thin prisms only that the ophthalmolo- gist uses — this has no practical importance. Hence we can neglect the position of the incident ray. The Uses of Prisms.— 1. To remove diplopia. 2. To ease the muscles, and so prevent muscle strain and subsequent diplopia (see page 176) . 3. To exercise weak muscles (see page 182). 4. To test the strength of the external ocular muscles. 5. To detect malingerers (see page 183). In trial cases the prisms are usually cut circular, so that they can be used in a trial frame ; the exact position of the base of the prism is usually marked by a line on the glass at right angles to the base. Rotating Prisms. — If two prisms of equal strength be placed in apposition in such a manner that the base of the one is in contact with the apex of the other, they neutralize each other, and if we rotate them in opposite directions we obtain the effect of an increasingly strong prism. Risley's Rotary Prism (Fig. 6) is made on this principle. If we place it in one side of a trial frame, both eyes being used, start from zero and gradually turn the button, we 8 THE REFRACTION OF THE EYE can ascertain the strongest prism the eyes can stand without having diplopia, or, if we are deaUng with a case of diplopia, we can ascertain the weakest prism that will procure " fusion " vision. Fig. 6. The numbers on the frame indicate the refracting angle in degrees. The instrument can give a total prismatic power of 30°. i fisms form no images and have no foci. Fig. 7. Lenses. — If two prisms are placed with their bases in contact, we have roughly a bi-convex lens (Fig. 7, a), and rays of light passing through it are bent towards the base of the prisms — i.e., the centre of the lens; in other words, they converge. If the prisms have their LENSES apices in contact, we have a bi-concave lens (Fig. 7, b), and the rays]are]bent towards the bases — i.e., outwards — and diverge. Spherical Lenses. — Besides the bi-convex (Fig. 7, a) and bi-concave lenses (b), there are plano-convex (c), Fig. plano-concave (d), converging concavo-convex or con- verging meniscus (e), and diverging concavo-convex or diverging meniscus (f). Rays of light passing obliquely through any of these forms of lenses are refracted or bent towards the thickest part of the lens. Fig. 9. The principal axis is a line drawn through the optical centre at right angles to the lens (Fig. 8, A o), and rays passing through this are not refracted; all other lines passing through the optical centre not at right angles to the lens are called " secondary axes " (Fig. 9, a '«). Rays passing along the secondary axes are refracted. 10 THE REFRACTION OF THE EYE but as the emergent and the incident rays are in the same direction, and the refraction in low-power lenses is very slight, the refraction can be ignored, and the rays assumed to pass along in a straight line. Convex Lenses. — Parallel rays passing through a con- vex lens unite on the opposite side of the lens at a point called the " principal focus " (Fig. 8, p f). At the principal focus an inverted real image of the object is formed. Let a b (Fig. 9) be an object at some considerable distance from the lens. Any ray passing from the point a through the optical centre of the lens c will be unrefracted {vide supra), and the image of a will be somewhere on this line on the other side of the lens Fig. 10. — let it be at ^; all other rays passing from A will be refracted on passing through the lens, and will focus at a. In the same manner an image of B is formed at b, and all other points between A and B will form an image between a and b, so that we get an inverted image a b oi a b formed at the principal focus of the lens. The distance between the principal focus and the optical centre is called the " principal focal distance " ; it is posi- tive, and convex lenses are known by the plus sign : + . Rays passing from the principal focus (p f) through the lens emerge as parallel rays on the opposite side (Fig. 8). Divergent rays from a point l (Fig. 10) beyond the principal focus f meet at a point / beyond the principal LENSES II focus f' on the other side of the lens. If the point L is twice the focal distance of the lens, then / will be at the same distance on the other side. These two points are called " conjugate foci," and are interchangeable; that is, the object may be at l or /, and the image is respectively at / or L. If a luminous point be between the convex lens and the principal focus, the rays will still be divergent when they leave the lens on the opposite side, and consequently no real image is formed; but a magnified virtual image is formed beyond the principal focus on the same side, at a point called the " virtual focus," and this virtual image Fig. II. is seen by an observer on the opposite side of the lens, the light from the points a and h appearing to thr^ observer to come from a' and h' (Fig. ii). Concave Lenses. — Parallel rays passing through a con- cave lens diverge, and consequently never come to a focus ; but these divergent rays, if prolonged backwards, will meet at a point f (Fig. 12). This point is the (virtual) principal focus of a concave lens. If an object be placed beyond the principal focus of a concave lens, an observer on the opposite side of the lens will see a virtual, erect, smaller image on the same side as the object; thus, rays from a and h will appear to 12 THE REFRACTION OF THE EYE come from a' and h' , and the object « 6 is seen as a' h' (Fig. 13). As concave lenses have a negative focal distance, they are denoted by the minus sign:]-. Cylindrical Lenses.— In addition to spherical lenses cyhndrical lenses are required — these are lenses cut out Fig. 12. of a cylinder; convex cylinders are cut from a solid cylinder (Fig. 14, a), concave cylinders from a hollow cylinder (Fig. 14, h), which may be regarded as the mould of convex cylinders. Cylinders have the property of not I Fig. 13. refracting any rays that pass along their axis, but rays passing at right angles to the axis undergo the maximum refraction corresponding to the strength of the lens. According to the angle at which the rays impinge upon the lens, they undergo more or less refraction, as this LENSES 13 angle is further away from, or nearer to, the axis of the cyUnder. A cylinder has no one focal point, but a line of foci parallel to its axis. Cylindrical lenses are employed to correct regular astigmatism. The axis of a cylindrical test lens is marked by a small line on the glass, or by making the sides of the lens, parallel to the axis, opaque. Fig. 14. Numeration of Lenses. — The lens whose focal distance is I metre is taken as a unit, and its refractive power is called one Dioptry or Dioptre (" d "). A lens of twice the power of this — viz., 2 d — has a focal distance of ^-; i.e., 50 cms.; a lens of half the power — viz., •5 D — has a focal length of 2 metres, and so on. The focal distance of a lens no = ' n Under the old system, a lens whose focal distance was I inch was taken as the unit, and a lens whose focal length was 10 inches was called jV* 3^ inches ^, and so on. The great disadvantage of this method of numeration was the inability to make it international, because the inch is not an international measure. To convert the old numeration into the new, divide the denominator into 40; thus, lens \ is V-==S d, and vice 14 THE REFRACTION OF THE EYE versa, Jo convert dioptres into inches, divide the dioptre into 40, and the result is the focal length in inches; thus, 4 D = -*3^= 10 inches focal length, expressed as to- The following table shows at a glance the approximate equiva- lent of the old and new numeration : )ioptres. Inches. Dioptres. Inches. •12 320 4 10 0-25 160 4-50 9 0.37 107 5 8 0-50 80 5-50 7 0-62 64 6 6| 0-75 53 7 ^1, 0-87 46 8 5" I 40 9 4i] 1-25 32 ID 4 1-50 26J II 3h 1-75 22i 12 3i 2 26 13 3 2'25 i7i 14 2f 2.50 16 15 2-§- 2-75 14 16 2J 3 13 17 2i 3-50 II 18 2i 20 2 Testing Lenses. — It is important to be able to test a lens and find out its optical value. Instead of going through the process of finding its principal focus, and measuring the distance of this from the lens centre, we place in front of it lenses of the opposite value; thus, if we wish to find the strength of a convex glass, we neutralize it with concave glasses. A finer test is to employ the parallactic movement. If we look at a distant object through a convex glass and move the glass, the object appears to move in the oppo- site direction; if we use a concave glass, the object appears to move in the same direction. So long as there is any movement we must place up concave or convex glasses, according as the displacement of the object is " against " or " with." In testing cylinders we have to ascertain not only the value, but also the direction of the axis. LENSES 15 When cylinders are moved in front of the eye in the direction of the axis, objects looked at through them are not displaced; but the smallest rotation of the cylinder causes displacement, which reaches its maximum when the movement of the cylinder is in the direction at right angles to its axis. In this position neutralize with cylindrical lenses of the opposite value, bearing in mind that displacement takes place " against " the movement so long as a convex lens predominates, and " with " the movement so long as a concave one predominates. The axes of the two lenses must coincide. When testing a sphero-cylindrical glass, the spherical lens should be first neutralized. A great saving of time is effected by testing glasses with the Geneva lens measure and the Maddox cylinder-axis finder. The Combination of Lenses — Convex Spherical Lenses. — The ordinary way for such lenses to be ground is to work half the power needed on each surface ; thus, when + 4* is required, each surface of the lens is made equal to +2, as if two plano-convex glasses of -1-2 had their plane surfaces cemented together. Another method of working a convex lens is to grind the surface away from the eye as a convex lens of higher power than is required, and the other surface concave of such a strength as to reduce the convex surface to the desired amount. Thus, when -1-4 is ordered, one surface can be made +7 and the other surface -3, or one surface can be -1-6 and the other -2. Such lenses are called " periscopic *'; they enlarge the field of distant vision, as the eye in all its movements is at the same distance from the surface of the glass, but their chief advantage is in enabling the glasses to be placed nearer the eye without being touched by the lashes. * In the following pages, the numeration of lenses will always be in dioptres, and " d " after the numeral will be generally omitted. l6 THE REFRACTION OF THE EYE Concave Spherical Lenses. — These are usually made with half the strength required, on each surface. A certain amount of periscopic effect may be obtained by grinding the surface nearer the eye more concave, and reducing the other: thus, —8 may be, and usually is, made — 4 on each surface, or the surface nearer the eye may be made —6 and the other — 2 ; or the lens may be ground as a diverging meniscus (Fig. 7, f) ; thus, if - 3 is required, the surface next the eye is ground as -5, and the other surface as +2. Cylindrical Lenses. — When a cylinder only is pre- scribed, it is ground on one surface, the other surface remaining plane. When combined with a spherical lens, it is usual to grind the sphere on one surface, and the cylinder on the other. When a convex sphere and cylinder are required, the periscopic effect can be pro- duced by grinding a concave cylinder on the surface nearer the eye, and increasing the spherical strength by the amount of the cylinder. Thus, supposing +2 cyl. axis vert, c:; +3 sph. is needed, it may be ordered thus: — 2 cyl. axis horizontal c^ +5 sph. In ordering glasses for mixed astigmatism (see page 137), the periscopic effect is produced by combining a convex cyhnder with a concave sphere, and mounting the latter next the eye. As it is very important to divide the strength of the lens between the two surfaces when dealing with high powers, a cylinder, if also required in such a case, must be worked on one of the spherical surfaces. These lenses are called Toric lenses, and any combination of spherical lens (•25 to 18), with cyHndrical lens (from •25 to 3) can be supplied. Thus, if — 14 sph. oj - 2 cyl. axis horizontal is required, one surface is made - 7, and the other - 7 sph. c::> - 2 cyl. These toric lenses are very useful in high myopia, and also in aphakia. Bi'Focal Lenses (see Presbyopia, page 151). — Where BI-FOCALS 17 different lenses are required for distance and reading, bi-focal lenses are generally prescribed. The earliest forms of these glasses were straight split bi-focals, also called " Franklin " glasses, the lenses being two separate lenses divided horizontally and in the middle. Against the many disadvantages of this form of bi-focal was the one advantage that the lower lens could be slanted and made more or less parallel with the book or paper that was being read. An improvement on these " split " bi-focals consisted having the reading addition cemented on by Canada dlsam, either as in Fig. 15 or as a small round wafer. Fig. 15. The disadvantage of both these forms was chiefly manifested by the dividing line between the lenses being visible and constantly causing annoyance to the wearer. Another disadvantage of the cemented bi-focals is the tendency of the balsam to dry or crystallize. The next improvement did away with the visible line, and these bi-focals are called " invisible bi-focals." They are of two kinds, one the so-called " Kryptok," where a concavity is ground in the lower part of the distance glass, and the reading glass, of a higher refractive index, is fused into it; the other, the final perfected form of invisible bi-focals is the " Luxe," which consists of one glass only. The glass is made from a solid piece of crown glass with the two lenses ground invisibly on its surface. The chief advantage of these " Luxe " l8 THE REFRACTION OF THE EYE bi-focals is that the centring of both portions is more under control, and there is no chromatic aberratioii, which is so often present in the fused form. Spherical Aberration. — In most lenses the rays passing through the peripheral part of the lens do not focus at the same spot as those which pass through the central portion. In convex lenses, when the peripheral rays focus in front of the central rays, the aberration is spoken of as positive ; and when the peripheral rays focus behind the central, as negative. The crystalline lens suffers from spherical aberration, but it is more or less hidden by the contraction of the pupil. During mydriasis this aberration may interfere considerably with vision, but may be corrected by placing in the trial frame an opaque disc with a central circular open- ing. If the refraction is being estimated, this opening should not be smaller than 4 mm. in diameter. CHAPTER II OPTICAL PROPERTIES OF THE NORMAL EYE The eye is constructed in the form of a photographic camera. As in the camera, there is a closed darkened box open in front, where there is an arrangement of lenses to focus an object on the back, at which spot there is the apparatus for receiving the perfectly-formed image : the plate in the camera, the retina in the eye. As in the camera, there are two conditions which must exist in the eye : firstly, the media must be transparent ; and, secondly, the focusing must be so arranged that a perfect image of the external object is formed on the retina — i.e., the principal focus of the eye must coincide with the retina. All deviations from this latter condition are called errors of refraction and accommodation. The Refraction of the Normal Eye at Rest— i.e., in the Absence of any Effort of the Accommodation — Dioptric Apparatus of the Eye. — The simplest form of a dioptric apparatus is when two media of different refrac- tive power are separated by a spherical surface. Such a system is represented by Fig. i6, where X y z is di spherical surface separating a less refractive medium on the left from a more refractive medium on the right. The line o A passing perpendicularly to the surface of the sphere and through its centre at N is called the " optic axis." All rays passing .^normally to the surface, such as R N and s N, like the optic axis, pass through n, and undergo 19 20 THE REFRACTION OF THE EYE no refraction; N, the centre of the sphere, is called the " nodal point." The point y where the optic axis cuts the sphere is called the " principal point." Rays c, d, parallel to the optic axis in the less dense medium, unite somewhere on the optic axis at the point F, called the " posterior principal focus." On the optic axis, in the less dense medium, there is another point (f'), called the " anterior principal focus," whence divergent rays passing into the denser medium are refracted, and become parallel to the optic axis as at zf. Fig. i6. These four points — the principal point, nodal point, and anterior and posterior principal focus — are called " cardinal points " of the system. In the eye the system is much more complicated. A ray of light passing into the eye meets the following sur- faces and media in the order named: Anterior surface of the cornea, substance of the cornea, posterior surface of the cornea, aqueous, anterior surface of the lens, sub- stance of the lens, posterior surface of the lens, and vitreous. Thus there are four surfaces and, if we include the air, four media. As the anterior and posterior sur- faces of the cornea are parallel, we may neglect the sub- stance of the cornea, and consider the two surfaces as one. Again, as the indices of refraction of the aqueous THE CARDINAL POINTS 21 and vitreous are identical (see page 4), we may assume them to be one medium. In this manner the eye is reduced to three surfaces and three media. These three surfaces — the cornea, and the anterior and posterior surfaces of the lens — are symmetrically centred round the optic axis of the whole system, which may now be reduced to a compound system, consisting of the cornea and a bi-convex lens ; we find the principal points p' p" (Fig. 17) and the nodal points n' n" of the cornea and lens ; and, finally, take the mean of these two points, Fig. 17. and get p the principal focus and N the nodal point. Such an eye is known as the " reduced eye," and was suggested by Listing. The positions of the cardinal points of the reduced eye are — Principal point, in the aqueous, 2 '3448 mm. behind the anterior surface of the cornea. Nodal point, in the lens, '4764 mm. from its posterior surface, and about 15 mm. from the retina. Posterior principal focus, 22 •81 9 mm. behind the an- terior surface of the cornea — i.e., on the retina of the normal eye. (This is the length of the standard eye.) Anterior principal focus, 12 '8 mm. in front of the anterior surface* of the cornea. 22 THE REFRACTION OF THE EYE The principal plane r p s (Fig. i8) is where the one surface of this reduced system passes through the prin- cipal point p which is considered the centre of refraction of the eye. The optic axis (o a) is an imaginary line passing through the centre of the cornea and the nodal point, and meeting the retina a little above and to the nasal side of the fovea. The nodal point corresponds to the optical centre, and, as we have already seen, all rays passing through it are unrefracted. We can now ascertain how an image is formed on the retina. Let X Y (Fig. i8) be an object in front of the eye; each Fig. I 8. point of this sends out a pencil of divergent rays, and all those which pass into the eye, by the dioptric system, are made to converge into a point on the retina. Each pencil of rays from the point x has a principal ray x a, which is normal to the surface, and, passing straight through the nodal point n without refraction, impinges on the retina at x'. The other rays from x are increasingly divergent, and are represented by x 6, x c; they undergo refraction, and converge together at some point on the principal ray, which in the normal eye will be at x'. In like manner we can trace the rays from the other extreme point Y, which forms an image at y', and so for all the other points. In tracing the formation of an image on the retina. SIZE OF RETINAL IMAGE 23 we can ignore all the rays from a point of the object, except the principal ray, which we trace through the nodal point; and by tracing all the luminous points from an object through the nodal point, we obtain in the normal eye an inverted image of the object on the retina. The nearer the object is to the eye, the larger will be its image, and vice versa. The size of the retinal image is therefore directly proportional to the distance of the object from the eye. It is sometimes important for the oculist to determine the size of the retinal image of an object in order to dis- cover the size of a diseased area; this can be estimated if the size of the object and its distance from the eye be known. The triangles A N B and a ^ h (Fig. 19) are similar, hence ah : hB : : « N : A n — that is, the size of the area on the retina is to the size of the object as the distance from the nodal point to the retina is to the distance of the nodal point from the object. Let the latter be 10 metres and the size of the object i metre; we know that the distance a; N is 15 mm. — consequently : ah : 1,000 : : 15 : 10,000; , 15,000 .-. ah = ^^ =1*5 mm. 10,000 24 THE REFRACTIOnIoF THE EYE The perfect type of eye is that in which the retina coincides with the posterior principal focus, and is called Fig. 20. Showing parallel rays focused on the retina in emmetropia (e), behind the retina in hyperopia (h), and in front of the retina in myopia (m) . the " emmetropic " eye (e, Fig. 20), and any deviation from this is called ametropia. VISUAL ANGLE ^5 The following table gives an idea of the relative frequency of the different forms of ametropia : (a) Emmetropia (see Presbyopia be- 2500 individuals whose sight after correc- tion was nor- mal and who had no disease of the eyes. :) Same refrac- tion in both eyes (O57) low) 9 (b) Hypermetropia . ^3 (c) Myopia 22 {d) Astigmatism — Hypermetropic 43« Myopic . 113 Mixed . 12 U^) Refraction different in the two eyes (Anisometropia) . . . . ^843 2500 5000 eyes (as above) — Emmetropia , ....... 56 Hypermetropia ....... 425 Myopia ........ 216 Astigmatism . . . . . . . .4303 5000 Of the 2500 individuals, 961 were presbyopic, and only 9 of these were emmetropic. If the posterior principal focus is beyond the retina, the eye is too short, and parallel rays, when they meet the retina, have not yet come to a focus, and only con- vergent rays come to a focus. This is called " hyper- opia " (h, Fig. 20). If the principal focus is in front of the retina, the eye is too long ; parallel rays focus in front of the retina, and only divergent rays focus on the retina. This condition is called " myopia " (m, Fig. 20). The Visual Angle and Visual Acuity. — Rays of hght, proceeding from the two extremes of an object into the eye, meet at the nodal point n (Fig. 21) before crossing and forming the inverted image on the retina, and the angle included at n is called the " visual angle." A n b is the visual angle of the object a b (Fig. 21). The size of the visual angle depends on the size of the object and its distance from the eye; thus, a' b', which 26 THE REFRACTION OF THE EYE is the same size as A b, subtends a larger angle, and the image is larger; and, again, a" b" subtending the same visual angle as A b would appear to be the same size, whereas it is much smaller. Fortunately, we do not gain our estimation of the size of objects by the visual angle alone; experience and comparisons with other objects of known size are brought into play, and enable us to correct any erroneous judgment. The smallest visual angle in which the standard eye can recognize an object is an angle of one minute, so that two points of light, such as two stars, separated by an angular interval of less than one minute would appear on the retina as only one point. Fig. 21. Test Types. — It is most important to have a standard measure for acuteness of vision, and Snellen has arranged test types on such a plan that each letter is made up of several parts, each of such a size that it subtends an angle of one minute vertically and horizontally, the whole letter subtending an angle of five minutes verticallj* and horizontally when read at the standard distance. Thus, in Fig. 22, the F is made out of twenty-five squares, each subtending an angle of one minute (the whole letter subtending an angle of five minutes) when read by the normal eye at 12 metres; and the l, which is constructed on the same plan, subtends the same angle when read by the normal eye at 6 metres. The numbers of the different-sized letters in Snellen's types represent the distance in metres at which the VISUAL ACUITY 27 standard eye can read them; in other words, at that distance they subtend an angle of five minutes. For instance, the largest type, d = 60 (see type at end of book), can be read by the normal eye at 60 metres, and it subtends the same angle as the type d = 24 read at 24 metres, and d =^ 6 read at 6 metres. The acuteness of vision is represented by a fraction which has for its numerator the distance in metres at which the type is read, and for its denominator the distance at which it ought to be read. The line d = 6 means that this type can be read by the normal eye at 6 metres, and if the patient under examination can read it at 6 metres, the fraction is | — that is, normal vision. If the patient cannot see a smaller type than d = 12 at 6 metres, his Fig, 22. vision == tV ; if D = 60 is the only letter that can be read at 6 metres, his vision = A — i-c-, one- tenth of the normal. If d = 60 cannot be read at 6 metres, the patient must be made to approach the type; if he can just read this letter at 2 metres, his vision is i~^', he has only one-thirtieth of normal vision. Although J is the standard of normal acuteness of vision, many eyes can see better — viz., |, or even J; i.e., such eyes can read at 6 metres type that the standard eye cannot read at a greater distance than 5 and 4 metres respectively. If the visual acuity is so lowered that the patient cannot see any letter at any distance, it can be measured by finding whether he can count fingers, and if so, at what distance, and failing this, by finding whether he 2S THE REFRACTION OP THE EYE can distinguish between black and white. If vision is even worse than this, we take him to the Hght and pass the hand in front of the eye — i.e., between the eye and the Hght ; if movement is recognized, we find out whether he can distinguish the direction of the movement. Finally, if he fails at all these tests, he should be taken into the dark room, and a strong beam of light should be directed on to the eye; if this is not perceived, vision = o; if it is perceived, we ascertain whether he has good projection, by reflecting the light on to the eye from different positions, and ascertaining whether he can tell whence the light is coming. Type for Near Vision. — As the " Schrift-scalen " of Professor Jaeger represent no standard, this type is being superseded by Snellen's, which is on the same principle as his distant type, the figure over the type signifying the greatest distance at which the normal eye can read it, and, of course, subtending an angle of five minutes at that distance. The sizes range from d = '5 to d = 4 (see type at end of book), j '2 (Jaeger) is the equivalent' of D 'S (Snellen). D = 0,5. JU to my boat, it was a very good one, and that he saw, and told me he would buy it of me for the ship's om and asked me what I would hare for it. D = 0,6. In this distress the mate of our vessel la3rs hold of the boat, and with the help of the rest of the men, they got her slung over the ship's side. D = 0,8. A little after noon I found the sea very calm, and the tide ebbed so far out, that I could come within a quarter of a mile of the ship ; D = l. In search of a place proper for this, I found a little plain on the side of a rising hill, whose front towards this little plain was steep as a house side. D = l,25. Then I took the pieces of cable which I had cut in the ship, and laid them in rows one upon another, within the circle between these two rows of stakes. D = l,5. When I had done this, I began to work my way into the rock, and bringing all the earth and stones, that I dug down, out through my tent. D=2,25. For in this way you may always damp our ardour. D = 3. I sai^T no one there. For the ensuiner D=60f200) D-36 (120) D=24 (80) D=I8(60) D-12 (40) DF O E D=9 (30) G L Z T O D«6 (20) L T R F P D-5 (16) A P O R F D CHAPTER III ACCOMMODATION When, with one eye closed, the other eye focuses a needle a metre from the eye, another needle placed half a metre from the eye will appear blurred. If A (Fig. 23) be the first needle, a clear image is formed by the exact focusing of it on the retina at a', Fig. 23. Fig. 24. while the image of B will be focused beyond the retina at b', the rays from B impinging on the retina in the form of a collection of diffusion circles. On the other hand, if the needle b be focused on the retina — i.e., if its image be clearly seen — the needle A 30 THE REFRACTION OF THE EYE will appear hazy or out of focus, because its image is focused in front of the retina, and, after crossing, the rays impinge on the retina as diffusion circles. Diffusion Circles. — Two points of light, if near one another and out of focus, appear as two diffusion circles overlapping each other if near enough (Fig. 24, a). As a line in focus may be considered to be an infinite number of points of light in focus, so a line out of focus consists of a series of overlapping diffusion circles (Fig. 24, b) which makes the line appear as a broad band, as Fig. 24, c. The further the rays focus from the retina, the larger will be the diffusion circles. In Fig. 25 both A and b are " out of focus," but b is more so than A, and consequently the diffusion circles formed by b Fig. 25. occup3 a larrer area; and, again, the larger the pupil the larger the area of diffusion circles, because as the pupil contracts it cuts off the outside rays. The alteration of the eye by its focusing mechanism is called accommodation. The photographer focuses by lengthening or shortening the distance between the back of the camera and the lens, but he could also focus by adding a convex or concave lens to that he is already using. It is in this latter way that the eye focuses; the eye cannot lengthen, but the lens can become more convex, which has the same result as adding a convex lens. In the normal standard eye, parallel rays, coming from a distance beyond 6 metres, are focused on the retina when the eye is at rest — i.e., when the apparatus of ACCOMMODATION 31 accommodation is not being used; but when the eye wishes to see clearly any object nearer than 6 metres, the lens must become more convex. After looking at the needle A, when we look at needle B and obtain a clear image, we are distinctly conscious of an effort, and the nearer we approach b to the eye the greater is the effort, till we reach a spot near the eye when no effort will produce a clear image, because the rays from the needle are too divergent to be focused on the retina. The nearest point to the eye at which the object is recognized as a perfectly clear image is called the near point "P." After looking at the needle close to the eye, and again looking at the distant needle, we are conscious of a relaxation of our efforts. How do we know that this focusing or accommodation is caused by an increased convexity of the lens ? The Mechanism of Accommodation. — If we take a patient into the dark room and hold a candle in front o the eye a little to one side, we shall see three images oi this candle in the eye. One, the brightest, is upright, the reflection coming from the anterior surface of the cornea; the second, duller, is also upright, and is the reflection from the anterior surface of the lens; and the third is inverted, duller, and smaller, and is from the posterior surface of the lens. The patient is told to look into distance, and the size and position of these images is noted, and then, carefully watching them, he is told to gaze at a near point. No change will be seen in the first image (proving the fallacy of the old theory that the cornea becomes more convex during accommodation), and little change in the third; but the middle image — viz., that from the anterior surface of the lens — becomes distinctly smaller and moves forward, showing that this surface has become more convex. In accommodation, then, the lens becomes larger in its antero-posterior diameter, and as it does not alter in volume, it becomes narrower in its equatorial dimensions. 32 THE REFRACTION OF THE EYE Fig. 26. — Diagrammatic Section of the Ciliary Region OF the Eye. C, Cornea; c S, Schlemm's canal; O s, era serrata; / p, pectinated ligament ; e F, Fontana's space ; T, tendinous ring ; m, merid- ional fibres; r, radiating fibres; c, circular fibres of the ciliary muscle; Z, zone of Zinn. The full lines indicate the lens, iris, and ciliary body at rest, and the dotted lines the same in a state of accommodation. (Reduced from Landolt.) ACCOMMODATIOK 33 We will now inquire how this change is brought about. According to Iwanoff, the ciliary muscle arises from a tendinous ring (Fig. 26, t) close to the insertion of the iris and Schlemm's canal {c S), at the posterior surface of the sclerotic, close to its junction with the cornea. The muscle then passes backwards, and may be divided into three parts: (i) The outermost part or meridional portion, passing into the posterior tendon (m), to be inserted into the choroid; (2) the radiating portion (r) ; and (3) the annular portion or circular muscle of Miiller (c), passing directly backwards and inwards respectively, to be inserted into an agglomeration of fibres called the " zone of Zinn " (Z). These fibres arise partly from the ciliary portion of the retina at the ora serrata (0 s) , and partly from the ciliary processes and the intervals between them, and they pass forwards and backwards, to be inserted into the anterior and posterior capsule of the lens. The annular muscle of Miiller is a sphincter, and does the principal work; hence it is always larger in hyperopia, because of the extra accommodation work necessary, and is badly developed in myopia. There are two theories as to the modus operandi of the ciliary muscle when accommodating. The old theory started by Helmholtz, and supported by Hess, is as follows : When the ciliary muscle contracts, it pulls forwards and inwards the capsule of the lens, the inward pull being specially brought about by the contraction of the circular muscle of Miiller. The contraction of the longi- tudinal fibres pulls forward the choroid and the portion of the ciliary body near it. By this process, they contend, the tension on the lens capsule is relaxed, and the lens, which has been in a state of compression, is allowed to assume a more convex form. The new theory advanced by Tscherning maintains 3 34 THE REFRACTION OF THE EYE that the action of the ciliary muscle is to increase the tension on the fibres of the suspensory ligament, and to alter the lens from a spherical to a hyperboloid form, and this theory is founded on the work of Thomas Young. According to this theory, the lens becomes more conical under accommodation, and the contraction of the pupil, that occurs at the same time, masks the increased aberration which results from the flattening of its periphery. The posterior surface of the lens does become slightly mere convex during accommodation, but it does not change its position, the increase of thickness of the lens being effected by the advance of the anterior surface. Tscherning's theory of accommodation is entirely supported clinically. Under the Helmholtz theory it is difficult to under- stand the possibility of meridional asymmetrical accommodation, and as difficult to believe in the possibility of obtaining 20 d of accommodative power which is frequently seen in young subjects. Lastly, the Helmholtz theory is totally against the idea of rest. Amplitude of Accommodation. — At rest, the eye is adapted for the most distant point it can see distinctly — ■ viz., its punctum remotum (R) ; while the greatest possible contraction of the ciliary muscle adapts the eye to the nearest point it can see distinctly — viz., its punctum proximum (P), which represents the greatest possible contraction. The force required to change the eye from R to P is called the " amplitude of accommodation," and is represented by the difference between the refraction of the eye at rest and the refraction when doing its utmost work. Donders represented the equation thus: III A~P~R or ' a = p-r. Where " a " equals the numbers of dioptres represented by the accommodation, " p " equals the numt^er of diop- ACCOMMODATION 35 tres represented by the eye when in a state of maximum refraction—/.^., when adapted for its nearest distinct point — and " r " equals the number of dioptres repre- sented by the eye at rest — i.e., when adopted for its furthest distinct point. In other words, " r " represents the static refraction of the eye. In emmetropia, as R is at " infinity, " r " can be ignored, .-.a = p. Therefore the ampHtude of accommodation is represented by the nearest distinct point ; if this is 9 cms. off, " a " = -f- = II — that is, the power of accommodation is equal to a lens of eleven dioptres. In myopia •' r " has a positive value. Take, for ex- ample, a person whose furthest distinct point with the eye at rest is 33 cms. (that is, a myope of 3), and sup- pose that his nearest distinct point is 7 cms. ; then a = p - r 100 100 = -7 5^ = 14-3 = II. In other words, 14 would represent his amplitude of accommodation if he were emmetropic; but being myopic to the extent of 3, we must subtract that, which leaves us 11 to represent his amplitude. In hyperopia, as we shall see later, " r " is negative; therefore the equation is a = p - (-^r) = p +r. Thus, an eye hyperopic to the extent of 5, having its near point at 25 cms. from the eye, has an amphtude of accommodation equal to a lens of 9. To see 25 cms. 36 THE REFRACTION OF THE EYE off, the eye requires an accommodation of 4 (-V/), but it has already expended 5 for distance, so that a = p - {- r) = 4 - (- 5) = 4+5 = 9- We thus see that to determine the ampHtude or range of accommodation we must find R and P. R is represented by the refraction of the eye at rest. P we find as follows : Take a tape graduated on one side in centimetres, and on the other in corresponding dioptres ; the zero-end of the tape is attached to the handle of a frame, into which may be introduced either a perforated diaphragm or a paper with fine print upon it, or threads or hairs ; or the ordinary near vision test card and separate measure may be used. The test object is brought towards the eye under examination (the other one being covered) until it begins to appear indistinct ; we then read off on the tape the distance of P from the eye, and the corresponding dioptres (p) representing the maximum refractive power of the eye. If from any cause, such as presbyopia or high hyperopia, the patient's near point is so far that the above tests cannot be employed, we place in front of the eye such a convex glass as will bring the punctum proximum (P) closer, and enable him to read d = .5 or see the words in the frame, such glass to be, of course, deducted afterwards. Thus, supposing a person with + 2 can bring the test object up to 25 cms. and no nearer, we read off on the other side of the tape 4, and we subtract the + 2 from this, which gives us p = 2 — that is, P is 50 cms. off. If he is an emmetropic presbyope, this represents his amplitude of accommodation. If he is hyperopic to the extent of 6, then a = 2 + 6 = 8. ACCOMMODATION 37 Or suppose the patient, being hyperopic and presbyopic, requires +5 to read at 33 cms., if his hyperopia = 6, then a = p + r = (3 - 5) + 6 = 4- We can also find the ampHtude of accommodaf ion by ascertaining the strongest concave glass the patient can " overcome." In emmet ropia such glass represents the amplitude of accommodation. In hyperopia the amount of hyperopia must be added, and in myopia the amount of myopia must be deducted. As an example, we find a patient who is hyperopic to the extent of 2 can still read J with - 4, but he cannot do so with - 5; thus his amplitude of accommodation is 4 + 2 = 6. It necessarily follows that to determine the amplitude of accommodation of an eye, its refraction must be accurately ascertained and the patient must wear the full correction of the error when the examination is made. The Region of Accommodation is quite different from the range, and gives very little idea of the work done. 1 —————— -^ WD a^ WD 00 R'lO'^'" P'-S'" i _ . lOD 2.0D a = too Fig. 27. Thus, the region of accommodation in an emmetropic eye, as Fig. 27 (i), is from infinity (R) to 10 cms. (P) in 38 THE REFRACTION OF THE EYE front of the eye, while in Fig. 27 (2), a myopic eye, it is only from 10 cms. (R) to 5 cms. (P) in front of the eye, and yet in each case the same amount of accommodation work is done, which is equal to a lens of 10. Accommodation is spoken of as absolute, binocular, and relative. Absolute accommodation is the full amount of accom- modation of one eye, the other being excluded. Binocular accommodation is the full amount of accom- modation which both eyes, converging, can exert together. Relative accommodation is the limit within which accommodation may be increased or decreased, the con- vergence remaining the same (see Convergence, page 54). CHAPTER IV CONVERGENCE Anatomical and Physiological Considerations. — The orbit con- tains the eyeball, the optic nerve, muscles, lachrymal gland vessels and nerves, and a quantity of fat. These structures are all firmly connected by a system of fasciae. Surrounding the eyeball, these fasciae are condensed in a fibrous capsule — the fascia bulbi or Tenon's capsule. This capsule consists of an external capsule and an internal capsule. It is perforated by the muscles just before their insertion into the globe, and its reflection unites with the cone of fascia surrounding the muscle ; prolonga- tions and thickenings of the orbital fasciae of these muscles are inserted into the margins of the orbit, and constitute the check ligaments.* The muscles which move the eye are six in number, and, with the exception of the inferior oblique, which arises from the anterior and inner part of the floor of the orbit, they all arise from the apex of the orbit. These muscles may be con- sidered as three pairs, each pair rotating the eye round a par- ticular axis. The four recti — viz., superior, inferior, internal, and external — -pass forwards, pierce Tenon's capsule, from which they receive a sheath, become tendinous, and are inserted into the sclerotic not far from the margin of the cornea, the most anterior insertion being that of the internal rectus, which is about 6 mm. from the margin of the cornea. The superior oblique passes forwards to the upper and inner angle of the orbit, where it becomes temporarily tendinous, and passes through a pulley, after which it becomes muscular again, and changes its direction, passing backwards and outwards through Tenon's capsule to be inserted (tendinously) into the sclerotic, at the back and upper part of the eye. The inferior oblique passes outwards and back- wards, underneath the inferior rectus, and then between the external rectus and the eye, to be inserted into the outer, pos- terior, and lower part of the eyeball, not very far from the entrance of the optic nerve. The axis of rotation of the internal and external recti is ver- tical, and that of the superior and inferior recti horizontal, with the inner extremity more forward than the outer (Fig. 28) . That * See Maddox, " Ocular Muscles," 1907, page 26, 39 40 THE REFRACTION OF THE EYE of the oblique muscles lies also in the horizontal plane, with its anterior extremity tilted outwards. The movements of the eyeball are produced by the association of various muscles, as shown below: I. Elevation. — The movement of the eye straight up is pro- duced by the superior rectus and inferior oblique, probably obi 6UP, Fig. 28. — Diagram of the Attachments of the Muscles OF the Left Eye and of their Axes of Rotation as seen from Above. (Michael Foster.) The attachments of the muscles are shown by the beginning of the thick lines, and the direction of the pull is shown by the arrows, v x represents the visual axis, and h h a line at right angles to it. The axis of rotation of the internal and external recti, being perpendicular to the plane of the paper, is not represented ; that of the other muscles is indicated by the broken lines. steadied by the internal and external recti, the superior rectus assisting in the elevation of the lid. 2. Depression. — Looking straight downwards is produced by the inferior rectus and the superior oblique, steadied by the lateral recti, the inferior rectus assisting in the depression of the lower lid. 3. Abduction. — The eye is turned straight;^ out by the external CONVERGENCE 41 rectus, assisted at the extremity of its action by the superior and inferior recti. 4. Adduction. — The eye is turned straight in by the internal rectus, assisted at the extremity of its action by the superior and inferior recti. When both eyes look to the right, we have contraction of the Fig. 29. — Diagram of the Connections of the Nuclei of the Lateral Recti Muscles. (After Ross.) C C, Cortex of right and left cerebral hemispheres; i, 2, fibres of the pyramidal tract uniting C, the cortex of the right hemisphere, and r' and er', the nuclei of the left internal and external rectus; i', 2', fibres of the pyramidal tract connecting the cortex of the left hemisphere with r and er, the nuclei of the right internal and external rectus muscles ; c, fibres of the corpus callosum uniting identical regions of the two hemispheres; c', commissural fibres connecting the spinal nucleus of the internal rectus of one eye with that of the external rectus of the opposite eye ; c", suggested com- missural fibres connecting the nuclei of the two internal recti. right external and left internal recti, and when they look to the left, contraction of the left external and right internal recti. Movement of the eyes up and in is produced by i and 4 — viz., superior rectus, inferior oblique, and internal rectus, movement down and out by 2 and 3, and so on. 42 THE REFRACTION OF THE EYE The external rectus is supplied by the sixth nerve, the superior oblique by the fourth, and the others by the third. Convergence of the eyes is produced by the associated move- ments of both the internal recti. The nuclei {r r', Fig. 29) of that part of the third nerve which supplies these muscles may be connected by fibres {c"), illustrating the principle that there is bilateral association of the nerve nuclei of muscles bilaterally associated in their action (Broadbent). This explains the con- vergence of a covered eye. A. Graefe says that one of the factors causing the covered eye to converge is a " Convergenzgefiihl," or, as Hansen Grut expresses it, a " Nahebewusstsein " — a con- sciousness of nearness. Landolt denies this, and asserts that the excluded eye fixes correctly through the connection between accommodation and convergence alone. It is important to remember that when a stimulus passes pri- marily to the nucleus of the internal rectus, it is associated with the same muscle of the opposite side, and convergence takes place; whereas the conjugate movements of the eyes to the right or left are produced by stimuli passing primarily to the nucleus of the external rectus, which nucleus is connected with the nucleus of the internal rectus of the opposite side (Fig. 29). We may have both these stimuli occurring at the same time — viz., primary stimulus to the internal recti to converge, and to the external rectus of one side associated with the internal rectus of the other side — to produce lateral movements of the eyes. The oculo-motor centre (Fig. 30, o.m.c.) is situated beneath the floor of the aqueduct of Sylvius. It includes (i) the accommoda- tion centre (a), lying most anteriorly near the middle line, and (2) the pupil constrictor centre (p) . The nucleus of the internal rectus (i.R.) lies further back. Filaments pass along the third or oculo-motor nerve from these centres to the ciliary muscle, the sphincter of the iris and the internal rectus, and are so associated that contraction of the ciliary muscles for accommodation, of the pupils, and of the internal recti for convergence, are all three associated in their actions. One impulse — viz., a psychical impression, a wish to look at a near object — passes from the motor centre in the cortex of the brain to these nuclei, and the result of this one impulse is the united action of these different muscles; the action is not always simultaneous, for convergence often lags behind accommodation (see page 56). Many people can voluntarily squint inwards, but they will be found to accommodate for a near point at the same time; some few can, however, do so without accommodating, and in such cases the psychical impression probably passes straight to the nucleus of the rectus internus by vs' (Fig. 30). Binocular Vision. — Man has binocular vision — that is, the image from an object falls upon the retina of each eye simultaneously, and in normal binocular vision on exactly the same region of the retina; for if the images BINOCULAR VISION 43 did not overlap, two images would be seen, and so-called " double vision " would be the result. The absence of double vision does not necessarily imply the presence of normal binocular vision with fusion of the two images, for one eye may be blind or its image suppressed by the brain (monocular vision). Many people use one eye only, for years, without discovering the fault. The best and quickest test for determining whether binocular Fig. 30. — Scheme showing the Oculo-Motor Centre and Some of its Connections. (Adapted from Erb.) P5, Psychical impression (the wish to accommodate being the stimulus) ; ps', psychical impression for voluntary converg- ing strabismus; a, accommodation centre with motor nerve to ciliary muscle, and p, centre for the sphincter of the iris with motor nerve, the two forming the oculo -motor centre, o.M.c; I.R., internal rectus centre, with motor nerve to internal rectus muscle; o.n., optic nerve from retina to o.c, optic centre, and connected with p, the papillary centre; X is the seat of the lesion causing reflex pupillary immobility. vision is present or not, is Snellen's apparatus, described on page 153.* Whereas, then, in discussing accommodation we con- sidered the eye simply as an optical apparatus, now we * Any of th3 tests for latent deviation, mentioned later, may also be employed. 44 THE REFRACTION OF THE EYE must consider the two eyes together as forming one whole, and on their proper associated movements must depend perfect binocular vision. If binocular vision be impossible, through some great defect of the optical apparatus or the muscles, no attempt will be made to produce it, and no strain will follow. On the other hand, apparently normal binocular vision may exist; but to produce this, a demand in excess of the power is put upon a muscle or a set of muscles, and the result is strain, either producing or tending to produce the symptoms of muscle strain. The Relation of the Two Eyes to Each Other in Normal Distant Vision. — Michael Foster says that the primary position of the eyes is " that which is assumed when, with the head erect and vertical, we look straight forwards to the distant horizon; the visual axes of the two eyes are then parallel to each other and to the median plane " — that is, in ideal binocular distant vision, the eyes being at rest and all the muscles in equilibrium with respect to each other, the visual axes are parallel. Test for Latent Deviation of the Eyes for Distance. — If a person with normal vision be directed to look at an object in the distance, and one eye be covered for twenty or thirty seconds, if there be any latent deviation it becomes as a rule manifest, and on uncovering the eye there will be diplopia for a brief space of time, the covered eye moving (in order to fuse the two images) — in, if there be latent divergence, and out, if convergence. A more accurate method of conducting this test is to destroy the possibility of binocular vision — i.e., fusion — by means of a prism, with its base up, placed before one eye, or, better still, by the apparatus suggested by'^Maddox, called the " glass rod test "; by which means we can not only at once detect concealed deviation, but can also measure the amount. The Maddox Test. — A glass rod (Fig. 31, a) is arranged O ON CO N O Csi :j5 4<<^ CM in o 00 O GL XI T J) o - fi <=a <=a <=> % x: o c £ o o « uJ ** 00 J ^ tO I o "I 05 ^ 5 ^© MADDOX ROD TEST 47 in a metal disc, which fits into the trial frame.* If this rod be placed before one eye, the other eye remaining uncovered, and a small flame be looked at from a distance of more than 4 metres, the eye in front of which the rod is placed sees the flame merely as a streak of light, and, the images of the tv/o eyes being so dissimilar, there is no desire on the part of the brain to fuse them; conse- quently the two eyes assume their position of rest. If the rod be placed horizontally in front of the right eye, there is a vertical streak of light, and if this streak coincide with the image of the candle seen by the left eye, the visual axes are parallel (orthophoria) ; but if it Fig. 31. do not, then when the streak is on the same side as the rod (in this case the right side) there is latent convergence (homonymous diplopia), when on the other side there is latent divergence (crossed diplopia). If a scale be used as suggested by Maddox (see plate), the number on the scale through which the streak of light passes records the amount of diplopia ; or prisms may be put up in front of the other eye, or the rotary prism used (see page 7). The weakest prism that causes the two images to coin- cide records the amount of diplopia. The Maddox * Fig. 31, b, represents a simple form of this apparatus which can be made by uniting four or five glass rods with seaUng-wax. This must be held before the eye, as it does not fit into a trial frame. 4^ THE REFRACTION OE THE EYE distance scale is marked for 5 metres, and roughly every 3j° represents a metre angle. To be quite exact, every 3° 40' or 32 cms. is a metre angle. If the scale be used at 4 metres, then every 25*5 cms. represents a metre angle. If we wish to measure vertical deviations, we turn the rod vertically, and thus obtain a horizontal streak of light. If this streak pass through the middle of the flame there is no vertical deviation, but if it be above or below there is hyperphoria of that eye which sees the lower image — i.e., if the streak of light be lower there is a tendency to upward deviation (latent hyperphoria) of the eye in front of which the rod is placed. To measure the vertical deviation we must use a scale, similar to that in the Plate, placed vertically. Before this test is applied any refractive defect must be corrected. By making a large number of examina- tions by this method, we can easily prove the correctness of the statement, ihs^., for all practical purposes, the visual axes of the two eyes in normal binocular vision are parallel. So much for what is called the " static equilibrium " of the ocular muscles. Now we proceed to examine the dynamic condition — that is, the relation of the muscles in binocular near vision; in other words, during con- vergence. Convergence " is the direction that the eyes must give to their lines of fixation in order that they may be simultaneously directed toward the point of fixation." When both eyes are fixing an object 6 metres (or more) distant, they are parallel, and C (which represents con- vergence) = o; when the eyes simultaneously fix an object I metre off in the median line, both internal recti contract and the eyes converge ; convergence is then said to be I metre angle, C = i m.a. This metre angle is the unit of convergence. If the eyes converge to a point 50 cms. off, then C = -Vxr = 2 m.a.; if 20 cms. off, C = ^■^^- = 5 m.a.; and if the object be 3 metres off. AMPLITUDE OF CONVERGENCE 49 C = i = *33 m.a. In Fig. 32, E e is the base line con- necting the two eyes, and E r' and e r' are two lines at right angles to this base, and therefore parallel. If the two eyes look at a point R, the angle r' e r is the " metre Fig. 32. (After Nagel and Landolt.) angle," or, better still, as r' e R is equal to E R p, the latter may be called the " metre angle." To Nagel belongs the credit of devising this method of measuring the amount of convergence. The metre angle (or " Meter- 4 50 THE REFRACTION OF THE EYE winkel," as he calls it) of convergence corresponds to the dioptre of accommodation. Thus, an emmetfope who is fixing binocularly a point i metre off is using I dioptre of accommodation, and convergence is i m.a. ; and if the point be 25 cms. off, he is using 4 dioptres of accommodation, and his amount of convergence is -W- = 4 metre angles, and so on. Amplitude of Convergence. — ^We again use Bonders' formula, and, expressing the equation in metre angles, c a == c p — c r, where "c a" represents the amplitude, "c p" the maximum, and " c r " the minimum, of convergence. When R is at finite distance (Fig. 32), we have ca^cp- cr; that is, the amplitude of convergence is the amount of convergence required to direct the visual axes of the two eyes simultaneously to the point P, starting from the binocular distant point R. When the visual axes are parallel, " r " can be ignored, and the equation stands — c a = c p. When the visual axes diverge, E r", e r", the axes will, if prolonged backwards, meet at a point - R, which is negative; the equation will then be — ca = cp- (-cr) = cp+cr. We distinguish the equation from that used in accommodation by prefixing or affixing a "c," thus : ca=:cp-cr, a": = pc-rc. The Punctum Remotum of Convergence. — Just as the punctum remotum of accommodation is the expression of the refraction of the eye when completely at rest, so the punctum remotum of convergence is the expression of the THE NEAR POINT 51 position of the eyes when at rest — that is, when the impulse to fusion brought about by binocular vision is removed — so that to find R we must find the latent position of the eyes for distance. This we do by the Maddox test, and the number of metre angles read off on the scale gives us " c r." When there is no latent deviation " c r " = o, when there is latent divergence " c r " is negative, and when latent convergence it is positive. To find " c p," the maximum of convergence, we direct the person to fix binocularly a small test object held, say, J metre from the eyes, equidistant between them and on the horizontal plane of the eyes. This may be a fine hair or wire stretched vertically in a frame, or it may be a luminous slit, as in Landolt's ophthalmo- dynamometer (Fig. 33); when the object is approached to such a distance that the test line appears double, we measure off the distance in centimetres, and divide this into 100, which gives us the number of metre angles that " p " is equal to. Suppose " c P " to be 10 cms., " c p " = "W = 10 m.a., and if c R be at " infinity," a = 10; but if there be latent divergence, say of i m.a., r = — I m.a., and a = 10 - (- i) = 10 + I = II m.a. In this test we must be careful to distinguish between mere haziness of the test object, which is the result of its being within the patient's accommodation near point, and doubling of it, because the near point of convergence is often nearer than that of accommodation. We should, therefore, always first ascertain the accommodation near point in each eye. It is generally considered that the normal amplitude of convergence is 10*5 m.a., although it may be 15 or even 17 m.a. 52 THE REFRACTION OF THE EYE The Relative Range of Accommodation and Convergence.— If the latent position of the eyes be tested, not only during the fixation of distant objects and of objects at a reading distance, but also for intermediate distances of fixation, it will be found that, as a rule, there is quite a gradual lagging of the non-fixing Fig. 33. — Landolt's Ophthalmo-Dynamometer. This apparatus rests on a candle, which, when lighted, causes the slit in the cylinder to appear as a luminous line. eye behind the fixing one : a gradual increase of latent divergence. This divergence is greater in myopia and less in hyperopia than in emmetropia. Fig. 34 represents the average curve of relative latent deviation in emmetropia. According to this figure, we see that with parallelism, or a condition almost approaching to CONVERGENCE 53 parallelism for distance, there is ^ metre angle of divergence on accommodating for ^ metre, and a whole metre angle for ^ metre accommodation — that is, that whereas, with both eyes fixing, on accommodating for J metre, 4 d of accommodation is used, and both eyes converge to a point using 4 m.a. of convergence, when the possibility of fusion is removed both eyes only con- verge to a point ^ metre off, using 3 m.a. of convergence. This is no proof of the existence of " insufficiency " of con- vergence ; all it shows is that the intimate relation between accom- modation and convergence is not absolute. All the more, then, should we expect to get latent divergence for near points when there is initial latent divergence for distance. When there is initial latent divergence for distance, the " lagging " of the convergence behind the accommodation for near points is -OC9, ID 22) 3D 4'JO m ^^ V -■is ?,m \ N K s N N S .Ut \ N \ 4-M i-J \ Fig. 34. (After Berry.) more marked than when the position of the eyes is parallelism, and this produces a " convergence insufficiency." We can ascertain the presence of latent deviation in near vision by the Maddox test. A scale (see plate, page 45) is held \ metre from the eyes, and a prism of 12°, base up, is held before the right eye. The scale consists of a horizontal line with fine print below it, in the centre of which is an arrow pointing upwards. The line is divided in degrees which are marked by figures, black on the right of the arrow, red on the left. Every 3^° from the arrow is marked by a small cross representing i m.a. The prism causes two lines and two arrows to be seen, and the patient is instructed to fix the upper arrow, or, better, the fine print just below it. When there is no latent deviation the two arrows are in a vertical line. When the lower arrow points to the left (red side) of the upper arrow there is latent divergence, and when it 54 THE REFRACTION OF THE EYE points to the right (black side) there is latent convergence for ^ metre, the amount of deviation being read otf on the scale. Graefe's " dot and line " test is inferior to the foregoing, as it does not record the amount of the defect. Maddox maintains as a result of his experiments that in near binocular vision there is always relative divergence — that is, con- vergence always lags behind accommodation. This convergence is composed of three factors: (i) " initial convergence " (this, of course, exists only when there is latent convergence) due to the relaxation of the external recti which are maintaining paral- lelism {p p, Fig. 35), and the eyes assuming their position of rest i i ; (2) accommodative convergence — i.e., the amount of con- vergence which is called forth by the accommodative effort which brings the axes to a a ; and, lastly, (3) the " fusion supple- ment," which is the result of the desire for single vision, and brings the axes to 0. This " fusion supplement " is demon- FiG. 35. (Maddox.) strated by holding a pen midway before the eyes of a patient at the distance of the convergence near point, and telling him to fix the tip of the pen; if now one eye is covered, this covered eye will markedly turn out, and, on uncovering, the patient will for a moment have diplopia, the eye making an incursion to recover binocular vision. The amount of the excursion on covering, or incursion on uncovering, represents the fusion supplement which the demand for binocular vision calls forth. This experiment can be made on most people, and is no proof of " insufficiency " of convergence. Although accommodation and convergence are intimately connected, this connection is not absolute. We can prove this experimentally by altering our accommodation without changing our convergence, as in looking at an object with both eyes before which we place weak convex and concave glasses, and also by altering our convergence without changing our accommodation CONVERGENCE 55 by placing before the eyes weak prisms, base in or out. The amount of dissociation between the accommodative and con- vergence efforts is limited, and varies with and in the individual ; it can be increased by practice, and it differs for varying degrees of accommodation and convergence. Fig. 36 shows the relative amount of accommodation that can be used with different degrees of convergence in an emmetrope aged 15. The horizontal figures record the degrees of convergence in metre angles, and the vertical figures record the degrees of accommodation in dioptres. The diagonal d d represents the /5 f8 /7 f€ fS /# /J /? // /o. 9 a 7 6 S 4- 5 2 / O — 1 — — 1 \ / !' y 1/ / / / / / / - - / h"^ / ?... ^ f_ 7^ — ] -A y / ^ ^ ^y A / ^ ^ y l/ y' y y^ / ^ ■ / / ^ "^ z / ^z V / 7 . / J^^'r _.J / 2 5 4-6 6 7 8 3 fO /t tZ /5 M$- /S ^ /7 m /9 2(i Fig. 36. convergence, starting from zero — i.e., " infinity " — and stopping at 5 cms. (20 metre angles). The vertical divisions between the upper curved line p p and the diagonal, represent the amount of maximum or positive part of accommodation, ascertained by the strongest concave glass that can be borne without prejudice to binocular and distinct vision, for any given point of convergence, and those between the diagonal and the lower curved line y v represent the amount of minimum or negative part of accommo- dation, ascertained by the strongest convex glass. Thus, take convergence for 6 m.a.: above we have 2*5 dioptres of positive accommodation, and below 3 of negative accommodation — that 56 THE REFRACTION OF THE EYE is, the relative amplitude of accommodation for 6 m.a. of con- vergence is 5*5 in this individual. It will be seen that when the convergence has reached lo m.a. the whole of the range of accom- modation is negative. Accommodation remaining fixed, we can estimate the amount of relative convergence by means of prisms ; the strongest prism, base out, that can be borne with fusion represents the positive, and base in, the negative part, of the amplitude of convergence, and, as Landolt has pointed out, we find that Fig. 36 can be made use of to represent this. The diagonal d d represents the accom- modation starting with eyes adapted for infinite distance; the positive portion of the relative range of convergence is on the right of the diagonal, and is represented by the horizontal divisions between d d and r r, and the negative portion is on the left. Thus for accommodation at 25 cms. — i.e., 4 dioptres — we see that we have 3 m.a. on the right and 3 '5 m.a. on the left — that is, while maintaining the same amount of accommodation, an adducting prism producing a deviation of 3 m.a., and an abducting prism requiring a diminution of 3-5 m.a., can be over- come by the eyes. Thus for 4 dioptres of accommodative power in this individual, an amplitude of convergence of 6-5 m.a. exists. It is fortunate for the ametrope that this dissociation between accommodation and convergence is possible. A hyperope of 3 D who fixes an object binocularly 7,^ cms. off must use an addi- tional 3 of accommodation — that is, he must use 6 altogether — but he will only require to converge to 3 m.a. If the association between accommodation and convergence were absolute, he would either have to converge to 6 m.a., and consequently squint, and thus lose binocular vision, or he could keep binocular vision on the condition that he did not accommodate for this near point; in other words, he has the choice between distinct vision and binocular vision — he cannot have both. Many hyperopes dissociate these two efforts, and can by practice and " nerve education " accommodate in excess of their convergence (see page 90). The difference in the power to dissociate these two efforts is one of the explanations of the well-known fact, that of two individuals having the same refractive defect, one will squint and the other not. The same necessity for dissociation between convergence and accommodation occurs in myopia. A myope of 3 d can see an object 33 cms. off without any accommodation, but must con- verge to the extent of 3 m.a. Thus he uses his convergence in excess of his accommodation. Donders stated that accommodation can only be maintained for a distance when, in reference to the negative, the positive part of the relative range of accommodation is tolerably great, and that the relative range of accommodation in ametropic eyes is quite different from that of emmetropic eyes, but that it tends to approach the latter when the correction of the error has been worn for some time. CHAPTER V THE OPHTHALMOSCOPE To understand the action of the ophthalmoscope, the following facts connected with the Optics of Reflection should be remembered : I. When light falls on a plane mirror (Fig. 37, A b), the angle of incidence is equal to the angle of reflection. The incident ray f d makes with the perpendicular p D an angle f d p, and the reflected ray D E also makes Fig. 37. an angle E d p, and these two angles are equal to one another. Both incident and reflected rays are in the same plane, which is perpendicular to the mirror. 2. "When parallel rays of light (Fig. 38, A b and c d) fall on a concave mirror, they are reflected to a focus (f) in front of the mirror, and this principal focus is midway 51 58 THE REFRACTION OF THE EYE between the mirror and the centre of curvature of the mirror (o) and on the principal axis. 3. Rays of light coming from a point near the mirror, but beyond its centre, as at L (Fig. 38), come to a focus (/) between the centre and the principal focus, and the two points are conjugate foci. The Ophthalmoscope. If by some contrivance we can manage to send rays of light from a spot in front of our eye into another eye, we shall get some of those rays returning to our eye after Fig. 38. being reflected from the retina of the observed eye, if the media be clear, and the pupil of the observed eye, instead of appearing black, will appear red. This can be done in the simplest manner by a piece of glass plate. If Ohd is the observed eye, and Ohr the observer's eye (Fig. 39), in front of which is inclined a glass plate G l, the rays of light passing from l are reflected partly at g l into Ohd, return along the same path, passing through the plate, and enter the observer's eye. As only a few rays find their way to the observer's eye, the light is very feeble. This was the principle of Helmholtz's first ophthalmoscope, and he improved THE OPHTHALMOSCOPE 59 it by placing together several glass plates, and thus increasing the luminosity. If for these glass plates a mirror with a central hole is substituted, more rays still will pass into the eye; and these rays returning, more will pass through the hole in the mirror into the ob- server's eye, and a brighter image of the fundus will be seen. A still greater improvement results if we use a concave mirror, as the light is more concentrated. Such is the simple ophthalmoscope — viz., a mirror with a central sight-hole supported on a handle. The ophthalmoscope has been further improved by adding an arrangement of lenses of different strength, which can be turned into position in front of the sight- hole, so that if the eyes of the observer or observed are ametropic, a clear image of the fundus can be obtained by the correcting lens. The Qualities of a Good Refraction Ophthalmcscope. — The mirror should be concave, with a focus of from 14 to 17 cms. It should be oblique, and capable of being turned round so that it can be used for either eye. This obliquity of the mirror enables the observer to approach very near the observed eye without cutting off any of the light, and also permits the correcting glass, when used, to be in a position parallel to the vertical plane of the eye. When the oblique mirror is not required, as in the " in- direct " method and in the " shadow test," a " straight " 6o THE REFRACTION OF THE EYE mirror should be substituted for it. This can be done by changing the mirrors, or, better still, by an arrangement like the nosepiece of a microscope, to which both mirrors are attached, either of them being turned into position as required. A further improvement can be made by the " straight " mirror being plane on one side and concave on the other, and fixed with a spring hinge, so that either side of the mirror can be used as desired. The mirror should be perforated; imperforate mirrors (with a central hole in the silvering) are not so good, as the glass reflects some of the light that should enter the observer's Fig. 40. — Morton's Ophthalmoscope. The rotating wheel is made to serve as a pupiliometer, the discs being numbered from i to 8 mm. eye. The aperture in the mirror should not be too small, otherwise too little light will reach the eye of the ob- server; its diameter should be about 3 mm. anteriorly (the glass side), and somewhat wider behind, and the sides of the tube should be well blackened. The cor- recting lenses of the ophthalmoscope should not be too small; they should have a diameter of not less than 5 mm. There should not be too many of them, and never more than two superimposed. The best plan is to have the glasses ordinarily used arranged round the rim of one disc, and those less used arranged, either on another disc, or on a movable quadrant. The number THE OPHTHALMOSCOPE 6l of ophthalmoscopes on the market is large, but the best, and certainly the most popular, is Morton's (Fig. 40). Fig. 41. — Electric Ophthalmoscope. The Electric Ophthalmoscope (Fig. 41).— This instru- ment has completely revolutionized direct ophthalmo- 62 THE REFRACTION OF THE EYE scopy. The management of the Ught, when using the old-fashioned instrument, has always been a trouble to the beginner or the practitioner who only occasionally uses the instrument; this trouble is removed in the electric ophthalmoscope because the Ught is concealed in a tube near the mirror and is fed by a battery in the handle. But even for the oculist who is an adept at using the old instrument the advantages of the electric ophthalmoscope are very marked. As the light has not to be considered, the instrument can be brought so near the eye that it can almost touch the cornea, and consequently a dark room is not necessary, as, by turn- ing the patient with his back to the window, we can easily examine the whole of the fundus, and, moreover, the patient can be examined in any position. A further improvement is obtained by using a Marple Mirror. This mirror, instead of having a central Fig. 42. — The Marple Mirror. opening, has a U-shaped one (see Fig. 42), with the result that there is little or no reflex from the centre of the cornea, and it is often quite possible to examine the macula through a pin-point pupil. With this instrument and a combined concave and plane mirror (Fig. 50, page 83), and a focusing lens, no further apparatus is required, and the old-fashioned refraction ophthalmoscope can be dispensed with. The convex lens or focus glass used in the " indirect " method should have a focus of about 8 cms. — i.e., be about 13 D — and should have a diameter of about 6 cms. The lens usually supplied with ophthalmoscopes is much too small. The glass should be kept clean and free from scratches. THE OPHTHALMOSCOPE 63 The Different Methods of Examining the Eye with the Ophthalmoscope. 1. The indirect method. 2. The direct method. 3. The " shadow test," or retinoscopy. The patient should be in a darkened room. The light used should be on an adjustable bracket if possible; any kind of light will do if it has a broad, steady, white flame, but the electric light in a ground- glass globe is the best, as it gives off less heat. Before commencing the ophthalmoscopic examination, the eye should be thoroughly examined by the oblique or focal illumination. For this purpose put the light on a level with the patient's eye, on the same side as the eye to be examined, and about 12-15 inches from it, and with the focus-glass throw a luminous spot on the cornea. By moving the lens about, the whole surface of the cornea, the anterior chamber, iris, and anterior surface of the crystalline lens, can be examined. This examination is further aided by viewing the illuminated spot through a strong magnifying-glass, and one of the best is Voigtlaender's. This preliminary examination gives valuable information as to the translucency of the media, etc. I. The Indirect Method. — Place the light close to the patient's head and a little behind, so that no light can reach the eye to be examined directly. Use the " straight " concave mirror, holding it about 15 inches from the eye, thus lighting up the fundus, and making the pupil appear red (if the media are transparent), and detecting opacities of the cornea, lens, and vitreous (the latter are best seen with a plane mirror and faint light) . Still using the same mirror, put up the focus-glass, holding it by the left index-finger and thumb, and 64 THE REFRACTION OF THE EYE steadying it by resting the remaining fingers of the left hand on the patient's brow. By this means an inverted image of the fundus is seen. This is called the " indirect method." The observer recognizes that the picture is inverted by slightly moving his head or the focus-glass, and finding that the image moves in the opposite direction. The manner in which this inverted image is formed is shown by the following figures. Fig. 43. (After Fick.) The focus-glass held in front of the eye makes the eye myopic, and, according to the refraction of the eye, this inverted image will be nearer or further from the lens. When the observed eye is emmetropic, the rays coming from the eye (Fig. 43, e) are parallel, and focus at the principal focus of the focus-glass; and, more- over, as the rays emerging from the eye are parallel, it does not matter where the focus-glass is placed ; nearer THE OPHTHALMOSCOPE 65 or further from the eye, the image must necessarily always be the same size. In hyperopia (Fig. 43, h) the rays emerging from the eye are divergent, and, passing through the focus- glass, they form a larger image than in emmetropia, and this image is further from the lens in front of its principal focus; on withdrawing the lens from the eye, the image is formed on the other side of the lens, nearer and smaller. In high hyperopia the image is so far in front of the focus-glass that the observer will have either to move back, or to accommodate, in order to get a distinct view of the inverted image. If with the mirror alone, still held at some distance from the eye, we can recognize fundus details nol in- verted — that is, in their true position — we are dealing with high hyperopia. In myopia (Fig. 43, m) the rays emerging from the eye are convergent, and form an inverted aerial image in front of the eye, and the focus-glass shows this image smaller than in emmetropia, and nearer to the lens — in fact, within its principal focus; on withdraw- ing the lens the inverted image becomes larger. In high myopia no focus-glass is required to see the fundus, as the rays proceeding from the eye are so convergent that they come to a focus at the punctum remotum and form an inverted image. In astigmatism the disc may appear oval, and the shape will alter as the focus-glass is withdrawn, accord- ing to the refraction of the different meridians. The advantages of the indirect method are — 1. The examiner is further from the patient than in the direct method (a distinct advantage in dealing with certain patients). 2. A general " bird's-eye " view of the fundus is obtained. 3. No correcting glasses are needed in the ophthal-' 66 THE REFRACTION OE THE EYE moscope; thus, a simple concave mirror with a central hole is sufficient. 4. It is sometimes easier to see the fundus when the pupil is small. In looking at the right disc, the patient should be directed to look past the observer's right ear, for the disc is on the nasal side of the posterior pole of the eye, and on looking at the left disc he should look past the left ear. It is important to remember that the patient must look with the eye not being examined ; therefore, in examining the left eye by this method, take care not to obscure the right eye with the hand that is holding the focus-glass. 2. The Direct Method.— As already stated above, this method is much simplified by the use of the electric ophthalmoscope. If the old-fashioned instrument is used the light must be brought quite close to the patient's head and slightly behind, and on the same side as the eye to be examined. The observer sits (or stands in a stooping position) close to the patient, and on the same side as the eye to be examined, using his right eye for the patient's right eye, and his left for the patient's left. Use the refraction ophthalmoscope (without the focus-glass) and the oblique concave mirror. Hold- ing the ophthalmoscope a few inches from the eye, reflect the light on to the eye and observe the red pupillary reflex through the central hole of the mirror, and then, without allowing the light to leave the eye, approach the eye as near as possible; in fact, the ob- server's forehead ought to touch the patient's forehead. The fault that most beginners make is not getting near enough to the eye. The observer must not ac- commodate, but look, as if trying to see through the patient's head, into distance. If the observer or patient have an error of refraction, the wheel of the ophthalmoscope must be turned until the suitable glass is found. To see the macula, the patient should THE OPHTHALMOSCOPE b'/ be told to look horizontally, in front; if the disc is to be examined, he should look slightly to the nasal side. Fig. 44. — Examination of the Erect Image when the Eye EXAMINED IS HyPEROPIC, EMMETROPIC, OR MyOPIC. (HaAB, after Fick.) In each figure three rays are shown emanating from a luminous point on the eye-ground. In hyperopia they diverge after leaving the eye, in emmetropia they are parallel, in myopia they converge : /, the posterior focus ; H, principal plane of the dioptric system of the examined eye ; Be., observer. The ophthalmoscope is not shown. Only a small portion of the fundus can be seen at one time, but this portion is considerably magnified 68 THE REFRACTION OF THE EYE (about 15 diameters), and consequently the minutest details are visible. By this method the refraction of an eye can be esti- mated, which as an objective method has, of course, a distinct advantage. The first duty of the observer — and most beginners find this very difficult — is to relax his accommodation. The person whose eye is being examined must also relax his accommodation, which can be done by direct- ing him to look at some object 5 or 6 metres off with the other eye, or, better, by paralyzing the ciliary muscle with a cycloplegic. If both the observer's and obr Fig. 45. the observed eye are emmetropic, all the details of the fundus will be clearly seen (Fig. 44, B). We can easily understand this, when we remember that rays passing from the mirror to the back of the eye that is being examined, are reflected as parallel rays if the eye be not accommodating and be emmetropic, and that parallel rays must be focused on the fundus of the observing eye if it also be emmetropic, and its accom- modation be relaxed (Fig. 45). If, on the other hand, the observer's eye under these circumstances accom- modate, the image, instead of being sharp, is blurred. It is not only necessary to observe these rules in order to get a clear picture of the fundus, but it is of para- THE OPHTHALMOSCOPE 69 mount importance if we wish to estimate correctly , the refraction of the eye we are examining. For this reason it is important that the observer should esti- mate his own refraction, and, if there be any error, correct it. If the observer be myopic, the fundus will be indis- tinct, just as is the case wuth all distant objects, for the rays coming from the observed ieye are parallel — that is, as if coming from a distant object. In order, therefore, to obtain a clear view of the fundus, the myope must use a concave glass, and the weakest concave glass he can see distinctly with will be the measure of his myopia, if his accommodation be relaxed . A hyperopic observer is in a somewhat better posi- tion, because he can see the fundus if he accommo- dates; but as he must relax his accommodation in order to estimate the refraction of the eye he is exam- ining, he must first find his own refractive defect and correct it. Unless he had his defect properly corrected in early youth, he has become so accustomed to use his accommodation that it will be most difficult-^almost impossible — for him to relax it, and the probability is that, although the convex glass he uses corrects his defect, he nevertheless cannot help using some accom- modation, and will thus overcorrect himself, render- ing himself myopic. It necessarily follows, therefore, that it is most difficult for a hyperope to estimate the refraction of an eye correctly by this method. He should use some other method, such as the " shadow test," which will be explained later. We have supposed up to now that the observed eye was emmetropic. We will proceed to examine the conditions that exist when the observed eye is myopic or hyperopic. Examination and Measurement of a Myopic Eye by the Direct Method. — The retina of a myopic eye is at the conjugate focus of an object situated at finite 7& THE REFRACTION OF THE EYE distance (see page 99); consequently rays proceeding from the retina of a myopic eye are focused at the far point when the accommodation is relaxed (Fig. 44, C). As this far point is at finite distance — in fact, near the eye — the rays are convergent; consequently they will not be focused on the retina of an emmetropic eye unless they are made parallel by using a suitable con- cave glass in the ophthalmoscope. This is done by turning the wheel of the instrument and bringing con- cave glasses before the opening, and the weakest con- cave glass required is the measure of refraction (if the accommodation of both the observer's and the ob- served eye is relaxed). The observer will, of course, be able, by using his accommodation, to see the fundus with a stronger concave glass than is required, but it will not then be the measure of the myopia. If the observer be a myope, and his myopia be not corrected with glasses, to ascertain the refraction of the observed eye he must deduct from the concave glass he requires the amount of his own myopia. When, for instance, the weakest concave he requires to see clearly the retina of the myopic eye is -5, and he himself is -2, then the observed eye is — 3. When he is hyperopic, he must add the amount of his hyperopia — i.e., when he has hyperopia of 2, and the weakest glass he re- quires is -5, the amount of myopia in the observed eye is - 7. The Examination and Measurement of a Hyperopic Eye by the Direct Method (Fig. 44, A). — The rays emerg- ing from a hyperopic eye are divergent (see page 85), and as they must be made parallel for an emmetropic ob- server if he wish to see the fundus clearly, a convex glass, representing the amount of hyperopia, must be turned into position. If the patient have hyperopia of 4, then + 4 must be used. The fundus could be seen clearly without a glass, by accommodation; but THE OPHTHALMOSCOPE 7 1 then, as it would be impossible to measure the amount of accommodation used, so would it be impossible to estimate the amount of hyperopia in the observed eye. A hyperope who is examining a hyperopic eye with the ophthalmoscope must deduct the amount of his own hyperopia from the strongest lens he requires to see the fundus with; i.e., if he be hyperopic to the extent of 3, and the strongest convex glass he can clearly see the fundus with, is +6, the observed eye has a hyperopia of 3 d. A myope, on the other hand, as he requires a weaker correcting glass, must add in dioptres the amount of the defect; thus, when he is myopic to the extent of 5, and requires no glass to see the fundus clearly, the eye that is being examined is hyperopic to the extent of 5. Again, when his myopia is 3, and the strength of the convex glass he can use is 2, the amount of hyperopia present in the observed eye is 5 ; or when he has myopia of 7, and he cannot see the fundus clearly with any glass less concave than 3, the amount of hyperopia present is 7 + ( - 3) — i.e., 4 d. To summarize, we may say that if an ametrope, to see clearly the fundus of an eye with the ophthalmoscope and to estimate correctly its refraction, requires — (i) A glass of the same kind as his own ametropia, but stronger, he must deduct the number of his own from that glass. Example. — He has a myopia of 3, and requires - 5 in the ophthalmoscope, then the error of the observed eye is - 2. (2) A glass of the same kind, but from one to ten dioptres weaker than his own ametropia, then the eye that is being examined has an ametropia of from one to ten dioptres of the opposite kind. Example. — He has a myopia of 6, and requires - 5 ; the refrac- tive defect of the observed eye is + 1 . If he require - 4, it is + 2, and so on. He has hyperopia +4, and requires +3; then the refractive error of the observed eye is - i , 72 THE REFRACTION OF THE EYE (3) A glass neither of the same kind nor strength, then the refraction of the observed eye is the opposite to that of the observer's, and the amount is equal to the addition of the number of dioptres of each. Example. — He has myopia of 5, and requires + 3 ; the refrac- tion of the observed eye is + 8. He has hyperopia of 3, and requires - 2 ; the error is - 5. It should be borne in mind that, to insure the exact measurement of the patient's refraction by means of the ophthalmoscope, the yellow spot must be looked at. If the patient be not under the influence of a mydriatic, this is not always easy, for not only does the pupil contract when the examined eye is turned towards the mirror, but the light reflex from the cornea interferes very much with the view unless the electric ophthalmoscope with Marple mirror is used; and, further, the absence of any large structure, such as the retinal vessels, makes it diihcult to secure the correct focus. As a rule, all that is seen at the macula is a slight stippling, produced by the irregular deposit of retinal pigment, and when this pigment is specially pronounced we get a bright ring or crescent at the fovea. This is the foveal reflex; and although it is slightly in front of the retina, the distance is so small that it can be ignored, and this foveal reflex can be focused and made use of in this manner, for ascertaining the refraction. If it cannot be used in this way, through being too faint, we must focus a small retinal vessel passing from the disc to the macula. The beginner will find that the easiest part to focus is the temporal side of the disc, for its margin here is generally very well defined. The Measurement of Astigmatism. — It is very diffi- cult, if not impossible, to diagnose low errors of astigmatism by the ophthalmoscope, but an error of one dioptre or more is revealed by portions of the fundus picture being out of focus, and by our inability THE OPHTHALMOSCOPE 73 to get a clear picture of all parts at the same time by any of the spherical glasses in the ophthalmoscope. Some ophthalmoscopes have cylindrical glasses fixed in them, but this is not at all necessary, as the astigma- tism can be approximately estimated without much difficulty by measuring the refraction of the meridians at right angles to each other in the following manner: Focus, for instance, the vessels that pass in a horizontal direction from the disc to the macula, and note the glass in the ophthalmoscope (the weakest concave and strongest convex) that is required to give a clear definition; this will give the refraction of the meridian at right angles to the horizontal one — viz., the ver- tical. Then focus the vessels that pass vertically upwards and downwards from the disc; this will give the refraction of the horizontal meridian, and the difference between the two glasses (if any) is the amount of the astigmatism (if any). When the chief meridians are not vertical and hori- zontal, but oblique, we can then, say, focus the vessels passing upwards and outwards from the disc, and when we have focused these vessels, if astigmatism exist, the vessels passing downwards and outwards will not be in focus, but will be either blurred or invisible, and we proceed to find the glass that is necessary to bring these latter vessels into focus, and so on. If the correcting glass be a large one, we must be care- ful to look through the centre, for if we look through the glass obliquely we shall get an appearance as if produced by astigmatism, which might not be present. In estimating the refraction by means of the ophthalmoscope, as above explained, the observer shoald approximate his eye as much as possible to the eye that is being examined, as the value of the lens is altered by altering the distance; a concave glass is weakened and a convex glass strengthened by removal from the eye. It is for this reaso.i that old people are often seen to wear their glasses low down o.i the nose, the strength of the CO a vex glass being slightly increased. This, of coarse, specially refers to lenses of high po.ver; therefore, the further away we 74 THE REFRACTION OF THE EYE hold the ophthalmoscope the more shall we overcorrect in myopia and undercorrect in hyperopia — i.e., the myopia of the eye being examined will be less, and the hyperopia more, than that represented by the ophthalmoscope glass. 3. The Estimation of the Refraction by the " Shadow Test " ; Retinoscopy ; Skiascopy. — Seated at a short dis- tance from the patient in a dark room, if we throw the light on to the patient's eye by means of an ophthal- moscopic mirror, provided the pupil is normal and the media are clear, we observe the red reflex of the fundus ; and if we gently rotate the mirror, the red reflex dis- appears, and darkness takes its place. The manner in which this darkness or shadow appears varies according to the refraction of the eye. We will examine the behaviour of the shadow under three conditions : 1. When the observer is beyond the patient's far point. 2. When he is within the patient's far point. 3. When he is exactly at the patient's far point. I. Let us suppose the surgeon Ob (Fig. 46, A) examin- ing the patient Pt by this method, and using the plane mirror, and we will assume Pt to have a refractive error of over I of myopia. Ob is seated i metre off Pt, and is consequently beyond P/'s far point. Ob reflects the light into Pt^s eye and observes the red reflex ; and if he rotate the mirror, making the light pass, say, across Pfs face from the nose to the temple, he will notice that the red reflex disappears, and that darkness takes its place, and in this example the darkness or shadow comes over the eye from the temple towards the nose — that is, in the opposite direction to the rotation of the mirror. Let us see how this has come about. In Fig. 46, for the sake of clearness, the mirror and the light have been omitted, and only the rays proceeding from P/'s fundus have been drawn. All luminous rays proceeding from the fundus of Pt Fig. 46. (After Fick.) RETINOSCOPY 77 through the pupil P p (Fig. 46, A) either do not reach the eye Ob, or they impinge on Ob's retina between P' and p\ Thus, all rays from p, from whatever part of Pt's fundus they come, must unite at p' of Ob if they are intercepted by 06' s pupil. Let a he a, luminous point on the fundus of Pt (who in this case is assumed to have a myopia of ov^ i), then at Pi's far point, somewhere on the line between a and the nodal point, an aerial image a' of a will be formed. Some of the diverging rays from a' will reach Ob, and, passing through the refractive media, will unite at a"', but as Ob's fundus intercepts these rays, a bright diffusion circle will be formed on the upper part ot P' p' {Ob's fundus), while the lower part of P' p' will be in darkness. Now, as our retinal images are projected inverted, Ob sees the pupil of Pt light below and dark above. If the luminous spot a descend to b in Pt, its image ascends to b\ and we have a bright area below in P' p', and Ob sees in P^'s pupil a bright area passing from below upwards. We thus see how in myopia of over i d, with the observer i metre from the patient, and using a plane mirror, the " shadow " moves against the rotation of t) ( mirror. 2. The reverse obtains when Ob is within Pt's far poin^. Let us suppose (Fig. 46, B) Pt to be hyperopic. The image of a will be at a', but those rays that pass through Ob's pupil are refracted, and meet at a" in front of the retina, and, diverging again, meet Ob's retina at p' as a diffusion circle ; in this case the bright area, being below, is projected inversely, and Ob sees P^'s pupil bright above and dark below, and if a moves down to b, it will be seen that Ob projects the bright area moving down also. Thus, with a plane mirror, if Ob be within Pt's far point, the shadow moves with the mirror; if Ob be seated i metre off Pt, this will occur in hyperopia, emmetropia, and myopia of less than i d. 78 THE REFRACTION OF THE EYE 3. £,astly, let us consider what happens when Ob is exactly at P^'s far point, which, of course, occurs if Ob be seated 1 metre off Pt, who has a myopia of i d (Fig. 46, C). The illuminated point a has its image a' exactly on the pupil of Ob, and as the ray p a' is re- fracted to p' , and the ray P a' to 0', the entire area P' p' is illuminated, and the entire pupil of Pt appears illumi- nated to Ob. Movement of « to 6 produces no effect; the area P' p' is still illuminated; but when the luminous point on P^'s retina passes below b or above a — that is, outside the area a b — it is focused on 06's iris, and no rays reach 06's retina ; consequently Ob sees the pupil Pj^ becoming suddenly dark, and there is no moving shadow. This point, when the observer's eye is exactly at the patient's far point, is called the " point of reversal," and the whole principle of retinoscopy is to find this point. In myopia Ob can move nearer to or further from the patient, and measure off the distance of the point of reversal, and so obtain the refraction of that particular meridian ; but in hyperopia this cannot be done, so that the best method is to work always at one fixed point — say I metre — and make the patient artificially myopic, if hyperopia or emmetropia exist, by placing before P^'s eye convex glasses ; if he be myopic, make him less myopic by using concave glasses. Let us now examine a patient. The patient's eyes should (if possible) be under the influence of a cycloplegic, which not only gives us a dilated pupil and makes the retinoscopy easier, but insures the relaxation of the ciliary muscle, which of course is essential. The patient should be seated in a dark room, with the light above or on one side of his head and slightly behind, so that no rays can reach the eye except from the mirror. We pro- vide ourselves with a set of test lenses and a trial frame, and seated, say, i metre off the patient, we reflect the light by means of the plane mirror into the patient's eye, "directing him to look at the sight-hole of the mirror. RETINOSCOPY 79 Suppose we are. examining the right eye, and rotate the mirror so that the Hght passes across from the patient's nose to the temple, and suppose we notice that as the Hght leaves the pupil a dark shadow takes its place, passing across in the same direction — i.e., from the nose to the temple — we know from Fig. 46, B, that we are within the patient's far point, and that we are dealing with a hyperope or emmetrope, or myope of less than i . Let us place in the trial frame + 2 : we find, say, that the shadow is still moving with the mirror; we are therefore dealing with hyperopia. Put up +4: the shadow now moves against the mirror, which means we are outside the patient's far point; put up +3, and we find on rotating the mirror that the pupil becomes suddenly dark, and there is no shadow following with the rotation, or passing against it. This, then, is the point of reversal. We have found the point of reversal with a +3 lens, seated i metre from the patient, which means that this meridian has a myopia of i with a +3 lens in front, and, deducting i from 3, leaves us 2 as representing the hyperopia. If the patient had been emmetropic in this meridian, a + 1 lens would have given us the point of reversal at i metre. If the patient's eye have a myopia of over i, when we are seated i metre off we must be outside his far point, whatever the amount of myopia, and the shadow moves " against " the plane mirror, and that glass which gives us the point of reversal represents the amount of myopia of that meridian with - i added if we are seated I metre off (or - 2 added if seated 50 cms. off, or - •5 added if 2 metres off) — -that is, if - 5 gives the point of reversal, - 6 is the amount of myopia. Some surgeons always aim at reversing the shadow — 'that is, they purposely go beyond the point of reversal, and slightly overcorrect. This is quite safe if allowance be made fof the overcorrection. < In the examples, we have been ascertaining the far 80 THE REFRACTION OF THE EYE point of one meridian only — viz., the horizontal; we must now proceed to examine the meridian at right angles — viz., the vertical — and if the same glass give us the point of reversal, we know that no astigmatism is present; but if there be a difference, that difference represents the astigmatism. When the astigmatism is great, and especially when one meridian is emmetropic or made emmetropic, the light is seen to pass across as a bright band (Fig. 47), and sometimes two bright bands are seen with a dark band in the centre, and as the bright bands approximate each other, the central dark band disappears, and one bright band remains. This has been called the " scissor movement." , Fig. 47. In oblique astigmatism, of course, the meridians are not vertical and horizontal, and when the astigmatism is marked, the appearance of the shadow is very character- istic, and a bright band is seen passing obliquely across the pupil, although we may be moving the mirror hori- zontally or vertically (Fig. 47). Suppose we are dealing with oblique mixed astigmatism, and, rotating the mirror horizontally, we observe a bright band fol- lowed by a shadow passing obliquely across the pupil " with " the plane mirror, we note the axis of this bright band, and also note that the meridian is hyperopic; if we then rotate the mirror at right angles to this bright band, we find that the shadow passes against the move- RETINOSCOPY 8l ment of the mirror, showing that this meridian is myopic. Suppose the point of reversal of the horizontal oblique meridian is obtained by -1-3, and that of the vertical by - I, by this we know that the refraction of the hori- zontal meridian is +2, and that of the vertical meridian is - 2, and there is therefore a total astigmatism of 4. The greater the ametropia, the nearer is the far point to the eye, and it is of great practical importance to remember that, the greater the ametropia, the less distinct is the shadow and the slower it moves; and as we approach the point of reversal by using correcting glasses, we obtain an increasingly defined shadow which Fig. 48. moves more and more rapidly. We can thus, at once, make a rough estimate of the degree and kind of ametropia. In Fig. 48, if R be the far point of the myopic eye, on rotating the mirror, the shadow moves from R to r' ; but if the myopia be less, and the far point at M, the shadow will have to describe the larger arc M m' in the same time — that is, it will move more quickly. In the same way, if the far point of a hyperope be at R (Fig. 49), the shadow will move more slowly than when the hyperopia is less and the far point at H. Some surgeons use the plane mirror at a distance of 4 metres always, and as only •25 d has to be deducted from the retinoscopy, this small amount can be ignored, 6 82 THE REFRACTION OF THE EYE and the point of reversal of a meridian represents the measurement of that meridian. When the surgeon is nearer than i metre, he must, of course, deduct more than i. For instance, suppose at 33 cms. the point of reversal of a meridian is obtained with +5, as his far point is J metre off, we have made the patient artificially myopic to the extent of 3, and we must deduct this from 5; therefore 5-3 (that is, 2) represents the hyperopia of this meridian. Many surgeons still use the concave mirror. The mirror should have a focus of 25 cms., and the observer should be seated a little over a metre from the patient. The movement of the shadow is the reverse of that which takes place with the plane mirror — that is, the shadow Fig. 49. moves " with " the mirror in myopia of over i, and " against " the mirror in myopia of less than i, and in hyperopia and emmetropia. This is easily understood if we remember that with a concave mirror the rays of light converge to the focal point of the mirror, and then cross and diverge ; consequently the image thrown on a screen by a concave mirror is inverted. [If we reflect a lighted candle on to a dark screen by a concave mirror held further from the screen than its focal distance, and if we then focus the divergent rays with a convex lens, we shall get an erect image, because the rays have been twice inverted, whereas with a plane mirror used in the same manner we obtain an inverted image, because there has been only one inversion.] If the observer be not emmetropic, he should wear his correcting glass. This, of course, especially applies if RETINOSCOPY 83 he be myopic. If he be hyperopic, he may correct his defect by accommodation if he choose. The point to be remembered is, that to practise retinoscopy accurately the observer requires a normal acuity of vision. He Fig. 50. may accommodate as much as he likes, as it does not affect the result. As the point of reversal is more definite when the shadow moves with, it is not a bad plan to use a plane ''^■^#;"'^'. ^ ^^ 4r -^ ^ Fig. 51. — Marple's Skiascopes. mirror when estimating hyperopia, and a concave mirror when estimating myopia. These two mirrors can be hinged together, and thus each mirror is the handle and cover of the other (Fig. 50). Marpie's skiascopes (Fig. 51), made by Meyrowitz of New York, are very useful, and obviate the necessity for keeping a 84 THE REFRACTION OF THE EYE separate test case in the dark room; they are designed to be held by the patient before the eye during retinoscopic examination. Each contains a series of six lenses, ranging from i to 6 dioptres, plus and minus respectively. In addition to these lenses there is on one side a movable slide containing a 6 d lens, which can be quickly slipped up over the other lenses one after the other, making further combinations from 7 d to 12 d. To determine smaller errors within i d, a slide containing three lenses -25, •50, and '75 d, respectively, is placed on the other side, and can easily be brought before the other lenses. On the skiascope containing the plus lenses the movable slide carries minus fraction lenses, and vice versa. CHAPTER VI HYPEROPIA Hyperopia or Hypermetropia. — The hyperopic eye is the undeveloped eye in which, with accommodation at rest, parallel rays come to a focus beyond the retina (Fig. 20, h), and only convergent rays focus on the retina; but as in Nature all rays are either parallel or divergent, it follows that the hyperopic eye at rest sees everything indistinctly. Rays coming from a point on the retina diverge, and, on passing through the dioptric system, emerge from the normal eye as parallel rays. In hyperopia, although they are not so divergent as they were before refraction, they still diverge if the eye be at rest, and therefore never come to a focus in front of the eye; Jut when prolonged backwards, they will meet at a point behind the eye — the punctum remotum. This punctum remotum of the hyperope is therefore not the actual focus of the distant rays, but the virtual focus, and is represented by the negative sign -R (Fig. 52). It will be seen from Fig. 52 that the more divergent the rays are in front of the eye, the nearer will their " backward prolongation " focus ; hence the nearer - R is to the eye, the higher will be the hyperopia. This is the same as in myopia — viz., the higher the myopia, the nearer is r to the eye; but the differ- ence is that in myopia R is in front of the eye, and in hyperopia it is an imaginary point behind the eye. «5 86 THE REFRACTION OF THE EYE ^ . ' Thus, the degree of hyperopia is in inverse ratio to the distance of the punctum remotum. In myopia this point can be measured directly, but in hyperopia it can only be done indirectly by employing convex glasses. Suppose the punctum remotum of a hyperope is 33 cms. behind the retina. We have seen that a convex lens whose focal point is 33 cms. is 3 d — that is, such a lens has the power of converging parallel rays to a point 33 cms. on the other side of the lens, and con- versely, rays diverging from a point 33 cms. in front of Fig. 52. Showing the punctum remotum of a hyperopic eye. such a lens become parallel on passing through. If this lens be put in front of the eye of this hyperope, it will so act that, assisted by the dioptric system of the eye, it will cause parallel rays to focus on the retina. Hence the measurement of hyperopia is that convex lens which enables the hyperopic eye, at rest, to see distinctly objects at a distance, and the focal length of such a lens represents the distance of the virtual far point from the eye. In the above example it was found that +3 was this lens, and we accordingly say that this eye has a hyperopia of 3. HYPEROPIA 87 A hyperope differs from a myope in that he can correct his defect up to a certain point; he can by accommodation produce the same effect on parallel rays as if a convex glass were placed in front of the eye. This apparent advantage brings with it many dis- advantages — viz., all the troubles incident to eyestrain. The hyperopic eye is never at rest; it has to accom- modate for distant as well as for near objects. The emmetrope's ciliary muscle is at rest when he is looking at any object 20 feet off, or beyond, but the hyperope's Fig. 53. Showing parallel rays focused on the retina of a hyperopic eye by means of a convex lens. eye is never at rest if he attempt to see distinctly; and, moreover, when he wishes to look at a near object, he starts with a deficit, which deficit is the amount of accommodation he required for distant vision. ' Thus, a hyperope of four dioptres, with five dioptres of accommodation, can focus distant objects clearly, but then he has only one dioptre left for near vision; this will only bring his near point to i metre from the eyes. Again, take a hyperope of two dioptres, with five dioptres of accommodation: he has only three dioptres available for accommodation for near objects; 88 THE REFRACTION OF THE EYE this brings his near point to 33 cms., but he is using the whole of his accommodative power for this, and it is impossible for him to do this for long without fatigue, and so we get all the symptoms of eyestrain. We have seen that in hyperopia a = p-(-r) = p+r (page 35), therefore p = a-r ; in other words, the fO /S 20 2S 50 3S 40 46 SO 66 GO 66 70 76 SO // m 3 \ H \ 7 \p fi \ 5 \, 4- N J \ ? k. •^/ Sj V a -/ --■ — •-- --- -- V ^ -_. .__ --■ ... .--. ? 'v ,T v^ ^