UNIVERSITY OF CALIFORNIA MEDICAL CENTER LIBRARY SAN FRANCISCO ^itebfc'K ^VB re* *r?^ PHYSIOLOGIC OPTICS DIOPTRICS OF THE EYE, FUNCTIONS OF THE RETINA OCULAR MOVEMENTS AND BINOCULAR VISION DR. M.fTSGHERNING ADJUNCT-DIRECTOR. OF THE~XABORATORY OF OPHTHALMOLOOY AT THE SORBONNE, PARIS AUTHORIZED TRANSLATION From the Original French Edition, Specially Revised and Enlarged by the Author BY CARL WEILAND, M. D. FORMER CHIEF OF CLINIC IN THE EYE DEPARTMENT OF THE JEFFERSON MEDICAL COLLEGB HOSPITAL OF PHILADELPHIA WITH 212 ILLUSTRATIONS &P47? TS7 SECOND EDITION PUBLISHED BY THE KEYSTONE E ORGAN OF THE JEWELRY AND OPTICAL, TRADES IQTH & BROWN STS., PHILADELPHIA, U. S. A. 1904 All rights reserved 171629 COPYRIGHT, 1900, BY B. THORPE PUBLISHER OF THE KEYSTONE Entered at Stationers' Hall, Condon, Eng. TRANSLATOR'S PREFACE. Physiologic Optics is a science which, on the one side, touches the highest philosophic problems of the human mind and, on the other side, keeps in intimate contact with the practical work of the ophthalmologist, who, in his daily work of refraction, can be guided safely only by its principles. Many are the text-books on this important subject. Some are mere compilations of older facts and some are written by men that soar so high above the field of the practical work of the ophthalmologist that their abstract scientific investigations lose almost all contact with these practical workers. The present book is neither a mere compilation nor an abstract theoretical investigation, but a collection of all the old and new scientific facts that have any bearing on the practical work of the oculist and optician. It is written by a man who lately has probably done more original work in this line than any other since Helmholtz and Bonders, and who, furthermore, has been in constant contact with practical ophthal- mology. Dr. M. Tscherning, who was born in Denmark in 1854, studied ophthalmology at Copenhagen under the philosophic mind of Hansen Grut. Since 1884 he has been adjunct-director of the laboratory of ophthalmology at the Sorbonne, where, since the deplorable disability of Javal, he himself has performed the functions of the director. This laboratory, which was founded in 1876 for Javal, after he had become widely known by his translation of the Physiologic Optics of Helmholtz, has given a new impetus to this science in France. Here Tscherning has made all his important original investigations, especially on ophthalmometry, the catoptric images of the eye, astigmatism, spherical aberration and accommodation. All this original work, as well as that of former investigators, is described in this book with great clearness and succinctness, almost entirely free from tedious mathematical encumbrances. Instead of long formuke, the experiment and simple geometrical deductions are employed to explain the observed phenomena. The translator has endeavored to reproduce the clearness and brevity of expression of the original as much as possible. How far he has succeeded in this, it is not for him to judge. This English edition, as has been indicated on the title page, contains many additions in the text by Dr. Tscherning, who has thus brought his book thoroughly up to date. The few notes, added by the translator, have been included in brackets with the letter W. appended. A list of illustrations and an index have been compiled to enhance the practical value of the book. It is true that some of the ideas expressed by the author, especially those about the use of mydriatics for ordinary purposes of refraction and the use of spectacles, are not in accord with current views about these subjects on this side of the Atlantic. But even those who cannot agree with the author on these questions, will find many new facts and ideas which will make a study of the book of great interest and profit. The translator only hopes that the reader may experience the same intellectual pleasure that he felt while reading and translating this work of one of our greatest investigators in the field of physiologic optics. CARL WEILAND, M. D., Philadelphia, U. S. A. TABLE OF CONTENTS BOOK I OCULAR DIOPTRICS CHAPTER I OPTIC PRINCIPLES PAGE 1. Optic Properties of Bodies I 2. Rectilinear Propagation of Light X 3. Reflection and Absorption 2 4. Regular Reflection 2 5. Plane Mirrors. Construction of the Image 3 6. Concave Spherical Mirrors 3 7. Convex Mirrors 6 8. Practical Remarks 6 9. Refraction 8 10. Quantity of Light Reflected. Total Reflection 8 11. Refraction by Plates with Plane and Parallel Surfaces lo 12. Refraction by a Prism 10 13. Refraction by a Spherical Surface II 14. Infinitely Thin Lenses 14 15. Theory of Gauss 18 Bibliography 26 CHAPTER II THE OPTIC SYSTEM OF THE EYE 16. Optic Constants of the Eye 27 17. Optic System of the Eye 31 18. Aperture of the System 34 19. Point of Fixation. Visual Line 36 20. Optic Axis. Angle a 36 21. Useful Image 37 Bibliography 38 CHAPTER III THE FALSE IMAGES OF THE EYE PAGE 22. General Remarks 39 23. The Images of Purkinje 40 24. Manner of Observing the Images of Purkinje 42 25. False Images of the Second Order 44 26. Manner of Observing the Sixth Image 45 Bibliograpy 46 CHAPTER IV OPHTHALMOMETRY 27. Principles of Ophthalmometry 47 28. Methods of Doubling 48 29. The Ophthalmometer of Javal and Schiotz 5 1 30. Results of the Measurement of the Cornea 54 31. Measurement of the Angle a 63 32. Determination of the Position of the Internal Surfaces 67 33. Determination of the Centers of the Internal Surfaces 68 34. Direct Determination of the Radii 70 35. General Remarks 7 1 Bibliography 7 2 CHAPTER V CIRCLES OF DIFFUSION 36. Definition 73 37. Line of Sight 74 38. Accommodation 74 39. Experiment of Czermack, Schemer and Mile 75 40. The Optometer of Thomas Young 75 41. Effects of the Stenopaic Opening 77 Bibliography 78 CHAPTER VI ANOMALIES OF REFRACTION 42. General Remarks 79 43. General Remarks on Ametropia So 44. Optometers 83 45. Myopia 84 46. Choice of Spectacles 87 47. Treatment of Myopia 88 48. Hypermetropia 9 49. Aphakia 9 2 Bibliography 94 CHAPTER VII SPHERICAL ABERRATION PAGE 50. Optic Principles , 95 51. Phenomena Dependent on the Spherical Aberration of Lenses 96 52. Aberration of the Human Eye. Experiments of Volkmann loo 53. Experiments of Thomas Young 101 Bibliography ..... l( 108 CHAPTER VIII CHROMATIC ABERRATION 54. Optic Principles 109 55. Chromatic Aberration of the Eye Ill 56. Experiment of Wollaston ill 57. Results 112 58. Phenomena of Dispersion, the Pupil being Partly Covered 113 59. Correction of Chromatic Aberration 114 Bibliography 114 CHAPTER IX REGULAR ASTIGMATISM 60. Optic Principles. Astigmatism Produced by the Form of the Surfaces 115 61. Defects of the Image 118 62. Astigmatic Surfaces 118 63. Astigmatism by Incidence 119 64. Astigmatism of the Human Eye. Historical 12 1 65. Physiologic Astigmatism 122 66. Corneal Astigmatism 122 67. Measurement of the Corneal Astigmatism 123 68. Regular Corneal Astigmatism 125 69. Relations between Ophthalmometric and Subjective Astigmatisms 125 70. Astigmatic Accommodation 129 71. Post-Operative Astigmatism 130 72. Keratoconus 131 73. Symptoms of Astigmatism 132 74. Examination of Astigmatic Patients . 133 Bibliography 136 CHAPTER X IRREGULAR ASTIGMATISM 75. General Remarks 137 76. Examination of the Eye with a Luminous Point , . . 138 77. Different Forms of Irregular Astigmatism .... 139 78. Rules for Analyzing the Figures of the Luminous Point 143 Bibliography 146 CHAPTER XI ENTOPTIC PHENOMENA PAGE 79. Manner of Observing Entoptic Phenomena 147 80. Analysis of Entoptic Phenomena 151 81. Entoptic Observation of the Vessels of the Retina 153 82. Other Entoptic Phenomena 156 Bibliography 159 CHAPTER XII ACCOMMODATION 83. Measurement of the Amplitude of Accommodation 160 84. Mechanism of Accommodation (Historical, A.) t 162 85. Mechanism of Accommodation (Historical, B.) 167 86. Personal Experiments I7 1 87. The Author's Theory of Accommodation 183 Bibliography 189 CHAPTER XIII OPHTHALMOSCOPY 88. Methods of Illuminating the Fundus of the Eye 190 89. Examination by the Erect Image 193 90. Examination by the Erect Image. Observations 197 91. Examination by the Inverted Image , 200 92. Ophthalmoscopic Examination of the Refracting Media 204 93. Skiascopy 205 Bibliography . , c 210 CHAPTER XIV THE PUPIL 94. General Remarks 211 95. Action of Mydriatics and of Myotics 212 96. Movements of the Pupil ....'. 2I2 97. Advantage of the Position of the Pupil near the Nodal Point . 215 Bibliography . . < . . 220 BOOK II FUNCTIONS OF THE RETINA CHAPTER XV CHANGES WHICH THE RETINA UNDERGOES UNDER THE INFLUENCE OF LIGHT PAGE 98. Retinal Purple .221 99. Movements of the Pigment Under, the Influence of Light 222 Bibliography 223 CHAPTER XVI THE LIGHT SENSE 100. Psychophysical Law of Fechner 224 101. Measurement of the Light Sense 228 102. Results 231 Bibliography 233 CHAPTER XVII THE COLOR SENSE 103. General Remarks 234 104. Phenomena of Contrast (Simultaneous) .... 238 105. After Images 241 106. Phenomena Dependent on the Variation of the Brightness of the Colors 243 107. Methods of Mixing the Colors 247 108. Results of the Mixtures of Colors 250 109. Abnormal Trichromasia 261 no. Color Blindness or Daltonism (Dichromasia) 263 111. Monochromasia . 269 112. Clinical Examination of the Color Sense 269 113. Hypotheses on the Mechanism of Color Vision . . 272 Bibliography .*-, ...... 275 CHAPTER XVIII THE FORM SENSE 114. Central Visual Acuity 277 115. Peripheral Acuity 282 Bibliography 286 BOOK III THE OCULAR MOVEMENTS AND BINOCULAR VISION CHAPTER XIX THE LAW OF LISTING PAGE 116. Centers and Axes of Rotation of the Eye 287 117. Law of Listing 289 118. Experiments of Meissner. Apparently Vertical Meridian 294 119. Historical 297 Bibliography 298 CHAPTER XX THE OCULAR MOVEMENTS 120. Jerking Movements of the Eyes 299 121. Relative Movements of the Two Eyes 299 122. Measurement of Convergence 301 123. Relations between Accommodation and Convergence 303 Bibliography ...,...., 303 CHAPTER XXI PROJECTION OF VISUAL IMPRESSIONS 124. Projection Outwards of Uniocular Vision 304 125. Projection of the Visual Field 304 126. Projection in Binocular Vision 307 Bibliography 312 CHAPTER XXII MONOCULAR PERCEPTION OF DEPTH 127. Influence of Accommodation 313 128. Indirect Judgment of Distance 313 129. Influence of the Parallax 315 Bibliography 3 l6 CHAPTER XXIII BINOCULAR PERCEPTION OF DEPTH 130. Influence of Convergence 3*7 131. The Stereoscope 3 1 / 132. Effect of the Stereoscope 3 22 133. Identical Points of the Retince 3 2 4 Bibliography 3 2 ^ CHAPTER XXIV STRABISMUS PAGE 134. Different forms of Strabismus 3 2 9 135. Measurement of Strabismus 136. Etiology of Concomitant Strabismus 137. Vision of Strabismic Patients 138. Treatment of Strabismus 335 Bibliography 337 CHAPTER XXV ^ OPTIC ILLUSIONS 139. Optic Illusions 33 8 Bibliography 34 Treatises to Consult 343 LIST OF ILLUSTRATIONS FIG. PAGE Frontispiece Portrait of the Author 1. Luminous Source, Opaque Body, Shadow and Penumbra I 2. Reflection on a Plane Mirror 3 3. Reflection on a Concave Mirror 4 4. Reflection on a Concave Mirror 4 5. Reflection on a Convex Mirror 6 6. Construction of the Utilized Part of a Mirror 7 7. Refraction 8 8. Total Reflection 9 9. Prism with Total Reflection 9 10. Refraction by a Plate with Plane Parallel Surfaces IO 11. Refraction by a Prism IO 12. Refraction by a Spherical Surface II 13. Refraction by a Spherical Surface 12 14. Refraction by a Parabolic Surface 13 15. Construction of Image Formed by a Thin Lens 15 16. Method of Measuring the Focal Distance of a Lens 17 17. Principal and Nodal Points ; Anterior and Posterior Focus 19 18. Construction of the Image of an Object 20 19. Construction to Find the Second Principal Plane 21 19 a. Construction of the Cardinal Points of Two Optic Systems 22 20. Construction to Find the Nodal Points of a Thick Lens 23 21. Optic System of the Eye 27 22. Optic System of the Eye of an Ox 28 23. Images of Purkinje of the Eye of an Ox (Dead) 29 24. Double Crystalline Images in a Case of False Lenticonus 29 25. Diagram of the Crystalline Lens 30 26. Position of the Cardinal Points of the Human Eye 32 27. Pupil of Entrance and Pupil of Exit 35 28. Reflections and Refractions by a Lens 39 29. Manner in which a Luminous Ray is Divided in the Eye 40 30. Position of the Seven Images in the Eye 41 31. Corneal Images of two Lamps Observed with the Ophthalmophakometer 43 32. The Ophthalmophakometer 44 33. Illustration of the Principle of Doubling 48 34. Doubling by the Two Halves of an Objective 49 35. Plates of Helmholtz 49 36. Doubling by an Objective, a Central Vertical Band of which has been Removed . . 50 37. Prism of Wollaston 50 38. Ophthalmometer of Javal and Schioetz S 1 39. Images of the Mires Seen Doubled . 5 2 40. Refraction by a Conical Cornea 54 41. Radii of Curvature of the Cornea 55 42. Diagram of Corneal Refraction 57 43. Forms of the Image of a White Square at Different Parts of the Cornea 5& 44. Keratoscopic Images of an Astigmatic Cornea 60 45. Keratoscopic Images of an Astigmatic Cornea 61 46. Keratoscopic Images of a Case of Keratoconus 62 46 a. Keratoscopic Image of an Eye with a Large Angle a 63 46 \ * = * (fig. 3), since the angles of inci- dence and reflection are equal, and i = BC< because the incident ray is parallel to the axis. It follows that C< = B<, but as the aperture is ' very small, we can consider B = Fig. 3. Reflection on a concave mirror. Q<&, therefore C< = Q4> = -J- , if C, the center; *, the focus. we designate the radius fcy R Fig. 4. Reflection on a concave mirror. Constructions of the image, I, of an object O; C, the center; *, the focus. AS = / t , A'S = f 2 , S$ = F, A = l lt A'$ = 1 2 . A ray passing through the center is perpendicular to the surface; it is consequently reflected on itself. OPTIC PRINCIPLES 5 CONSTRUCTION OF THE IMAGE. To find the image Bj of a point B (fig. 4), it suffices to trace the course of two rays which have emanated from that point; the image must be at the place where they intersect after reflection. After what has been previously stated we already know the course of three rays proceeding from the point B. i. The ray BM, which is parallel to the axis, passes after reflection through the focus ; 2. The ray B, which passes through the focus, is reflected parallel to the axis since the course of the rays is reversible; 3. The ray BC, passing through the center, is reflected on itself. Two of these rays suffice for the construction. By combining them, two by two, we obtain the three different constructions shown in figure 4. SIZE OF THE IMAGE. RELATIONS BETWEEN THE DISTANCES OF CON- JUGATE POINTS. Let us consider the line BA = O (fig. 40) as the object ; I is its image. And supposing SL = I and MS O, the triangles AB4> and SL4> on one side, and the triangles SM3> and A'B'4> on the other give us the relations . = i. = ^ or /! I, = FF (Neu-lnn)\ The formula _ = -JL can also be written = - 1 ; I r IK which is the formula we use later in ophthalmometry. As we have /! = f 1 F and I z = f 2 F, the formula of Newton /i k = FF can also be written F . F 111 Tf + TT lor A + 7r = F The first of these two formulas is that of HclmMts; and, as we shall see, it is altogether general. The second is identical with that of infinitely thin lenses. (1) In this formula and those which follow I designate by: 0, the object; 1, the image; RI, the radius of the first surface; R 2 , the radius of the second surface; FI, the anterior focal distance; Fo, the posterior focal distance; fi, the distance of the object from the surface; f, the distance of the image from the surface; ti, the distance of the object from the anterior focus; ? 2 . the distance of the image from the posterior focus; For mirrors and lenses surrounded with the same media on both sides we have F! = F 2 = F 6 PHYSIOLOGIC OPTICS By construction or formula we find that: i. The image of an object placed beyond the center is situated be- tween the center and focus. It is real, inverted and diminished; 2 . As the course of the rays is reversible, an object placed between the center and the focus gives an image situated beyond the center, and this image is real, inverted and enlarged; 3. An object placed between the focus and the mirror forms its image behind the mirror. This image is virtual, erect and enlarged. 7. Convex Mirrors. As in the case of concave mirrors, the focus is placed at an equal distance between the surface and center. The con- struction (fig. 5) is the same as in the preceding case, and the formulae Fig. 5. Reflection on a convex mirror. Construction of the image. C, the center; $, the focus. also, but the distances of the points situated behind the surface must be considered as negative; we have therefore The image of a real object is always virtual, erect and diminished; it is situated between the surface and the focus. 8. Practical Remarks. One can tell whether a mirror is convex, con- cave or plane by placing the eye near the surface. A convex mirror forms a diminished image of the eye, a concave mirror gives a magnified image (provided the eye is between the focus and the mirror). The image formed by a plane mirror is the same size as the object. To determine the focal distance of a concave mirror we can : i. Form the image of a distant object on a screen: the distance of the mirror from the screen is equal to the focal distance ; OPTIC PRINCIPLES 7 2. Place the screen by the side of a flame and find the distance from the mirror at which the image appears distinct. The distance of the mirror from the flame is double the focal distance, for since the object and image are, in this case, at the same distance from the mirror, this distance is equal to the radius of the mirror or double its focal distance. We de- termine the focal distance of a convex mirror by finding the position of the screen at which the reflex which the mirror forms of a distant flame has a diameter equal to double the diameter of the mirror. The distance of the mirror from the screen is equal to the focal distance, as a simple geometrical construction will show. For all small mirrors ophthalmo- metric processes are used. Concave mirrors, like convex lenses, make rays converge, while con- vex mirrors make them diverge. For this reason convex mirrors are used as ophthalmoscopes when it is desirable to have a very feeble light. A combination of a plane mirror with a convex lens acts like a concave mirror with a focal distance equal to that of the lens or half of it, accord- ing as the light traverses the lens once or twice (ophthalmoscope of Coccius). A combination of a plane mirror with a concave lens acts like a convex mirror. PORTION OF MIRRORS USED. Except in the case when an image is projected on a screen it is only a small part of the mirror that is utilized. We can find this part by constructing the image I (fig. 6) of the object Fig. 6. Construction of the utilized part AB of a mirror. O and by joining by straight lines its margin with the margin of the observer's pupil. These straight lines delimit the utilized portion of the mirror AB. We could also construct the image of the pupil and join this image to the object; the result would be the same. PHYSIOLOGIC OPTICS 9. Refraction. When a luminous ray strikes n. polished surface sepa- rating two transparent media it is divided into two, a reflected ray which is thrown back into the first medium and a refracted ray which continues its course in the second (fig. 7). The three rays are in the same plane which contains also the normal to the point of inci- dence. The angle of reflection is, as we have seen, equal to the angle of incidence, but the angle of refraction (formed by the normal and the refracted ray) is different. Its size is determined by the law of Descartes (Snellius). The ratio between the sine of the angle of incidence and the sine of the angle of re- fraction is constant, whatever may be the angle of inci- dence, as long as two media remain the same. Fig. 7. The symbol n denotes the index of refraction, and the index of air is generally adopted as the unit. The index of water in relation to air is | = 1.333, that of glass in relation to air is approximately \ = I o- The index of glass in relation to water is, then, -| -l- = -f , etc. In the formulae which follow n denotes the index of the second medium as compared with that of the first. 10. Quantity of Reflected Light. Total Reflection. The quantity of light regularly reflected increases with the angle of incidence, with the difference of index between the tzvo media, and lastly with the degree of polish of the surface. In air a highly polished glass surface reflects about 4 per cent, of incident light, if the angle of incidence is negligible. Good metallic mirrors reflect about two-thirds of the incident light. Total reflection takes place when light, propagated in a dense medium, meets at a large angle of incidence the surface which separates the dense medium from a rarer one. Let AB (fig. 8) be the surface separating the air from the water and O a luminous point in the water. OD is a ray which, on reaching the sur- face, is divided into two, DE which is refracted and DF which is re- flected and much feebler ; the next rays OG and OH are equally divided ; the emerging ray is always more and more refracted and loses more and more in intensity, while the reflected ray gains in intensity; and when the angle of incidence reaches a certain size, the emergent ray forms an angle of 90 with the normal, that is, it glances along the sur- OPTIC PRINCIPLES face. We designate as the critical angle the angle of incidence which corresponds with an angle of refraction of 90. In this case sin r = 1 ; therefore, sin ?, sin r = sin i = n. In our case n = 3/4, sin i = 0.75 and the critical angle is about 49. If the angle of incidence exceeds the critical angle all the light is reflected (total reflection) (OK, fig. 8). Air Fig. 8. Total Reflection. If we pour water into a glass and try to look obliquely from below upwards through the surface of the water this surface appears like an absolutely opaque metallic surface. No ray coming from above reaches the eye because all are deflected towards the bottom of the glass by refraction. If we dip a pencil in the water we see it mirrored in the surface; rays coming from the pencil reach the eye after total reflection at the sur- face of the water. As this form of reflection is the most com- plete of all, it is frequently used in optic ex- periments. The most usual application of it is in the rectangular prism; looking per- pendicularly at one of the faces we see an image of objects placed in front of the other face, formed by total reflection on the hypothenuse (fig. 9). Nor need the prism be rectangular; a prism of 60 gives a like result; but in every case the three faces must be polished. Fig. 9. Prism with total reflection. 10 PHYSIOLOGIC OPTICS 11. Refraction by Plates with Plane and Parallel Surfaces. The inci- dent ray and the emergent ray are parallel, for we have r = r (fig. 10). since the surfaces are parallel, and consequently also i = i. The emerg- ent ray has suffered a displacement towards the side whence the light Fig. 10. Refraction by a plate with plane and parallel surfaces. Fig. 11. Refraction by a prism. 12. Refraction by a Prism. Seen through a prism an object seems deflected towards the apex of the prism. The angle between the direc- tion along which the object is seen and that in which it really is found is called the deviation. If i (fig. n) is the angle of incidence, i : the angle formed by the emergent ray with the normal, A the angle of the prism. and d the deviation, we have for and therefore d = i + i 1 A d = i r + i 1 r l A = 180 x = r + r, d = i + i, A. The deviation is least when i = i lf the course of the rays is then sym- metrical, and we have : A = 2r and d = 2i 2r = 2i A. In the formula sin i = n sin r we can replace the sines by the arcs if the latter are small; therefore OPTIC PRINCIPLES 11 i = nr and d = 2nr A ... = (n-l).W If the prism is glass, we have n = | approximately, n I = \ Therefore the deviation produced by a weak prism is equal to half its angle. 13. Refraction by a Spherical Surface, Incident rays parallel to the axis reunite at the posterior forces 2 (fig. 12). The distance S4> 2 is Fig. 12. Refraction by a spherical surface. 4> 1( the anterior focus; 4> 2 , the posterior focus C, the center. known as the posterior focal distance; it is expressed by for we have C$2 _ sin r R. sin (i r) or, if the angles are small, C$ r r 1 R i r nr r n 1 Therefore 2 = -5-_ n 1 and 8*, - -5 + R = -^5_. After refraction the rays coming from the anterior focus $ are parallel to the axis. Its distance 4> S = F x is called the anterior focal distance and is expressed by F R F '- JT=1' indeed, we find this value by a calculation analogous to that by which we have found the posterior focal distance. (1) [The author here derives this formula from that for the least deviation. It may be derived in a more general way thus : d = i r + ii TI or for small angles d = nr r + nr^ n = ( 1) (r + n) (n 1) A.]- W. 1'2 PHYSIOLOGIC OPTICS We note that F 2 = F! + R = T.F, that is to say: i. The difference between the focal distances is equal to the radius; 2, The ratio between the focal distances is equal to the ratio between the indices of the corresponding media. 3. In fig. 12 we have 4> 2 S = *J C = F 2 The distance of the center from the posterior focus is equal to the anterior focal distance, and the distance of the center from the anterior focus is equal to the posterior focal distance. CONSTRUCTION OF THE IMAGE. To construct the image of a point situated outside the axis we can draw : i. A ray passing through the center: it is not refracted; 2. A ray parallel to the axis : it is refracted towards the posterior focus ; 3. A ray passing through the anterior focus : after refraction it is parallel to the axis. The point of intersection of two of these straight lines is the image. There are three possible constructions, therefore, by which we may obtain the image of this point. ^ H/ Fig. 13. Refraction by a spherical surface. Construction of the image. C, the cer tre ; 4> 1( the anterior, focns ; $ 2 . the posterior focus; O, the object; I, the image. AS =/ lf BS Fig. 13 shows the construction by means of rays 2 and 3. The triangles DA^ and ^SG and the triangles HM< 2 and 4> 2 BE being similar, we have the same relation as for the mirrors I - *\ - /, whence we deduce the two general formulae /! / = F, F, ami A : + Jl = J. h h OPTIC PRINCIPLES 13 The image is real and inverted when the object is beyond the anterior focus; it is smaller than the object if the distance of the latter from the surface is greater than 2F 1? larger if the distance is less than zF^. If the object is between the focus and the surface, the image is virtual, erect and enlarged and behind the object. If the surface is concave the radius is to be considered negative. The focal distances then become negative: F 1 =-- ir | n -, F, J^y, which indicates that the anterior focus is situated behind and the pos- terior focus in front of the surface. If, in this latter case, the rays pass from a dense medium (with index = n) into a rarer medium (with index = i), we must in the formulae replace n by -- The focal distances then become positive again : F x = rr, F 2 = ~. This is what happens when rays, after having passed through the first surface of a biconvex surface, meet the second. POWER OF A REFRACTING SURFACE. The refracting power of a sur- face is expressed in dioptrics by the inverse of the anterior focal dis- tance measured in meters: D = - = --^- (i) If for example the anterior focal distance is 24 millimeters (anterior surface of the cornea) the refracting power is D = -^ = 42 dioptrics. Fig. 14. Refraction by a parabolic surface. A, luminous point ; F, its image ; BG, normal; BH, radius of curvature. REFRACTION BY A SURFACE OF REVOLUTION OF THE SECOND DE- GREE. If the luminous point is on the axis, refraction at a given point (1) [In other words, we define the refractive power of a convex surface at a certain point B (fig. 14) as the dioptric power of an infinitely thin plano-convex lens obtained by cutting off a piece of the refracting surface by a plane at right angles to the normal at B and very near to this point. Such detached plano-convex lens, surrounded by the first medium, has a posterior focal distance F 2 equal to the an- terior focal distance ^ equal to - - and a refracting power = -=- =. -=- = n 71 1 r o -=- r i If the surface is not a sphere but a surface of revolution of the second degree, we must replace R by the normal N at the- point B]. W. 14 PHYSIOLOGIC OPTICS B (fig. 14) takes place in the same manner as if the surface was replaced by a sphere drawn around the point G where the normal BG meQts the axis. If we designate as N the normal BG, the refracting power of the surface at the point B is therefore D = n ~ . We can indeed calculate the focal distances for a surface of revolution exactly as we have done for the sphere, and we find the same ex- pressions by replacing R by N. It is well to note that it is the normal BG and not the radius of curvature BH which enters into the formulae. These remarks are of importance for the theory of accommodation and of keratoconus. 14. Infinitely Thin Lenses. The theory of lenses is very simple if we can neglect the thickness. We designate as axis the straight line which joins the two centers of the surfaces, and as optic center the point where this axis crosses the lens. This point enjoys this property that a ray passing through it crosses the lens without deviation. FOCAL DISTANCE OF A BICONVEX LENS. Let us designate the radii of curvature of the two surfaces as Rj and R 2 . Incident parallel rays which meet the first surface are refracted towards the posterior focus, the distance of which, as we have seen, is equal to ^~. This point now acts as the object for the second surface; as it is behind the latter its distance is to be considered as negative. In the formula fi is therefore equal to ir? F x has the value of ^\ and F 2 of ^ri( 13). We have therefore n tVo Rn The posterior focus of the lens is deduced, therefore, from the ex- pression OPTIC PRINCIPLES 15 The anterior focal distance is equal to the posterior focal distance, for it is clear that on rotating the lens the expression -p~ remains the same. We must replace Rj by R 2 , and vice versa, which does not change the expression. CONSTRUCTION OF THE IMAGE (fig. 15). To construct the image A' of a point A we can draw : i. The ray AC passing through the optic center: this ray suffers no deviation ; 2. The ray AD parallel to the axis : after refraction this ray passes through 2 ; 3. The ray A^ passing through the anterior focus: after refrac- tion this ray is parallel to the axis. p. Fig. 15. Construction of the image formed by a thin lens. BC =/ lf B'C =/ 2 , C*j These three rays intersect at the point A, but two suffice to find this point. The triangles AB^ and S^CE on one side, and the triangles DC4> 2 and 4> 2 B'A' on the other give us, as in the case of the mirrors, the relations : which can also be written i.i i h -7- = ~ET By the formula or by construction we find the following relations between object and image : I. If the object is beyond the focus, the image is real and inverted, and on the other side of the lens. It is enlarged if the distance of the object from the lens is less than double the focal distance, diminished in the contrary case. If the distance of the object from the lens is equal to double the focal distance, the object and image are of the same size. 10 PHYSIOLOGIC OPTICS 2. If the object is between the focus and the lens, the image is virtual, erect and enlarged; it is on the same side of the lens as the object, but farther away. If, after having placed a strong lens on a printed sheet, we withdraw it gradually from the sheet, looking through it at some distance we see at first an erect image which is virtual and situated back of the lens and which increases in size the farther we remove the latter, until the sheet is at the focus; at that moment the image disappears (it becomes so large that a single point fills the entire field of the lens). Withdrawing the lens still farther we see an inverted image situated between the lens and the eye. It is enlarged at first, but rapidly diminishes according as the lens is removed. CONCAVE LENSES. While biconvex lenses and plano-convex lenses, which act in the same manner, make incident rays converge, concave lenses make them diverge. The formula of the focal distance remains the same, but as the surfaces are concave the radii must be considered as negative : The focal distance is therefore negative also, that is to say the focus is on the side from which the rays come. Incident parallel rays continue their course as if they come from the focus situated on the same side as the object. The construction of the image is analogous to that which we have employed for biconvex lenses. It gives us the same relations as before with the necessary changes of the signs : I /, F 11 1 and - o k t\ -/, As long as the object is real, the image is virtual, erect and smaller. It is at the focus when the object is at infinity. According as the latter approaches the lens, the image does likewise^ 1 ) MENISCI. A lens, one surface of which is convex and the other con- cave, is called a meniscus. According as the radius of the convex sur- face or that of the concave surface is smaller the meniscus is convergent or divergent (positive or negative). The positive meniscus is thicker in the middle, the negative is thicker towards the edges. These rules are valid, however, only when the thickness is negligible, which often does not happen. (!) Generally the object and image move in the same direction in all cases of refraction, in an opposite direction in cases of reflection. OPTIC PRINCIPLES 17 METHODS OF MEASURING THE FOCAL DISTANCE OF A LENS. The method most frequently employed by oculists consists in looking at exterior objects through the lens, subjecting the latter to slight dis- placements. We then notice that exterior objects are displaced in the same direction as the lens if the latter is concave, in the contrary direc- tion if it is convex. In other words, if the eye is in front of the middle of the lens the rays reach it without any deviation; but if the eye is placed before a peripheral part of the lens it receives rays deflected by reason of the prismatic effect of the glass, and this effect is greater in proportion as the part through which the eye looks approaches the periphery (fig. 16). To determine the focal distance of a lens we find in the test case the glass which neutralizes it (i). Fig. 16. But we must remember that the numeration of the glasses in the test case is frequently not very exact. Lenses have the same curvature on both sides ; we have therefore -J- = 2 (n B ~ l ; the index of the lens is approximately n=i.$, which means that the focal distance and the radius are nearly the same length (-J- = 2 (1 - 5 B ~ 1} = ~). It was customary for a long time to number lenses according to their radius of curvature ; as the index is generally a totle more than 1.5, it would follow that the strong lenses would have a focal distance somewhat less than the number they bear, but in the case of convex glasses the error would be nearly compensated for by the influence of the thickness of the glass. Later, numeration by dioptrics (2) was introduced; and to obviate the necessity of changing the moulds in which glasses are ground the manu- 1 i) We can also use with advantage the American spherometer, a little instrument with which we measure the radius of curvature and thus indirectly the refracting power of the glass. (2) [In 1872 Monoyer, of France, first proposed the term "dioptrie." He says in the Annales d'Ocu- listique, Vol. 68, page 111 : " C'est le pouroir dioptrique de la lentitte d'un metre ou 100 centimetres de lon- gueur focale qui doit servir d'unite. Cette unite nous I'appellerons unite metrtque ou decimale de refraction ou simplement DIOPTRIE si Von veut biens nous permettre ce ntologivme derive conformement aux usages scientiflqucs. This term has been adopted all over the world and in English can have only one philo- logically correct translation, that is dioptry. This correct form has been employed, instead of diopter, all through this work ]W. 18 PHYSIOLOGIC OPTICS facturers simply wrote the numbers in dioptrics on such of the old lenses as most nearly corresponded with such numbers. It is only re- cently that lenses have been manufactured strictly according to the dioptric series. For all these reasons it may be useful for an oculist to be able to de- termine the focal distance directly. For convex lenses we need only form the image of a distant object on a screen. The distance of the lens from the screen is the focal distance. For the concave lenses we place a flame at a great distance so that it forms its virtual image at the focus of the lens ; we then place a screen behind the latter and find the position to give to it in order that the luminous circle formed by the lens would have a diameter equal to double that of the lens. The dis- tance of the latter from the screen is the equal to the focal distance. We can determine the radii of curvature by means of reflection images, by following the formulae which we have given for the mirrors. Knowing the radii and focal distance we can calculate the index by the formula -jr = (n-i> (^- + -^-). REFRACTING POWER OF A LENS. The refracting power (D) of a lens is expressed in dioptrics by the inverse of the focal distance measured in meters : We can better realize the meaning of this expression if we recall the fact that we expressed the refracting power of a surface by the inverse of the anterior focal distance, 1jL ^ . The refracting power of an in- finitely thin lens is, therefore, simply the sum of the refracting powers of its two surfaces. The refracting power of an optical system composed of several in- finitely thin lenses placed very ne, . one another is equal to the sum of the powers of the lenses. 15. Theory of Gauss. If the lenses are not so thin that their thick- ness can be neglected, nor placed so near one another that we can neg- lect their distances, we can find the position and size of the image by construction or by calculation by the rules which we have given for re- fraction by spherical surfaces : we construct or calculate in the first place the image formed by the first surface; this image then serves as the object for the second surface and so forth. But it is much simpler to use the theory of Gauss. We will briefly explain the essential points of this theory, which is applicable to every optical system composed of OPTIC PRINCIPLES 19 spherical surfaces, supposing that the system be centered, that is to say that all the centers of the surfaces are on the axis and that the aperture of the surfaces is small. According to the theory of Gauss, every optic system has six cardinal points, namely : Two principal points, 1^, h 2 (fig. 17) ; Two nodal points, K x , K 2 ; One anterior focus, ^ ; One posterior focus, 2 . The anterior focal distance, F 1 = ^ h lt is the distance of the anterior focus from the first principal point ; it is equal to the distance of the second nodal point from the posterior focus, K 2 3> 2 - The posterior focal distance, F 2 h 2 2 . Its direction is therefore DH. 2. The ray GB, which passes through the anterior focus 4> 15 must, after refraction, be parallel to the axis : It will then take the direction EH. Fig. 18. Construction of the image I of the object O. L*^ = / x . 4^ h t = F lt L/^ =f l M* 2 = I,, *, h, = F 2 , Mft, =/, 3. The ray GK 15 directed towards the first nodal point, takes, after refraction, the direction K 2 H, parallel to its first direction. The triangles GL^ and Eh^^ on one side and the triangles D/L>4> 2 and HM4> 2 on the other give the relation We have, therefore, as before l^ / 2 = F x F 2 , and we can deduce the other general formula -^- + ~jj- = I. Note that / t is reckoned as F from the- first principal point, f 2 on the contrary from the second prin- cipal point. METHODS OF FINDING THE CARDINAL POINTS OF A GIVEN SYSTEM. a. CONSTRUCTION (fig. 19). We draw an incident ray parallel to the axis and we construct its course by the law of Descartes or by the for- mulae which we have given for refraction by spherical surfaces. We thus find the posterior focus. We then prolong the incident and emerg- ent rays; their point of intersection is situated in the second principal plane, and the perpendicular let fall from this point on the axis marks OPTIC PRINCIPLES 21 the second principal point h 2 . Repeating the same construction with a ray parallel to the axis, coming from the other side, we find in the Fig. 19. Construction to find the second principal plane. same manner the anterior focus and the first principal point. Knowing these four points we can deduce the position of the nodal points, since the distance of the first nodal point from the anterior focus is equal to the distance of the second principal point from the posterior focus, etc. b. CALCULATION. Let us designate by A and B the two optic sys- tems which we wish to combine, their focal distances by F\ and F' 2 (for the system A) and by F'^ and F" 2 (for the system B), and the distance of the posterior focus of the system A behind the anterior focus of the system B, by d. We can then find the cardinal points of the combined system by means of the following formulae in which y indicates the dis- tance of the anterior focus of the combined system behind the anterior focus of the system A, and y 2 the distance of the posterior focus of the combined system in front of the posterior focus of the system B. . F',F", d The deduction of these formulae offers no difficulties. An incident ray, parallel to the axis, will pass after refraction by the system A, through its posterior focus, and, after refraction by the system B, through the point 4> (fig. 190) ; the posterior focus of the compound sys- tem. Its prolongation meets the prolongation of the incident ray at D 22 PHYSIOLOGIC OPTICS so that h 2 is the second principal plane of the compound system. After the formula of Newton we have 2/2 = _ F'^F", On the other hand the figure gives us the relations : a F' 2 F 2 F', (y, + F"J T'-d + F", -y 2 + F", r F - - d + F", ' F' (d + F"! _ F', F", We find the value of y x and F x by supposing the light to come from the other side. Knowing thus the focal distance and the position of the foci it is easy to calculate those of the other cardinal points. 4 /^ /' ^ -Z) 19a. In the case which the figure represents, d is negative, since the pos- terior focus of A is situated in front of the anterior focus of B ; F! and F 2 are, therefore, also negative, as well as y^ and y 2 ; the compound system acts as a concave lens. If d the focal distances are infinity : incident parallel rays are again parallel after refraction. Such a system is called telescopic; a telescope focused on infinity by an emmetropic observer is an illustration of it. The distance d, the sign of which determines the character of the compound system is often called the interval; in the cases which interest us it is nearly always positive. OPTIC PRINCIPLES 23 SPECIAL CASES. As the focal distances are proportional to the in- dices of the first and last media, they ought to be equal if the first and last media are identical, which is true for nearly all optical instruments. In this case the distance of the anterior focus from the first principal point is equal to its distance from the first nodal point, that is to say the first principal point coincides with the first nodal point and the sec- ond principal point with the second nodal point. This is what occurs in the case of thick lenses, in which case we can find the nodal points by a simple construction. Let Q (fig. 20) be the center of the first surface ; C 2 that of the second ; C 2 A any radius what- ever of the second surface, and Q B a radius of the first surface parallel to C 2 A. Let us draw the straight line AB, which represents the course of a ray in the interior of the lens; DB and AE indicate its direction outside the lens. It is easy to see that these two straight lines are parallel; the angles i are, in fact, equal, since the angles r are equal. Prolonging DB and AE they cut the axis at the two points K! and K 2 , which are the two nodal points. The point O is the optic center of the lens. It is the image of K x in rela- tion to the first surface, and that of K 2 in relation to the second surface. In an infinitely thin lens, the nodal points and the principal points all coincide with the optic center. If the entire system is represented by a simple refracting surface, both Fig. 20. Construction to find the nodal points principal points coincide with of a thick lens. , . points with the center. The mirrors may be considered as dioptric systems, in which the last medium has an index equal to that of the first medium, but with the contrary sign, since the rays run in a contrary direction. The two principal points coincide with the surface, the nodal points with the center, and the focus is at an equal distance between the two (since F! = F 2 ). The compound reflecting systems likewise have only one principal point and one nodal point, and the focus is situated at an equal 24 PHYSIOLOGIC OPTICS distance between them. Such, for example, is the case in the compound systems which give rise to the images of Purkinje in the eye. EXAMPLE i. To find the cardinal points of the crystalline lens. Suppose the crystalline lens has a thickness of 4 millimeters, that the radius of the anterior surface is 10 millimeters and that of the posterior surface 6 millimeters. Let us take 1.33 as the index of the aqueous humor and the vitreous body, and suppose that the index of the crystal- line lens in relation to these liquids is about 1.06. In this case each of the systems A and B is represented by a single refracting surface. The focal distances of the system A are: R 10 n 1 ~" 0.06 _ , 10 X 1.06 __ 177 2 ~~ 1 ~ 0.06 those of the system B are : 1.06 l.Oti The interval d is the distance of the posterior focus of the system A from the anterior focus of the system B; the former is situated at 177 millimeters behind the anterior surface, the latter at 106 millimeters in front of the posterior surface ; the thickness of the crystalline lens being 4 millimeters, we will have ^=177 miljimeters + 106 millimeters 4 millimeters = 279 millimeters, and _ F" x F", _ 106X100 _ ~~^~ 279 167 X 106 279 = 63.4 The anterior focus of the crystalline lens being situated at 106 milli- meters behind the anterior focus of the first surface C, which is at 167 OPTIC PRINCIPLES 25 millimeters, its distance as far as that surface will be 167 106 = 61 mil- limeters, and as the focal distance is 63.4 millimeters, the first principal point of the crystalline lens will be placed at 2.4 millimeters behind the anterior surface. The second principal point will be situated at an equal distance, at 100 38 63.4 = 1.4 millimeters, that is to say, 1.4 mil- limeters in front of the posterior surface. Both focal distances are equal, as they must be, since the surrounding media are alike. The refracting power of the crystalline lens would be with these data 6 - 3 ^ = 15.8 D. EXAMPLE 2. Let us consider the cornea as a simple refracting sur- face with a radius of 8 millimeters surrounded in front by air (n = i), behind by the aqueous humor (n = 1.33 = f ). The distance of the anterior surface of the cornea from the anterior surface of the crystalline lens is 3.6 millimeters. To combine the cornea with the crystalline lens the cardinal points of which we have just found. Here the cornea forms the sstem A. Its focal distances are : *-.-**-- The principal points coincide with the surface. The focal distances of the system B are those found above for the crystalline lens. The interval d is the distance of the anterior focus of the crystalline lens as far as the posterior focus of the cornea: d = 6i mm. + 32 mm. 3.6 mm. = 89.4. With these data we find for the entire optic system of the eye : 24 X 32 89.4 = 8.6 mi The following table gives a general idea of such an optic system. By position of a point we mean the distance of that point behind the sum- mit of the cornea. 26 PHYSIOLOGIC OPTICS Simplified Eye. Index of aqueous humor and vitreous body 1.33 the crystalline lens 1.41 Radius of curvature of the cornea 8 mm anterior surface of the crystalline lens. . 10 mm posterior surface of the crystalline lens . . 6 mm Depth of the anterior chamber 3.6 mm Thickness of the crystalline lens 4 mm Anterior focal distance of the cornea 24 mm Posterior focal distance of the cornea 32 mm Focal distance of the crystalline lens 63.4 mm Position of the anterior principal point of the crystalline lens 6 mm posterior principal point of the crystalline lens 6.2 mm Anterior focal distance of the eye 17 mm Posterior focal distance of the eye 22.7 mm Position of the anterior principal point of the eye 1.6 mm posterior principal point of the eye 1.9 mm anterior nodal point of the eye 7.3 mm posterior nodal point of the eye 7.6 mm anterior focus of the eye 15.4 mm posterior focus of the eye 24.6 mm Kefracting power of the cornea 42 D. crystalline lens 16 D. eye 59 D. We shall see in the following chapter that the data with which we have made these calculations are not rigorously exact; nevertheless, they give a very close approximation, generally sufficient for our pur- pose. Later I shall have recourse more than once to this system, which I call the simplified eye, to distinguish it from the complete optic system of which we shall treat in the following chapter. Bibliography. Complete development of the system of Gams in the introduction to the physiologic optics of Helmholtz. Among the numerous treatises on geometric optics, I shall cite: Jamin and Bouty. Cours de physique de I'Ecole Polytechnique, 1886. Pouillet-Muller. Lehrbuch der Physik und Meteorologie, 8th edition. Braunschweig, 1872. Of an easy study. Wiillner (Ad.). Lehrbuch der ExDerimentalphysik. II. Leipzig, 1877. Lorenz (L.). Die Lehre vom Licht. Leipzig, 1877. Among the more complete works, but of a more difficult study, we shall cite : Verdet (E.). (Euvres. Paris, 1872. Herschel (Sir J. F. W.). Light. London. 1845. In French by Verhulst (P. F.) and Quetelet (A.). Paris, 1829. Heath (K. S.). A Treatise on Geometric Optics. Cambridge, 1877. Gariel (G. H.). Etudes d'optique geometrique. Paris, 1889. The beautiful works of E. Abbe resulted in considerable progress in geometric optics dur- ing the last twenty years. We will find an account of them in Czapski (S. ), Theorie der optischen Instrumente, Breslau, 1893, and, in a more easily accessible form, in the new edition of Pouillet-Muller, by Pfaundler (L.) and Luoamer (O.), Braunschweig, 1897. CHAPTER II. THE OPTIC SYSTEM OF THE EYE. 16. Optic Constants of the Eye. By means of the theory of Gauss we can calculate the cardinal points of any optic system if we know the position and curvature of the surfaces and the index of the media. To calculate the optic system of the eye we must know, therefore, as ex- Fig. 21. The optic system of the eye (left), C 1? C 2 , C 3 , C 4 , the centers of the four surfaces in their natural order; AB, optic axis ; L, visual line. actly as possible those numbers which are frequently called the optic constants of the eye. Those which I have given in the examples in the preceding chapter are only approximate. The following table gives the constants of an eye, which I have measured as carefully as possible (fig. 21): Optic Constants of the Eye. Position of the anterior surface of the cornea posterior surface of the cornea 1.15 mm anterior surface of the crystalline lens 3.54 mm posterior surface of the crybtalline lens 7.60 mm Radius of the anterior surface of the cornea 7.98 mra posterior surface of the cornea 6.22 mm anterior surface of the crystalline lens 10.20 mm posterior surface of the crystalline lens 6.17 mm 27 28 PHYSIOLOGIC OPTICS Index of the air cornea aqueous humor Total index of the crystalline lens, Index of the vitreous body accepted 1 1.377 1.3365 1.42 1.3365 The positions and radii of the surfaces as stated are according to measurements which I made by methods which I shall mention later. The only difference of any importance between them and those found up to the present arises from the thickness of the crystalline lens which, in his schematic eye Helmholtz put down as 3.6 millimeters, certainly too small a number to be considered an average. I have also added the numbers for the posterior surface of the cornea which I was the first to measure. As to the indices which cannot be measured directly on the living eye I have put down 1.377 for the cornea after a measurement of Matthiessen, which I also have verified. Those of the aqueous humor and vitreous body are very exactly known ; we can, indeed, determine them with great exactness by means of the refractometer of Abbe, or by other analogous methods. Less is known of the index of the crystalline lens than of the other optic constants of the eye. It must be noted in the first place that this body is not homogeneous; its index gradu- ally diminishes starting from the center of the nucleus towards the periphery. The curvature of its layers diminishes also towards the periphery, so that each layer takes the form of a meniscus, the concavity of which is greater than the convexity. This conclusion follows as well from anatomical researches as from optic observations which I made on the eye of an ox after death (i). There is, indeed, frequently produced, in the Fi e- 22 - ~ P tic g y stem f tlie eye of an ox (twice enlarged), crystalline lens, after death, a differentiation between the cortical masses and the nucleus, probably caused by the im- bibition of water by the superficial parts. In consequence of this process (1) The optic constants of such an eye are as follows (fig. 22) : Radius of the cornea 15 millimeters Position of the anterior surface of the crystalline lens 6 posterior surface of the crystalline lens 17 Radius of the anterior surface of the crystalline lens 14 posterior surface of the crystalline lens 8 anterior surface of the nucleus 8.5 posterior surface of the nucleus 7 THE OPTIC SYSTEM OF THE EYE 29 there is produced on the surfaces of the nucleus quite a regular reflec- tion, so that instead of two reflection images we see four (fig. 23), when Fig- 23. Images of Purkinje of the eye of an ox (dead). (Flame of a candle.) a, image of the cornea ; 6, image of the anterior surface of the crystalline lens; c, image of the anterior surface of the nucleus; d, image of the posterior surface of the nucleus; , image of the posterior surface of the crystalline lens. the crystalline lens is exposed to the light of a flame. Now, the position of these images indicates that the curvature of the surfaces of the A B Fig. 24. Double crystalline images in cases of "false lenticonus." After Demicheri. A. Looking straight in front. a, image of the cornea ; 6, image of the anterior surface of the crystalline lens ; c, image of the anterior surface of the nucleus; d, image of the posterior surface of the crys- talline lens, which coincides, for this direction of the look, with that of the posterior surface of nucleus. B. Looking outwards. a, image of the cornea ; b, image of the posterior sur r ace of the crystalline lens; c, im- age of the posterior surface of the nucleus. 30 PHYSIOLOGIC OPTICS nucleus is considerably greater than that of the crystalline surfaces. Dr. Dcmicheri has recently described cases of alterations of the human crystalline lens in which we can also observe four crystalline images ; their position also indicates a greater curvature of the surfaces of the nucleus (fig. 24). It has long been known that, as a result of this peculiar construction of the crystalline lens, its total index, that is to say, the index of an imag- inary lens having the same form and the same focal distance as the crystalline lens, is greater, not only than the mean index of the crystal- line layers, but even than that of the nucleus. To account for this paradoxical phenomenon, we may suppose the crys- talline lens divided into two parts, the nucleus and the cortical part, supposing the index uniform in each part, but greater for the nucleus. On account of its great curvature and high index, the nucleus (a, fig. 25) would then have a very considerable refracting power, which, however, would be diminished by the influence of the cortical layers which act as two concave lenses (b, b). It is clear that if the index of these layers were higher their influence would be greater, and the refracting power of the whole crystalline lens would consequently 1 Fig. 25. be weaker. Thomas Young placed the index of the center of the nucleus at 1.412, and by calculation therefrom he deduced 1.436 for the total index. Later Listing gave 1.455 f r the total index, a number adopted by Helmholts, but which is decidedly too high. For his new schematic eye this latter author later adopted an index (1.4371) which was nearly identical with that of Young. More recently Matthiessen tried to determine the law after which the index of the crystalline lens varies from the center towards the periphery, and to calculate from it the total index. According to him the difference between the total index and that of the superficial layers would be double the difference between the index of the nucleus and that of these cortical layers. He has found 1.437 as the total index, and the average of his measurements of the central index approaches very close to the figures of Young. Measurements which I have taken after a new method, in collaboration with Dr. Stadfeldt (i), seem, however, to show that the law of Matthiessen can be considered only as an approx- imation, and, on the other hand, the observations of those who have (1) According to the measurements of Stndfddt, which I shall mention later on, the mean index of the crystalline lens would be 1.435, and the refracting power of the crystalline lens would be on an average 19 D. (varying between 17 D. and 24 D.). THE OPTIC SYSTEM OF THE EYE 31 operated on cataract seem, as we shall see later, to call for a lower total index. Awaiting the result of new measurements I adopt the number 1.42. Thanks to the special structure of this organ the refracting power of the crystalline lens is some dioptrics stronger than it would have been if its index had been uniformly equal to that of the nucleus. In comparison with the total refraction of the eye the increase is not con- siderable ; it might easily have been obtained by a slightly greater curva- ture of one of the surfaces. The teleologic reason for this structure is rather to be sought in the mechanism of accommodation. For, this mechanism would be, as I understand it, impossible without the two peculiarities which characterize the structure of the crystalline lens : the increase of density and the increase of curvature of the layers according as we approach the center. Another advantage of this structure of the crystalline lens consists in making weaker the images of the eye which I call harmful (miisibles), and which I shall mention farther on. 17. Optic System of the Eye. Applying the theory of Gauss to the data which we have just stated, we find the following results: A. Optic System of the Cornea. Position of the first principal point 0.13 mm second principal point 0.14 mm first nodal point 8.08 mm second nodal point 8.07 mm anterior focus 24.53 mm posterior focus 32.47 mm Anterior focal distance 24.40 mm Posterior focal distance 32.61 mm Refracting power 40.98 D. B. Optic System of the Crystalline Lens. Position of the first nodal point 5.96 mm second nodal point 6.14 mm Focal distance of the crystalline lens 62.46 mm Refracting power 16.01 D. Combining these two systems, we find the complete optic system of the eye. C. Complete Optic System of the Eye. Position of the first principal point 1.54 mm second principal point . 1.86 mm first nodal point 7.30 mm second nodal point 7.62 mm anterior focus 15.59 mm posterior focus 24.75 mm Anterior focal distance 17.1 3 mm Posterior focal distance 22 89 mm Refracting power : 58.38 D. 32 PHYSIOLOGIC OPTICS Thanks to these data we may eliminate, so to speak, the entire real optic system of the eye. In the system which we have just calculated we take into consideration only the course of the rays in the air before en- tering the eye, and their course in the vitreous body after emergence from the crystalline lens; their course between the an- terior surface of the cornea and the posterior surface of the crystalline lens re- mains unknown to us. Fig. 26. Position of the cardinal points of the human eye (magnified four times). A! h 2j principal planes ; K l K 2 , nodal points. We note that the refracting power of the cornea is 2.5 times greater than that of the crystalline lens. The sum of their refracting power is not far from being equal to the refracting power of the eye, because the nodal points of the cornea are quite near those of the crystalline lens (i). The following little table shows the refracting power of each of the surfaces : Anterior surface of the cornea -f- 47.24 D. Posterior surface of the cornea 4.73 D. Anterior surface of the crystalline lens + 6.13 D. Posterior surface of the crystalline lens 4- 9.53 D. Total -j- 58.17 D. The posterior surface of the cornea has, up to the present, been neg- lected by authors ; we see that it has a certain importance. Its value is negative and almost as great as that of the anterior surface of the crys- talline lens. We shall see that it seems to play a part in certain forms of astigmatism. Nevertheless, we commit only a very small error by neglecting it, (1) The refractipg power of the eye would be exactly equal to the sum of the powers of its compo- nent systems, if the anterior principal point of the crystalline lens coincided with the posterior nodal point of the cornea, or if we consider the cornea as a single refracting surface, with its center. In the formula of paragraph 15 (page 22) _F/ i jw i 1 ~ d we would have, indeed, in this case d FI' + FI", which gives 111 THE OPTIC SYSTEM OF THE EYE 33 that is to say, by supposing that the substance of the cornea does not exist; the anterior surface simply separating the air from the aqueous humor. By eliminating the negative influence of the posterior surface, the total refraction of the cornea should increase, but the power of the anterior surface diminishes nearly as much, since we replace the index of the cornea by the weaker index of the aqueous humor. In our case we would, by thus simplifying the matter, have found a refracting power of the cornea equal to 42.16 D. instead of 40.98 D., that is to say, we would have committed an error of 1.18 D. or about 1/50 of the total power of the eye. The right eye, the optic system of which I have calculated (in the hori- zontal meridian), is the only one of which up to the present time we pos- sess complete measurements. It is important to note that it is not to be considered as an average. The radius of the cornea is two or three- tenths of a millimeter above the average, and the length of the axis of the supposed emmetropic eye, which we have found equal to 24.75 mm., is probably also a little above the average. This eye is, therefore, to be considered relatively large, the more so as the person to whom it belongs is pretty tall in stature. A light degree of astigmatism with the rule would also act in the same way. I have measured some other eyes, but not a sufficient number to be able to establish an average. The figures which I have just given apply only to the eye of the adult. The eye of the new-born child is much smaller (the axis meas- ures about 17 mm. instead of 24 mm.), so that we might expect to see the curvature of all the surfaces increased in the same proportion. This is not so : according to the concordant measurements of AxenfeUl and Holth the cornea of the new-born child differs but little from the adult cornea. This latter varies as we shall see between quite wide limits (40 to 47 dioptrics) and the values which we find in the new-born child are near the higher limit. Compensation for the diminution of the axis is made by the crystalline lens. According to the measurements of Stadfeldt the crystalline lens of the new-born child is as thick as that of the adult, but the diameter is 6 mm. instead of 8 or 9 mm., whence it follows that the curvature of the surfaces is very great. Following are some figures according to Stadfeldt:. Radius Radius Ant. surface. Post, surface. Thickness. Diameter. Adult 1 l mm 6 mm 3.6 mm New-born 4.5 mm 4 ram 3 9 mm 6 mm 34 PHYSIOLOGIC OPTICS Supposing that the index is the same as in the adult, the crystalline lens of the new-born child would, therefore, be nearly twice more re- fracting, and the crystalline refraction in the latter would not be very far from being equal to the corneal refraction. 18. Aperture of the System. The theory of Gauss supposes that the aperture of the system is very small, which is by no means the case in the eye, and many errors committed in questions of ocular refraction seem to me due to the fact that we do not sufficiently take into account the large aperture of the system. In optic instruments an aperture over ten or twelve degrees is scarcely accepted. Supposing that the pupil has a diameter of 4 millimeters, the aperture of the cornea would be 20 degrees ; and a pupillary diameter of 4 millimeters is rather insufficient, for it must not be forgotten that we generally examine our patients with a very strong light. In the ordinary circumstances of life, the pupillary diameter is most frequently greater (5 or 6 millimeters), whence results a series of errors which would be still greater but for the special precautions taken to neutralize them in part. We must bear in mind that the pupil is seen neither in its real posi- tion nor at its true size : it appears moved forward and enlarged on ac- count of the refraction through the cornea. It is easy to determine its apparent place and size. In our general formula, -^ -f- -^- = 1, we must put the values of the cornea of the simplified eye, F = 24, F 2 = 32, and the distance of the anterior surface of the crystalline lens and of the pupil from the anterior surface of the cornea, f 2 = 3.6, and we find / x = 3.04. And if the real size is 4 millimeters, we put in the formula -- = L the values O = 4 mm , F 2 = 32 mm , / 2 = 3.6 mm 32 mm = 28.4 mm ; therefore The pupil appears, therefore, moved forward about 0.5 mm. and en- larged by the same quantity. The iris appears at the same time swelled in front. What we see is, therefore, a virtual image of the iris and of the pupil. We call these images apparent iris and apparent pupil. They are aerial images. Rays which, in the air, are directed towards a point of the apparent pupil are, after refraction by the cornea, directed towards the corresponding point of the real pupil. If we imagine the iris and pupil seen, through the crystalline lens, by an eye located in the vitreous body, the pupil would no longer appear THE OPTIC SYSTEM OF TEE EYE 35 in its place, but the displacement would be less ; it would be seen nearly o.i mm. farther back than it is in reality, and enlarged 0.2 mm. Rays coming from a point of the real pupil would proceed in the vitreous body as if they came from the corresponding point of the crystalline image. If we had constructed the corneal image and the crystalline image of a point of the pupil, we would then know that a ray directed towards the former would pass, after refraction by the cornea, through the same point, and, after refraction by the crystalline lens, through the crystal- line image of the point. The apparent pupil belongs therefore to the incident rays as does the first principal point or the first nodal point, and the crystalline image of the pupil belongs to the emergent rays. The luminous cone which enters the eye is limited by the apparent pupil; in its course between the cornea and the crystalline lens, it is limited by the real pupil, and, in the vitreous body, by the crystalline image of the pupil. There are analogous phenomena in most optical instruments, wherever a diaphragm is between two lenses; Professor Abbe has proposed the names of pupil of entrance and pupil of exit for the images of the diaphragm. We have seen that the principal planes are each the image of the other, and that they have this characteristic that the object and image are of the same size. In the formula -|X -f- - = 1, the distances marked 1 are calculated to start from the first principal point, those marked 2 to start from the second principal point. But in this formula we can as well calculate the distances from any other pair of points, one of which is the image of the other. We might measure, for example, from the pupil of entrance and pupil of exit. We would thus have in figure 27 the relation ~~ + ^ =1 Fig. 27. oa, pupil of entrance; 66, pupil of exit; O, object; I, image; 4> 1} anterior focus ; 4>j, posterior focus. and we could find the image of an object by constructions analogous to those in which we have used the principal planes. The only difference is this: if an incident ray meets the first principal plane at a distance 36 PHYSIOLOGIC OPTIC8 from the axis equal to y, the emergent ray also cuts the second princi- pal plane at a distance from the axis equal to y. But if the incident ray meets the pupil of entrance at a distance from the axis equal to y, the emergent ray cuts the plane of the pupil of exit at a distance from the axis which is to y in the same relation as the diameter of the pupil of exit is to that of the pupil of entrance. In our case it would be the re- lation of -g-. This mode of procedure is often more convenient than the classic method, more especially because it is easy by this construc- tion to calculate the diameter of the luminous cone. 19. Point of Fixation. Visual Line. To distinguish an object clearly it is necessary to fix it, that is to say, to place the eye in such a way that its image is formed on the fovea. The point fixed and the fovea are therefore conjugate foci. But we would be greatly deceived if we thought that the entire fovea corresponded with the point of fixation. The anatomical fovea has an extent of 0.2 mm. to 0.4 mm. (Henle) or of 0.75 to 1.50, seen from the posterior nodal point (at 1 6 millimeters from the retina). Looking at the sky the fovea would cover, therefore, a part having two or three times the diameter of the moon, which corresponds to a half degree. The point of fixation is much smaller in dimension, for 'we can readily tell whether we fix the right border or the left border of the moon. Generally when two points closely approach each other we can still tell which one is fixed as long as we can see that there are two. It was Javal who specially insisted on this fact, to which he at- tributed great importance for the theory of binocular vision. We designate as the visual line the ray which goes from the point fixed to the first nodal point, and which, consequently, after refraction, reaches the fovea as if it came from the second nodal point. If, in the aphakic eye, we neglect the posterior surface of the cornea, the visual line passes through the center of curvature of the anterior surface ; it is, therefore, perpendicular to that surface. In a normal eye it is never far from being so, since the nodal points are very near the center of curva- ture of the anterior surface of the cornea. The direction of the visual line does not depend on the position of the pupil. In cases of pupillary displacement it may happen that the ray which represents the visual line does not enter the eye. We shall see later (page 64) how we may determine experimentally the direction of the visual line in the eye. 20. Optic Axis. Angle . An exact centering would demand that the four centers of curvature, or the three, if we neglect the posterior THE OPTIC SYSTEM OF THE EYE 3T surface of the cornea, would be on the same straight line. The center- ing of the eye is never exact, but the deviations that we can establish are often small. In some cases I have, however, found defects of cen- tering relatively large in eyes, too, which functionally should be con- sidered normal. The defect which I have most frequently met consists in this, that the center of curvature of the cornea is situated (as much as a quarter of a millimeter) below the axis of the crystalline lens. Neg- lecting these deviations the optic system of the eye may be considered as centered around a straight line which is called the optic axis of the eye. The fovea not being placed on this line, it does not coincide with the visual line ; it is directed outward and downward from the visual line and forms with it an angle of 5 to 7, called the angle (fig. 21). We shall see later that the anterior surface of the cornea is not spher- ical: it is flattened towards the periphery so that it may be compared to an ellipsoid of revolution around the long axis. Certain authors designate as the angle the angle which the line of vision forms with that axis which passes through the most curved part of the cornea (the summit). Generally the axis of the cornea very nearly coincides with the optic axis of the eye, so that both definitions amount to the same thing. But we shall see that the comparison of the form of the cornea to that of an ellipsoid is very defective. Hence it may be better to retain the old definition. We can compare the optic system of the eye with that of an opera glass. If the optician, by a defect of workmanship, had placed one of the lenses a little obliquely, or if he had placed the middle of this lens a little outside the axis of the instrument, this defect would correspond with a defect in the centering of the eye. If, on the contrary, the ob- server looked a little obliquely through the glass, the visual line would form with the axis of the glass an angle which would correspond with the angle . 21. Useful Image. The optic system of the eye forms a dioptric image, real, inverted and diminished, which is projected on the retina as the photographic image is formed on the screen of the dark chamber. The comparison between the eye and the dark chamber dates from the invention of this instrument (Porta, Leonardo da Vinci). But although we had from that time all the elements necessary to understand the construc- tion of the eye, there continued, however, to prevail much confusion on this question, more especially because people could not be brought to admit that the image which serves for vision was inverted. It was 38 PHYSIOLOGIC OPTICS Kepler (1604) who first explained the formation of images in general and was led to suppose the existence of an inverted image on the retina, an image which was later demonstrated by Scheiner on an eye from which he had removed a part of the sclera and of the choroid. But, besides this image which I designate as the useful image, because it serves for vision, there is formed in the eye a series of other images which I have designated as false images of the eye, and which will form the subject of the following chapter: Bibliography. (Euvres ophthalmologiques of Thomas Young, edited by Tscherning, p. 134-137. Listing (J.). Dioplrik des Auges in Wagner, Handwb'rterbuch der Physiologic. Tscherning (M.). Beitrdge zur Dioptrik des Auges in Zeitschrift fur Psychologie und Phys- iologie der Sinnesorgane, III, p. 429. Matthiessen. Die neueren Fortschritte in unserer Kent- niss von dem optischen Baue des Auges der Wirbelthiere in Beitrdge zur Psychologie und Phys- iologie der Sinnesorgane, dedicated to Helmholtz on the occasion of his 70th anniversary. Stadtfeldt (A.). Hecherches sur I'indice total du cristallin humain. Journal de Physiologie et Pathologic. November, 1899. CHAPTER III. FALSE IMAGES OF THE EYE. 22. General Kemarks. If we place a flame at some distance from a lens, we notice on the same side with the light two reflected images of the flame, one for each surface. Placing the eye on the other side of the lens at some distance, we see the dioptric image, which is real, and, besides, a small, indistinct image due to a double reflection in the in- incident Ray Ray Harmful Ray Useful Ray , > i^ost Ray Fig. 28. Reflections and refractions by a lens. terior of the lens, a first reflection produced by the posterior surface, and a second by the anterior surface (fig. 28). The rays which form this latter image undergo, besides, a refraction by each surface of the lens. The small image is real ; we can, indeed, receive it on a screen held near the lens. The incident light is thus divided into three portions: useful light which forms the dioptric image of which we generally make use, the light lost by reflection on the surfaces, and lastly, the light reflected twice, which I call harmful (nuisible). This harmful light may, indeed, enter the eye which is observing the useful image, where it is often a cause of 89 40 PHYSIOLOGIC OPTICS annoyance, because it does not contribute to the formation of that image. A simple lens loses about 8 per cent, by reflection, and the harmful light represents only 1/500 of the incident light. In complicated instruments much more of the light is lost. In the ophthalmometer of Javal and Schioetz, the loss is about 33 per cent. In the human eye we may also distinguish between the useful light which passes through the surfaces, the light lost by reflection, and the harmful light, which, having suffered two reflections, returns again towards the retina. But the eye has this peculiarity that, of all optic instruments, it is that which loses least light (about 2 per cent.). The harmful light is also reduced to a minimum, but feeble as it is, it is visible nevertheless. The useful light forms the dioptric image which serves the purpose of vision; the lost light forms four false images of the first order, called Fig. 29. Manner in which a luminous ray is divided in the eye. A, incident ray. I, II, III, IV, lost rays corresponding to the four images of Purkinje; V and VI, harmful rays corresponding to the fifth and sixth image ; VII, useful ray. images of Purkinje, one for each surface ; they correspond to rays I, II, III and IV, fig. 29. The harmful light forms a series of false images of the second order, of which one only is visible (rays V and VI, fig. 29). 23. The Images of Purkinje. These images were described at the beginning of this century by the scientist whose name they bear, but one of them, the second, was lost sight of until I described it again some years ago. (i) The first of these images, that due to the anterior surface of the cornea, is produced by a single reflection, the others are formed by rays, which, after having suffered one or several refractions, are at first reflected, then undergo still other refractions before emerg- ing from the eye. The optic systems which produce these images are, therefore, quite complicated, but we can always replace them by a single reflecting surface, which I call the apparent surface. (1) See Biix, however. Oftalmometriska Studier. Uppsala, 1880, p. 63. FALSE IMAGES OF THE EYE 41 Suppose, for example, that we wish to study the third image of Purkinje, that produced by reflection at the anterior surface of the crys- talline lens. Neglecting the weak refraction by the posterior surface of the cornea, the rays suffer, besides reflection, two refractions, one on en- tering and the other on emerging from the eye. Now, we can replace Fig. 30. Position of the seven images in the eye. The object is supposed to be situated at 20 degrees below the yisual line. this series of refractions and reflections by a simple reflection on the ap- parent surface. We find the position of this surface by finding the posi- tion of the image of the real surface, seen through the cornea, in the same manner as we have already found the position of the apparent pupil, by means of the formula ^ + -jf- = 1 ; with the values of the simplified eye we have F = 24 mm., F 2 = 32 mm., f 2 = 3.6 mm., which gives the position of the apparent surface, f = 3 mm. We then find the position of the center of the apparent surface by finding in the same manner the image of the center of the real surface seen through the cornea (f = 13.5, which gives f z = 17.5). The apparent surface being at 3 mm. and its center at 17.5 mm., it must perform the function of a convex mirror of 14.5 mm. radius, placed three millimeters behind the cornea. The focus is at an equal distance between the surface and the center, that is to say at 10.2 mm. behind the cornea; it is therefore very nearly at this place that the third image of Purkinje is formed. We can also use the apparent surface to calculate the size of the image, follow- ing the formula-?- = ~ (see page 5.) To make the same calculation for the posterior surface of the crys- talline lens, we must first calculate the refracting system composed of the cornea and of the anterior surface of the crystalline lens, and then the 42 PHYSIOLOGIC OPTICS images of the posterior surface and of its center, seen through this system. With the exception of the anterior surface of the crystalline lens, the apparent surfaces differ only slightly from the real surfaces. The three first surfaces being convex their images are erect, while that of the fourth is inverted. The object being generally at quite a distance, the images are formed very near the catoptric foci of the apparent surfaces. The first, second and fourth are nearly in the pupil- lary plane, while the third is situated at 7 or 8 mm. behind this plane (fig. 30). Besides, the third image easily disappears behind the iris when the eye makes a slight movement, which makes this image more difficult to observe than the others. 24. Manner of Observing the Images of Purkinje. The first linage, that of the anterior surface of the cornea, is much the brightest; its observation offers no difficulty. To observe the second image we place ourselves as when we wish to examine a patient by oblique illumination, and we examine the eye with a magnifying glass, a lens of 10 D. for example, but without concentrat- ing the light on the eye. Examining the corneal image of the flame, we shall see when it approaches the border of the pupil, and still better, when it shall have passed it, that it is accompanied by a small image which is situated near it. The more the images approach the edge, the more distant they are from each other; near the edge the distance may exceed a millimeter, and the small one is frequently still visible when the large one has already disappeared, giving way to the irregular reflex of the sclera. The small image is always situated between the large image and the middle of the pupil, which indicates that the posterior surface is more curved than the anterior surface. Suppose, indeed, that we used two lamps, one on each side, and consider the distance separating the two lamps as the object (fig. 31). It is then clear that the image of the posterior surface is smaller than that of the anterior surface, which indi- cates that its curvature is greater. At the middle of the pupil the small image is not visible, because it coincides with the large one ; they are, indeed, situated at the same distance from the summit of the cornea. The third image, the largest, always preserves, whatever we may do, a more or less diffuse appearance, due to the fact that the index varies in the superficial layers of the crystalline lens. To observe it we place ourselves as before, requesting the person whose eye is being examined to look in a direction which nearly bisects the angular distance between the eye of the observer and the flame. By moving his eye slightly from FALSE IMAGES OF THE EYE 43 side to side the observer will quite easily see the image which presents itself as a broad glow, pale and more or less diffuse, and which changes position at the least movement of the observed eye. Fig. 31. Corneal images of two lamps, observed with the ophthalmophakometer. The small images beside the large ones are due to reflection by the posterior surface of the cornea. After having found the image, we can concentrate the light on the eye; by this means we magnify the image, which soon fills the entire pupil. If the light is bright the pupil frequently appears white, as if the eye was affected by a ripe cataract, and we may, by examining it with the magnifying glass, thus observe anatomical details which we cannot discover in any other way. I recommend to clinicians this exam- ination, of which I have nowhere found a description, (i) To make the experiment under the best conditions we must select a lens of large aper- ture, place the luminous source at quite a distance and hold the lens in such a way that its focus coincides with the catoptric focus of the surface. The third image is, as we shall see, of great importance for the study of accommodation. The fourth image does not generally offer any difficulties to the ob- server. It is observed under the same conditions as the preceding one, by directing the look of the observed person a little towards the lamp. (1) Rings of DEMICHERI. Demicheri has recently (Bulletin of the Society of Ophthalmology of Paris) described phenomena of coloration which are observed by this method in the pupil in certain affections of the crystalline lens. The middle of ' zone, then by a yellow zone, and lastly eration was one of more or less mature cataract. over, the crystalline lens appeared intact, the pupil was tilled by this examination with an intense red, so that one would have thought it filled with blood. These colors are probably phenomena of inter- ference due to the reflection on the finely reeded surface of the crystalline mass, nearly like the colors which mother-of-pearl presents, but the conditions under which they are produced are still unknown. loratiou which are observed by tins memoa in tne pupil in certain affections e middle of the pupil appeared blackish blue ; it was surrounded by a green , and lastly by a red zone, near the pupillary border. The case under cotisid- less mature cataract. In a case which I have examined, and in which, more- 44 PHYSIOLOGIC OPT! CIS It is small and distinct. Being inverted it moves in a direction contrary to that of the others. For a more minute examination of these images my ophthalmophako- meter may be used (fig. 32). It is composed of a small telescope, sup- . 32 The Ophthalmophakometer. ported on a stand, and of a copper arc movable around the axis of the telescope, and bearing a scale, the zero of which coincides with this axis. The radius of the arc is 86 centimeters. The head of the observed person is fixed by a head-rest in such a manner that the eye which we are to examine is at the center of the arc. On the arc move several cursors, which carry electric lamps. Each lamp is enclosed in a tube closed in front by a plano-convex lens, which concentrates the light on the observed eye. I will speak later of the manner of using the instrument for measuring the internal surfaces of the eye. 25. False Images of the Second Order. All the reflected rays which emerge from the eye to form the images of Purkinje, with the exception of those of the first image, meet surfaces which again reflect a part of the light; this light is extremely feeble for most of the surfaces; it is only on meeting the anterior surface of the cornea that there is reflected sufficient light to be visible. Thus there are formed two more images, the fifth, produced by a first reflection on the anterior surface of the crystalline lens, and a second reflection on the anterior surface of the FALSE IMAGES OF THE EYE 45 cornea, and the si.vth, due to a first reflection on the posterior surface of the crystalline lens and a second reflection on the anterior surface of the cornea. As the rays return towards the retina, these images are subjective. The optic systems which produce these images are very complicated. They are calculated, too, by the formulae which we have explained on page 21. The focus of the fifth image is near the posterior surface of the crystalline lens. It is, therefore, at this place that this image of a distant object is formed. Before reaching the retina the rays are so dispersed that they are no longer visible ; I, at least, have not been able to discover the least trace of this image. Theoretically we ought to be able to make it visible by bringing the object nearer, since the image and object move in the same direction as in all the refracting systems, but the experiment did not succeed. In fact, when the flame with which we are working is moved near enough to the eye, the useful image becomes transformed into a diffusion circle, which fills the greater part of the field and prevents one's seeing anything else. The focus of the sixth system is, on the contrary, very near the retina of the emmetropic eye ; the image is also generally easy to observe. 26. Manner of Observing the Sixth Image. We choose, in a half- darkened room, a point of fixation situated some distance away, and, having fixed this point, we give to the candle, held in the hand, a to-and- fro horizontal motion, moving it towards and away from the visual line without, however, reaching it. We, then, notice on the other side of the visual line a pale image of the flame. Some people see the phenomenon sufficiently distinct to be able to discern that the image appears inverted, the retinal image being erect. We discern more clearly the form of the image when we cause the candle to pass below the visual line ; the image then passes above, and we see that its apex is directed downwards. Myopes see the image with greater difficulty ; they often succeed better when using their correcting glasses, but they must then guard against confounding it with the images pro- duced by repeated reflections between the cornea and the glasses. It seems that there are persons who cannot perform the experiment successfully. If the anterior chamber is unusually deep it may, indeed, happen that the focus of the system is quite a distance from the retina, but we ought then to be able to succeed by moving the flame towards the eye or away from it. We see, therefore, how very advisable it is that the harmful light be reduced to a minimum; in fact, if the index of the superficial crystalline 46 PHYSIOLOGIC OPTICS layers had been higher, the sixth image would have had more brilliancy, and we would be affected with an annoying monocular diplopia. And right here we must pause to wonder at the enormous sensitiveness of the retina, for the brightness of the sixth image is really only ^ m of that of the useful image. One can study the sixth image more closely, by means of the ophthal- mophakometer, by placing oneself in the place of the person examined, and by fixing the middle of the objective of the telescope, which cor- responds to the zero of the division. Placing the arc horizontally, and putting the lamp A which slides on the arc at some distance from the telescope, we see the image appear on the other side. We bring one of the cursors of the arc to coincide with the image, so that we may read its position on the scale. We, then, notice that the image is only approximately symmetrical with the lamp, in relation to the visual line. By causing the arc to rotate 180 in such a way as to bring the lamp into a position symmetrical with the former, we notice that the image no longer coincides with the cursor. This is on account of the angle . If the visual line coincided with the optic axis, the two positions of the image corresponding to two positions sym- metrical with the lamp, ought to be symmetrical. We can use measure- ments of this kind to determine the size of the angle . It was while using the ophthalmophakometer that I found this image, which I described as new in 1891. But Coccius had seen it previously, and Otto Becker had given the explanation of it in 1860 in a memoir which is very little known. Heuse described it again in 1872, but gave an erroneous explanation of it. The images of Purkinje have no interest as far as the function of the eye is concerned, but they are of great importance for the physiology of vision. It is, indeed, by a study of them that we can determine the form and position of the refracting surfaces of the eye. The study of these images constitute ophthalmometry, to which we will devote our attention in the following chapter. Bibliography. Purkinje (I. E.). Commentatio de examine physiologico organi visus et systematis cutanei. Vratislaviae, 1823. Becker (O.). Utber Wahrnehmung eines Eeflexbildes im eigenen Auge, Wiener medicinische Wochewchrift, 1860, p. 670-672 and 684-688. Heuse. Ueber die Beobachtung einer neuen entoptischen Erscheinung. Oraefe's Archiv. Bd. 18, 2, p. 236. M. Blix. Oftalmometriska Studier. Upsala, 1880. Tscherning. Recherches sur la qua- riZme image de Purkinje; Arch, de physiol., 1890. Tscherning. Theorie des images de Pur- kinje et description d'une nouvelle image. Arch, de physiol, 1891. Tscherning. Sur une nouvelle image d la fois catoptrique et dioptriqve de Vcdl humain et une nouvelle methode pour determiner la direction de Paxc optique de I' ceil. Bulletin de la Societe francaise d'ophtalmologie 1891, p. 203. CHAPTER IV. OPHTHALMOMETRY. 27. Principles of Ophthalmometry. The basis of ophthalmometry is the formula -2- = - r =^-orR = ~- (see page 5 ). To determine the radius R of the small convex mirror which forms the anterior sur- face of the cornea, we measure the image I of an object O, placed at a given distance /. There is never any difficulty measuring either the object or the distance; it is, therefore, to the measurement of the image that we must devote our attention. We may say at once that we generally use as objects the distances separating two flames or two white objects (mires). The image, then, is the distance separating the images of the flames or of the mires. The method most used by physicists for such measurements consists in placing a micrometer at the focus of the objective of the telescope with which the image is observed. The objective forms an image which coincides with the micrometer, the graduations of which permit the size of the image to be read directly by observing it through the eye piece. It has been attempted to use this method for ophthalmometry, but without success. As the observed eye cannot be kept absolutely quiet, the image is constantly changing its place in relation to the mi- crometer, which makes a fairly exact measurement impossible. This is why Helniholts introduced into ophthalmometry another prin- ciple which he borrowed from astronomy, where the same problem present itself, that of doubling (dedoublement). It seems, however, that the method had already been used for the same purpose by Thomas Young. Suppose that we desire to measure the distance I separating the two- points a and b (fig. 33,1), and that we have a process which permits us to see everything doubled at a certain distance D. By this means in- stead of the two points a and b we would see four, a^ and a 2 , b^ and b 2t . 47 48 PHYSIOLOGIC OPTICS and the distance a x a 2 would be equal to b^ b 2 and to D, while the dis- tance a t b i = a 2 b 2 = l (fig. 33,2). Suppose, now, we could make the doubling vary. By increasing it we would reach a point when a 2 and b^ would coincide (fig. 33,3) which would take place at the moment when l ~' objects separated flames so that a and Of b form two luminous points we ob- tain more exact measurements by giv- '* J ing one of them the form of two points ^ situated on the same vertical (fig. 33,4); at the moment of contact the image of b is placed exactly between the two points a. Instead of making the doubling vary, we can make I vary, which is brought about by varying the object (displacing one of the lamps) until contact is obtained. Generally it is useful to employ a certain degree of magnification in order to have easy measurements, and this suggests the use of a tele- scope placed at some distance from the eye; instruments with short focus, more or less resembling microscopes, are not practical because it is impossible to keep them in focus, the observed eye not being able to remain sufficiently quiet. Thus, we would only have to affix our doubling apparatus to our tele- scope and place conveniently two flames or two white surfaces which would serve us as objects, and we would be ready to begin our measure- ments. 28. Methods of Doubling (Dedonblement). a) A first method consists m dividing the luminous cone which meets the objective, into two halves, an upper and a lower, and displacing each half laterally, one to the right, the other to the left. We can obtain this effect : i. By placing before the upper half (i) of the objective a weak prism, apex to the right, and before the lower half another, apex to the left. (1) I am supposing here and in what follows that it is the horizontal meridian we are measuring. OPHTHALMOMETR7 49 2. Instead of prisms we can use plane parallel plates, placed obliquely but in a symmetrical manner in relation to the axis of the telescope. Such plates placed obliquely (see page 10) have the effect of displacing the object laterally, each on its own side; the effect is, therefore, the same as that of prisms, and the plates give better images. This is the system employed by Helmholtz, who made the doubling vary by changing the inclination of the plates, and later by Leroy and Dubois, who used a constant doubling by making the object vary. 3. We can saw the objective in two and displace the upper half a little to the left, the lower half a little to the right (fig. 34). It is easy to see that this method must produce a doubling of the f ^\. image, since the optic center of the objective is, so to speak, divided into two halves, displaced laterally in rela- tion to each other. This method gives very good images and less light is lost, since we obviate the reflection on the surfaces of the prisms or plates, but the instrument is very difficult to construct; the displacement of the two halves of the objec- tive, in relation to each other, must be made, indeed, with an exactness that is expressed in hundredths of a millimeter. None of these methods is very practical, because all of them call for a very exact adjustment of the instrument to find the meridians of the astigmatic eye (see ch. IX). If the eye is displaced a little during the measurement, we may find false directions for these meridians. Helm- holtz remedied this inconvenience by placing himself very far (at I or 2 meters) from the patient, which calls for a room prepared for this pur- pose and makes measurement pretty difficult. b) A second method consists in dividing the objective into two lateral halves, and displacing laterally each half of the incident luminous cone. Such an arrangement can be obtained : i. By placing in front of the objective a double prism with apex ver- tical ; 2. By placing before each half of the objective a plate with plane, parallel surfaces, forming an angle with the axis of the telescope (fig. 35)- These are the plates of Helmholtz which are placed side by side instead of being placed one above the other. 3. We can obtain the same effect by removing a vertical band from the middle of the objective and cementing to- Flg ' ^ gather the remaining parts (fig. 36). Systems of this order offer no difficulty in finding the meridians, but 50 PHYSIOLOGIC OPTICS Fig. 36. they have another inconvenience : contact depends much on the exact- ness of the adjustment. If, after having ob- tained contact the observed eye is displaced a little, so that the instrument is no longer exactly in focus, contact ceases. We may thus obtain totally false measurements of astigmatism if the observed eye is displaced between the two measurements. This inconvenience is partly got rid of in the model of the Javal and Schioetz ophthalmometer which the optician Kagenaar, of Utrecht, con- structed. It uses a combination of the methods b, 1 and &, 2, a combina- tion of two very weak prisms forming an angle between them ; the apex of the prisms is inwards. c) The best method, however, is to employ doubly-refracting crystals. Coccius had recourse to a plate of spar ; Javal and Schioets used a Wollas- ton prism. This prism (fig. 37) is composed of two rectangular quartz prisms, which are cemented together so as to form a sin- gle very thick, plane parallel plate. The two prisms are cut differently in the crystal; one * has the apex parallel to the axis of the crystal, the other *'\ perpendicular to it. Each ray '"'d which passes through the Fig. 37. Prism of Wollaaton. prism is divided into two, and each of the two new rays is deviated a little so that they are nearly symmetrical in relation to the incident ray. (i) By all other systems which I have mentioned the incident cone is divided into two half cones, which are a little displaced in relation to each other; the prism of Wollaston on the contrary pro- duces two entire cones of half the intensity. The instrument of Helmholtz must be considered as an instrument for the laboratory. Investigators, like Danders and Mauthiier, used it for measuring the eyes of some patients, but its use was so difficult that Mauthne? exclaimed: "Ophthalmometry must be understood as ophthalmoscopy, only it is much more difficult." Besides it necessitates (1) [A detailed theory of this prism, together with a calculation of the angles, can be found in the Thtorie de rophtalmom&trie de la cornte by Dr. Tscherning in Javal's M&moires d'oplitatmomttrie, Paris 1891.] W. OPETHALMOMETR7 51 a dark room, and the complete measurement of the cornea calls for not less than 32 measurements. It is only by the labors of Javal and Schioets that ophthalmometry has become a clinical method. 29. The Ophthalmometer of Javal and Schioetz. The instrument (fig. 38) is composed of a telescope which carries a copper arc movable around the axis of the telescope, and with a head-rest on which the head of the patient is supported; when the telescope is adjusted to the level of the eye of the observed person, the latter is at the center of the arc. Two white mires slide along the arc, and it is the distance separating them which serves as the object. By moving one of the mires on the arc, the Fig. 38. Ophthalmometer of Javal and Schioetz. size of the object is made to vary until it corresponds with the doubling of the prism which is constant. The telescope has two achromatic objectives between which is the Wollaston prism, placed so a-s to double in a direction exactly parallel to the plane of the arc. It is, besides, pro- vided with a Ramsden eye piece with a spider's thread. Each observer must begin by focusing the ocular on the thread; then the instrument is adjusted for the level of the observed eye by displacing it forwards or backwards. We then see the images of the two mires doubled (fig. 39), and by displacing the mire on the right, contact is obtained. This done 52 PHYSIOLOGIC OPTICS we can read the distance of each mire in degrees from the axis of the telescope on the scale of the arc, and the sum of the two figures indicates the corneal refraction. I have supposed the cornea in question spher- ical, otherwise we would have to begin by finding the principal meridi- ans ; but I shall reserve the description of the measurement of the astig- matic eye for the chapter on astigmatism. Generally the patient must look into the tele- scope; it is only when we wish to measure the peripheral parts of the cornea also that we make him look in other directions. The graduation of the arc is in degrees, but the doubling is so chosen that each degree corre- sponds with one dioptry. This calls for an expla- nation. Javal and Schioetz have taken as the index of the aqueous humor 1.3375 (i); the refracting power of the cornea ex- pressed in dioptrics would be, therefore (see page 13) : 03375 or, expressing R in millimeters, 337.5 D = "K and K = 337.5 With this formula we calculate the following table, which gives the relation between the refracting power of the cornea, expressed in diop- trics, and the radius expressed in millimeters : Dioptrics. Radius. 40 D. 8.44 mm 39 D. 8.65 mm 38 D. 8.89 mm (1) This value of n, very nearly correct, was selected in order that, in the following table, 43 D- would correspond exactly to 7.5 mm., which is convenient in order to regulate the instrument by & sphere type of 7.5 mm. Refraction. Radius. Refraction. Radius. 50 D. 6.75 mm 45 D. 7>5 mm 49 D. 6.89 mm 44 D. 7.67 mm 48 D. y.Ogmm 43 D. 7.85 mm 47 D. 7.18 42 D. 8.04 mm 46 D. 7.3 4 mm 41 D. 8.23 mm OPETEALMOMETR7 53 Placing the value which we have just found for R in the formula _ I ' R we find 337.5' in which formula I designates the image which, at the moment of con- tact, is equal to the doubling. Let us designate by a the linear length of a degree ; if this length must correspond to one dioptry, the object which corresponds with the image I must have the size Da, therefore Da - 2im ~ 337^ or 2/1 337.5 On the other hand as a must be one degree long, we have 1 a 360 ~ : 27J-J therefore 2*1 2fl a = 360 337.5 and In order that a degree of the arc may correspond with one dioptry, the doubling of the prism must be, therefore, 2.94 mm. This is what has been done. The radius of the arc (/) has been selected so that the linear length of a degree may be 6 millimeters (5 millimeters in the new model). In the last models of the instrument certain details have been changed, but the principle remains the same. We may add, furthermore, that, in order to measure the As, one of the mires has a special form "in steps," each of which corresponds to one dioptry. A keratoscopic disc enables us to study the general form of the cornea. UTILIZED PART OF THE CORNEA. It is only a very small part of the cornea that is used for the measurement. Making the construction in the way indicated on page 7 we see that the images of the mires are formed by reflection on two small parts of the cornea situated about 1.2 mm. from the visual line. Rotating the arc these two parts move describing a concentric ring around the visual line. This ring is the only part of the cornea which 54 PHYSIOLOGIC OPTICS sends light into the objective, and consequently also the only part on which the instrument can give information. The parts situated outside or inside this ring may have curvatures quite different from those indi- cated by the instrument. Suppose, for the moment, that we have to do with a conical (hyperbolic) cornea: what we would measure would be the radius of BG of the circle BE (fig. 40), which touches the surface Fig. 40. of the cornea at B and E (see page 13). Generally this circle coincides quite closely with the "optic" part of the cornea ; but if we want to make very exact measurements we must always take into consideration this source of errors. EXACTNESS OF THE MEASUREMENTS. With a good illumination an experienced observer would not easily be led astray to the extent of a quarter of a dioptry, which corresponds to almost -~ of a millimeter of error for the radius. Absolute reliance cannot, therefore, be placed in the second decimal of the measure of the radius. Bonders and Homer arrived at very nearly the same results using the ophthalmometer of Helmholtz. Still more accurate results may be obtained by using trans- lucent mires which are illuminated from behind by electric lamps. In these conditions an experienced observer can almost guarantee exact- ness to a tenth of a dioptry or thereabouts. 30. Results of the Measurement of the Cornea. The radius of the cornea (at the summit) varies between 7 and 8.5 mm. It is extremely rare to find a cornea the radius of which is not situated between these limits, except in cases of keratoconus. The curve (fig. 41) shows the distribution of the different curvatures in a certain number of men (emmetropes) whom I examined in collabo- OPHTHALMOMETRY 55 ration with Dr. Bourgeois. The average was 43.1 D = 7.8 mm. It is noticeable, however, that these same measurements show that the radius is greater in persons tall in stature and with a large cranial circumfer- ence, (i) Now the persons whom we examined were indeed of tall stature (cuirassiers). It may be, therefore, that the average length of the radius may be slightly smaller than that which I have just indicated. It would be an error to think that one radius rather than another corresponds with emmetropia. As Javal says an elephant and a mouse may both be emmetropic despite the fact that their corneal radii must necessarily be very different. It seems that we can express the 35 30 25 20 15- 10- 5- 7.17 7.33 7.49 7.66 7.81 8.02 8.23 8.43 mm Fig. 41. The abscissas indicate the radii of curvature of the cornea in millimeters, he ordinates the number per hundred of emmetropes in whom we meet the radius of curva- ture in question. relation by saying that in the emmetropic eye there exists a constant relation between the radius of curvature of the cornea and the length of the ocular axis, so that the ocular shell of different emmetropic eyes would always be a reproduction of the same type, a little enlarged or a little diminished. The existence of the myopia and hypermetropia of curvature (corneal) is not yet demonstrated (2) except, perhaps, for certain cases of very high hypermetropia which approach microphthal- mia ; but their existence is beyond doubt. If I except cases of astigmatism, different in both eyes, it is very rare to find a difference, ever so slightly noticeable, between the corneal re- (1) Steiger has since found a still more manifest relation between the radii of the corneas and the distance between the eyes. (2) See, however, the communication of Sulzer to the Congress of the French Society of Ophthal- mology, 1896. 56 PHYSIOLOGIC OPTICS fraction of the two eyes of the same person, even in cases of anisome- tropia. Amongst the cuirassiers mentioned above there were not more than two per cent, who showed a difference exceeding a half dioptry between the two eyes. EXAMINATION OF THE PERIPHERAL PART OF THE CORNEA. Up to the time when Javal and Schioetz made a clinical method of ophthal- mometry there was little known of the form of the cornea. The ophthal- mometer -of Helmholtz being too complicated to make many measure- ments, one was limited to measuring three points of a meridian, that which corresponds to the visual line and another at some distance on either side. As the peripheral radii were found to be greater than the central radius, and as, in consequence, the cornea could not be consid- ered as a sphere, the curvature of the second degree which approached nearest the meridian measured was calculated (see fig. 42). Thus it was that the idea was disseminated that the form of the cornea (non-astig- matic) would be that of an ellipsoid of revolution around the long axis, which axis would be directed outwards from the visual line and form an angle of about 5 () with this line. This idea differs widely from the reality; the cornea does not resemble an ellipsoid. Helmholtz in- sisted from the start on the fallacy of the comparison. After the construction of modern ophthalmometers it became much easier to study this question. The second model of the Javal and Schioetz ophthalmometer is provided with a very large keratoscopic disc divided into graduations of 5 by concentric rings. After having made the usual measurements, during which time the patient looks at the center of the objective, the measurement is repeated making him look 5 to the left, 10 to the left, etc. ; and, after having thus measured the right half of the horizontal meridian we measure the left half. We repeat the measurements for the vertical meridian. Measurements of this kind have been made in Paris by Sulzer and Eriksen (fig. 42) ; these measure- ments confirmed the assertion of Aubert and Matthiesen who, using the ophthalmometer of Helmholtz, had said that the cornea could be divided into two parts, a central one, which is approximately spherical and which we call the optic part, and a peripheral one or basilar part, which is much flattened. Eriksen reckoned as belonging to the optic part that part the refraction of which does not differ more than one dioptry from the central refraction. Its extent varies a little in different eyes. Follow- ing are the limits of the optic part compared with those of the entire cornea, after Eriksen: OPETHALMOMETRT 57 Optic Part. Outwards 16.5 Inwards , 14 Above 12.5 Below.. 13.5 Cornea. 44.7 40.1 38.5 42.2 The figures are the averages of measurements made on 24 eyes. The total width of the cornea is, therefore, not much less than 90, and that of the optic part is about 30, or a third of the entire width. 30 2S 30" , its distance from the retina by a and the distance of the distinct image from the retina by d, we have for the diameter of the circle of diffusion the expression If, instead of a luminous point, we observe an object the image of which is formed in front of or behind the retina, each point of the object produces on this membrane a circle of diffusion which is overlapped by the next circle, except near the borders of the diffuse image. There is also formed around the shape of the object a border, the width of 73 74 PHYSIOLOGIC OPTICS which is equal to half of the diameter of a circle of diffusion, and the intensity of which diminishes towards the periphery. The object is, therefore, seen a little enlarged and with ill-defined borders. 37. Line of Sight. When we perform the act of sighting we try to -make two points, situated at different distances, coincide ; as we can only see one point distinctly at once, it is generally supposed that we make the image of one of the points coincide with the center of the circle of diffusion of the other. Now the center of the circle of diffusion cor- responds with the middle of the pupil ; it would be necessary, therefore, to place the second point on the line which joins the point which is fixed to the center of the apparent pupil, a line which is called the line of sight. This reasoning is subject to caution. Indeed, in order to be able to sight, it is necessary to see the second point pretty distinctly, which requires that it be not too far removed, optically, from the point fixed. The circle of diffusion of the point of sight is, therefore, so small that we commit only a very small error when we consider it as a point. We must also note that the rule according to which the circle of diffusion should everywhere have the form of the pupil, is not strictly correct. By reason of astigmatism and other irregularities of the eye, there nearly always exists, as we shall see in chapter X, a part in front of or behind the focus, where the circle of diffusion is far from having the form of the pupil ; it assumes more or less irregular forms, and the light is no longer distributed in a regular manner. In sighting, then, we make the image of the point fixed coincide with the brightest part of the circle of diffusion, which has nothing to do with the center of the pupil. In order not to complicate the terminology, it would, therefore, be preferable to dispense with the expression line of sight. 38. Accommodation. We know that the eye can change its focus, adapting itself for shorter distances than that for which it is adapted in a state of repose. Holding a book at 50 centimeters and placing a veil between the book and the eyes, at 20 centimeters, we can see distinctly, sometimes the threads of the veil, and sometimes the letters. If we illuminate the fundus of an emmetropic eye with the aid of a plane mirror, by using a flame placed at a great distance, we see a distinct image of the flame projected on the fundus of the eye, if the observed person looks in the distance. If, on the contrary, he fixes an object located nearer, the image forms a circle of diffusion which, most fre- quently, fills the entire pupil. The contrary takes place when the flame is placed at a short distance. CIRCLES OF DIFFUSION OF THE RETINA 75 39. Experiments of Czermak, Scheiner and Mile. Looking towards .an illuminated surface (the sky, for example) through a pin-hole made in a dark screen, we see the opening under the form of a circle of diffusion. If we move a second screen, held nearer the eye, in front of the opening, it seems to move in a direction contrary to that in which it really does move. If, on the other hand, we move the second screen in front of the first, it seems to move in the direction of its real displace- ment (Czermak). Looking towards an illuminated surface through two openings, the distance of which is smaller than the diameter of the pupil, we see two circles of diffusion which partly overlap. A needle is then placed so that we see it in the part common to the circles of diffusion, and another farther away in the same direction. That one of the two needles which we fix is seen single, the other double. If it is the nearer needle that is seen double, the image on the left disappears, if we cover the opening on the right, (i) If it is the other needle that is seen double, the con- trary takes place (Scheiner). It is easy to repeat this experiment with a lens, and it is also a very good way of determining the focal distance of the latter (by replacing the needle by a luminous point). If we look at the more distant of the two needles in the experiment of Scheiner through a single small opening, we shall see that a slight movement of the screen causes the nearest needle to move in the con- trary direction. On fixing the nearer of the two needles the other seems to move in the same direction as the screen (Mile). It is easy to account for these phenomena when we sketch the course of the rays, not forgetting that the eye inverts the phenomena when projecting them outwards. 40. Optometer of Thomas Young. (2) The experiment of Scheiner forms the basis of the optometer of Thomas Young, which appears to ( 1) To reader the experiment more striking to my pupils, I had a plate of red gelatine glued in front of the opening on the right. But, after having explained the theory of the experiment, I met with very vigorous protestations ; all declared that it was the needle on the right which appeared red. It is thus, in fac", when we look towards the sky, but we must not conclude from this that it is the needle on the right which belongs to the opening on the right. The phenomenon is analogous to that of colored shadows, of which I will speak in chapter XVII. If one places oneself in such a way that the needle is eliminated, it is the image on the left which appears red. One of my pupils, M. Johnsson, has studied the chromatic phenomena which are observable under the same circumstances, by looking at the needle towards the sky, but without the interposition of the colored plate. One sees them specially well by dilating the pupil and using the slits of the optometer of Young. When the needle is situated on the near side of the point which is fixed, one of the images is seen green, the other purple ; each image is bordered with red on the side which looks towards the other image, with blue on the opposite side. These phenomena, which depend on the chromatic aberration of the eye, are not yet well explained. (2" 1 Not being able to procure any part of this instrument, I had it constructed again by M. Werlein, modernizing it a little. 76 PHYSIOLOGIC OPTICS me to be one of the most important instruments for the study of physi- ologic optics. It has the form of a little rule. On one of the faces is drawn a fine white line on a black ground. We look along this line, through a lens of + 10 D. In front of the lens moves a small horizontal rule, in which are different groups of slits (fig. 5$a). Placing the two slits, which are at the middle of the horizontal rule, in front of the lens, they act like the openings in the experiments of Schemer. Each point Fig. 55. Kules of the optometer of Young. of the line appears double, except that which is seen distinctly ; an emmetrope, not using his accommodation, must, therefore, see two lines which intersect at the punctum remotum, or artificial far point, at 10 cm. from the eye. To determine the refraction of any person we make him look in the instrument, and put a small cursor at the place where he sees the lines intersect. A dioptric scale, placed along the line, then permits the refraction to be read off directly. We then determine the near point (punctum proximum) in the same manner. The other groups of slits permit the determination of the refraction of the different parts of the pupillary space. We can also use the little vertical rule (fig. 51^) which has the form of a very pointed triangle ; by lowering it more or less, we eliminate a smaller or greater part of the middle of the pupil. The instrument does not lend itself very well to the examination of patients, for it is quite difficult for an inexperienced observer to use it without using his accommodation. For one who can control his accom- modation, the instrument permits the measurement simultaneously of CIRCLES OF DIFFUSION OF THE RETINA 77 the refraction and the amplitude of the accommodation; the refraction can be determined in different meridians by making the instrument rotate around its longitudinal axis. It was thus that Young discovered the astigmatism of his own eye. The observations made with this optometer are, moreover, of the greatest importance for the study of the nature of accommodation (see chapter XII). 41. Effects of the Stenopaic Opening. Looking through an opening smaller than the pupil, we diminish the circles of diffusion so that objects which we first see dimly become more distinct. This is why myopes see better at a distance by looking through a small opening. We can also make use of it as a magnifying glass ; we can, indeed, move very close to the eye the object which we desire to examine, and in this way obtain a very large retinal image. The more the diameter of the opening is diminished, the more distinct the image becomes, but it loses at the same time in brightness. We cannot exceed a certain minimum limit without blurring by diffraction the distinctness of the image, (i) As the stenopaic opening effaces, so to speak, the effect of the anom- alies of refraction, it is harmful in all cases in which we desire to deter- mine refraction. This is why we place patients with their backs towards the window when we examine their vision. We must also avoid the small apertures in the ophthalmoscopes which are used to determine refraction; a too strong illumination is equally hurtful. Fig. 56. Magnification by means of the stenopaic opening. Examining an object placed very near the eye through a stenopaic opening, we shall see that the object seems to enlarge as we gradually move the screen away 'from the eye. Following is the explanation of this fact. (1) Looking at a luminous point which we see distinctly, through a very fine opening, we observe that it becomes enlarged into a small luminous surface surrounded with brilliant rings. This effect of diffraction begins to make itself slightly felt starting from an aperture of the pupil or of the opening of about 2 millimeters. 78 PHYSIOLOGIC OPTICS Let AB (fig. 56) be an object, and A^ its image formed by the optic system of the eye. As the object is near the eye, the image is formed quite a distance behind the retina. To determine the position of the indistinct image on the retina, we draw the ray Ac passing through the middle of the pupil of entrance; after refraction it continues its course as if it came from c lt the center of the pupil of exit. Its direction is AV-,, since it must pass through A', the image of A. The point a is, therefore, the middle of the circle of diffusion which A forms on the retina, and ab is the diameter of the image of diffusion. Let us now interpose the screen EE with its stenopaic opening. The only ray which passes from A through this opening takes the direction AK and, after refraction, the direction K X A' ; it meets the retina at a t and a^ b 1 is the size of the retinal image. We see that this image is larger than ab and that it would become larger still if we moved the screen farther away. Myopes looking at distant objects through a stenopaic opening see them diminish if the opening be moved away a little. Bibliography. The study of the influence of circles of diffusion on vision has been very much neglected by modern authors. The best work done on this question is the fol- lowing, which dates from the last century. Jurin (J.). Essai sur la vision distincte el indistinct*, in Robert Smith, Cours complet d'op- tiquc, translated by Pezenas, Paris, 1767. Scheiner (C.). Oculus. Innspruck, 1619. Mile (J.). Pogg. Ann., XLII, 40. (Euvres de Young edited by Tscherning, page 112. Tscherning (M.). L'optomdre de Young et son emploi. Arch, d e physiol. October, 1894. CHAPTER VI. ANOMALIES OF REFRACTION. 42. General Remarks. We have thus far treated the optic system of the eye as if it were perfect, but it has really many defects. Helmholts- said that if an optician had delivered to him an optic instrument as im- perfectly made as the eye, he would have considered himself within his right in refusing it ; expressing himself in quite forceful language. The remark of M. Mascart appears to me nearer the truth. He said that the eye has all possible defects, but only to such an extent that they are not harmful. We have already seen that this is the case with diffraction, which begins to make itself felt, starting from a pupillary diameter of 2. millimeters, almost the lowest limit of this diameter. It is the same with chromatic aberration, spherical aberration, etc. An optician need not be so careful with an objective, the images of which are intended to be magnified five times, as with another the images of which are to be magnified twenty or thirty times. In the same way eyes frequently have all the visual activity we can expect considering the retinal structure, and a greater degree of optic perfection would be superfluous. It is true that many eyes which are considered normal, have optic defects which diminish their visual acuity, which should be nearly double that called normal acuity; but for most occupations, the acuity known as normal amply suffices. We can divide anomalies of refraction into three groups: i. ANOMALIES "OF THE SCREEN." a. Axial myopia. Screen is too far away from the optic system. b. Axial hypermetropia. Screen is too near the optic system. c. Oblique position of the screen. This last anomaly is not generally recognized. It seems to play a part in diminishing the visual acuity in certain forms of very high myopia, in which the summit of the staphyloma does not correspond exactly with the fovea. It is evident 80 PHYSIOLOGIC OPTICS that, if the optic system of the eye were perfect, all the rays emanating from a point would meet exactly in a point on the screen, and the obliquity of the latter would play no part, for the extent of distinct vision is so small that the difference of distance of the different parts of the image from the optic system cannot have much influence. But if the rays do not meet exactly in a point, as is nearly always the case, it is clear that the circle of diffusion on the retina must be larger when the retina is placed obliquely, and that this must diminish visual acuity. 2. ANOMALIES OF THE REFRACTING SURFACES. Myopia ) \ of curvature. Hypermetropia j Regular astigmatism. Spherical aberration. Chromatic aberration. Keratoconus. Lenticonus. Aphakia. Luxation of the crystalline lens. All the forms which are classified under the name of irregular astigma- tism. 3. ANOMALIES OF THE INDICES. False lenticonus. The anomaly which Demicheri has recently described under the name of false lenticonus is the only anomaly of the indices which has been established up to the present. In these cases we see with the ophthalmo- scope the same play of shadows that is characteristic in keratoconus ; it is due to a great difference of refraction between the middle of the pupil which is very myopic (as high as 10 D. and more), and the periphery which is hypermetropic (3 to 4 D). The explanation is probably to be found in a diminution of the index of the peripheral layers of the crys- talline lens, a change which must diminish the refraction of the peri- pheral parts of the pupil and greatly increase the central refraction, following the explanation which we have given on page 30. We find in these cases the images of Purkinje doubled (see page 29), the surfaces of the nucleus giving rise to a quite regular reflection; these cases are analogous to that which I have found in the case of the eye of a dead ox, probably also due to the imbibition of water by the superficial parts. 43. General Eemarks on Ametropia. We designate as the far point (punctum remotum) the place for which the eye is focused when in a state ANOMALIES OF REFRACTION 81 of repose. It is, therefore, the conjugate focus of the fovea. By mak- ing an effort of accommodation, the eye can focus itself for shorter dis- tances. The nearest point for which the eye can adapt itself is called the near point (punctum proximum). We generally express the distance of the near point and that of the far point in dioptrics ; the difference between the two numbers is called the amplitude of the accommodation. The determination of the far -point is quite easy, and forms an important part of the work of the oculist ; that of the near point is not very certain, since its position depends on an effort of the patient, the strength of which may vary from day to day ; for that reason the determination of the near point is frequently neglected in clinics. We consider as normal the emmetropic eye, that is to say, an eye such that, in a state of repose, the image of distant objects is formed on the retina. In the myopic eye this image is formed in front of, in the hyper- metropic eye behind, the retina. We designate these two anomalies under the common name of ametropia. The emmetropic eye has its far point situated at infinity, that of the myopic eye is at a finite distance. As to the hypermetropic eye, its remote point is virtual. It is necessary that the rays converge before entering the eye in order that they may re- unite in a point on the retina. This point towards which the rays must converge, before entering the eye, and which is consequently situated behind the latter, is the far point; its distance is to be put down as nega- tive. The degree of ametropia is indicated by expressing in dioptrics the distance of the eye from the remote point, (i) In the great majority of cases, myopia and hypermetropia are due to an anomaly in the length of the eye: the myopic eye is too long, the hypermetropic eye too short. An increase or a diminution of I milli- meter in the axis of the eye corresponds to an ametropia of two dioptrics and a half. Let us place in the formula of Newton, / x / 2 = F t F 2 , the values of the simplified eye F x = 17 millimeters, F 2 = 22.7, and we will have /! / 2 = 386, in which formula / x is the distance of the far point from the anterior focus and / 2 the distance of the retina from the posterior focus of the eye. If L = 1 millimeter, / x = 386 millimeters, which cor- responds to about 2.5 D. ; if / 2 = 2 millimeters, / t = 193 millimeters or about 5 D., and so on. Myopia is corrected by placing in front of the eye a concave glass so that the image which it forms of distant objects may be situated at the (1) From which part of the eye one should start to calculate ametropia is a disputed question; it seems to me that the simplest way is to calculate it, starting from the summit of the cornea. Some have preferred to calculate it from one or other of the cardinal points of the optic system, but as these points have not the same position in all eyes, nor in all the meridians of the same eye, nor even for all parts of the same meridian, confusion would result. 82 PHYSIOLOGIC OPTICS far point of the eye. On account of the distance of the glass from the eye its focal distance is a little shorter than the distance of the eye from its far point. The subjective examination always results, therefore, in our finding a somewhat higher myopia than really exists. The difference is insignificant for low degrees of myopia, considerable for high de- grees. If we move the glass away from the eye, its effect diminishes. When selecting the correcting glass, we must take great care to select the weakest concave glass which corrects, because young myopes see as well with stronger glasses, the excess of correction being neutralized by accommodation. After having found the correcting glass, we may try the effect of moving it gradually away from the eye. If the patient continues to see well the glass is too strong. Hypermetropia is corrected by means of a convex glass, which brings the image of the distant object to the far point situated behind the eye. The focal distance of the glass being a little greater than the distance of the eye from the far point, the correcting glass is a little weaker than the hypermetropia. The hypermetrope can increase the strength of his glasses by moving them a little away from the eye. The correcting glass is the strongest convex glass which the patient tolerates without loss of visual acuity, but he can also see as well with weaker glasses by using his accommodation. The retinal image of an object seen under a given angle is larger in the myopic eye and smaller in the hypermetropic eye than in an emme- tropic eye, because the distance of the posterior nodal point from the retina is greater in the myopic eye, less in the hypermetropic eye. But, this effect disappears when we correct the ametropic eye, by plac- ing the correcting glass so that its optic center coincides with the an- terior focus of the eye. Then the image is always the same size, what- ever the ametropia may be. For, the rays AO and BO (fig. 57) pass through the lens without deviation and are parallel, after refraction by ANOMALIES OF REFRACTION 83 the optic system of the eye, so that the size of the image is always the same, whatever may be the distance of the retina. If we place the cor- recting glass in front of the anterior focus, the retinal image of the myopic eye is smaller, that of the hypermetropic eye larger, than the image of the emmetropic eye, which is easy to see by a construction analogous to that of fig. 57. We first construct the image formed by the glass, and draw the rays passing through the extremities of this image and through the anterior focus. Patients often say that the concave glasses diminish objects. This may be attributed to the fact that the glass is placed in front of the anterior focus, or simply to the fact that exterior objects, seen distinctly, appear smaller, because of the disappearance of the circles of diffusion. But the cause may also be that the glass is too strong; for if the patient uses his accommodation the anterior focus approaches the eye and the image becomes smaller for this reason. 44. Optometers. The use of the test case lenses and of the visual acuity chart, placed at a distance, is always the best of the subjective methods. A very great number of optometers have been constructed, but none of them has succeeded in superseding the test case ; they have this defect in common that they superinduce an effort of accommoda- tion which makes the myopia appear too strong. The best are those which are operated at a great distance, like the optometer of Javal, but even these seem sometimes to give too strong degrees of myopia. The optometer of Javal is composed of two discs, nearly like the discs of the ophthalmoscope for refraction, but much larger : one of the discs has spherical lenses, the other cylindrical lenses; a special mechanism permits the axis of all the cylindrical lenses to be adjusted in the direc- tion we desire. Other optometers are founded on the use of a single convex lens; by displacing the object in relation to this lens, we can form the image of it at any distance whatever, and thus find the place where it appears distinct. Optometers of this kind have been con- structed by Coccms, Bonders, Sous, and many others. The optometer of Grade was a Galilean telescope; we know that myopes are obliged to shorten their opera glasses to see distinctly. By providing the opera glass with a scale it may, therefore, be used as an optometer. So also may the telescope, the use of which was proposed by Hirschbcrg. Among all these optometers I shall mention specially only that of Badal, on account of its admirable principle. It is composed of a single convex lens, the focus of which coincides with the anterior nodal point of the eye. The position of the latter is made secure by an eye-rest. A 84 PHYSIOLOGIC OPTICS diminished copy of the chart of Snellen is placed on the other side of the lens, movable forwards and backwards. By displacing the object we can make the image appear anywhere, and it is easy to see (fig. 58) that the retinal image remains always the same size, no matter whether the Fig. 58. Principle of Badcti. object is at. bb or at aa, etc. We can therefore measure the visual acuity with this optometer. The same result is obtained by making the focus of the lens coincide with the anterior focus of the eye (fig. 59). Fig. 59. 45. Myopia. There exist two forms of axial myopia, one which de- pends on near work, and one which does not. (i) Myopia from near work appears usually at an age ranging from 6 to 15 years; it often stops at the age of 25 years. It attains medium degrees and does not seem to exceed the limit of 9 D. Complications, except staphyloma, are rare. Dangerous myopia is sometimes congenial and stationary ; as a rule it develops in early infancy, and continues to increase during the whole life. At the age of 20 years it generally exceeds 9 D. This form of myopia is to be considered as a malignant choroiditis, and it is to it that dangerous complications of myopia belong; like most choroidal affec- tions it seems to be a little more prevalent among women. In 1882 and 1883 I examined about 7,000 young Danish conscripts, by determining their refraction by means of the upright image. The influence of near work is seen in the following list: (1) Even eliminating these two forms of myopia, it is probable that there would still remain a cer- tain number, due to a congenital disagreement between the optic system and the length of the axis of the eye, for it is not probable that all normal eyes are constructed so as to be exactly emmetropic. But myopia between 2 D. and 9 D. is so rare among uneducated persons, that this third form must com- prise only light degrees. ANOMALIES OF REFRACTION 85 Myopes. Students 32 per cent. Persons employed in offices and in trade 16 Artists, etc 13 Tailors, shoemakers, etc 12 -,,- f Workmen (hard labor) 5 per cent. \ Agriculturists (peasants) 2 The distribution of the two forms of myopia in the two groups was the following: I II In all. 2,336 5,187 Myopes < 9 D. 407 (17 per cent.) 169 ( 3 ) Myopes > 9 D. 13 (0.56 per cent.) 38 (0.73 ) 90 *f 80 SS 60 * sow 20 S| oil Hyper- a e v z netronia 9 7 S 5 metropia D Myopia Fig. 60. Distribution of the anomalies of refraction among the young population of Copenhagen. Educated. Uneducated. We see that the very great frequency of myopia in the educated classes 86 PHYSIOLOGIC OPTICS comprises only the lowest degrees. The very high degrees are rather more frequent in the illiterate (fig. 60). Among the peasants I have even met more cases of myopia greater than 9 D. than of myopia between 2 D. and 9 D. It is, therefore, a great exaggeration to regard myopia from near work as a public calamity, as is done especially in Germany. One exag- geration leads to another. It was thought formerly that myopic eyes were stronger than others because they did not become presbyopic. After the discovery of the ophthalmoscope very grave complications in cases of strong myopia were continually met with, and thus originated the idea expressed in the celebrated phrase of Bonders, "I do not hesi- tate to declare that every myopic eye is a diseased eye," a phrase which Cohn adopted as his motto in the first of the great compilations of statistics of school children ever made. Later, many others were made, but without important results. They show conclusively that myopia is more frequent and more pronounced in the higher classes of the schools ; but as the pupils of these classes are older, and as the myopia is a condition that develops with age, these statistics do not establish definitely the influence of near work. A satisfactory explanation of the mechanism by which near work produces myopia has not yet been given. Danders named three factors : first, the inclined position of the head which produces hyperemia of the globe with a tendency to distention; second, the fatigue of the eyes, which would be the result of prolonged reading, and which would also produce hyperemia; third, the compression which the external muscles would exercise on the eye, during convergence for a near point. Arlt, who, by his autopsies, proved for the first time in 1854 that myopia is due to a lengthening of the globe, laid special stress on the action of the superior oblique while reading. The eye being directed downwards, this muscle may, indeed, compress one of the veins and thus produce the development of hyperemia. Stilling tried to further develop this theory by finding the predisposition to myopia in a special form of the orbit (very low Hypoconchid) which would give to the muscle a direc- tion more likely to compress the eye. In spite of the slight degree of accommodation which myopes need (i), (1) It is possible that myopes often accommodate more than we think. la low degrees they fre- quently work within their far point, because by bringing the work near they can see more detail. As to high degrees, other circumstances may bring about a quite remarkable accommodation. This is why Jzval said that a myopic eye may be focused at once for the extremities and the middle of a line of a book. If the myopia is 10 D., the length of the line is 10 cm., and if the ends of the line are seen dis- tinctly without accommodation, the patient is obliged to accommodate about two dioptries when read- iag the middle, unless he keeps the book or his head in continuous motion, or contents himself \vith seeing diffusely a part of the line. ANOMALIES OF REFRACTION 87 the theory of the accommodative origin of myopia has, however, many believers, and I think they are right; but as the mechanism of accom- modation was scarcely known until recent times, it is not wonderful that the solution of the problem of myopia from near work was sought in vain. 46. Selection of Spectacles. Although myopia from near work is not to be considered as a true diseased condition of the eye, it always causes a disagreeable feeling which it is our duty to prevent as much as possible. As it is near work which produces myopia, young myopes must be made to work at as great a distance as possible; and, on account of the probable influence of accommodation, we must suppress the latter as much as possible, or annul it. We are very frequently consulted on the question of glasses by parents who are worried at seeing their children become myopes. If the myopia is low, under three dioptrics, we give correcting glasses for distant vision, and nothing for near vision, (i) rec- ommending the patient to be careful as to the distance of the book while reading. We place the normal distance for work at 33 centimeters. If the myopia exceeds three dioptrics we give for near vision correcting glasses diminished by 3 D. For example, if the myopia is 6 D. we give 3 D. for near vision. For distant vision we may give correcting glasses or a supplementary glass to superimpose on the spectacles. But, in giving concave glasses for near vision we must forcibly impress upon myopes the necessity of observing the minimum distance of 33 centi- meters when working; otherwise the glasses would be rather harmful by superinducing an effort of accommodation which might cause the myopia to increase. When the myopia exceeds 9 D., it becomes necessary to regard it as dangerous, and great care in the use of the eyes must be recommended. Generally it is preferable not to completely correct myopia, but only sufficiently so that the patient may not be too much annoyed in moving around. As the acuity is frequently diminished we can no longer insist on as great a distance for near work; thus we may give correcting glasses diminished by 4 to 5 D. for near work, which places the far point at 25 or 20 centimeters respectively. The patient must be advised never to work with his head lowered; in the latter case where the dis- (1) [In the United States we prefer to let these myopic patients wear their glasses constantly, especially as these eyes are usually more or less astigmatic. The success of this method is proved by the careful in- vestigations of Dr. S. D. Risley. See his article on School Hygiene in the System of Diseases of the Eye iby Norris and Oliver, Philadelphia, 1897.] If. 88 PHYSIOLOGIC OPTICS tance of the work is 20 cm. a desk must be used. Patients frequently ask us for advice as to illumination. No artificial light, except an arc lamp, is hurtful to the eyes; the stronger it is the better, because arti- ficial illumination never attains the degree of illumination of a bright day; but it may be useful to protect the eyes with a shade. When the myopia is very high, spectacles are frequently of no service, as the patients do not accept them. It is then necessary to restrict near work as much as possible. For distant vision a small telescope some- times gives good service. In order to obviate the necessity of accom- modation, patients should be advised to lengthen it as much as possible. 47. Treatment of Myopia. Each of the two theories by which myopia from near work has been explained has given rise to a treat- ment of this defect. The theory of convergence led to the attempt to stay the progress of myopia by performing a tenotomy of the external rectus as soon as there was a slightly pronounced latent divergent strabismus (which was called insufficiency of the internal recti exophoria). Certain surgeons performed thousands of operations of this character: the result was very doubtful, and we may consider this operation as abandoned. The theory of accommodation led to treatment by atropine ; but, before speaking on this subject, I shall say a few words on the use of atropine for the determination of refraction, a method which is still very much in vogue in some countries. De Wecker held decided views on the abuse of atropine in ophthalmic practice, and, as far as its use for the determination of refraction is con- cerned, I am in perfect agreement with him. We know that young hypermetropes are accustomed to correct part of their hypermetropia by using their accommodation, and that they cannot relax this accom- modation without becoming trained to it by means of convex glasses > at least as long as they fix a specified object. To make all the hyper- metropia manifest we must instil atropine in order to paralyze the ac- commodation. It is this perfectly correct observation which gave rise to the idea that generally a better determination of refraction would be obtained by using atropine, and which resulted in the ciliary muscle being held responsible every time a difference of refraction before and after the instillation of atropine was found. By putting atropine in the emmetropic eye we often find a light degree of hypermetropia, which Bonders was wont to explain by assuming a "tonus of the ciliary muscle." Frequently also we see myopia diminish slightly under the influence of atropine, and this diminution ,has been attributed to the existence of a ANOMALIES OF REFRACTION , 89 "spasm of accommodation," which would disappear as soon as the ac- commodative muscle would be paralyzed. These errors originated in the belief that refraction must necessarily be the same in the whole pupillary space. It is nothing of the kind: there nearly always exist differences which are frequently very consider- able. Thus there is in my eye a relatively great difference, nearly 4 D., between the upper border and the lower border of the pupil (see page 145). When we instil atropine, the pupil is dilated and the basilar posi- tion of the cornea, which is much flattened, comes into play. As the flattening of these parts is often considerable enough to over-correct the spherical aberration, we find that the refraction of these peripheral parts is generally less than that of the central parts. A quite slight dilatation of the pupil suffices in order that the area of these parts, which, in ordinary conditions, are excluded, may be greater than that of the ordinary pupil ; it is this fact which makes us judge specially by them in the determination of refraction. If the peripheral flattening of the cornea is less, or if the extent of the optic part exceeds the ordinary limits, which sometimes happens, we may, thanks to the spherical aber- ration, obtain an increase of refraction by instilling atropine. Such cases have been observed, among others by Javal; they were very diffi- cult to explain with the ideas which have been held on the subject up- to the present, since it could not be supposed that the use of atropine could cause a spasm of the accommodation. We observe like phenomena with photographic objectives the aberration of which is not well cor- rected ; the focus changes on changing the aperture of the diaphragm. Except in cases of latent hypermetropia, we obtain, therefore, generally a better idea of ocular refraction by the ordinary examination without atropine. Atropine treatment has been used in cases of progressive myopia; the ciliary muscle would be kept paralyzed for 15 days or a month, in order to arrest the progress of the myopia, the special purpose being to coun- teract the spasm of accommodation, which was supposed to be the cause of the progress of the myopia. This treatment does not seem to have been effective. In cases where the eyes are exposed to great danger, for example in detachment of the retina, it may, however, be useful to procure for them complete rest by instilling atropine and forbidding work altogether for some time. Some years ago, on the advice of Fukala, the profession began to treat high degrees of myopia by removing the crystalline lens, generally by a discission followed by extraction. This treatment, which Danders pro- 4)0 PHYSIOLOGIC OPTICS nounced criminal at a time when surgical operations were more dan- gerous than now, often seems to give very good results, not only because those operated on become emmetropic or nearly so after the operation, but also because they gain considerably in visual acuity for distance. We have already seen that the size of the retinal image of the myopic eye, corrected by a glass placed at the anterior focus, is equal to the image of the emmetropic eye. Now, in the emmetropic eye the retina is situated about 16 millimeters behind the posterior nodal point; in a myopic eye, which has become emmetropic by the extraction of the crystalline lens, the retina is situated at the posterior focus of the cornea or about 24 millimeters from the nodal point. As the size of the image depends only on this distance, we see that the linear enlargement of the image by the operation is about a half. Often it gains still more because the correcting glass is placed not at the anterior focus but a little in front, which has the effect of diminishing the image. The loss of accom- modation, which is, indeed, of very little use to myopes of a high degree, cannot counterbalance these advantages ; nevertheless there is reason for prudence in recommending this operation, for it is not without danger. When making the discission (followed by paracentesis) we may fear glaucomatous complications or iridocyclitis as a consequence of a too great swelling of the crystalline lens. If extraction is performed an accidental loss of the vitreous body may sooner or later produce a detachment of the retina. 48. Hypermetropia. The hypermetropic eye is too short. The retina being too near the optic system, the hypermetrope cannot, without an effort of accommodation, reunite on the retina parallel or diverging rays. When the hypermetropia is high, the amplitude of accommoda- tion diminishing with age, there comes a time when the patient can no longer correct his hypermetropia by accommodation (absolute hyper- metropia). The degree of hypermetropia is expressed by the strongest convex glasses with which the patient can distinguish distant objects distinctly. To disclose all the hypermetropia, it is often necessary to paralyze the ciliary muscle by means of atropine, because the patient has formed the habit of accommodating as soon as he fixes an object, and he cannot suddenly rid himself of this habit even when we put before his eye a convex glass which should eliminate any necessity of accom- modation. That part of hypermetropia which we cannot make man- ifest by the ordinary examination is called latent hypermetropia (Bonders) ; it diminishes with age, and it need not be regarded as a very definite ANOMALIES OF REFRACTION 91 quantity. We can often, by working a little with the patient, make him accept stronger and stronger glasses. In the dark room where the patient does not fix, hypermetropia frequently becomes manifest in its entirety which permits it to be determined with the refraction ophthal- moscope or by skiascopy. ACCOMMODATIVE ASTHENOPIA. The hypermetrope, being obliged 10 use part of his accommodation to neutralize his defect of refraction, generally becomes fatigued more quickly than the emmetrope by near work. The essential symptom of this accommodative asthenopia is that, while reading, the letters become blurred. When this symptom appears, the patient reads with ease for some time ; then the letters begin to be- come indistinct, so that he is forced to rest a while. If he begins again he gets along well for a shorter time than before, after which the same phenomenon is reproduced. If the patient still continues there super- vene fatigue, orbital pains, etc.; but these phenomena are secondary, and we must not, from their appearance, decide on hypermetropia as the cause in the absence of the essential symptom, viz., the indistinctness of the letters after reading for some time. We need no longer attribute the complaints of patients to a low degree of hypermetropia. Low degrees of hypermetropia manifest themselves, as a rule, only by the premature appearance of presbyopia. We may easily correct a low degree of hypermetropia, even in young people, but we must not expect to obtain great results. The complaints of the patients have generally other causes. Boehm, Stellwag and others recommended the use of convex glasses in cases of accommodative asthenopia, but to Danders belongs the credit of having brought them into general use. His labors, indeed, con- tributed greatly to dispel the fear which earlier oculists had of strong convex glasses. They considered asthenopia as the forerunner of amblyopia, and believed that the giving of convex glasses was conducive to the development of the latter. Hypermetropes generally prefer a great distance for work in order not to fatigue their accommodation. But, when the hypermetropia is very high, which demands an effort of accommodation much too fatiguing, we see patients choose a very short distance, moving the book to within a few centimeters from the eyes. They see better, thanks to the considerable enlargement of the retinal images. It is true that they are blurred; but, on bringing the object nearer, the circles of diffu- sion increase less quickly than the images, and moreover, the patients can diminish them by winking their eyelids. 92 PHYSIOLOGIC OPTICS The rule of Donders for the selection of spectacles was to correct the manifest hypermetropia plus one-fourth of the latent, that is to say, to give, for young people, convex glasses a little stronger than those which they accept for distant vision. I consider this rule a wise one; others correct all the hypermetropia. Generally the patients are dis- satisfied at the beginning, before becoming accustomed to the spec- tacles; the glasses annoy them, and it is advisable to forewarn them that they will do so for some time. This annoyance is greater the stronger the glasses, which is one reason for not correcting all the hypermetropia. Another reason is that patients are much more annoyed when, for one reason or another, they cannot wear the glasses, since they have lost the habit of overcoming their hypermetropia by accom- modation. If the hypermetropia is low or medium (i to 3 D.) there is no reason for giving glasses for distant vision, at least to young people who easily correct their hypermetropia by accommodating; we may leave them ff ee in this regard. If the hypermetropia is high or if there is a tendency to strabismus, the glasses must be worn constantly, (i) 49. Aphakia. It is very rare to find true hypermetropia which ex- ceeds 7 D. (see fig. 60). The higher degrees are met with only in aphakia (absence of the crystalline lens). The degree of hypermetropia of the aphakic eye can be calculated by means of the formula^- -j- -^r- = 1. With the values of the simplified eye we have F x = 24, F 2 = 32, / 2 = 24.7, which gives / = 81.2. The far point is therefore situated at 81.2 mm. behind the cornea; the eye will be corrected by a convex glass of 96 millimeters = 10.4 D., placed at 15 millimeters in front of the cornea. We find, in fact, that nearly all the emmetropes operated on for cataract are corrected with a glass of from 10 to ii dioptrics. But it would be an error to apply this number to the ametropias, and to think that we could always find the post-operation refraction by dimin- ishing the ante-operation refraction by n D. To find the correcting glass for ametropias we must calculate it in the same way as for emme- (1) [In this country our reasoning upon this point is quite different. As people with hypermetropia, higher than 3D., accommodate with great difficulty, they do not keep it up very long at a time or some- times avoid to correct accommodation by reading very near with diffuse but enlarged images as has been so well explained by the author. They thus frequently rest their eyes more than the persons with lower degrees of H. who use their accommodation more constantly and on that account show more asthenopia. At any rate the constant correction of the lower degrees of hypermetropia has relieved many cases of obstinate asthenopia.] W. ANOMALIES OF REFRACTION tropes. It is thus that Dr. Stadfeldt has calculated the following little table : Before \ TT 7 operation f H. 5 H. 3 H. 1 E M.I M. 3 M. 5 M. 7 After )rr 15 operation f H. 13.8 H. 12.5 H. 11.3 H. 10.6 H. 10.1 H. 8.9 H. 7.8 H. 6.6 Bef r . e IM.Q operation f M. 11 M. 13 M. 15 M. 17 M. 19 M. 21 M. 23 M. 25 After ) H 5 5 operation ( H. 4.4 H. 3.4 H. 2.3 H. 1.3 H. 0.2 M. 0.8 M. 1.8 M. 2.7 Comparing this table with the following table which has been made up from a series of results from operations published by Pflueger, we see that the agreement is sufficiently satisfactory. Before operation M 10 Mil M 12 M 13 M 14 M 15 M 16 M 18 M 22 After H5 H 5.5 H 3.5 H 3.5 H 3.5 HI H 2.5 M 2 M 2 Dimmer has directed attention to a slight source of error in the ordi- nary examination of aphakics. The lenses of our test cases are biconvex, while those which the optician makes for patients are generally sphero- cylindrical, the cylindrical surface being turned towards the eye. Now, the optic center of biconvex lenses is situated at the middle of the lens, while that of plano-convex glasses is situated at the apex of the convex surface. It follows that the spherical effect of the sphero-cylindrical glass is a little greater than that of the biconvex glass, having the same focal distance, the posterior focus being situated a little nearer the glass in the former case. The error may reach a half dioptry. For some time test cases have been manufactured in Austria in which the strong convex glasses are plain on one side. Ostwalt has laid stress on the influence which the distance of the glass from the eye exerts on the power of sphero-cylindrical glasses. Suppos- ing, for example, that an eye is corrected by + n D. with + 3 D. cyl., placed at 15 millimeters in front of the eye. Such a glass has, in one of the principal meridians, a focal distance of 91 millimeters, in the other of 71 millimeters. The far point of the eye is thus found in one of the meridians at 91 mm. 15 mm. = 76 mm. (13.1 D.), in the other at 71 mm. 15 mm. = 56 mm. (17.9 D.). Its astigmatism is, therefore, really 4.8 D. and not 3 D. As far as the subjective examination is con- cerned this difference plays no part, since the glasses with which we examine our patients are at the same distance from the eye as those which the patient will wear, but it is not so with the ophthalmometer, 94 PHYSIOLOGIC OPTICS which tells the true astigmatism of the eye; we must recollect, there- fore, that in this case the number furnished by the ophthalmometer is higher than that which suits the patient. In the case of simple cylin- drical glasses the same influence makes itself felt, but to a much less extent ; a convex cylinder of 6 D. thus corresponds with a true astigma- tism of 6.5 D., a concave cylinder of 6 D. with 5.5 D. Bibliography. Donders (F. C.). On the Anomalies of Accommodation and Refraction (>f the Eye. London, 1864. Mauthner (L.). Vorlesungen iiber die optischen Fehler des Auges. Wien, 1876. Landolt (E.). La refraction et V accommodation de V whlch suffers the Displace- ment. We can thus prove that the eye is slightly displaced, a little upwards when we wink the eyelids, a little downwards when we open the eye very widely. When we lean the head to one side the eye undergoes a slight displacement in the direction of the weight, etc. The phenomena are especially striking when we instil eserine, because the field is then very small. The displacement of the cross may then reach a fourth or a third of the entire extent of the field. Fig. loio. Entoptoscope. a, plan- chette of wood; 6, rod: c, copper plate, perforated; 4 thread. ENTOPTIC PHENOMENA 151 80. Analysis of Entoptic Phenomena. a). OBSERVATION OF THEIR PARALLAX (Listing). By fixing different points of the entoptic field, we observe that the entoptic phenomena are displaced in the field. If the corpuscle which gives rise to the shadow is behind the pupillary plane, the shadow moves in the same direction Fig. 102. Parallax of the entoptic phenomena. as the visual line (fig. 102, a, b). Taking the position b, the visual line is directed upwards; the shadow has descended to near the lower border of the field, but seems to have ascended (by the projection out- wards). It is easy to see that we have the contrary parallax if the object is in front of the pupillary plane, and that it disappears if the object is in this plane. As the movement is greater in proportion as the object is more removed from the pupillary plane, we can thus form an approximate idea of the position of the corpuscle. b). MEASUREMENT OF THE DISTANCE OF THE CORPUSCLE FROM THE RETINA (Brewster, Bonders and Doncan). To measure this distance Breivster proposed to use two luminous points. We then see two circles of diffusion which partly overlap, and each corpuscle produces two shadows. We measure the distance between the two shadows of the same object and the diameter of the free part of one of the circles DE (fig. 103) ; the ratio between these two measurements is equal to the ratio between the distance of the object from the retina and that of the pupil from the retina. Let A and B (fig. 103) be two luminous points which must be in the anterior focal plane of the eye, d the middle of the pupil, o the object, 152 PEJSIOLOaiC OPTICS p and p! the shadows and c and q the centers of the circles ol diffusion. Since the points are in the focal plane, dc is parallel to op and dc to op lt Fig. 103. Determination of the position of an entoptic object. After Brewster. therefore: "^ = ^ > anc * figure 103 b shows that cq = DE = R -f- if R is the radius of the circle of diffusion. We can make measurements by using as a luminous source a sheet of white paper strongly illumi- nated. We look through two stenopaic openings towards this sheet and we notice the places where the shadows are projected as well as the borders of the circles (Bonders) . Doncan made the measurements & double vue by comparing the entoptic phenomena with a scale seen with the other eye. c). EXAMINATION OF THE REFRACTION OF THE OBJECT. So far, we have treated the entoptic phenomena as shadows, and the objects which produce them as opaque bodies. Most frequently, this is not the case, as they are more or less transparent; but their refraction is different from that of the surrounding parts, whether their surface has a different curvature, or whether their index is different. It is easy to see (fig. 104) that the more refracting objects must con- centrate the light so that the entoptic image becomes luminous and surrounded by a dark border; this is the case with the images of the corneal specks. On the contrary, if the object is less refracting than the surrounding parts, the image is dark, with a more luminous border. The difference is specially marked in the case of the star figure of the crystalline lens, which, in some people, appears dark, in others luminous, thus indicating that the refraction of the corresponding parts is some- ENTOPTIC PHENOMENA 153 times greater, sometimes less than that of the surrounding parts. If we make the experiment by placing ourselves at a great distance, and making the eye strongly myopic, we should have the phenomena in- verted. Fig. 104. The drop on the cornea causes convergence of the rays which pass through it so that we see a luminous center surrounded by a shadow. In the experiment which we have just noted (fig. 104), the dark border is due to the fact that part of the rays which should illuminate it are made to converge towards the middle of the entoptic image, by the interposition of the corpuscle. This border is always diffuse and fre- quently somewhat pronounced; it must not be confounded with the diffraction ring which surrounds the images along the border of the pupil when the luminous point is very small. This ring, which some- times may be double or triple, is always very thin and very distinct. 81. Entoptic Observation of the Vessels of the Eetina (Purkinje). a). If, in a dark room, we hold a candle at some distance from the eye while we look directly in front, we see the retinal vessels greatly magnified projected on the dark portion of the room. They appear dark (of a deep blue) on a somewhat more luminous ground (orange). If we move the candle towards or away from the visual line, the vessels seem displaced in the same direction; if, on the contrary, we move the candle around the visual line, the vessels seem to move in the direction opposite to that of the candle. The fovea appears without vessels: in my eye it offers a kind of starlike appearance; in others (Burow) it appears as a luminous disc, limited by a crescent-shaped shadow. The explanation of these phenomena has been given by H. Muller. By refraction there is formed at a (fig. 105) a retinal image of the candle; the part of the retina thus illuminated sends diffuse light in all direc- tions. The vessel v intercepts the rays av, so as to form the shadow b on the sensitive layer of the retina; it is this shadow that we see (the retina is represented too thick on the figure ; really the shadow is very near the vessel). Illuminated directly, the vessel also forms a shadow 154 PHYSIOLOGIC OPTICS on the sensitive part situated behind it ; but this shadow is not usually perceived, because it is always formed at the same place (and because the sensitive layer has thus become accustomed to it) or, perhaps, be- cause the part of the retina which is behind the vessel, being always covered, is never fatigued and consequently remains much more sensi- tive, so that the little light which passes through the vessel produces as strong an impression on this part as the full light on the remainder of the retina. Fig. 105. Entoptic observation of the vessels. (After H. Muller.) It seems that the vessels form in ordinary circumstances negative scotomata, like the spot of Mariotte, although it may be difficult to ob- serve them, except near the papilla, because of the instability of the fixation (see chap. XVIII). b). We concentrate with a convex lens the light of a flame on the sclera, as far as possible from the border of the cornea. By bringing the focus somewhat on the sclera, we see dark vessels on an orange ground. The vessels move in the same direction as the luminous focus. On concentrating the light on the internal part of the sclera we succeed in seeing the luminous focus itself under the form of a red sun near the external border of the visual field. The explanation is analogous to that of the preceding case. The light of the image of the flame, formed on the sclera, passes through this membrane and the choroid, and disperses in the interior of the eye where it forms vascular shadows at unusual places. H. Midler meas- ured the distance ab (fig. 106), separating two successive positions of the luminous focus, and the displacement /5 of the shadow of a vessel corresponding to this displacement of the light. With these data, he calculated that the vessel should be 0.17 to 0.33 mm. in front of the sensitive layer. This experiment seems to prove that it is the layer of EXTOPTIC PHENOMENA 155 the cones and rods that is the sensitive layer, for the distance of the small vessels near the macula from the layer with the cones is very nearly the same (0.2 to 0.3 mm.). Another phenomenon, also due to the influence of the light which passes through the sclera and the choroid, is observed when we place ourselves near the luminous source, a window for example, so that one eye may be illuminated while the other is in the shade. After a little while we then observe, on closing the eyes alternately, that the white objects seen with the illuminated eye present a greenish tint, while they appear reddish to the other eye. The light which passes through the sclera and the choroid is colored red by the blood of the latter mem- brane. This red light "fatigues" the retina of the illuminated eye, which has the effect of making white objects assume a greenish tint. The other eye sees them red by contrast. When we read in full sunlight, we sometimes see the letters vividly colored red. The phenomenon is probably of the same kind as the preceding. The red light, which passes through the membranes of the eye, comes to be added to the light which passes through the pupil. It is not sufficiently great to perceptibly change the tint of the white paper, brightly illuminated by the sun, but it colors red the black letters, which send back only very little of the white light. c). Looking at the sky through a stenopaic opening, we see very dis- tinctly pictured the granulated ground and the delicate vessels which surround the macula ; but the stenopaic opening must be kept in continuous motion, otherwise the phenomenon disappears. If we look at the sky without the stenopaic opening, the shadow of the vessel is too short to reach the sensitive layer. The same phenomenon is frequently ob- served when working with the microscope : when we illuminate the field with daylight, we see the vessels by placing the eye at the ocular and giv- ing it a to-and-fro motion. The musca of the vitreous body may also be very well observed Fig. 106. - Entoptic obser- vation of the vessels by il- m this way. lumination of the sclera. When making this experiment, as well as the preceding one, we sometimes see the vessels become luminous ; this is due to the fact that the parts of the sensitive layer on which the shadow falls, in ordinary circumstances, are now exposed to the light, which acts much more strongly on these parts than on the remainder. 150 ^ 88. Other Entop tic Phenomena. a). Looking towards the sky. \\ o very frequently see bright points which seem to move lively and then to disappear, giving place to others (Pti/ v , \ The phenomenon is often more pronounced if we look through a cobalt glass. This phenomenon is explained by the pressure which is exerted on the sensitive layer by a globule of blood which is stopped in a very narrow capillary, (i) 6), By compressing the eye for some time, we can see the retinal vessels and even notice the blood globules magnified about 50 times. The retinal vessels appear bluish; but, before perceiving them, we see those of the chorio-capillary membrane, red on a black ground (Vierordt, LaiWifi). It seems that this experiment, which Young had already made, would not succeed with everybody f). A pressure localized on a small part of the sclera gives rise to a pkosphcnc which, like every other retinal impression, is projected in the opposite direction. Making the experiment in darkness, we notice that the phosphene has the form of a feebly luminous disc, surrounded by a bright border, corresponding to the inflection of the retina. "With very prominent eyes Young succeeded in producing a phosphene cor- responding to the macula: exterior objects which were in the position of the phosphene were still visible, but presented very pronounced de- formities. If we exert on the eye a pressure sufficiently strong uniform, the entire visual field is darkened in consequence of the anemia of the retina. On making, in a dark room, rapid movements with the eyes, we observe two luminous circles corresponding to the places of entrance of the optic nerves and due to the traction produced by these nerves during the movement. e). On making an effort of accommodation in a dark room, we some- times see a very large luminous circle, which is attributed to the trac- tion which the ciliary muscle exerts on the interior membranes of the eye during accommodation (phosphene of accommodation of Csermak). I did not succeed with this experiment. /). A weak electric current makes visible at the moment of clc the dark papilla on a blue ground, if the current is ascending; whitish blue on a dark orange ground if the current is descending: on opening the current we have the phenomena reversed. If the current is strong, we see all the colors of the spectrum mixed. (1) [Another and rery probable explanation of this phenomenon assumes that we observe in the littJebritht bom some reiattT^y empty capillary spaces, produced by small temporary local stoppages of the circulation in the capillaries of the retina. See the paper by the translator in the QpAOotm* Jta*r< February, 1900.]- IT. BSTOPTIC PBBSOMESJL 157 g). On looking towards the sky through a Xicol prism, we see the brushes of Haidinger, an indistinct cross, one of the arms of which is yellow, the other blue; the phenomenon rotates with the nicoL Some persons can see the phenomenon, but less pronounced, without a nicoL A), Phenomena of Diffraction* in the Eye. Looking toward* a very in- tensely luminous point we see it surrounded with an infinity of very fine, many-colored radiations, the whole of which is known under die name of ciliary corona. Its extent varies with the intensity of the luminous point. If the latter is very bright (a reflected image of the sun) the diameter of the corona, may reach 8 degrees or more. The cause of the phenomenon is, in all probability, to be found in the fibrous structure of the crystalline lens. Besides the ciliary corona, most people see around the entire luminous source a somewhat vivid diffraction ring A, presenting the colors in the well-known order: red outside, brae inside. The diameter of the ring (blue) is about 3 degrees. The space which separates it from the lumin- ous source is filled with the ciliary corona. Druault and Solomonsohn have recently described a second, larger ring B (6 to 7 degrees in diameter), winch seems to appear in every one when the pupil is dilated. It presents the colors in the same order as the first, but it is more irregular, and composed of radial striae. Making these observations with monochromatic fight, the ciliary corona, presents itself under the form of a luminous dust, which is concentrated towards the periphery so as to form the two rings which I have just described. Quite near the luminous source we see one or two black, very fine rings, due to diffraction by the border of the pupiL The ring A is probably due to the epithelial cells of the cornea, and analogous to the rings which we observe on looking through a glass plate covered with grains of lycopodium. On covering a larger and larger part of the pupil with a screen, we see the entire ring become indistinct and disappear at once. Schioetz has shown that on exposing the cornea, to the action of distilled water for some time, as in the experiment of Young, page 168, we observe a pretty system of rings, the first of which corresponds almost to the ring A. We must note, however, that Druavlt, on looking through a dead cornea, showed the existence of a ring, the dimensions of which scarcely differed from those of the ring A, and which was undoubtedly due to the endothelium of the membrane of Descemet: he could remove the entire epithelium of the anterior surface without producing the least change in the ring, which would, on the contrary, disappear as soon as he touched the endothelium. 158 PHYSIOLOGIC OPTICS The ring B, which was previously described by Danders, is due to the crystalline fibres which act as a grating. If we cover a part of the pupil with a screen, we see a part of the ring disappear while the remainder does not change. Druault succeeded in reproducing the phenomenon with dead crystalline lenses. The rings which glaucomatous patients see resemble these rings, but are generally larger (10 to n degrees). As the size of the rings is in- versely proportional to that of the corpuscles which produce them, it is probable that the origin of the glaucomatous rings is to be found in the deepest layer of the corneal epithelium, the cells of which are much smaller than the superficial cells (Schioetz). Placing a drop of blood in the conjunctival sac we obtain a very pretty ring (diameter 7.5 degrees for the yellow) surrounded by a second paler ring. The space between the first ring and the light is not black, as for the other rings here de- scribed, but yellowish or maroon (Druault). These rings seem analogous to those sometimes seen by persons affected with conjunctivitis. i). I recently described a kind of entoptic phenomenon which I ob- served in the following circumstances. We surround a lamp with a transparent shade, made of some layers of colored tissue paper, for ex- ample. We place ourselves at some meters distance, and interpose an opaque screen, in which has been cut a vertical slit, between the lamp and the eye ; the distance of the screen from the eye may vary between 30 cm. and several meters. We close the left eye and fix with the right Fig. 106a. Entoptic phenomenon. eye a point on the screen, situated near the right border of the slit. To begin, we hold the head so that the eye may be in darkness. Then we move the head so that the eye enters into the luminous pencil which passes through the slit while maintaining fixation at the same place. ENTOPTIC PHENOMENA 159 At the same moment we see the phenomenon appear under the form of two blue arcs, feebly luminous, but bright, which go from the slit towards the position of the blind spot by turning around a fixed point (fig. 1060). The phenomenon lasts only a moment; an instant later the arcs become narrow, the interior which was black is filled with a blue glow, and the whole disappears, to reappear again with the least motion of the eye. To see the phenomenon with the left eye it is necessary to fix the left border of the slit. According to a communication from Dr. Crzellitzer the phenomenon was described by Purkinje in a publication which I have not at my dis- posal. It seems very prevalent ; among persons whom I have examined in this regard, I have met only a single one who has not been able to see it. The form of the arcs recalls the course of the nerve fibres at this place. The appearance resembles that of certain phosphorescent bodies, by the bluish color and by the impression which it gives of being feeble and yet bright at the same time ; we again find the same appearance for different other phenomena which we observe in darkness, for instance the after image of Purkinje (see page 242), the trace which the im- pression of a red coal leaves on the retina, and so forth. Bibliography. (Euires de Young, edited by Tscherning, p. 71, 140 and 168. Purkinje (J. E.). Beitrdge zvr Kentniss des Sehens, 1819, p. 89, et neue Beitrdge, 1825, p. 115. List- ing (J.). Beitrag zur physiologischen Optik. Gb'ttingen, 1845. Doncan (A.). De corporis vitrei structurd. Utrecht, 1854. Brewster (D.). Transactions of the Royal Soc. of Edinb., XV, 377. Miiller (Heinrich). Verh. der med. physik. Gesdlschaft zu Wurzburg. IV, V. Haidinger. Ueber das directs Erkennen des polarisirten Lichts und der Lage der Polarisations- ebene. Poggend. Ann. 1844. Darier (A.). De la possibilite de voir son propre cristallin Ann. d'oc. t. CXIV, p. 198, 1895. Schioetz (H.). Om nogle optiske equeskaber ved Cornea. Christiana, 1882. Druault (A.). Sur la production des anneaux colores autour des flammes. Arch, d'ophtalmol, Mai, 1898, et Compte rendu du Congres 47.44 mm Total index 1.4545 1.4519 1.4414 Later, he supposed for the schematic eye an index of 1.4371, which would give for the living eye in repose a focal distance of 50.62 mm. and for the eye in accommodation 39.07 mm. To explain the mechanism of accommodation Helmholtz announced the following hypothesis, which he gave, however, only as probable: in a state of repose the crystalline lens is kept flattened by a traction exerted by the zonula. When the ciliary muscle, of which he considered 166 PHYSIOLOGIC OPTICS the anterior extremity as fixed, contracts, it draws the choroid slightly forward, which relaxes the zonula. Having become free, the crystalline lens then swells by its own elasticity, approaching the spherical form. This hypothesis does not seem to have been at first generally ac- cepted, (i) Hencke, and other authors, tried to explain the phenomena observed by other hypotheses. After having discovered the supposed circular fibres of the ciliary muscle, H. Mulkr thought that this muscle changed the form of the crystalline lens by a direct pressure, an idea which was abandoned when it became known that the ciliary body never touches the crystalline lens. On the other hand, the hypothesis of Helmholts was strengthened by the experiments which Hensen and Voelkers performed on dogs. They thrust very fine needles into the eye a little behind the ora serrata ; on stimulating by the electric current the ciliary ganglion, they saw the free extremity of the needle describe a movement backwards, which proves that the choroid is drawn forwards. The phosphene of Czermak, which had also been seen by Purkinje, also indicates a traction forwards of the interior membranes of the eye. By examining eyes on which an iridectomy had been performed, Coccius also established during accom- modation, phenomena which could militate in favor of the hypothesis of Helmholts (swelling of the ciliary processes, at least apparent diminution of the diameter of the crystalline lens, and an increase in the width of its border, that is to say, of the very peripheral part which is seen black with the ophthalmoscope). Thanks to these observations, thanks also to the ever increasing fame of Helmholts, his theory ceased little by little to be disputed, and his followers, more loyal than the king, proclaimed as certain what he had himself, with much reserve explained as probable. (2) Thus, Mauthner declared the question of accommodation definitely solved by the theory of Helmholts. Before explaining the mechanism of accommodation as I intend to, I must add some remarks to the historical explanation which we have (1) See Bonders. Anomalies of the Refraction of the Eye. London, 1864. (2) Great men are, indeed, too reserved through fear of their followers. HelmhoUz formed the idea of comparing the cornea to an ellipsoid, and although he said intentionally that the cornea does not resemble such a surface, this idea has so taken root that it will be difficult to eradicate it. It is so also with his ideas of accommodation ; if we take the trouble to compare the cautious terms which he used, Avith the mode of expression of his followers, we shall see the difference. The participation of the pos- terior iurface of the crystalline lens in accommodation, which everybody considers as certain, had for Helmhottz merely the character of a grand probability. Measuring his three living eyes, he found for the crystalline lens a thickness about %mm. less than that of dead crystalline lenses ; and he added : " On the other hand, it seems to me very improbable that I have committed an error of a%mm. mak- ing these measurements." In the modern treatises we read, on the contrary : " If we remove the crys- talline lens of the eye of a young person, AVC see it immediately assume a spherical form," etc. ACCOMMODATION 167 just read, and which is classical, because there have been authors who have expressed ideas on accommodation in my opinion more correct than those in vogue up to the present time. First, I will make an objec- tion. If it is true that the crystalline lens, in repose, is kept flattened by a traction exerted by the zonula, we should expect to find the dead crystalline lens, taken from the eye in its capsule, in a state of maximum accommodation, or perhaps even still more swollen, since it is no longer exposed to any traction. The followers of Helmholtz have, indeed, strongly insisted on the fact that he found the dead crystalline lens thicker than the living crystalline lens in repose, although the difference does not seem to exceed the limit of error (see page 71) ; but, if we take the trouble of examining his numbers (page 165), we shall see that his dead crystalline lenses were by no means in a state of accommoda- tion. He measured in all three living eyes and found, as radii of the anterior surface of the crystalline lens in repose, 11.9 mm., 8.8 mm. and 10.4 mm., while for the dead eyes he found 10.16 mm. and 8.87 mm. His autopsies, therefore, by no means tell in favor of his hypothesis. It is so also in the case of the measurements which Stadfeldt under- took recently. He measured eleven living human crystalline lenses in a state of repose, with the ophthalmometer ; the radius of curvature of the anterior surface of the crystalline was on an average 10.6 mm., while the average of the same radius of the six dead crystalline lenses, taken from the eye in the capsule and measured with the ophthalmometer of Javal, without being exposed to any traction, was 11.4 mm. 85. Jttechanism of Accommodation. Historical, B. It was Young who first demonstrated that accommodation was effected by an increase of curvature of the crystalline surfaces. Moreover, he had more exact ideas on what happened during accommodation than those which are actually now in vogue. He wrote his celebrated treatise on the mechanism of the eye in 1801, and it is truly astonishing that nearly a century should have passed before his book was understood and before we came to know as much as he. Before proving that the accommodation is effected by an increase of curvature of the crystalline lens, he begins by showing that there can be question only about an increase of curvature, either of the cornea or of the crystalline lens, or of a lengthening of the globe, and he eliminates, as theoretically impossible, the other hypotheses which had been proposed. Let us now pass to his analysis. a. ACCOMMODATION is NOT EFFECTED BY AN INCREASE OF CURVATURE OF THE CORNEA. Young proved this thesis by a series of experiments, 168 PHYSIOLOGIC OPTICS Young.) several of which closely approach our modern ophthalmometric methods. Observing the corneal image, he did not discover the least change during accommodation; he obtained, however, a very visible change by exerting a pressure on a peripheral part of the cornea, and this change of curvature is much less considerable than that which would be necessary to explain accommoda- tion. It is evident that a change of the cornea sufficient to explain accommodation would have been very visible. Young, who experi- mented with his own eyes, was at this time 27 years old, and his amplitude of accommoda- tion measured about 10 D. Actually, we can easily measure a quarter of a dioptry. His most conclusive experiment consisted in P uttin ? the e >' e Under Water < fi * Io8 ) : he took a weak objective of a microscope which had very nearly the same refraction as the cornea, filled the tube with water, and placed it before his eye also plunged into water. In these con- ditions, the action of the cornea, which was surrounded by the liquid on both sides, was eliminated and replaced by that of the objective. Now in this experiment the amplitude of the accommodation remained intact. b. ACCOMMODATION is NOT EFFECTED BY AN ELONGATION OF THE GLOBE. To prove this fact Young employed a method which he could use because he had very prominent eyes. He turned the eye inwards as much as he could, and applied against its anterior surface a strong iron ring; then he thrust the ring of a little key on the external side between the eye and the bone, until the phosphene reached the fovea. The rings were kept at a fixed distance. Placed between the iron ring and that of the key, the eye could not lengthen. He should therefore, if accommodation was effected by a lengthening of the globe, either find it abolished, or see in every case the phosphene, due to the pressure, extend over a much greater surface. But in these conditions the accom- modation remained unaltered, and the width of the phosphene did not change. c. PERSONS OPERATED ON FOR CATARACT HAVE LOST ALL TRACE OF ACCOMMODATION. By measuring with his optometer persons operated on for cataract, Young easily succeeded in proving this fact. d. He then explained the direct proofs of the increase of curvature of the crystalline lens. It was to these experiments that I alluded when I ACCOMMODATION 169 said that he had, on accommodation, ideas which are ahead of our own time. I again performed these experiments some years ago, and it was by starting from them, by repeating them and adding others to them, that on the mechanism of accommodation I have come to form ideas which differ materially from those which have been current up to the present. It was impossible for Voting to describe clearly the mechanism of accommodation, because at that time the non-striped muscle fibres were unknown, which kept him from suspecting the contractility of the body known later as the ciliary muscle ; he was thus led to postulate the con- tractility of the crystalline lens, an hypothesis which he soon abandoned. His researches in this direction necessarily could not but remain fruit- less. The ciliary muscle was discovered, at the same time and separately, by Bowman and Bruecke (in 1846). Ideas on the structure and function of this muscle have varied considerably. Sometimes the anterior ex- tremity, sometimes the posterior extremity has been considered as fixed ; sometimes the mobility of both extremities was taken for granted (Donders), sometimes both were considered fixed. The oldest descrip- tions seem to be the best, especially that of H. Milller; most of the modern works seem influenced by the hypothesis of Helmholtz. Accord- ing to H. Milller, we must distinguish between a longer superficial part (fig. 109) composed of longitudinal fibres which are inserted in front on the sclera, near the canal of Schlemm, and which are lost behind in the choroid, and a deep part, also com- posed in greater part of longitudinal, but shorter, fibres, and not going so far either in front or behind, as the superficial fibres. These fibres are not inserted in the sclera. The deep- est layer is composed of oblique or even circular fibres. Milller thought that they formed a true sphincter, but the existence of such a sphincter is by no means proved; after holding for some time a circular direction, these fibres seem to change their course and to continue in the deep Fig. 109. Ciliary muscle of man. ( After H.Muller.) a, cornea ; 6, sclera ; c, iris ; d, ciliary process; e, canal of Schlemm; /, longitudinal fibres; g, circular fibres; h, transitional fibres of the ciliary muscle. 170 PHYSIOLOGIC OPTICS longitudinal fibres. It seems that at least a part of the deep longitudinal fibres ends thus ; others seem to end free, without insertion, in the part of the muscle which goes towards the anterior chamber. By dividing a hardened eye into two halves by a longitudinal section, we easily discover the small white triangle of the ciliary muscle. If we then exert a traction upon the iris in order to separate the ciliary body from the sclera, we do not tear the muscle from its insertion near the canal of Schlemm, but we divide it into two leaflets, both of which end, behind, in the choroid. In the fresh eye there also always remains a part of the muscle adhering to the sclera as Mannhardt had already observed. When making this experiment we produce an appearance which forcibly recalls the ciliary muscle of certain animals (the cat, for example, fig. no), in which the muscle is divided in front into two parts separated by a pro- longation backwards of the space of Font ana. Among the authors who have reached a result differ- ent from that of Helmholtz, I shall mention Mannhardt, who, by a study of the com- parative anatomy of the ciliary muscle, reached the conclusion that it is the pos- terior extremity of the mus- cle which should be consid- ered as fixed, and that ac- commodation must be pro- duced by a traction exerted by the ciliary muscle on the zonula. He was vigorously attacked by H. Mutter, and his work scarcely attracted attention because it could not be considered that a traction on the zonula could produce an increase of the curvature of the crystalline surfaces. We cite, moreover, the remark- able observations of Foerster (1864), according to which the tension diminishes in the anterior chamber during accommodation. He ob- served several patients in whom he performed paracentesis so that the iris and crystalline lens were nearly in contact with the cornea. When Fig. 110. Ciliary part of the eye of a cat. a, Ciliary muscle dividing in front into two leaflets ; b, canal of Fontana ; c, cornea ; d, iris. ACCOMMODATION 171 the patient made an effort of accommodation, the middle of the cornea became depressed to assume its old form by the relaxation of the accom- modation. It must be noted, however, that the phenomenon persisted after instillation of atropine. In persons having a corneal fistula he obtained an almost immediate effect from atropine by placing a drop in the conjunctival sac and making an effort of accommodation, the liquid being sucked into the anterior chamber by the diminution of tension. These beautiful observations, which Arlt declared equivalent to physiologic experiments, are scarcely explicable by the theory of Helmholts. 86. Personal Experiments. Finally I come to my own experiments on accommodation: the first (i) are derived from the statements of Young. i The amplitude of accommodation diminishes tozvards tJte periphery of the pupil. a. ABERROSCOPIC PHENOMENA. We have already seen that with the aberroscope (see page 102) most persons see the shadows concave towards the periphery. But, on making an effort of accommodation, the form of the shadows changes: they turn their concavity towards I II Fig. 111. Change of aberroscopic phenomena during accommodation. I, Repose. II, Accommodation. the middle, which indicates that the refraction increases towards the middle (fig. in). After what we have said on page 98 it follows that the central refraction must have increased more than the peripheral refraction. 172 PHYSIOLOGIC OPTICS Some people in a state of repose see shadows straight or slightly con- cave towards the middle. In such people this deformity becomes still more pronounced during accommodation. b. CHANGE OF THE CIRCLE OF DIFFUSION. If we observe a distant luminous point, after having made the eye myopic, it appears under the form of a luminous disc, the brightness of which is generally uniform or concentrated at the middle. During accommodation we see it change its appearance; we see a feebly luminous disc surrounded by a bright border. According to the explanation given on page 98, this observa- tion means, like the preceding one, that the spherical aberration is over- corrected during accommodation, that is to say, that the central accom- modation is greater than the peripheral accommodation. Although accommodation may increase the refraction of the eye by many diop- trics, the circle of diffusion increases only slightly, at least when the pupil is dilated. Figure 112 shows the appearance of the circle of diffu- sion of an emmetropic eye ; rendered 8 D. myopic by a convex lens, this- Fig. 112. Appearance of the luminous point (right eye of Professor Koster, treated with cocaine). eye sees the circle of diffusion represented by a, figure 113, while b, same figure, represents the form under which it sees a luminous point by mak- ing an effort of accommodation of 8 D. without a lens. The pupil was- dilated. The explanation of the phenomenon is easy : let us imagine the pupil and circle of diffusion divided into corresponding zones ; it is clear that if the accommodation is everywhere the same, all the zones of the ACCOMMODATION 173 diffusion circle ought to increase, while, if the accommodation dimin- ishes towards the periphery, the outside zones increase little or nothing and the central zones, on increasing, come to partly cover the peripheral zones. This is the reason why the circle of diffusion is surrounded dur- Fig. 113. The same eye as in figure 112. a, Appearance of the luminous point, the eye being rendered myopic 8 D. with a convex lens (Repose). 6, Appearance of the luminous point, without lens, the eye accommo- dating 8 D. Measured with the optometer of Young, the central accommodation was 8 D. ; the pe- ripheral accommodation (at 2.5 mm from the axis) was 3.3 D. ing accommodation with a bright border, without increasing much in diameter. c. MEASUREMENT WITH THE OPTOMETER OF YOUNG. The opto- meter of Young enables us to measure directly the difference between the central accommodation and peripheral accommodation. We measure the central accommodation with the two nearest slits (see page 102), which we place as nearly as possible at the middle of the pupil, and the peripheral accommodation with the triangular plate which we lower just enough to be able to still see the two lines. In this way we prove that at the border of the pupil (supposed to be five millimeters) the amplitude of the accommodation is only half the central accommodation or still less. If, after having dilated my pupil to the utmost (with a mixture of cocaine and homatropine), I use an interval of 7 millimeters, my ac- 174 PHYSIOLOGIC OPTICS commodation which, at the middle of the pupil, is 2.5 D. to 3 D., dimin- ishes nearly to zero (0.2 D.) on the borders. Here are some measure- ments: Central amplitude (interval 0.75 mm.). 9.8 D. Peripheral amplitude (interralSmm.). 4.2 D. 8 D. 3.3 D. 7.5 D, 3.7 D. 6 D. (1) 3 D. 4 D (1) 2 D. Mme T 6.7 D. 3.8 D. Tschernine . . 3 D. 1.25 D. We find still more considerable differences between the central and peripheral accommodation, by placing the two slits sometimes at the middle of the pupil, sometimes near the borders: AMPLITUDE OF ACCOMMODATION Temporal border. Center. Nasal border. Demicheri (Homatropine) 6 D. 2 D. 4 D. (1) ID. MmeT 5 D. 6.7 D. 5 D. Tscherning (Homatropine) 0. 25 D. 3 D. d. SKIASCOPIC EXAMINATION. Observations a and b are easy to make, but they require that the observer be young, that his pupil be well dilated and that he be master of his accommodation ; observations with the optometer of Young, as well as those with the ophthalmometer, which I shall describe forthwith, are quite delicate and require special instruments. But we possess in skiascopy with a luminous point a very convenient means of studying the nature of accommodation. To make the observation we select a child or a young person whose pupil is well dilated with cocaine. It is better to select a person whose pupil is well dilated, who is almost emmetropic, and who has not too much aberra- tion in a state of repose. We place the lamp, surrounded with its perfo- rated screen, at one side of and a little behind the observed person and we project light on his eye by means of a concave mirror, which forms the image of the opening at 15 to 20 cm. from the observed eye, in which position we place a mark of fixation. As long as the observed person does not accommodate, the condition of Jackson is not fulfilled, and we see the pupil entirely illuminated, but at the moment when the observed person fixes the fixation mark the ring of over-corrected aberration appears with all desirable distinctness. The phenomenon is espe- (1) The accommodation was weakened by the influen of homatropine. ACCOMMODATION 175 cially striking if we compare the appearance of the accommodated eye with that of the non-accommodated eye, made myopic with a convex glass (fig. 1130). We have observed (page 99) that we see luminous, under these circumstances, the parts of the observed pupil which send Fig. 113a. Skiascopic examination of accommodation, a, Appearance of the emmetropic eye made myopic with a lens of -{- 5 D. 6, Appearance of the same eye, accommodating 5 D. without lens. light into the observing eye. Placed at 50 cm. the existence of the ring indicates, therefore, that there are, towards the borders of the pupil, parts, the myopia of which does not exceed 2 D., for otherwise the rays proceeding from these parts would have already crossed the axis, and would not enter into the observing eye. To determine the degree of aberration produced by accommodation, we approach nearer and nearer the point of fixation ; the ring becomes thinner and thinner, but it is rare that it disappears completely before the accommodation attains a very high degree. I have thus shown that a central accommodation of 8 D. accompanied a peripheral accommodation of 2 D. in a case in which the pupil was very large. The condition was, therefore, still more pro- nounced than in the cases which I examined w r ith the optometer. The phenomena may present themselves a little differently if the positive aberration is very pronounced in a state of repose, but on making the calculations we obtain the same result. 2 During accommodation the anterior surface of the crystalline lens in- creases in curvature at the middle, while it is flattened towards the periphery. I place the arc of the ophthalmophakometer horizontally, and attach three incandescent lamps to it, so that they are on the same horizontal line and just far enough apart for all three images formed by the anterior surface of the crystalline lens to be visible in the pupil. I direct the look of the observed person so that the three images are situated near the 176 PHYSIOLOGIC OPTICS upper border. In a state of repose they are arranged in a straight line (fig. 1 14 a) or following a curve slightly concave towards the center (fig. 115 A); during accommodation, they form a curve convex towards the a b l 6 2 b 3 Fig. 114. Reflection images, on the anterior surface of the crystalline of my right eye, of three lamps placed on a horizontal line, a, in a state of repose; b l b 2 6 3 , in different stages of accommodation. Highest accommodation 3 D. with cocaine. middle (fig. 114 b lt b 2 , 6 3 , 115 B), and the curvature of which is more pronounced in proportion as the accommodation is greater. It is easy to see that this phenomenon indicates a greater curvature at the middle than towards the periphery : indeed, let us suppose for an instant that we have added three other lamps, which would form their images near the lower border of the pupil, and let us consider as objects Fig. 115. Reflection images of the right eye of Mme T. A, in a state of repose ; B, during accommodation (after a drawing of Professor Hosier}. a, corneal images; b, images of anterior surface of the crystalline lens. Accommodation of 6 D. the distances between the two lamps situated on the same vertical line. We would thus have three equal objects, the images of which would be of the same size in a state of repose (aa, fig. 116), which indicates that the curvature is the same everywhere ; but, during accommodation, the image (b, fig. 116) of the middle is considerably smaller than the other two, b b it which indicates that the curvature is greater at this place. We observe an analogous phenomenon on the cornea, in cases of keratoconus. The keratoscope of De Wecker and Masselon is formed by a white square on a black ground. On examining a case of keratoconus with this instrument, and causing the look to be so directed that the ACCOMMODATION 177 apex of the keratoconus coincides with the axis of the instrument, we see the sides of the image of the square assume the form of curves turning their convexity towards the middle (fig. 117). Repose Accommodation Fig. 116. We might think, from these phenomena, that the curvature of the peripheral parts increases during accommodation, but less than that of Fig. 117. Deformity of the corneal image of a white square in a case of keratoconus. (After Masselon.) the central part. Nothing of the kind: the peripheral parts undergo a real flattening which causes, however, an increase of refraction. To understand this fact, which might appear paradoxical, we must recall what I have said on page 13 on refraction by surfaces of the second degree. Outside of the axis, it is the normal and not the radius of curvature which, for refraction (and also for reflection), plays the part of the radius of the sphere, supposing that the luminous point (or, in the case of reflection, the observing eye) is on the axis. In figure 118, BDE represents a curve of the second degree, AF its axis, BH the radius of curvature at the point B, BG the normal at this 178 PHYSIOLOGIC OPTICS point and the dotted curve a circle drawn with BG as radius. The luminous ray AB is refracted in the direction BF, exactly as if the sur- face were replaced by the circle BE. The measurements which we have made with the optometer of Young enable us to calculate approximately the form of the surface, and the calculation will explain at the same time what I have just said. Let us suppose that all the accommodation is effected by the anterior surface, and let us take the experiment of Demicheri as an example. He had, at the middle, an accommodation of 7.5 D., at 2.5 mm. from the axis an accommodation of 3.7 D. Let us suppose 10 millimeters for the radius Fig. 118. Refraction by a parabolic surface. of the anterior surface in a state of repose and 1.06 for the index of the crystalline lens in relation to the aqueous humor. We express the refrac- tion of the surface by the inverse of the anterior focal distance -~ = -- oToicrs = 6 D. During accommodation the central refraction increased 7.5 D. ; the refraction of the surface would be, therefore, at this place 13.5 D. Whence we obtain the radius p Q by the formula n "~J=M 6 Po Po = 13.5 D., which gives p = 4.44. At 2.5 mm. from the axis the accommodation was 3.7 D., the refraction of the surface in a state of accommodation 6 D. -f 3.7 D. = 9.7 D., and the normal N, at this place, would be found by the formula ~ = 9.7 = -~ , which gives N = 6.1 mm. We can then find the radius of curvature p , at this place, by the formula 1C 3 P s=s ^i wm ' cn holds good for all surfaces of the second degree. It gives P = 12 millimeters. We see that the surface is already flattened at this place during accommodation, and it is manifestly flattened still more farther towards the periphery. If a small part of the accommodation is effected by the posterior surface, as is probable, the flattening of the anterior surface towards the periphery must be still greater, for it is ACCOMMODATION 179 probable that the part of the accommodation which is due to the pos- terior surface diminishes relatively much less quickly towards the pe- riphery. Supposing that the portion of the accommodation due to the posterior surface be i D., as well at the center as near the border of the pupil, we would have for the anterior surface /><> = 4.8 mm., p = 14.2 mm. The surface would have the form of a quite flattened hyperboloid (fig. 119), the apex of which would correspond very nearly with the optic axis of the eye, and would be found a little outside the visual line. It is interesting to observe that among all the surfaces of the second degree having p = 4.8 mm., it is this hyperboloid which most nearly approaches the form of the surface in a state of repose. Accommodation is effected, therefore, by a minimum de- formity. 3 By placing the cursor A of the oph- thalmophakometer above the telescope, and requesting the observed person to look towards the latter, we observe, when he makes an effort of accommodation, the fol- lowing phenomena (fig. 120) : I. The image of the anterior surface of the crystalline descends quickly towards the corneal image, and is finally hidden be- hind the latter. It is this displacement which has been described by Cramer. Towards the end of this phase the pupil- lary contraction begins. II. This movement ended, the small image of the posterior surface of the crys- talline descends in its turn by a slow and abrupt movement. Its dis- placement is much less than that of the large image ; and, while the latter moves in a straight line, the small image is displaced in a curve with its concavity turned towards the middle. The pupillary contraction is greatest during this phase. III. When the observed person relaxes his accommodation, the small image again ascends to resume its old place with a quick movement, as if moved by a spring. Fig. 119. Deformity of the crys- talliue surfaces during accomo- dation. The full curves indi- cate the shape in a state of repose, the dotted curves the accommo- dative shape. (Accommodation 7D.) 180 PHYSIOLOGIC OPTICS IV. This movement ended, the large image re-ascends in its turn ; its movement is rather slow, and as if hesitating. The accommodative phenomena seem, therefore, to take place in two steps. i " in tv Fig. 120. The four apparent phases of accommodation. Corneal image. O Image of the anterior surface of the crystalline. Image of the posterior surface of the crys- talline. A, accommodation ; B, relaxation. Fig. 121. Eight eye of Mme T. Displacements of the image of the posterior surface during accommodation, observed with the ophthalmophakometer. C, by fixing the telescope; D, by looking to the right; G, by looking to the left; H, by looking up- wards ; B, by looking downwards. The large white spot is the corneal image, the two small white spots indicate the position of the image of the posterior surface of the crystalline in a state of repose and during accommodation. The arrows indicate the direction of the displacement which takes place when an effort of accommodation is made. ACCOMMODATION 181 During the displacement of the small image, the large one is con- cealed behind the corneal image, so that we cannot see whether it is displaced or not; it is not easy to find a direction of the look such that we can follow the two crystalline images during the entire accommoda- tive displacement. Sometimes they are concealed behind the corneal image, sometimes behind the iris. I have, however, succeeded in doing so by using two lamps, one for each image ; in this way, we can satisfy ourselves that the large image undergoes a slight displacement down- wards at the same time as the small one, but this displacement of the large image is concealed by the corneal image when we perform the experiment as I have just described. It is especially easy to observe the displacement downwards of the large image, if the direction of the look of the observed person is such that the image in repose is placed near the internal or external border of the pupil. The movement of Cramer then takes place in a horizontal direction. Having reached the end, the image makes a bend, becoming displaced a little downwards, but this latter displacement is much less than that of the small image. I may add that the small image is displaced downwards, whatever may be its posi- tion in the pupil (fig. 121), which indicates that the cause can be sought neither in the increase of curvature of the surface, nor in a displacement forwards or backwards of the crystalline lens. But this displacement downwards of the image is combined with a quite small centripetal dis- placement, which also takes place whatever may be the position of the image in the pupil, and which is probably due to a slight recession of the posterior surface. The observation has again been made by Hess and Heine. They have found that the displacement of the small image takes place downwards, whatever may be the position of the head ; if we lean the head on the right shoulder, the displacement of the small image takes place towards the side which is downwards, that is to say, for the right eye towards the temporal border of the pupil, for the left eye towards the nasal border. I was able to verify this observation, which seems to indicate that the change takes place under the influence of the weight. Hess also observed that an entoptic figure, situated on the posterior surface of the crystalline lens, is displaced downwards by a maximum accommodation, whatever may be the position of the head. 4 Other Phenomena Accompanying Accommodation. We have seen that Hueck discovered a slight advancement of the anterior surface; Helmholtz confirmed this observation. It is possible that we may some- times meet such a displacement, although the experiment of Helmholtz 182 PHYSIOLOGIC OPTICS did not succeed very well with me. and although I am not sure that his observations do not admit of another explanation. In the eye with which I have made my experiments, the anterior surface did not ad- vance ; the part corresponding- to the pupil did not change its place, but the part covered by the iris receded with this membrane. There is formed during accommodation, at the anterior surface of the iris, a circular depression (fig. 122), the peripheral border of which, corre- sponding to the ciliary body, rises in a peak, while the central border pre- sents a very gentle slope, corresponding to the anterior surface of the crystalline lens. I commend this observation, which was already made by Cramer, but which has often been regarded as proving an enlarge- ment of the anterior chamber in the angle of the iris ; it is easy to see that the most peripheral parts of the posterior partition of the anterior chamber do not recede. The phenomena are not always equally pro- nounced, but we can nearly always find at least a trace of them in young subjects. We can make the observation by oblique illumination, but the use of the magnifying glass (monocular) is not to be recommended; binocular vision is necessary in order to properly account for the change in the level of the iris. When the phenomenon is quite pronounced, we thus obtain a quite distinct idea of the conical form which the anterior crystalline assumes during accommodation. As to the posterior surface of the crystalline lens, its changes are less manifest. We have seen that the catoptric phenomena seem to indicate a slight increase of curvature. The posterior surface remains very nearly in its place during accommodation ; sometimes, however, we ob- serve phenomena which seem to indicate that it recedes a little. Fig. 122. Change of the anterior chamber during accommodation ; a, repose ; b, accommodation. The much-discussed question of knowing whether the thickness of the crystalline lens changes during accommodation is very difficult to decide, because the change, if it exists, does not exceed the limit of an error of observation. Influenced, perhaps, by the observation of Helmholts, I had thought an increase of thickness established. Recently I took up the subject anew in collaboration with Professor Koster; we went to much trouble without being able to reach a definite result. ACCOMMODATION 183 87. The Author's Theory of Accommodation. After the observations which I have just described in the preceding paragraph, and which can be briefly expressed by saying that accommodation is effected by the tempo- rary formation of an anterior le-nticonus, the hypothesis of Helmholts does not seem tenable ; for it is not easy to conceive how such a mechanism could produce a flattening of certain parts of the crystalline lens and at the same time an increase of curvature of the other parts. I have already observed that the curvature of the anterior surface of the crystalline lens of the dead eye corresponds with that of the living crystalline lens in a state of repose, and not at all with the accommodated crystalline lens. But the difference between the dead crystalline lens and the accommodated crystalline lens is still more striking, if we consider not only the curvature at the middle, but the form of the entire surface, because the anterior surface of the accommodated crystalline lens is flattened towards the borders, as I have just explained; in the dead eye the curvature, on the contrary, increases considerably towards the borders, the surface having the form of an ellipsoid of revolution around the short axis. This fact, which was already established by Krause, (i) is especially very striking if we examine the eye with the ophthalmo- meter, as I explained on page 61. The most usual way is to remove the prism, and observe the image of the keratoscopic disc. As long as CAB Fig. 122a. Reflection images on the anterior surface of the dead crystalline len*. A, at the center ; B and C, towards the borders. the ophthalmometer is placed in the direction of the axis of the crystal- line lens, the images of the circle are round, but, if we displace the in- strument so as to form the image near the border, it changes into an (1 ) Hclmholtz seems to have been lecl into error by the celebrated measurements which Jean Louis Petit had made at the commencement of the eighteenth century. Most of the measurements of Petit are very exact, but those of the curvatures of the surfaces are without any value. He had a series of copper plates cut in the form of arcs of circles of different radii. His only means of determining the curvature of the surfaces of the eye consisted in finding the arc of the circle which seemed to him to conform to the surface. The measurements of Krause are astonishingly good if we consider the manner in which he made them. He cut a fresh eye in two, along the axis, placed one-half of it in water under a micro- meter and examined with a microscope of little magnifying power. 184 PHYSIOLOGIC OPTICS ellipse with the long axis vertical. Comparing figure 1220, with those on page 62, we see that the deformity of the surface is quite the contrary of the conical form. Following are the radii of curvature from 5 to 5 of an eye measured by Holth, compared with those which I have cal- culated for the eye of Demicheri in maximum accommodation: Age o 5 10 15 20 Dead eye 28 12,4 mm 12 mm ll mm 9 mm 7 mm Accommodated eye.. .. 25 5.6 mm 5.9 mm 7.0 mm 18.0 mm 79.2 mm We see that we can scarcely suppose a more pronounced difference (fig. I22b). I, therefore, set myself to study the physical qualities of the Fig. 1226. A, the dead crystalline lens ; B, the accommodated crystalline lens. The dotted lines indicate the form of the surfaces of the second degree, to which the majority of crystalline surfaces most nearly approach. crystalline lens, by using especially the lenses of horses, which are very large and consequently easily handled, and I have found that we cannot consider the crystalline lens as a simple elastic body in the sense of Helmholtz. The contents of the crystalline lens are composed, in the adult, of two parts, the nucleus, which cannot change its form, and the superficial layer which, on the contrary, possesses this faculty to a very high degree; its consistence is very nearly that of a solution of very thick gum. I call this layer the accommodative layer in order to show that it is due to it that the eye can accommodate itself. According a% age advances, the nucleus increases while the accommodative layer ACCOMMODATION 185 diminishes and with it the amplitude of accommodation. The whole is surrounded by a capsule which is inextensible or very nearly so (Hoc- guard). It has always been supposed that a traction exerted on the zonula must flatten the crystalline surfaces, while a pressure exerted on the borders would have, on the contrary, the effect of increasing their curva- ture. Nothing of the kind : a pressure exerted on the borders has, on the contrary, the effect of flattening the surfaces, while a traction exerted on the zonula increases the curvature of the surfaces at the middle, while flattening them towards the periphery. To verify this fact we take the crystalline lens from the eye of an ox or a horse, which must not be too old, with the capsule and zonula of Zinn. It is easy to see that by compressing the borders the surfaces are flattened; to> observe the effect of traction we take hold of the zonula on both sides, very near the crystalline lens, and, by pulling, we can, on looking at the crystalline lens sideways, see that the anterior surface, assumes a hyperbolic form (fig. 123). But we obtain a better idea of the deformity by studying the catoptric images. We place the crystalline lens with the anterior surface uppermost on a table and fix above it, at some distance, an opaque ring on which we have stretched a sheet of transparent paper; by illuminating this sheet of paper we see the catoptric image of the ring formed on the anterior surface of the crystalline lens as a black circle. We can also replace the ring by a big lens. The size and distance of the ring must be chosen so that the image may be sufficiently large, and placed so that the image may be centered with the crystalline lens. Then, by exerting a traction we see the circle change into an oval, the short axis of which cor- responds with the direction of the traction, which proves that the curvature increases in that direc- tion. The experiment succeeds the more easily the larger the ring. If we place the ring so that its image is near the border of the crystal- line lens, we see it lengthen in the direction of the traction, which indi- Fig. 123. Crystalline lens of the ox twice enlarged: The dotted line indicates the form which the crystalline lens assumes: A, by a lateral pressure ; B, by a traction exerted on the zonula. The arrows indi- cate the direction of the forces. 186 PHYSIOLOGIC OPTICS cates a flattening in this direction. Dr. Crzcllitzer has recently con- structed an instrument by means of which we can exert a traction on the zonula in all directions at once, and with which we can still better imitate accommodation. Instead of the ring we may use two candles placed so that their images are in the direction of the traction; on stretching we see them make a centripetal movement analogous to the movement discovered by Cramer, but much less extended. Indeed, on the one hand, it is probable that these animals (i) have not a very well developed accommodation, and on the other hand, it must not be for- gotten that in the eye the displacement appears nearly doubled by the magnifying action of the cornea. The experiment can be considered only as an imitation of accommodation on a large scale ; but the fact that we can obtain an increase of curvature by a traction exerted on the zonula is beyond doubt. Furthermore, we should scarcely expect any other result. I have several times emphasized the fact that the nucleus has a much more pronounced curvature than the surfaces of the crystalline lens, and more- over, that it cannot change its form unless we crush it. Glancing at figure 124, we readily understand that by exerting a traction on the zonula the peripheral parts must flatten, while at the middle the curvature increases on ac- count of the greater resistance and curvature of the nucleus. And the result will be the same if there is no nucleus, as is the case in young people, only if the curvature and resistance in- crease towards the center. The increase of curvature of the central layers is visible on any preparation of the crystalline lens. The increase of resistance finds its optic expression in the increase of index towards the center. By traction on the zonula we have obtained changes analogous to those which we observe during accommodation, and it seems to me that the structure of the ciliary muscle lends itself very well to the produc- tion of such traction. We have seen that it is composed, for the most (1) Dr. Stadfddt later verified the results with human crystalline lenses, which he placed in a cork ring, fixing two opposite parts of the zonula with very fine needles. He measured the curvature of the surfaces with the ophthalrnometer ofJaval and Schioetz, and then determined the position of the focus, or rather that of the focal lines, with a microscope. In consequence of the traction, he always caused astigmatism, the maximum of curvature corresponding to the direction of the traction. On a crystal- line lens belonging to a person aged 38 years, he thus produced an astigmatism of the anterior surface of 4 D. The posterior surface was only very slightly influenced. The astigmatism disappeared with the traction. Fig I'j4. Optic system of the eye of the ox (magnified twice). ACCOMMODATION 187 part, of longitudinal fibres, that the most superficial fibres are inserted in front on the sclera, near the canal of Schlemm, while the middle fibres end free near the surface which lies towards the anterior chamber, and that the deepest fibres are combined with the oblique and circular fibres which, perhaps, form their terminations. The muscle has the form of a little triangle, the external surface of which rests on the sclera, while the internal surface is turned towards the vitreous body and the anterior surface towards the anterior chamber. During contraction the antero- external angle remains fixed, the antero-internal angle recedes, as we can see directly in the anterior chamber, and the posterior extremity advances as the experiments of Hensen and Voclkers prove. The reces- sion of the anterior part exerts on the zonula the traction which pro- duces the deformity of the anterior surface; the advancement of the posterior extremity exerts on the choroid a traction which has the effect of sustaining the vitreous body and indirectly the crystalline lens, so that the latter does not recede under the influence of the traction. As far as the actual result is concerned, it matters little to which of the two actions we attach the greater weight. Let us conceive, for example, a moment when the anterior extremity may be fixed : the result of the contraction of the muscle would be that the crystalline lens, on account of the traction exerted on the choroid, would be pushed a little forward, which would produce also a traction on the zonula, which would suffice for the deformity of the crystalline surface. It may be that there exist, in this relation, individual differences as the disagreement between the observations of Helmholtz and my observations seems to indicate, (i) I think that this theory explains quite satisfactorily the greater part of the phenomena which accompany accommodation. It explains, in the first place, the deformity of the anterior surface; the direction of the zonula in the living eye is such that the effect of the traction must act almost exclusively on the anterior surface. It explains also the change of level of the iris and the diminution of tension of the anterior chamber (by the recession of the peripheral parts of the crystalline lens and iris). The phenomena observed by Coccius are probably due to an optic (1) According to certain authors (Arlt, Iwanoff), the ciliary muscle differs in myopes and hyperme- tropes. If this is so, we might, perhaps, find the predisposition to myopia in a special structure of the ciliary muscle. It is, indeed, clear that the more the superficial fibres are developed the greater must be the traction exerted on the choroid, and this traction has evidently for its object the protection of the sclera against the increase of tension during accommodation. If the posterior extremity of the muscle were fixed, the sclera would be exposed to this tension every time one would accommodate. In view of this relation, it may be interesting to observe that the eye which I examined, in which the an- terior surface of the crystalline lens did not advance during accommodation, is myopic about 6 D., and that that one of the three eyes of Helmholtz which showed the least advancement was slightly myopic. 188 PHYSIOLOGIC OPTICS illusion. Holding the crystalline lens of a horse in front of a red ground we see this color through the whole crystalline lens, except at a quite narrow border where the red rays undergo total reflection. By exerting a traction on the zonula, this border enlarges at the expense of the transparent part, which makes one think of a diminution of the diameter of the crystalline lens. We have not succeeded, up to the present, in explaining satisfactorily the singular phenomena which I observed when the accommodation attained its maximum (page 180). I had attributed them to a displace- ment downwards of the crystalline lens, due to an unequal traction on the zonula. But since Hess and Heine have shown that the displacement takes place following the weight, this explanation must of necessity be abandoned. Hess supposes that the crystalline lens falls downwards by the relaxation of the zonula, as stated by Helmholts, but apart from the fact that the hypothesis of Helmholtz must be rejected for other reasons, it is not easy to any longer suppose, in view of the manner in which the crystalline lens is fixed on the vitreous body, that it can fall downwards unless the anterior part of the vitreous body is displaced also. The fact that the movement of the small image is much wider than that of the large one (i), indicates in every case that there can be no question of a displacement directly downwards, but rather a see-saw movement downwards and backwards. Among other explanations which might occur to us, that of a deformity due to a displacement of the crystalline mass in the interior of the capsule would perhaps be the most probable. As to the contraction of the pupil which accompanies accommodation, it is evident that it has the effect of eliminating the peripheral parts of the crystalline lens, which, by reason of their flattening, would render the image too poor. We know also that when the pupil is dilated with an alkaloid which has little or no effect on the accommodation (cocaine or homatropine), near sight diminishes relatively more than far sight; this phenomenon is often attributed to a diminution of the amplitude of accommodation, but at least with cocaine I have only very rarely been able to prove a real diminution of this amplitude. We must note, however, that eyes which have a strong spherical aberration correct this aberration by accommodation ; these eyes may, therefore, see relatively better near at hand than far away, when the pupil is dilated. (1) A slight displacement of the look downwards would give analogous phenomena. When the eye makes a movement, the displacement of the images is in direct relation with the distance of the center of curvature of the surface in question to the center of rotation of the eye. The displacement of the small image is relatively large because the center of curvature of the posterior surface of the crystalline lens is situated very far forward in the eye. ACCOMMODATION 189 When, in a paracentesis, we allow the aqueous humor to escape, we know that the crystalline lens and the iris come to be applied against the cornea, without this membrane noticeably changing form. In all probability, the crystalline lens is then in the state of highest accommo- dation, because it could not make such a movement without exerting a strong traction on the zonula. While performing paracentesis on a rabbit's eye, Mannhardt claims that he saw also the accommodative displacement of the images of Purkinje, by means of the ophthalmoscope of Cramer. It becomes probable, therefore, that the pupillary contrac- tion, which accompanies the escape of the aqueous humor, is accom- modative. But the pupillary contraction accompanies the escape of" the aqueous humor even in a dead eye ; by introducing the point of a Pravas syringe into the anterior chamber, it is easy to dilate or contract the pupil at will by injecting or removing the liquid. This contraction is, therefore, purely mechanical, and it then becomes probable that the accommodative contraction of the pupil is so also, although this mech- anism is not yet clearly elucidated. Bibliography. Petit (J. L.). Memoire ur le crynfallin de VceH de Fhomme. Hist, de 1' Academie des Sciences, 1730. Krause (C.). Poggendorfs Annalen, 1834-36. Max Lan- genbeck. Klinische Beitrdge zur Chirurgie und Ophthalmohgif. Gottingen, 1849. Cramer (A.). Het Accommodatievermogen der Oogen. Haarlem, 1853. Translated into German by Doden. Leer, 1855. Helmholtz (H.). Ueber die Accommodation des Avges. Archiv fiir Ophtalmologie, I, 2. Griife (A.).v. Fall von acquirirter Aniridie ah Btitrag zur Accommoda, tionslehre. A. f. O. VI F, 2. p. 150. Briicke (E.). Anatomixche Beschreibung des menschlichen Augapfels. Berlin, 1847. Bowman (William). Lectures delivered in the London Royal oph- thalmic hospital Moorfields, 1847. Miiller (Heinrich). Ueber einen ringfb'rmigen Muskel am Ciliarkorper des Menschen und ilber den Mechanismus der Accommodation. A. f. O., Ill, p. 1. Mannhardt. Bemerkungen ilber d(n Accommodationsmuskel und die Accommodation. Arch, fur Opht., IV, 1. Hueck (A.). Die Bewegung der Krystattinse. Leipzig, 1841. Coccius (A.). Ueber den Mechanismus der Accommodation des menschlichen Auges. Leipzig, 1867. Forster (R. ). Zur Kenntniss der Accommodafionsmechanismus. Kl. M. f. A., 1864 p. 368. Rochon-Duvignaud. Recherches sur F angle de la chambre anterieure et le canal de Schlemm, Paris, Steinheil, 1892. Tscherning (M. ). Etude sur le mecanisme de V accommodation. Arch, de phys., January, 1894. L'optometi-e de Young et son emploi. Arch, de phys., October, 1894. Recherches sur les changements optiques de I'ceil pendant 1 J accommodation. Arch, dephys., Janu- ary, 1895. Theorie des changements optiques de I'ceil pendant F accommodation. Arch, de phys. January, 1895. Crzellitzer (A.). Die Tscherningsche Accommodativnstheorie. Grafe's Ar- chiv, XLII, 4, 1896. Stadfeldt (A.). Die Veranderung der Lime bei fraction der Zonula. Kl. M. f. A., December, 1896. Crzellitzer (A.). Zonularspannung und Linsenform. Bericht der Heidelberger Gesellschaft, 1896. He?s (C.). Arbeiten aus dem Gebiete der Accommoda- tionslehre. Grafe's Archiv, 1896-99. Heine (L.). Die accommodation Linsenverschiebungen im Auge. Grafe's Archiv, 1897. Tscherning (M.). The Theory of Accommodation. Oph- thalmic Review, April, 1899. Tscherning (M.). La surcorrection accommodative de Vaber- ration de sphericite de I' ceil. Journal de Physiologic, March, 1899. CHAPTER XIII. OPHTHALMOSCOPY. 88. Methods of Illuminating the Fundus of the Eye. It has been known from the remotest times that the pupil of certain animals (dog, cat, etc.) can appear luminous. The phenomenon was thought to be analogous to the production of light by the glow-worm (phosphorescence) ; in reality it is due to the existence of the tapetum, a part of the choroid the retinal surface of which is strongly reflecting and has a metallic reflex : its purpose is not very well elucidated. As to the human pupil, it has been known for a long time that it may, in very rare cases, appear luminous after the development of an interior tumor of the eye (amaurotic cat's-eye). Beer also remarked the ocular glow in certain cases of aniridia. Towards 1850 dimming and Bruecke discovered the method of making the pupil of the normal eye appear luminous, and Hclmholtz in 1851 achieved the great invention of the ophthalmoscope which was destined to revolutionize ophthalmology. Like every other object the fundus of the eye sends back light when it is illuminated. Let A (fig. 125) be a luminous point for which the Fig. 125. eye is accommodated. This point sends into the eye the cone ABC, the rays of which reunite at D. This point, being illuminated, sends the rays in all directions; those contained in the cone ABC emerge from the eye to meet at a point A. Generally, therefore, the eye can send back light to a point which has first sent the light to it, and if in ordinary circumstances the pupil of the eye appears black, it is because the pupil 190 OPHTHALMOSCOPY 191 of the observing eye, being black, cannot send light back into the ob- served eye. In order that it may appear luminous, a luminous source must be placed in front of the observing eye; this is what we do by means of the ophthalmoscope. Following are the different circumstances in which we can see the pupil luminous : a. The pupil of albinos is seen red because the fundus of the eye is illuminated by the light which has passed through the sclera. If we cover the eye with a screen pierced by an aperture corresponding to the pupil, the latter appears black. By concentrating a bright light on the sclera by means of a lens, we can make the pupil of a normal eye luminous, especially if the person has a fair complexion. b. If, in the case of figure 125, the eye is not exactly focused for the luminous point, the latter illuminates on the retina a circle of diffusion (ab, fig. 126). This circle sends back the light not only in the direction Fig. 126. of the luminous point, but also in neighboring directions : thus the point a sends back the cone BaC which, outside the eye, takes the direction ABCd, so that the observing eye o may be placed in this cone. Placing a lamp at some distance from the observed eye and sighting near the border of the flame, from which we shelter ourselves by a screen, we can frequently see the pupil luminous, especially if it is a little large and if the patient does not fix the flame. The experiment succeeds more easily if the observed eye is strongly ametropic, because then the rays, having emerged from the eye, soon diverge greatly, so that the observing eye may easily find a place in the luminous cone. If the eye is not ametropic we can make it so by means of a strong lens or by putting it under water, or, as Bellarminoff has lately done, by placing a plate of glass in contact with the cornea so as to eliminate the refracting power of this membrane. By this latter means we can make the fundus of the eye visible for several persons at once. In the case of amaitrotic cat's-eye, the presence of the tumor in the interior of the eye makes the latter strongly hypermetropic, so that the fundus becomes easily visible. 192 PHYSIOLOGIC OPTICS c. PRINCIPLE OF THE OPHTHALMOSCOPE OF HELMHOLTZ. Let AB (fig. 127) be a plate of plane, parallel glass and L a lamp which sends light towards this plate. The greater part of the light passes through the plate, but a part is reflected towards the observed eye, D. It enters this eye and illuminates the retina. The latter sends back light towards the plate : a part of this light is reflected towards the lamp L, but the greater part passes through the plate and enters the observing eye C, which, consequently, sees luminous the pupil of the observed eye. To Fig. 127. Principle of the ophthalmoscope of Hdmholtz. compensate for the loss of light which, proceeding from L, passes through the plate, Helmholts used several plates, placed one behind the other. d. PRINCIPLE OF THE ORDINARY OPHTHALMOSCOPE. We obtain a more intense illumination by means of a silvered mirror; the observer looks through a small portion from which the coating has been removed or which has been perforated. As a concave mirror concentrates the light it illuminates better than a plane mirror, and the latter better than a convex mirror, (i) Generally it is useful to have a good illumination ; but we sometimes see better the very delicate changes in the fundus of the eye by using a weak illumination, and very delicate opacities of the (1) The clearness of the retinal image of the flame which is formed in the observed eye is the same in all cases, but the image is larger when we use a concave mirror than when we use a plain or convex mirror. One can verify this for oneself by putting one's eye in the place of the observed eye. The image of the flame which one then sees in the mirror corresponds to the illuminated part of the retina ; it is larger in the case of the concave mirror than with the plane or convex mirror. Placing the flame behind the mirror, one sees, in the same circumstances, the opening as a luminous circle which cor- responds to the part of the fundus of the eye which the observer can see at once (ophthalmoscopic field). OPHTHALMOSCOPY 193 vitreous body or of the crystalline lens disappear if the illumination is too strong. The ophthalmoscope is the only practical means of illuminating the eye. Nevertheless, a different method may sometimes prove service- able. We place the lamp behind the observer so that the light reaches the observed eye by glancing along the head of the observer; we concen- trate the light on the eye with a lens. When the pupil is dilated we can thus see the fundus of the eye feebly illuminated, and we often dis- tinguish very distinctly details situated far forward in the vitreous body (tumors of the ciliary body, detachments, etc.). 89. Examination by the Erect Image (Helmholtz). The conditions for seeing the pupil luminous were known, before Helmholte, by the re- searches of Gumming and Brucckc, and Babbage seems to have already illuminated the pupil with a mirror from a small portion of which the coating was removed for observation purposes; but none of these scientists thought of studying the conditions under which this ocular glow can form an image of the fundus of the eye. When preparing the lectures, in the course of which he was to illus- trate for his class the methods of making the pupil appear luminous, Helmholtz proposed to himself the problem to be solved, not a difficult task for an experienced physicist. He easily succeeded in solving it theoretically, and then constructed the first ophthalmoscope by com- bining some glass plates with the lenses of a test case ; after some days of hard work he succeeded in seeing the fundus of the living eye which no one had ever seen before him. Helmholtz used examination by the erect image. Suppose that the observer is emmetropic (if he is not he must correct his refraction) : he can then see the fundus of the eye of another emmetrope without any further aid, since the rays emerging from the observed eye are parallel. If the observed person is not emmetropic he must be made emmetropic. We, therefore, look for the strongest convex glass or the weakest con- cave glass with which we can see the fundus of the eye distinctly: this glass indicates at the same time the refraction of the eye ; but the ob- server must cultivate the habit of not using his accommodation, other- wise the results will be false. The refraction which we find with the ophthalmoscope ought to be in agreement with that found by subjective examination. It must be noted, however, that the glass of the ophthal- moscope is generally a little farther away from the eye examined than a glass placed in a frame. We find therefore, as by the subjective method, 194 PHYSIOLOGIC OPTICS too low a number for hypermetropia, too high a number for myopia, and the error is more pronounced in the case of an ophthalmoscopic examination on account of the greater distance. For low degrees of ametropia it is insignificant; for high degrees, especially of myopia, it is sufficient to make the determination fallacious. Latent hypermetropia is generally disclosed by ophthalmoscopic examination because in the dark room the patients do not fix. MAGNIFICATION. To obtain a numerical expression of ophthalmo- scopic magnification, we may compare the retinal image, formed in the observing eye, of an object (the papilla of the fundus of the examined eye) with the retinal image which the observing eye would have of the same object, placed free in air, at the working distance of the observer. We often make this distance 20 centimeters. Let us suppose that both eyes, that of the observer and that of the observed person, are emmetropic. Let O = AB (fig. 128) be the object of the fundus of the observed eye ; we draw the rays AC and BD parallel to the axis. These two rays will intersect at the anterior focus 3^, and all the other rays proceeding Patient Fig. 128. Observer from A and B are parallel to either of these ; among other rays ^E and 4>\G which, prolonged, pass through the anterior focus of the observing eye. After refraction in this eye these rays are parallel and determine the size of the image, I. Designating by F the anterior focal distance of the observed eye, by F\ that of the observing eye, the two similar triangles CD4> X and EG4>\ give the relation : JL F/ i O F! ' We see that, if the optic systems of both eyes are alike, I is equal to O. The papilla of the observed eye forms in the observing eye an Image equal to itself. By placing the fundus of the eye free in the air at the OPHTHALMOSCOPE 195 working distance, equal to 20 centimeters, the retinal image Ij of the object O (fig. 129) would be found by the formula 200 By multiplying this formula by the preceding one, we obtain the magnification in the erect image : 200 mm By supposing 15 millimeters for F a , the magnification would be about 13, but this number is arbitrary, since the working distance has been chosen arbitrarily. Fig. 129. Observer If the observed eye is myopic, the magnification is greater, supposing that the correcting glass is beyond the anterior focus of the observed eye, as is always the case. The construction is the same as in the pre- ceding case, but on meeting the concave glass the rays C^ and D<^ t (fig. 130) are made more divergent. The rays ^E and &\G which are Patient Fig. 180. Observer parallel to them diverge, therefore, more than in the preceding case, which makes the image I x greater. If there is a case of a myopia of 19C PHYSIOLOGIC OPTICS curvature the magnification is still greater; the point 4^ is, in fact, situated nearer the observed eye, which causes the rays HK and LM, and consequently also the rays ^E and ^G to diverge still more. In the hypermetropic eye the reverse takes place. It follows that in an astigmatic eye we see the papilla elongated in the direction of the meri- dian of greatest refraction. OPHTHALMOSCOPIC FIELD. According to Helmholtz we find the ophthalmoscopic field, that is to say, the aggregate of the parts of the fundus of the eye, visible simultaneously by joining by straight lines the middle of the pupil of the observing eye to the borders of the pupil of the observed eye, and by making these straight lines undergo the same refraction in the observed eye as if they were rays. Figure 131 shows that the field is greater in the hypermetropic eye, smaller in the myopic eye, if the observing eye is beyond the anterior focus of the observed eye, as is always the case. As it is the border of the pupil of the observed eye which limits the field, we increase it by instilling atropine. Patient Observer Fig. 131. Construction of the ophthalmoscopic field. This is an instance of inverse constructions which we frequently use in geometric optics; to know what points of the fundus of the ob- served eye can send back rays into the pupil of the observing eye, we reverse the problem by imagining the pupil of the observing eye lumin- ous and finding what parts of the fundus of the observed eye it can illuminate. The result is the same on account of the reversibility of the optic processes. In reality the field is a little larger than that which we have found by our construction, since we have reduced the pupil of the observing eye to a point; from -the point d, situated outside the field, some rays could still enter the observing eye through the lower parts of the pupil. To have the field complete it would be necessary to construct, not the image p i of the center of the pupil p, but the image of the entire pupil or rather of the opening of the ophthalmoscope, formed by the OPHTHALMOSCOPY 197 optic system of the observed eye. We would thus obtain a larger field, but the parts near the border would be very slightly illuminated. 90. Examination by the Erect Image. Observations. To tell the size of intra-ocular objects, it is customary to compare them with the dia- meter of the papilla; we thus say that the width of a staphyloma is the fourth or half of the diameter of the papilla. The attempts which have been made to obtain more exact measurements by means of a micro- meter (Bonders, Lcroy) have not given practical results. The refraction is usually the same for the entire fundus of the eye. According to Young, if we suppose a sphere drawn around the eye with the distance of the far point as radius, the position of the retina is such that it is everywhere found at the place where the best images of objects situated on this sphere would be formed. A certain degree of astigma- tism by incidence is inevitable for the peripheral parts; but the retina is here found between the two focal lines almost at the place which would correspond with the circular diffusion spot. Thanks to this arrangement, we can use the papilla for the determina- tion of refraction by the erect image; generally its refraction scarcely differs from that of the macula. There are exceptions to this rule, how- ever. For instance, I examined on consultation a young man in whom a myopia of 4 D. was indicated, while a colleague, very experienced in determination by the erect image, and myself found, each for himself, emmetropia by the ophthalmoscope. It was later established beyond doubt that the patient had really a myopia of 4 D. Then, asking our- selves whether the myopia might not be due to a spasm of accommo- dation, we resorted to a treatment by atropine, but without changing the result. Analogous differences seem quite frequent in cases of ex- cessive myopia, by reason of the elongated form of the globe. A difference between subjective and ophthalmoscopic refraction may therefore be due: i to a greater distance of the correcting glass from the observed eye (see page 194) ; 2 to the fact that a latent hyperme- tropia may become manifest in the darkness ; 3 to the fact that the papilla may have a different refraction from the macula ; 4 to simulation. To judge of the depth of a papillary excavation we can measure the difference of refraction between the edge and pit of the excavation, keeping in mind that a difference of one dioptry corresponds to almost a third of a millimeter. We can measure by the same process the tume- faction of the papilla in cases of optic neuritis, the distance of an opacity of the vitreous body from the retina, etc. 198 PHYSIOLOGIC OPTICS Another means of judging whether one point is situated in front of another consists in making slight movements of the head (with the ophthalmoscope). We shall then see the nearer point make a move- ment in a contrary direction in relation to the other point (parallax). The magnification of 13 which we have found for the erect image has nothing to do with the apparent size of the papilla, which depends on the distance to which we project the image without knowing it. When we begin to use the ophthalmoscope, the papilla frequently ap- pears very small, and generally its size seems to vary for different ob- servers. I have noticed a phenomenon of the same kind when looking at a luminous point (see page 138). If the point is very distant the circle of diffusion appears very large to me. But if I observe a luminous point placed at the focus of a lens of 20 D., held in front of my eye, the point appears extremely small, and this although the retinal image ought to be exactly the same in both cases. Accommodation is often charged with playing a part in this optic illusion, but we must observe that it takes place even if every trace of accommodation be excluded. It rests on an unconscious conclusion relatively to the distance of the object (see chapter XXII). The macula is usually difficult to see : most frequently the pupil must be dilated. The fovea is sometimes visible as a dark spot with a small whitish point in the middle; its place is marked in every case by the peculiar manner in which the vessels come from all sides to disappear in its vicinity. We never see a trace of the yellow color which is so striking in the dead eye ; certain authors have, therefore, considered this yellow coloration as a phenomenon due to changes after death, and this idea seems confirmed by an observation which I have made. We gen- erally suppose that if we do not see the yellow color of the macula, it is because the yellow light is drowned by the red light reflected by the blood. I, therefore, thought that we should be able to see it by illumi- nating the eye with a strong sodium flame. The blood does not reflect this light or reflects it only slightly, and the appearance of the fundus of the eye recalls that of photographic illustrations of ophthalmoscopic images; we see the vessels black on a gray ground, but the macula, which we should expect to find illuminated, remains at least as dark as in ordinary ophthalmoscopy. The red color of the fundus of the eye is due to the vessels of the choroid ; wherever the choroid is defective we see the white background of the sclera, in cases of coloboma for example. It is curious that we never see a trace of the retinal purple with the ophthalmoscope. In the OPHTHALMOSCOPY 199 normal state the retina is completely transparent ; we see only its vessels. Sometimes we can, however, distinguish it as a grayish veil in the parts near the papilla. If the black pigment be strongly developed, the fundus of the eye appears of a uniform deep red. If it is but slightly developed, the fundus has often a marble or spotted appearance due to the meshes of the vascular network of the choroid. Most normal eyes have a physiologic excavation or cup of the papilla which has the appearance of a whitish spot. It is then easy to see, by the erect image, that the bottom is more myopic than the border; we see indistinctly the vessels of the excavation when those of the borders appear distinct and vice versa, at least when the excavation is a little deep. The physiologic cup never reaches the borders of the papilla. We can be certain that an excavation is pathologic only when it reaches the borders everywhere. We frequently perceive in the normal eye a pulsation of one or several of the large veins. During the systole the tension of the globe increases enough to compress the large veins near their starting place where the intra-venous tension is weakest. At the moment of diastole the tension of the globe diminishes, the pressure ceases and the veins empty them- selves, (i) The pulsation of the arteries is nearly always a sign of glaucoma ; the tension of the globe is so high that the arteries remain empty, except at the moment of systole. The papilla is generally limited by a very thin white border, some- times surrounded by an incomplete black border, formed by the pigment of the choroid. The white border is called the scleral border; it is attributed to the visibility of the sclera between the choroid and the papilla. Sometimes it is larger and mistaken for an incipient staphyloma. One can see the red fundus of one's own eye by looking in a mirror held before a flame. A luminous pencil passes through the opening of the ophthalmoscope, enters the eye, is reflected by the retina, emerges from the eye, meets the mirror, and is again reflected towards the retina. If the course of the rays permit, for example if the eye is emme- tropic and the mirror plane, we may even distinguish the details. We (1) [Lately Dr. S. Turk has studied this question again in a number of persons with irregular heart- beat (arythmia). These observations prove that the venous narrowing is independent of the entrance of the arterial pulse wave into the eye, and he infers that the cardiac systole produces not the narrowing, but the dila- tation of the veins. He further shows that this venous pulsation cannot be caused by a rhythmic inter- ference with the exit of the blood from the vena centralis retinee because a dilatation, caused in this way, ought to be propagated opposite to the direction of the blood-current. He, therefore, considers this phenomenon caused by a propagation of the arterial pulse wave through the capillaries into the veins which is accounted for by the relatively high extravascular pressure in the eye (Engelmann'sArch.f. Physiol.,1899).] W. 200 PHYSIOLOGIC OPTICS see at the same time the catoptric image of the cornea as a large circle of diffusion. Auto-ophthalmoscopes have been constructed as well as ophthalmo- scopes, by means of which several observers can see simultaneously the fundus of the eye. Another way of examining oneself consists in observing with one eye the image of the other formed by a looking-glass; we can in this way perform ophthalmoscopy of the left eye with the right eye by the in- verted image, and we can, with a small concave mirror placed not far from the eye, observe the images of Purkinje, etc. It was by working thus with my own eye that I observed for the first time the conical deformity of the anterior surface of the crystalline lens during accom- modation (page 176). 91. Examination by the Inverted Image. This examination was in- troduced into oculistic practice by Ruete in 1852. It was especially adopted and developed by the Berlin school (Graefe), while the Vienna school (Jaeger) especially used the erect image. As the Berlin school held for a long time a more influential position, examination by the in- verted image was for a long time more used than the other. The two methods, however, merit a place side by side. The inverted image gives a less magnification and a larger field: it is, therefore, very useful for studying the general appearance of the fundus of the eye, while the erect image serves especially for the study of the details and for the determina- tion of refraction. Examination by the inverted image is made by holding a strong convex lens (most frequently -f- 13) at a distance from the eye almost equal to its focal distance. This lens forms a real and inverted image of the fundus of the eye, situated on the other side of the iens, in the vicinity of its second focus. It is this image that the observing eye sees when accommodating, or, which is better, by looking through a convex lens of about 4 D., placed behind the mirror. If the examined eye is emmetropic, the rays leaving the eye are parallel and the image is formed at the focus of the lens ; if it is myopic the image is a little nearer, if hypermetropic a little farther than the focus. In the latter case the observer is frequently obliged to move back a little in order to see the image distinctly. MAGNIFICATION. If we use a lens of + 13, the magnification is about five times for an emmetropic eye. Let ab = O (fig. 132) be an object in the fundus of the observed eye. We draw the ray be parallel OPHTHALMOSCOPE 201 to the axis : it passes, after refraction, through the anterior focus of the eye 4> 15 and the other rays coming from b are parallel to it, since the eye Fig. 132. is emmetropic. One of these rays db' passes without refraction through the optic center of the lens, and it is on this ray db' that the image b' of b is formed, in the focal plane of the lens. The two triangles pc^ and dfb' are similar: we have, therefore, <. $ > that is to say, the magnifi- cation is equal to the relation between the focal distance of the lens and the anterior focal distance of the eye. The anterior focal distance of the eye being 15 millimeters and that of the lens 77 millimeters, the magnifi- cation is -J?- or about 5. We can increase the magnification by using a weaker lens, but the image at the same time moves away from the lens so that the observer is obliged to move back, which makes this way of increasing the image of little practical value. In cases of persons operated on for cataract it may be useful to use a stronger lens (+ 18) to obviate the necessity of moving away. M E II Fig. 133. After Bjcrrum. INFLUENCE OF REFRACTION OF THE EXAMINED EYE ON THE MAGNIFI- CATION. A glance at figure 133 suffices to show that if we place the lens so that its focus coincides with the anterior focus of the eye, the 202 PHYSIOLOGIC OPTICS magnification is the same whatever may be the refraction of the exam- ined eye (principle of Badal). (i) If the lens is nearer the eye, as is generally the case, the magnification is greater in the hypermetropic eye, less in the myopic eye (fig. 134). For this reason the papilla of the astigmatic eye is seen elongated in the Fig. 134. After Bjerrum. direction of the meridian of least refraction; by moving the lens away the other meridian is elongated and finally that which corresponds to the meridian of greatest refraction is seen to be the greater just as by the erect image. OPHTHALMOSCOPIC FIELD. In order that the field may be as large as possible, the lens must be at a distance from the eye almost equal to its focal distance. Under these circumstances the image which the lens forms of the pupil of the observed eye is very large and fills the entire lens; the iris disappears from the field. We construct the field as for the erect image, by supposing the center (P, fig. 135) of the pupil of the observing eye luminous and finding what part of the fundus of the eye it could illuminate. In drawing figure 135, it has been supposed that the image P x of the center of the pupil of the observer coincides with the nodal point K of the observed eye, so that the "rays" Aa and "Bb suffer no refraction : ab is therefore the field, and we note that it does not depend on the pupil of the observed eye, since the cone AP X B does not touch its borders. The field is limited only by the borders of the lens ; it is therefore preferable to use a large lens as they do in England. If we move the lens nearer or farther away, so that a larger part of the cone AP B coincides with the pupil, it may happen that the latter may be too small, so that the iris intercepts the (1) This is exact only if the ametropia is axial. In case of & myopia (hypermetropia) of curvature, the anterior focus is situated near the eye in proportion as the refraction is greater. Repeating the construction of figure 133, we see that by making the focus of the lens coincide with the anterior focus of the eye the magnification is greater in the case of myopia. The astigmatic eye has two anterior foci, one for each principal meridian ; to obtain the same magnification in both meridians, the focus of the lens must be nearer the eye than the more distant anterior focus. OPHTHALMOSCOPY 203 most peripheral rays. The field is then limited by the iris of the ob- served eye, which may be seen through the lens. If the pupil is small, it may be difficult to hold the lens exactly at the proper place for the iris to disappear ; this is why dilatation of the pupil is advantageous. It must be noted, furthermore, that a small part of the field is well illumi- Patient ? Obaenrer Fig. 135. Construction of the ophthalmoscopic field by the inrerted image. nated. If we use a concave mirror of 20 centimeters focus, as is cus- tomary, we see at the fundus of the eye a quite distinct image of the flame (because the image formed by the mirror is almost at the focus of the lens so that the rays which meet the eye are almost parallel) ; it is only the part of the field which corresponds to this image that is illumi- nated ; the remainder is in darkness. The illuminated portion may be increased by using a plane mirror, but the illumination is then less bright. We can see the inverted image without any lens if the patient is myopic more than 6 D. ; by moving the head from side to side, we make sure that the vessels are displaced in the contrary direction, for we can also see the fundus of the hypermetropic eye (by the erect image) at a sufficiently great distance. The visual field is very small and the magnifi- cation often so great that one vessel may fill half of the field. The ex- istence of this image is sufficient to establish the diagnosis of a strong myopia. It is often difficult to examine the high degrees of myopia by the erect image, and by the inverted image the enlargement is some- times not sufficient. We can then use this image which the myopic eye itself produces, by magnifying it ; we make no change from the ordinary way of examining with the inverted image ; it is only necessary to move the lens far enough away for the image to be formed between the lens and the observed eye. The lens then produces an enlarged virtual image of this inverted image, which is also inverted and situated farther be- 204 PHYSIOLOGIC OPTICS hind ; to see it distinctly it is often necessary to place oneself very near the lens, especially if one uses a convex glass behind the mirror. We can thus obtain an enlargement nearly as great as by the erect image (Dcmicheri). We can use the examination by the inverted image for the determina- tion of the refraction of the eye, by measuring the distance from the observed eye at which the inverted image is situated, since this distance varies with the refraction of the eye. This method, which was proposed by Schmidt-Rimplcr, has never become very popular. The appearance of the fundus of the eye is very nearly the same with both methods. W r e must except the macula, however, which, by the inverted image, often presents itself under a special form, as an oval spot, with the long diameter horizontal, a little larger than the papilla ; this spot is dull, a little darker than the rest, and surrounded by a bright circle, corresponding to the convexity of the border of the fovea, which acts as a kind of convex mirror. Analogous reflexes often appear also on other parts of the retina, especially in young subjects. Differences of level are observed by the parallactic displacement which is obtained by subjecting the lens to a slight to-and-fro movement. 92. Ophthalmoscopic Examination of the Refracting Media. To ex- amine the transparency of the refracting media it is preferable to use a weak illumination ; we use preferably a plane mirror or even a convex mirror. De Weckcr recommended the use of the plates of Helmholtz for this examination. We see, indeed, the shadows which the opacities produce by intercepting a part of the rays sent back by the fundus of the eye. If the fundus is strongly illuminated, and if the obstacles are not completely opaque, they allow a part of the light to pass and the shadow is less complete. It is useful to use a strong magnifying glass for this examination in order that we may place ourselves very near the eye. Otherwise many of the small corpuscles may escape in the exam- ination. It is quite rare for these opacities to be visible by the light which they themselves reflect. It may happen, however, that we can see the red color of hemorrhages situated far forward in the vitreous body, or the white color of certain opacities, especially when using the light in such a manner that it falls very obliquely along the head of the observer. In cases of synchisis scintillans the observing eye receives light regularly reflected by the surfaces of the small crystals situated in the vitreous bodv. UPHTHALMOSCOPY 205 93. Skiascopy. This method of examining ocular refraction was discovered by Cuignet, who described it under the ill-chosen name of keratoscopy. It was Parent who specially developed the method, and it was he who first gave the correct explanation of it. The observer takes his place at one meter from the patient, whose eye he illuminates with a plane mirror ; by rotating the mirror around a vertical axis we see the luminous spot on the face of the patient move in the same direction. The illumination of the pupil follows the same direction, whether the patient be hypermetropic, emmetropic or very slightly myopic. If the myopia is over I D., the pupillary light is dis- placed in the contrary direction, and if the myopia is equal to I D., we do not see the light move in the pupil. The luminosity diminishes uniformly in the entire extent of the pupil to disappear suddenly. Fig. 136. Skiascopy. Plane mirror. L, lamp ; M lt first position of the mirror ; L n image which it forms of the lamp ; J lf retinal image. M 2 , second position of the mirror; L 2 , image of the lamp ; I 2 , retinal image. The examination of figure 136 shows that the retinal image moves in the same direction as the mirror. If the observed person is hyper- metropic, emmetropic or myopic less than I D., it is the erect image that the observer sees. The light seems to him to move on the retina, as it really does. If, on the contrary, the myopia is greater than I D., he sees the light move in the contrary direction, because the light comes to him from the inverted image which he observes. To determine the degree of ametropia, we place before the eye of the patient stronger and stronger glasses, until the shadow covers the entire pupil at once ; the patient has then a myopia equal to i D. If we use a concave mirror we see, as in the preceding case, the luminous spot move on the face of the patient in the same direction as 206 PHYSIOLOGIC OPTICS the mirror. But the retinal image of the flame moves in a contrary direction: we see, indeed, on figure 137, that the image of the flame (L x L 2 ) formed by the mirror goes in a direction contrary to that of figure 136, whence it follows that it is the same for the retinal image. t Fig. 137. Skiascopy. Concave mirror. The letters have the same signification as in figure 136. The observer also sees the ocular glow move in an opposite direction if the observed person is emmetropic, hypermetropic or myopic less than I D. and in the same direction if the myopia is greater than I D. Skiascopy is important in the search for astigmatism if we do not dispose of it with an ophthalmometer. If the mirror be moved in the direction of one of the principal meridians, everything happens as in a non-astigmatic eye. But if the movements of the mirror take place in another meridian, the shadow is seen to move in a direction which forms an angle with that of the mirror. This is due to the elliptical form of the diffusion spot. If we draw an ellipse with oblique axes on a sheet of paper, and observe it through a smaller circular aperture, while giving it a horizontal movement, it is almost impossible not to give way to the illusion that the motion takes place in an oblique direc- tion. We then find the motion to give the mirror in order that the displacement of the ocular glow takes place parallel to that of the mirror. We then determine the refraction of the principal meridians in the ordinary way. When the ametropia is considerable, the glow is quite feeble and the boundary between the light and shade is curved. If on the contrary the eye is almost corrected, we see the glow very bright and its border is very nearly straight. OPHTHALMOSCOPT 207 The explanation of this fact, which has given rise to a lively discus- sion, is quite simple. As the lamp (or its image formed by the mirror) is far from the observed eye, there is formed in the emmetropic eye a small pretty distinct retinal image of the flame (fig. 138, A). As all the light is concentrated on this small image, it is quite bright and although it is small, it nevertheless fills the field because the latter is also very small, as it is easy to see by using the construction we have given for O Fig. 138. The thick circle indicates the limits of the skiascopic field : A, in an emme- tropic eye ; B, in a strongly ametropic eye. The square in A represents the image of the flame ; in B, it changes into a large spot composed of circles of diffusion. the ophthalmoscopic field. The right border of the ocular glow cor- responds with the border of the retinal image of the flame. In the ametropic eye the field is large, and the retinal image is displaced by a diffusion spot, much larger and consequently not so bright. Each point of the distinct retinal image is replaced by a circle of diffusion of the same form as the pupil of the observed eye; as the latter is generally round, the spot also takes on a round form (fig. 138, B) more pro- nounced in proportion as the ametropia is greater. It is easy to prove the exactness of this explanation: if we use as luminous source a very long, bright line, the border of the ocular glow remains straight, even in the case of strong ametropia, because the superposition of the circles of diffusion cannot then produce a round form. Likewise, if we give the pupil a triangular form, by placing a stenopaic opening of this form before the eye of the observed person, the shadow retains also its rectilinear border, for the supposition of triangular diffusion spots can- not give a round form to the diffusion spot. But in neither case does the observer see a distinct image, because his eye is accommodated for the pupillary plane of the observed eye, 2Q8 PHYSIOLOGIC OPTICS while the image which he observes is in front of (M) or behind (H) this plane. And as it is not focused for the image, the latter is seen vaguely, each point being represented by a circle of diffusion, the border of which, as always, corresponds with the border of the pupil of the observer. THEORY OF LEROY. The explanation which Leroy has given of skiascopy, and which is widely accepted, especially in Germany is in Patient Observer Fig. 139. thorough agreement with that of Parent which I have just explained. Let a (fig. 139) be an illuminated point of the retina of the observed eye, supposed to be myopic, and a' its image.' From the observed eye then starts the luminous cone ba'c, of which the part a'mo enters the observ- ing eye. This eye sees luminous the part of the pupil which sends rays to it, that is the part bp, while pc is dark because the rays which conic Fig. 140. B from this part are intercepted by the iris of the observer. This Leroy somewhat subtly expressed by saying that the shadow is produced by the iris of the observer. We can imagine the pupil of the observer projected through a' on the pupil of the observed person (fig. 140, A) ; the part of this latter which it would cover would appear luminous. In regard to the theory of Parent, we would say that the observer sees the point a but dimly, that is to say as a diffusion circle the border of which, OPHTHALMOSCOPY 209 as we know, corresponds to the border of the pupil of the observed eye. The two theories are therefore two different ways of saying the same thing. But were the curved form of the shadow explained by the form of the pupil of the observer it would be wrong, because the phenomena do not change if the observer looks through a triangular aperture placed in front of his pupil. The form of the pupil of the observer plays no part, for in reality it is not a luminous point which is found on the retina, as the theory of Leroy supposes, but an image of the flame of which ad (fig. 139) is a section. The border of the image which \ve use is, therefore, a straight line perpendicular to the plane of the paper, and it would be necessary to repeat the construction of Leroy for each point of this straight line. We would thus obtain a series of projections of the pupil of the observer, which would delimit the part of the pupil of the observed eye which appears luminous (fig. 140, B). It is easy to see that the form of each diffusion circle has no influence on the form of the border of the shadow. PARACENTRAL SHADOW. When one is near correction, one often sees the shadow move irregularly. Bitzos has described a paracentral shadow: a part of the pupil, near the center, appears dark, while the borders are still illuminated. This phenomenon indicates that the refrac- Observer Patient Fig. 141. Theory of the paracentral shadow. tion is not the same everywhere in the pupil; it frequently makes im- possible a very exact determination of the refraction. We must not, therefore, expect a very exact determination by skia- scopy, as is the case also for subjective measurement and determination by the erect image, simply because the very idea of ocular refraction does not permit of very great exactness. Here is the explanation of the paracentral shadow. Let us suppose an eye emmetropic, but with a strong spherical aberration so that the 210 PHYSIOLOGIC OPTICS peripheral parts of the pupil may be myopic. The rays coming from a luminous point of the retina would then have the direction indicated on figure 141. An eye, the pupil of which would be at P would receive rays i and 3 and would see luminous the parts corresponding with the pupil, while at 2 the pupil would appear dark, since the ray 2 would not enter the pupil. The observing eye would, therefore, see a bright center separated from equally bright borders by a dark ring. If P be displaced a little downwards, it would receive all the rays drawn on the figure, but some on the other half would not enter it, which would give the phenomenon of paracentral shadow. This shadow is, therefore, nothing else than the manifestation of spherical aberration. We have seen that the appearance which indicates aberration consists of a luminous ring towards the borders of the pupil, separated from the central light by a dark zone; tilting the mirror slightly the central light becomes partly joined to the ring and the dark part assumes the form described by Bitzos. I have several times emphasized the advantages which skiascopy with a luminous point presents for the study of optic anomalies of the eye. It also lends itself very well to the ordinary measurement of refraction. At the critical moment when the movement of the light changes its direction the far point of the observed eye coincides with the pupil of the observer. As, on the other hand, the principle of Jackson demands that the image of the luminous source coincide with the far point one is led to use a plane mirror and to place the flame, surrounded by its opaque screen, quite near the eye of the observer. But, in order to observe the luminous band of astigmatism and the ring of aberration, we must place the lamp by the side of and a little behind the patient. Bibliography. Cumming (W.). Medico-chirurgical transactions. XXIX, p. 284. Briicke (E.). J. Mutters Archiv fur Anatomic und Physiologic, 1847, p. 225. Helmholtz (H.). Beschreibung eines Augenspiegels zur Beobachtung der Netzhaut am lebenden Auge. Ber- lin, 1851. Kuete (Th.). Der Augenspiegel und das Optometer. Gottingen, 1852. Coc- cius (A.). Ueber die Anwendung des Augenspiegels, nebst Angabe eines neuen Instruments. Leipzig, 1853. Cuignet. Keratoscopie. Recueil d'opht., 1873-74. Parent. Diagnostic et determination objective de V Astigmatisme. Kecueil d'opht., 1881. Leroy (C. J. A.). Le phenomene de P ombre pupillaire. Rev. gen. d'opht., 1887, p. 289. BellarminofF. Neues Verfahren den Augenhintergrund zu besichdgen. Munch, med. Wochenschrift, 1888. Bit- zos (G.). La Skiascopie. Paris, 1892. Demicheri (L.). Examen ophtalmoscopique d Fimage renversee sur les yeux fortement myopes. Ann. d'oc., 1895. The theory of the ophthalmoscope is found explained in several treatises on ophthalmo- scopy. The following small book is to be recommended on account of its brevity and clear- ness: Bjerrum (I. ) (of Copenhagen). Instructions pour Temploi de I'ophtalmoscope. Translated by Grosjean. Paris, Steinheil, 1894. CHAPTER XIV. THE PUPIL. 94. To properly understand the working of a dioptric instrument, we must not only know the position and power of the refracting sur- faces, but also the size and position of its diaphragm. I have already referred to the difference between the size and position of the apparent pupil and the real pupil, and observed that the pupil is generally dis- placed a little to the temporal side. Its size varies in different people ; generally it diminishes with age, and finally becomes quite small in old people. As a rule it is larger in myopes than in hypermetropes, at least in appearance, for the anterior chamber of myopes is often deeper, which makes the pupil appear larger. In cases of complete amaurosis, the pupil is immovable and very large, except when the amaurosis has a spinal origin, in which case the pupil is often greatly contracted. The pupil contracts and dilates under many different influences ; these movements are very complex and, for the most part, still imperfectly elucidated. All agree on the existence of the sphincter, while that of the dilatator is disputed, although physiological observations make its exist- ence probable. The movements of the pupil are under the influence of the motor oculi and the great sympathetic. Cutting the motor oculi produces a dilatation of the pupil, much less, however, than that which may be pro- duced by atropine. The contractions which accompany accommodation and incidence of light cease at the same time, as well as accommodation itself. The contraction which accompanies incidence of light is, there- fore, produced by a reflex action between the retina and the optic nerve on the one hand and the oculo-motor on the other. It must be noted, however, that Brown-Sequard produced a contraction of the pupil by concentrating light on an enucleated rabbit's eye, according to which experiment the light would also have a direct influence on the muscles of the iris. An irritation of the oculo-motor produces a contraction of the pupil, an irritation of the great sympathetic at the neck produces, 211 212 , PHYSIOLOGIC OPTICS on the contrary, a marked dilatation, while the cutting of this nerve contracts the pupil. 95. Action of Mydriatics and Myotics. The instillation of a drop of a solution of atr opine (0.5 per cent.) produces a marked dilatation of the pupil; it paralyzes its movements as well as the accommodation: the effect generally lasts eight days. If we use a much-diluted solution, the effect does not last so long and the action on accommodation is much less pronounced. To explain why the dilatation by atropine is much greater than that obtained by cutting the motor oculi, it is supposed that it acts at the same time by irritating the terminal fibres of the great sympa- thetic. Homatropine (0.5 per cent.) dilates the pupil, but it generally does not act to any extent on the accommodation if the solution is pure, (i) Its effect lasts twenty-four hours. Cocaine (5 per cent.) dilates the pupil, but does not act on the accom- modation; at least I have not been able to find any effect on my own eye. (i) A mixture of homatropine and cocaine dilates the pupil still more than either one of these alkaloids by itself. Such a mixture is recom- mended, therefore, for investigations of accommodation, the more so because the pupil is dilated some time before accommodation begins to diminish. Scopolamine (J per cent.) produces complete paralysis of accommodation, with a very marked dilatation of the pupil which we can further increase by adding cocaine. With a solution of eserine (0.5 per cent.) we obtain a very great contrac- tion of the pupil, and the accommodation reaches its maximum. I have obtained with eserine a little greater amplitude than I could produce spontaneously. It is doubtful whether eserine acts directly on the sphincter, or whether the contraction of the pupil is analogous to that which always accompanies accommodation. 96. The Movements of the Pupil. i The pupil contracts under the influence of light (reflex by the optic nerve). It is not alone the light which strikes the retina of a particular eye, but also that which enters the other eye, which causes the contrac- tion. The pupils are equal in size, even if one eye is exposed to a much stronger light than the other. If the pupil does not contract when the light strikes the retina of the same eye, and does contract when it strikes (I) Other observers maintain the contrary; the differences are perhaps individual ; perhaps due to the fact that they use different preparations. THE PUPIL 213 that of the other eye, we may infer a complete amaurosis of the eye in question. In complete darkness the pupil reaches its maximum dilata- tion, so that the iris is often not visible (i) (Colin, CL Dubois-Reymond). This fact has been demonstrated by taking photographs of the eyes in complete darkness: we illuminate them with mixtures of powders, the light of which does not continue long enough to give the pupil time to contract. It is not easy to reconcile this observation with every-day experience, which shows that the reaction of the pupil to light depends on the oculo-motor, the cutting of which produces only a medium dila- tation. It is manifest that the object of this contraction of the pupil is to regulate the quantity of light that enters the eye. 2 The pupil contracts during accommodation. To examine the func- tions of the pupil we must see whether it contracts : a) when the light strikes the retina of the same eye ; b) when the light strikes the retina of the other eye; c) when the patient makes an effort of accommodation. We know that accommodative contraction may exist without the reac- tion to light, and vice versa (Argyll Robertson). The accommodative con- traction has this peculiarity that even the most peripheral parts of the iris show a centripetal movement, which is not generally the case for the reaction to light (Hueck). The object of this contraction is to eliminate the action of the periph- eral parts of the crystalline lens, which do not sufficiently accommodate. 3 The pupil contracts when the aqueous humor escapes. I have already remarked that this contraction is also observed after death (Arlt), so that it must be considered as a purely mechanical phenomenon, which we may identify with accommodative contraction. I have made some experiments to elucidate the nature of this contraction ; before describ- ing them it is important to speak of the posterior chamber, the existence of which has been disputed. On examining an eye by oblique illumination, we easily see that the border of the iris is in contact with the crystalline lens. We also see this very well by examination with the third image of Purkinje, which I have mentioned page 42, or by examining an eye affected with mature cataract. If we remove the crystalline lens from the eye, or if it be dis- located, the iris shows at each movement of the eye the trembling known as iridodonesis; Helmholtz and others were led to infer from these facts the non-existence of a posterior chamber ; there exists, nevertheless, a (1) If the iris is not visible at all, it is an apparent phenomenon, due to refraction through the cor- nea, for if we plunge an eye, the pupil of which is dilated to this extent, in water, the iris becomes im- mediately visible (Stadfcldt). 214 PHYSIOLOGIC OPTICS small space filled with liquid between the crystalline lens, the ciliary body and the peripheral parts of the iris. We sometimes see in perfect eyes a slight trembling of the peripheral parts of the iris when the eye makes a movement. The observation of Arlt, showing that we still see the pupillary con- traction after paracentesis has been performed on the dead eye, struck me forcibly. To verify it I introduced the point of a Pravaz syringe into the anterior chamber ; by depressing or withdrawing the piston we can make the pupil contract or dilate at will. By removing nearly all the contents of the anterior chamber I was able to reduce the diameter of the pupil to i or 2 mm. On the contrary, by forcing the injection as far as possible, the dilatation may extend so far as to make the iris disap- pear, (i) It is true that one part of the change is only apparent, as Stadfeldt has shown: the more the pupil recedes, the more enlarged it is seen through the cornea; but on examining the eye under water, we find a very noticeable change. The phenomenon is difficult to ex- plain ; it is not due to the mere effect of pressure, for we may compress the eye all we want to without observing any change in the diameter of the pupil ; nor is it due to a difference of pressure between the chamber and the posterior part of the globe, for, by injecting liquid into the vitreous body or by removing it, we no longer produce any change of the pupil. I also injected a solution of gelatine into the anterior chamber, and then, by hardening the eyes slightly, I obtained pretty fair casts. Under these circumstances the posterior chamber is also always injected; the cast forms a prismatic ring, with an anterior surface corresponding to the iris, a posterior surface corresponding to the anterior surface of the crystalline lens and an external surface corresponding to the ciliary body. But, between the crystalline lens and the part of the iris next to the pupil, we never find any gelatine, or if there is any, it is so thin a layer that it is destroyed in the work of preparation. 4 During sleep the pupil is greatly contracted, even in amaurotic persons, whose pupil generally is large and motionless. The pupil is also contracted during narcosis, and generally when a person is in agony : at the moment of death it is generally greatly dilated; this dilatation dis- appears immediately. In spite of the pupillary contraction during sleep the reaction to light persists. 5 On examining the pupil with a magnifying glass we observe rhythmic contractions, which, at least in part, correspond to the systole, (1) When we increase the pressure much, the cornea becomes opaque; we can make it almost as white as the sclera ; as soon as the pressure ceases, it again becomes transparent. THE PUPIL 215 and which are due to the fact that the vessels are filling with blood. The contraction is greater when the systole coincides with an expiration. We cannot explain in this way all the slight contractions of the pupil which are observed with a magnifying glass. 6 We observe a dilatation of the pupil following fright ; it also accom- panies dyspnea, vigorous muscular action or a sharp irritation of any sensitive nerve. 97. Advantage of the Position of the Pupil near the Nodal Point. Young remarked that if the pupil had been situated farther forward in the eye the apparent size of objects would have changed every time we made an effort of accommodation. We have seen that the image of a point for which the eye is not accommodated, forms a circle of diffu- Fig. 142. sion, the center of which, corresponding to the middle of the pupil, is frequently brighter on account of spherical aberration ; if the pupil is not too large we may consider this center as a vague image of the point. Suppose that, in a state of repose, the eye is focused for the object AB (fig. 142). The image of the point A is formed at A l on the line AM passing through the nodal point. During accommodation the image is moved forward to A 2 . To find the place where the diffuse image is formed on the retina we draw the ray Ap passing through the middle of the pupil of entrance : after refraction, this ray must pass through p v (i), the middle of the pupil of exit, and through A 2 ; the diffuse image is (1) On the fiarure we suppose that p and pi coincide ; really they are about 0.7 millimeters apart. 216 PHYSIOLOGIC OPTICS therefore formed at A 3 and the image of the entire object A 3 B 3 is smaller than the distinct image A x B . In the human eye we may ob- serve a slight effect of this kind by using our accommodation while observing distant objects; it is more pronounced when we replace the pupil by a stenopaic opening, at some distance from the eye. The position of the pupil near the nodal point has probably still an- other advantage. One of the first qualities that we require in a photo- graphic objective is that it be rectilinear, that is to say, that the images of the straight lines placed peripherally in the field be straight, and not curved. We usually obtain this effect by placing the diaphragm in the nodal plane, and the position of the pupil near the nodal point of the eye seems to play a part for the correct vision of objects seen indirectly. Nevertheless, the eye is not rectilinear. It follows from a series of experiments described by Helmholtz that, in indirect vision, the straight lines appear in the form of curves, the concavity of which is turned towards the point fixed. If we desire to repeat these experiments, we must place ourselves so that no other line, which we know to be straight, is in the field, for example by stooping over a large table. i We place on the table a small piece of paper A (fig. 143), which serves as a point of fixation, and two others, B and C, as far as possible from A, without ceasing to see them distinctly in B indirect vision. While fixing A, we try to place a fourth piece, D, on the straight line which joins B and C. We shall nearly always place it too far inwards. 2 If we place on the table a strip of paper with parallel borders, 8 to 10 centimeters in width, and fix the center of it, the borders appear concave towards the point of fixation. The strip, there- fore, appears larger at the middle than towards the ends. 3 Guided by theoretical considerations, the value of which may appear doubtful, Helmlioltz designed the hyperbolic chess-board, of which figure 144 is an illustration diminished in the proportion of 3/16. In accordance with his theory, he found that, placed at a distance of 20 centimeters, for which the chess-board was calculated, he saw the curves assume the appearance of straight lines when he fixed the middle. When he stood at a greater distance, the lines appeared to have the curvature which they really had ; moving nearer and nearer, he saw the curvature THE PUPIL 217 diminish and finally completely disappear. The distance at which the curvature disappeared was each time almost exactly 20 centimeters. If he approached nearer still, the lines presented the reverse curvature, appearing concave towards the middle. Fig. 144. Hyperbolic chess-board of Helmhoitz. 4 Another experiment of the same kind consists in placing- a circular piece of cardboard in the periphery of the visual field; above or below we see it elongated in the horizontal direction, while on the two sides it appears elongated in the vertical direction. We can express all these phenomena by saying that the visual field is seen narrowed towards the periphery. Let us suppose the plane visual field divided into equidistant zones, and suppose that we gave an illus- tration of it by making the zones diminish towards the periphery. We would thus obtain analogous deformities ; the straight lines would be represented by curves concave towards the middle (see page 98). A circle placed peripherally in the field would become narrower in the radial direction, and so forth. To explain these observations, Hclmholts called attention to another observation which he made, and which is itself a consequence of the law of Listing (see chapter XIX). Standing in front of a wall we look at a point A situated on a level with the eyes; we then raise the look, without changing the position of the head, towards the horizontal line which forms the upper edge of the wall. Moving the look rapidly along this line, we see it concave, with the concavity turned downwards exactly as we would see it in indi- rect vision by fixing the point A, if it was sufficiently distinct. Faithful to the empiric theories by which he tried to explain most 218 PHYSIOLOGIC OPTICS observations on physiologic optics, Helmholtz supposed that this illu- sion was the cause of the preceding one. Surveying the line with the look it appears curved on account of the law of Listing, and it is because we have thus learned that it appears curved that it does usually appear so in indirect vision also. We must note that this way of observing the line, namely by surveying it with the raised look, appears altogether unusual. I do not think that before making this experiment I ever looked at a line in this way, as it would be more natural for me to raise my head to look at it, and in this case the illusion disappears. It is, therefore, not easy to understand how I would have known that the line ought to appear curved. But the following experiment is still more at vari- ance with the explanation in question. I had con- structed a small artificial eye (fig. 145), all the dimen- sions of which approached as nearly as possible those of the human eye. The cornea and the crystalline lens are of glass, and have the same curvature as in the human eye; in order to remedy somewhat the exces- sive refraction of the crystalline lens, I filled the eye Fig"l45. with a mixture of glycerine and water, the index of Artificial eye. which is a little higher than that of the vitreous body. The retina is replaced by a hollow hemisphere of ground glass, having nearly the curvature of the retina of the human eye. Although the refraction may not be absolutely identical with that of the human eye, the difference, however, cannot be very great. With this eye I repeated and succeeded in all the experiments cited above (fig. 146). The image of the black strip has the borders convex towards the periphery; in order that the borders of the image appear straight those of the object must be concave. The image of a circle appeared shrunken in the radial direction, etc. The experiment with the chess-board of Helmholtz is still more conclusive. As long as the eye is at a great distance, the image is like the object; but, according J f* window as we move the eye nearer, the curvature of the lines artificial eye. becomes obliterated, and very close to the drawing the lines of the image appear concave on the inside. I tried to determine the place where the direction of the curvature changes, or in other words the place where the figure appears most rectilinear, and each time I found THE PUPIL 219 a distance of 20 centimeters, at least as exactly as when making the experiment with my own eye. According to this experiment it seems to me beyond doubt that all these deformities depend primarily upon the form of the retina. Pro- jecting a plane on a hollow sphere, we necessarily obtain towards the periphery a narrowing of the projection analogous to that which we have found for the eye. It is possible, however, that the position of the pupil in front of the nodal point may play a certain part, for the illusion appears to me rather more pronounced if I look through a stenopaic opening, which acts as an artificial pupil placed in front of the eye. This touches one of the fundamental questions of physiologic optics. I wish to speak of the antagonism between the nativistic and the empiric ideas. Although this question is beyond the scope of the present work, I shall consider it for a moment. Looking at a window, the visual sense tells me that it is square. How can the eye give this information ? The nativists, among whom we must first mention Hering, say that, by an unknown congenital mechanism, the retinal impression gives directly to the mind the idea of the form of the object. We could express this idea by saying that, by an un- known mechanism, the mind sees the retinal image. The empiricists, among whom Helmholtz is the most celebrated, say that the retinal image gives us primarily no information on the form of the object, that it is only a "sign" of the object, almost as the letter A is the sign of a certain sound ; by the movements of the eyes and by information furnished by the touch, we learn that this sign is to tell us that the object is square ; Helmholtz expressed his ideas thus : "As for me, I think it probable that the figure, form and position of the true retina, as well as the deformities of the retinal image, are absolutely unconcerned with vision, provided the image be distinct in its whole length, and that the form of the retina and that of the image remain perceptibly invariable from one moment to another. We have absolutely no knowledge of the existence of our retina." Under the influence of Darwin, an effort was made (Bonders) to recon- cile the two schools by saying that the qualities in question are the result of experiences, not of the individual, but of the species. Under- stood in this sense the empiric ideas scarcely differ from the nativistic ideas, the qualities being then congenital in the same sense as, for example, the actual form of our organs, and we would then have to distinguish sharply between what we may suppose learned by the same individual and what is due to the experience of the species. 220 PHYSIOLOGIC OPTICS The empiric theories are more attractive because they make an attempt at explanation, while the nativistic theories exclude all hope. But it would be necessary to apply them only to the phenomena for which they readily adapt themselves, and it seems to me that the great physicist of Berlin has gone too far in being willing to deny the relation between the illusions here described and the deformities of the retinal image. It seems to me that there must exist a mechanism by which we can account for the existence of these deformities. Bibliography. The opposition to the too free application of empiric ideas does not date from yesterday. See (Euvres de Young, p. 239. " We are certainly obliged every mo- ment to call experience to our aid in order to correct the errors of one of the senses by com- parison with the perceptions of the others. [But] it seems to me that some scientists go too far when they assert that the use of all our senses is derived from experience alone with- out being willing to admit the existence of an instinct on a par with it," etc. Arlt (F.). Zur Anatomic des Auges. Arch. f. Ophth. Ill, 2. Du Bois-Reymond (G.). Ueber Photographieen der Augen bei Magnesiumblitz. Arch. f. Physiologic, 1888, p. 394. Tscherning (M.). La contraction de I'iris accompagnant I'ecoulement de Fhumeur aqueuse. Bull, de la Soc. fran9. d'opht., 1885, p. 305. Tscherning (M.). Quelques consequences de la loi de Listing. Ann. d'oc., Sept., 1888. Tscherning (M.). La deformation des objels rus indireetf- ment. Bull, de le Soc. franc, d'opht., 1895, p. 403. BOOK II FUNCTIONS OF THE RETINA CHAPTER XV. CHANGES WHICH THE RETINA UNDERGOES UNDER THE INFLUENCE OF LIGHT 98. -- The sensitive layer of the retina is, in all probability, that with the cones and rods. Besides the fact that the very structure of the layer makes this hypothesis probable, it is further strengthened by the experi- ments and measurements of H. Midler (on the entoptic vision of the vessels, see page 155) as well as by observations on visual acuity. But we have not succeeded in explaining in a satisfactory manner the mech- anism by which light is transformed into nervous action. We have suc- ceeded in proving a certain number of changes which the retina under- goes under the influence of light, and we have studied on the other hand the functions of the retina, which are now very well known, but we have not succeeded in explaining their mutual relations. RETINAL PURPLE. If we examine the eye of an animal which has been left in darkness for some time before enucleation, we find that the external segment of the rods has a purple color which disappears very quickly under the influence of daylight, passing through a yellow tint. The cones have not this coloration and the fovea of the human eye, which is composed of cones only, is without color. If we expose the eye of a living rabbit to daylight for a quarter of an hour, the purple first changes to a yellow and then completely fades away. Placing it so that the image of a bright object, a window for example, may be formed on the retina, we can thus obtain a permanent image (optogram). If, after having caused the purple to fade away, we leave the animal in darkness, the purple color returns gradually, provided that the retina be in contact 221 222 PHYSIOLOGIC OPTICS with the pigment cells. It is not necessary that they be the pigment cells of the same animal : if we place the retina of one eye in the place of that of another eye the reproduction of the purple is also effected in darkness. Vision does not depend on the retinal purple, since there is no purple in the fovea, since rabbits whose retinae we have allowed to fade away completely are not blind, and since there are certain classes of animals, serpents for example, in which the purple is wanting. The retinal purple was discovered by Boll in 1876 ; subsequently Kuehne labored much with the question, studying especially the chemical proper- ties of the retinal purple and yellow. The enthusiasm with which the discovery of Boll was first received quickly grew cold when it was seen that it did not give a direct explanation of the mechanism of vision. Some time ago the question was again taken up and an effort made to put the retinal purple in relation, on the one hand, with the vision of certain colors, on the other with the adaptation of the retina to very feeble light. These efforts, some of which will be mentioned later on, have, up to the present, only a hypothetic character. 99. Movements of the Pigment under the Influence of Light. By ex- perimenting with frogs, Boll observed yet another phenomenon depend- ent on the influence of light. He observed that it was easy to separate the retina from the epithelium when the animals are left in darkness for an hour or two before death. If the animal has been exposed to light for a certain period before enucleation it is, on the contrary, difficult to separate them, and if we sever the retina we find it covered with black pigment spots which adhere to it. We know that the epithelial cells send prolongations between the rods which they separate from one another. In darkness the pigment is found massed between the exterior segments of the rods, but under the influence of light it is displaced so as to cover the terminal surface of the rod, and is projected among the rods, sometimes even to the external limiting membrane. The external segment of the rod is swollen at the same time. Analogous phenomena have been described in the eyes of birds, mammals, and also in a human eye. Van Gendercn Stort made a step in advance in the biology of the retina by using a method by which the retina is hardened in a very little while (nitric acid) ; instead of cutting the retina with a microtome he hacked it with a razor. He showed that there is yet another change which the retina undergoes when exposed to light. In an animal left in darkness some time before death, we find the internal part of the cones long CHANGES WHICH THE RETINA UNDERGOES 223 and filiform, and the length differs for different cones so that the latter are arranged in several rows quite a distance from the limitans externa. If, on the contrary, the animal has been exposed to light, the internal part of the cones is shortened and swollen : all the cones are placed in a A B Fig. 146a. Section of the retina of a frog. After Van Genderen Stort. A, in darkness; B, in light. row along the limitans externa (fig. 1460). According to Van Genderen Stort the retinal purple is also in the cells of the pigment epithelium, and it is probably secreted by these cells. He thinks that the pigment dis- placement has for its object the protection of the rods against light, and that it is due to this fact that the epithelial cells send, under the in- fluence of light, prolongations between the rods, almost like the cells, called chromatophores, which make the skin of some lower animals change color under the influence of light. Van Genderen Stort was kind enough to make a present of some of his beautiful preparations to our laboratory. The phenomena are so distinct that the first glance at the preparation enables one to tell whether the animal was exposed to light or not. We must note further that Knehne observed certain galvanic phenom- ena dependent on the action of light on the retina. Bibliography. Boll (P.). Du Bois-Reymond?. Archir.f. Anat. u. Physiol, 1877, p. 4. Boll (F.). Monatsber. d. Akad. Berlin, 1877, Jan. 11. Kuehne (W.), in Hermann (L.). Handburh der Physiohgie. Leipzig, 1879. Van Genderen Stort. Acad. d 1 Amsterdam, June< 28, 1884. CHAPTER XVI. THE LIGHT SENSE The functions of the retina are divided into three classes: the light sense, the color sense, and the form sense. The light sense is the faculty of recognizing the different luminous intensities. 100. Psychophysical Law of Fechner. According to this law the smallest difference of perceptible illumination is a constant fraction (about i per cent.) of the total illumination. Fechner came to formulate his law by the following observation. One day he found a scarcely perceptible difference of brightness between two clouds, and was much surprised to see this difference persist on looking through a quite dark smoked glass. He called this law psychophysical because, finding it also for other senses, he was led to consider it as a general law of perception. If, for example, a line must have a length of 105 millimeters in order that we can tell with certainty that it is longer than another of 100 millimeters, we will also find that a line must be at least 210 millimeters for us to be able to tell with certainty that it is longer than another of 200 millimeters. In both cases the relation between the smallest perceptible difference and the total length is the same, one-twentieth. It is so also if we examine the smallest perceptible difference between two weights, and so with the other senses. We notice that our senses differ in this respect from most of our instruments. With an ordinary double decimeter, the shortest distance that we can measure (I do not say estimate) is a half-millimeter; the smallest measurable difference between two lines would be, therefore, a half-millimeter, and this whatever may be the length of the lines to be measured. To determine the ratio between the smallest difference of perceptible illumination and the total illumination, Fechner used the following ex- 221 THE LIGHT SENSE 225 periment which had already been described in the middle of the last century by Bouguer and by Lambert. The former had also observed the fact on which Fcchner later based his law. i Let us place at some distance from a screen two candles, A and B (fig. 147), of equal intensity I, and place between the candles and the screen a stick so that it forms two shadows a and b on the screen. The shadow a is formed by A, and consequently illuminated only by B ; the Fig. 147. Experiment of Bouguer. shadow b receives light only from A, and the remainder of the screen receives light simultaneously from B and A. By moving B away from the screen, the shadow b becomes weaker and weaker, and when the distance of B from the screen is nearly ten times that of A it ceases to be visible. 2 We replace the candles by others of one-half less intensity, and repeat the experiment : we find, as in the preceding case, that the shadow ceases to be visible at the moment when the distance of B from the screen is about ten times that of A. And we shall find the same result, whatever may be the intensity of the candles. The law of Fechner is thus verified. Suppose that, in case i, at the moment when the shadow disappears, B is at 500 centimeters from the screen, A at 50 centimeters. We know that the illumination is proportional to the intensity of the luminous source, and inversely proportional to the square of the distance. A gives, therefore, to the screen an illumination of &p , B an illumination of ftp > while the shadow b receives an illumination of pr only. The differ- ence between the illumination of the screen and that of the shadow is therefore : ,1 I 50 2 ^ 5002 and the ratio between this difference and the illumination of the screen is * 226 PHYSIOLOGIC OPTICS I 5002 i _L i _L_ 102 + : 1Ul 5l 2 + 500 2 or __!_, since the measurement is not very exact. In case 2 the relation is 1/21 5U0 2 = 1 1/2 I 1/2 I : = 101 50 2 '" 5002 It is consequently the same in both cases. The law of Fechner explains many of the phenomena daily observed. If, after having performed with the candles the experiment cited above, we open the shutters so that the daylight strikes the screen, the shadows disappear. The difference between the illumination of the shadow and that of the screen remains the same, but the ratio between this differ- ence and the total illumination of the screen is much below the fraction of Fechner. We read as well in the evening, with a gas light, as in day time, although the illumination in day time is enormously more powerful, because the ratio between the light reflected by the black letters and that reflected by the white paper remains the same. In a space illuminated by a very powerful lamp, the flame of a candle held at some distance from the screen produces a shadow of it, because it absorbs a part of the light of the lamp. If we move the candle nearer the screen, the illumination increases and the shadow disappears, although the difference of brightness between it and the background remains the same. The law of Fechner is true only for medium degrees of illumination. If the illumination becomes very feeble, the difference must be relatively much more considerable. We read very well with a gas light ; but if we lower the flame much we cannot read any longer, although the ratio between the light reflected by the letters and that reflected by the paper remains the same. It is possible that this difference may be due to what is called the retina's own light, an expression by which we designate the feeble glow which may still be perceived in a completely dark room, and which is due to internal causes (friction of the blood in the vessels of the retina against the sensitive layer, perhaps also processes in cer- tain parts of the brain, etc.). We can conceive that, if this light is added to that reflected by the printed sheet, the difference of brightness between the letters and the white sheet may fall below the limit of Fechner. The law of Fechner also ceases to be applicable when the THE LIGHT SESSE 227 light is very strong. This is why we cannot see the spots on the sun with the naked eye, on account of the dazzling, but very well with a smoked glass. But, within the very extended limits which correspond almost to the limits of illumination which we use, the law of Fechner is verified with very great exactness. It is not absolute, however : in order to dis- tinguish very fine shades, it seems that there is a certain illumination which is most favorable, viz., that which approaches the light of a clear day. The acuity of the light sense may be expressed by the inverse of the fraction of Fechner. If the latter be T Jg- , we say that the acuity of the luminous sense is equal to 100; if, by greatly diminishing the illumina- tion, the fraction rises to -&- we say that the acuity is only 50, and so forth. We could illustrate the relation between the light sense and the illumi- nation by a curve which would have a form like that of figure 148. The division of the horizontal line would indicate the degree of illumination, beginning on the left by complete darkness, and terminating on the 3- o a, 6 c- & Fig. 148. right by the light of the sun. The ordinate of each point of the curve would measure the acuity of the light sense. As long as the illumina- tion is very weak, the eye sees nothing: when it reaches a certain degree which, in the figure, is marked by the letter a, the eye begins to be able to distinguish white objects. This degree of illumination, w r hich forms the lowest limit of visibility, is called threshold ("Reizschwelle"). As long as the illumination remains so feeble, the light sense is not very acute ; the perceptible differences are considerable. But the acuity increases quickly, and when the illumination has reached a certain degree, b, the acuity reaches the degree which it holds for a long time, until the illumination has attained the power c. It is for the part be that the law of Fechner is true, but not exactly, for this part of the curve is not alto- gether straight. It reaches its highest point at M. If we increase the light still more, the luminous sense falls quickly; 228 PHYSIOLOGIC OPTICS there is again need of very considerable differences of light in order that the differences may be distinguished. Let us designate by a the smallest difference of appreciable sensation. If a light of a certain intensity I produces a certain sensation S, there is need of an intensity I + T J I = -}JJ- I to produce the sensation S -f- a, an intensity of -}JJ- I + -}JJ- X ^ = I ( JJJ- ) 2 to produce the sensation S + 20, an intensity of I (-}JJ-) 8 to produce the sensation S + 30, and so forth. It is under this form that the law was promulgated by Fechncr, for the fact itself was known since the works of Bouguer at the commencement of the eighteenth century. The right by which we make the differences designated by a equal to one another may be disputed. 101. Measurement of the Light Sense. We usually limit ourselves to determining: i The threshold, the lowest limit at which the eye begins to distinguish anything (corresponding to the point a of the curve) ; 2 The least difference of brightness which we can distinguish by ordinary illumination, corresponding to B6 or to Mm (fig. 148). It is this determination which we have just made with the candles. We determine the threshold (i) with the photo ptometer of Foerster (fig. 149). It is a box painted black inside. The patient looks through two apertures, corresponding to his eyes a and a lf towards a white surface, placed at the far end of the box, on which are traced large black marks T. The only light which can penetrate into the box comes from a square window F, the aperture of which we can change and which is placed beside the apertures through which the patient looks. Behind the window, which is covered with oil paper, burns a standard candle L. The minimum aperture of the window permitting the patient to see the black marks gives the threshold. The test is not very exact ; it is difficult to obtain very uniform answers, and adaptation enormously influences the result. The photoptometer of Charpentier, also intended to determine the (1) It is doubtful whether the determination of the threshold is really anything else than the deter initiation of the fraction of Fechner for a very weak illumination. Theoretically, for the detennina tion of the threshold, it ought to be required that the eye can compare a very weak light with absolute black; but we cannot produce absolute black on account of the retina's own light. THE LIGHT SEXSE 229 threshold, consists of a tube, 22 cm. long and 5 cm. wide, the extremities of which are closed by plates of ground glass A and B. At the middle of the tube are placed two lenses of n cm. focal distance, and between them a diaphragm with changeable aperture. On illuminating the plate A the lenses project an image of it on the plate B, the brightness of which image we may cause to change by changing the aperture of the diaphragm. It is the plate B which serves for the observation ; for the protection of the eye of the observer we may add to it a second tube blackened internally, the length of which corresponds to the distance for work of the observer. An eye-shade which permits of exact adapta- tion to the borders of the orbit excludes all extraneous light. The minimum aperture of the diaphragm which permits the observer to distinguish the plate B, determines the threshold. In every instrument of this kind the difficulty consists especially in rinding a luminous source which can give a constant and uniform illumination. In order to determine the smallest perceptible difference we can use the method with the candles, described above. Another method consists Fi^. 150 Disc of AJaxson. in the use of the disc of Masson, a white disc of which sectors of different sizes have been blackened (fig. 150). By subjecting this disc to a suffi- ciently rapid rotation, we see three gray rings separated by white inter- vals. Supposing that the sector a is 20, the sector b 10 and the sector c 5, and supposing, which is not strictly true, that the black does not reflect any light at all, the brightness of the three gray rings would be 340, 350 and 355, if we place the light of the white rings at -360. The difference between the exterior gray rings and the white will be 5, and 230 PHYSIOLOGIC OPTICS the relation between this difference and the white will be 3 ^- = - 7 *- > which represents the value of the fraction of Fcckner of the examined subject, if he can distinguish the three images. If he can distinguish only two, the fraction of Fechner is ~ = ^-, and so forth. A great number of rings must be used ; the illumination must be good, and the patient must not be too far away, in order to eliminate the influence of a diminished visual acuity. It is evident, however, that we cannot completely elimi- nate it; the acuity may be so poor as to prevent the patient from dis- tinguishing anything. To obtain an impression of a uniform gray with the disc of Masson, it is necessary that it rotate with a certain speed, about 20 to 30 times per second. If the disc carries several black and white sectors, alternat- ing, the speed may be less. In case the speed is not sufficient, the disc gives a scintillating impression and we often observe on it very beautiful Fig. 150a. A, Disc of Helmholtz; B, Disc of JBenham. colors. The disc A (fig. 1500) has been described by Helmholts: with a certain speed the external ring shows very vivid colors, among which the red and green predominate; they are often arranged in a manner which recalls a series of short spectra, as we observe them with grat- ings. But the phenomena are very changeable; in the second ring, which has only four sectors, the yellow and blue predominate with this speed, but only to a slight extent. If we increase the speed the external ring gives a uniform gray, while the second ring assumes the appearance which the external ring had previously. In figure 1500, B represents the disc of Benham. If we make it rotate in the direction of the arrow, the arcs form concentric circles which present quite vivid colors in the fol- lowing order, starting from the middle: red, brown, olive-green, blue. Making the disc rotate in the opposite direction, the order of the colors THE LIGHT SENSE 231 is reversed. The most beautiful of the colors is the red ; the circles seem traced in blood. The nature of these phenomena is not yet elucidated. We must not think that it is due to a decomposition of the white light, for the experi- ment succeeds perfectly when illuminating the disc with homogenous light, providing it is sufficiently strong. We even see colors of this kind when looking towards the homogenous sodium flame. Another method of studying the power of distinguishing differences of brightness consists in examining the visual acuity for pale letters, the brightness of which we can determine by comparing them with the rings on the disc of Masson. This method, which was described by Javal, was later developed by Bjerrum. It would be better to have a series of tables of visual acuity with paler and paler letters, but generally one suffices; Bjerrum recommended the use of letters, the brightness of which is one-twelfth weaker than that of the background. For these letters, a normal individual has an acuity of about one-third the acuity which he has for black letters on a white ground. It is evident that this method cannot be considered as an exact measure of the light sense, since the visual acuity plays a great part in the response of the patient. In order to eliminate to a certain extent this influence, one can use one's own eye as a control, by lowering his visual acuity by means of a convex glass, until it is equal to that of the patient. 102. Kesults. The threshold of the normal eye was determined by Aubert. He found that the weakest light that we can distinguish is that of a sheet of white paper illuminated by a candle placed at a distance of from 200 to 250 meters. The threshold varies much with the state of adaptation of the eye ; placed in a dark room, we do not at first dis- tinguish objects which we see very distinctly later on when accustomed to the darkness. For the determination of the threshold it is, therefore, necessary to leave the patient some time (as much as 20 minutes) in the darkness, with eyes bandaged, before beginning the examination. It seems that, by this stay in the darkness, the entire curve (fig. 148) is displaced towards the left, and also to its extreme limit, for on leaving the darkness the eye is dazzled by an illumination which it usually bears very well. The fraction of Fechner varies in normal persons between ~ and -,,- (0.55 to i per cent.). For a very weak illumination, the light sense of the macula is less acute than that of the surrounding parts; by fixing a point a little to one side of it, we better distinguish objects the brightness of which 232 PHYSIOLOGIC OPTICS differs only slightly from that of the background, for example, when we try to distinguish very dim stars. According to certain authors, Parinaud for instance, this phenomenon must be attributed to the fact that the fovea does not possess the faculty of being able to adapt itself to very weak illuminations like the rest of the retina, and this difference is ex- plained, because the fovea, composed of cones, has no retinal purple, which is considered as the organ of adaptation. This hypothesis is con- firmed by another fact, namely, the knowledge that the time of repose which the eye requires to reach complete adaptation is nearly the same (about 20 minutes) as that which is necessary for the reproduction of the purple. It is possible, however, that the inferiority of the macula may be partly due to its yellow pigmentation. The pigment absorbs a part of the blue rays, which, as we shall see, play a dominant part in vision by weak illuminations. The threshold is displaced upwards in patients suffering from hemera- lopia. It seems, however, that, in many cases, there is question rather of an anomaly of the adaptation, which requires much more time to take place than in the normal eye. Leaving a person affected with hemeralopia in darkness, he continues to improve for some time. We can prove the existence of hemeralopia with the phptoptometer of Foerster, or by examining the visual acuity while we lessen the illumina- tion. Hemeralopia is a constant symptom of pigmentary retinitis ; we meet it as often in cases of syphilitic retinoHchoroiditis, sometimes in cases of detachment of the retina or in glaucoma. It is extremely rare in cases of pure atrophy of the optic nerve. In cases of idiopathic hemeralopia, we find nothing in the fundus of the eye; this disease is often congenital and hereditary, and therefore incurable ; if, on the con- trary, the disease has existed only for a short time, its prognosis is favorable; it sometimes has an endemic character. It may happen that the peripheral part of the visual field only is affected ; we then establish the existence of the disease by examining the visual field with a weak illumination. We sometimes meet cases in which the fraction of Fechner is in- creased; in which, consequently, the patients cannot distinguish gray from white. This affection is met with especially in cases of atrophy of the optic nerve and in central scotoma. One of the first cases of this kind was observed at the clinic of Hansen Grut, at Copenhagen, and described by Krmchcl. It was a patient who presented himself, saying that he did not see well enough to find his way. Examined with the ophthalmoscope, the papillae were whitish, the visual acuity was normal, THE LIGHT SENSE 233 and the visual field was only slightly contracted. It was puzzling, there- fore, to explain the complaints of the patient until the idea of examining him with the disc of Masson presented itself: the fraction of Fechner had increased to ^ . The patient distinguished perfectly black on white, but was unable to distinguish between gray shades, as they present themselves, for example, in street paving; whence the difficulty which he experienced finding his way. We sometimes meet patients who claim that they see better when the illumination is low (nyctalopia). Examining their visual acuity, we find, however, that it does not increase when we lessen the illumination (at least in cases in which we have not to do with a purely optic phenom- enon : this is why a central leucoma becomes less annoying when the pupil is dilated). But, on comparing these persons with a normal person, we note that by lessening the illumination the acuity of the normal person diminishes more quickly than that of the patient. If the normal person has an acuity three times that of the patient by ordinary illumination, it may happen that on diminishing the illumination both would have the same visual acuity. Persons suffering from a central scotoma sometimes complain of nyctalopia for a like reason. We have seen, indeed, that the superiority of the macula over the rest of the retina diminishes with the illumination, so that with a very weak illumination the fovca does not see so well as the rest of the retina. We can under- stand, therefore, that a central scotoma may cause relatively less annoy- ance when the illumination is weak. We must recall, too, the quantitative measurement of the light sense in persons affected with cataract. The patient ought to be able to recognize the illumination of an ordinary lamp at a distance of 4 to 5 meters, or that of a candle at 2 meters, and its projection must be good, that is to say, the patient must be able to tell the direction in which the luminous source is located. If the patient does not satisfy these condi- tions, we may conclude that there exists an affection of the fundus of the eye, which compels us to make an unfavorable prognosis. Bibliography. Bonguer (P.). Essai cToptique. Paris, 1729. Bouguer (P.). Traite d'optiquesur la gradation de la lumidre. Paris, 1760. Lambert (J. H.). Photometria. Augustse Vindelic, 1760. Masson. Etudes de photometric electrique. Ann. de physique et chimie, 1845, t. XIV, p. 129. Fcerster. Ueber Hemeralopie und die Anwendung eines Photometers im Gebi'te der Ophthalmologie. Breslau, 1857. Fechner. Elemente der Psychophysik. Leip- zig, 1860, 2 vol. Klein. De V influence de Vedairage sur Vacuite visuelle. Paris, 187;-5. Krenchel (V). in Klin. Monatsbl.fur Augenheiik. February, 1880. Bjerrum (J.). Under. -(r- gelsen of Synet. (Danish). Copenhagen, 1894. Cbarpentier (A.) La lumiere et lescoulevr*. Paris, Baillere, 1888. The work of Lambert is first in importance. A German translation with notes by Anding, has just appeared at W. Ostwald. Die Klassiker der exakten Wissentchaften. Leipzig, 1892. CHAPTER XVII. THE COLOR SENSE. 103. General Eemarks. On analyzing any color with the spectro- scope, we find no other tints than those which compose the solar spec- trum, mixed in different proportions. The only colors which would seem to form an exception, the brownish colors, are really red and yellow colors of slight intensity, more or less mixed with white. To examine the color sense, therefore, we may limit ourselves to the study of spectral colors and their mixtures. We have thus the advantage of experimenting with pure colors, which are easily definable by the wave length of the rays. The use of colored papers, although very convenient, has many drawbacks, in consequence of the impossibility of defining exactly the color of the paper used, so that another experimenter may be able to procure a similar tint. On the contrary, if we obtain a result with spectral light of a certain wave length, the experiment may be described in a very exact manner, the only condition which may be left uncertain being the intensity of the light used. On analyzing blue spec- tral light with the spectroscope we find only blue, while the light reflected by a paper of this color contains, besides blue, most of the other colors of the spectrum. There is another way of procuring pure colors, for the incandescent vapors give monochromatic light, at least approxi- mately. Thus the sodium flame gives yellow light of a wave length of 0.59 /Jt, the lithium flames red light (0.67 /*), the thallium flame green light (0.54 ,u), and the strontium flame blue light (0.46 /^). But, as a rule, these flames are in less common use than spectral light. The light which passes through colored glasses is generally far from being monochro- matic ; we must, however, except red glasses, colored with oxide of copper, which, when they are a little dark, allow scarcely any but red rays to pass. Among liquids we sometimes use the solution of bi- chromate of potash, which absorbs the blue extremity of the spectrum, and the solution of sulphate of copper-ammoniac, which absorbs the red, 234 THE COLOR SENSE 235 the yellow and part of the green. A mixture of both allows a quite pure green light to pass. 1 3 ( I ) E : i ( I H i 70 1 1 1 60 Mill 1 I 1 1 1 t i il . 1 1 1 1 i , , -1 ^_. A^_ _^ \ JA^ A^ .. -^- .^~ J\^ J Red Orange Yellow Green Blue Indigo Violet H H 1 1 1 1 r 1 1 1 eol 1 1 1 1 1 1 1 i t 1 I , ,"1 i I 1 t 1 I i i ,1 , Red Orange Yellow Green Blue Indigo Violet Fig. 151. I. Spectrum of refraction. II. Spectrum of diffraction. The numbers indicate the wave length in hundredths of p. We distinguish between the spectra of refraction, formed by means of prisms, and the spectra of diffraction, which are obtained by allowing light to pass through a grating, that is to say, a glass plate on which a great number of very fine parallel lines have been traced. The spectra of refraction are preferable because they are, generally, purer than the spectra of diffraction. They have this inconvenience that the relative width of the different colors varies with the prism used. The red and orange colors are reduced to a relatively small space, while the blue and violet colors are stretched out over a large surface. In the spectrum of diffraction, the distance between the different colors is, on the contrary, proportional to the difference of the wave length (fig. 151), so that all the spectra of diffraction are alike and form, so to speak, the normal spectrum. The yellow is at the middle of the spectrum ; the red and orange occupy half, the green, blue, indigo and violet the other half. As landmarks in the spectrum, we frequently use the lines of Fraun- hofcr, the wave lengths of which have been very exactly determined. Say, 236 PHYSIOLOGIC OPTICS for example, that the rays, which we use, are situated at half the distance between E and F; on the scale of figure 151 we see that the light used must have had a wave length of 0.50 to 0.51 /* . It is better, however, to determine the wave length directly, which is easily done by means of a grating. I have already observed that there are in the spectrum rays beyond the red which are not visible. The extreme visible red corresponds nearly to a wave length of 0.8 //. The colors then follow in the well- known order : red, orange, yellow, green, blue, indigo, violet. Beyond the violet come ultra-violet rays, which are not visible under ordinary conditions, but which can be observed by means of a photographic plate, or by receiving them on a fluorescent screen, or simply by eliminating all other light according to the method given on page 109. They are then seen with a certain grayish color, which is, perhaps, partly due to the fact that the retina is fluorescent. We distinguish colors according to their hue (ton), their purity or tint (saturation) and their brightness or shade (intensite). The tone or hue de- pends on the wave length alone, or, in other words, on the position of the color in the spectrum : the red has a different hue from the green, etc. The saturation or purity depends on the white which is found added to nearly all existing colors, except those of the spectrum: the less white there is, the greater the purity of the color. The intensity or bright- ness depends on the quantity of light. If we have formed a spectrum by means of a certain luminous source, and then increase the intensity of this source, the intensity of all the colors of the spectrum increases at the same time. The hue changes constantly in the spectrum : that is to say, if we take light from two different parts of the spectrum, we cannot make them alike by changing their brightness. The change reaches its greatest rapidity in the green-blue part of the spectrum, where even a variation in the wave length of o.ooi /* produces a change of hue; the rapidity diminishes towards the extremity, and in the extreme parts of the red and violet the hue remains the same (Kocnig and Dieterici). According to Kcenig we can distinguish about 160 different hues in the spectrum. On the other hand, according to the same author, the eye can distinguish about 600 different degrees of brightness between the threshold and dazzling light. This is true for white and probably also for the different hues of the spectrum, but the total number of different impressions between which the eye can make a distinction is, however, less than one would think in view of these indications, for when the brightness be- THE COLOR SENSE 237 comes very great or very feeble, the color disappears as we -shall see forthwith. On examining the spectrum it is easy to see that our sensations of colors form a continuous series. We begin with the red, which passes from orange to yellow, etc., and end with the violet, the tint of which presents an analogy to the red. The intermediary color between the red and violet, purple, is not found in the spectrum, but it would be possible that Greeu Yellowish -Green Bluish-Green Yellc Blue Violet Purple Fig. 1.V2. Table of colors after Newton. this color would be produced by ultra-violet rays if the retina were not fluorescent. We can, therefore, represent the gamut of the colors by a closed curve. The simplest form we can give to this curve is that of a circle (fig. 152), replacing, however, the part corresponding to the purple by a straight line ; we shall soon see why. We suppose all the colors of the spectrum placed on this circle in their natural order. At the center is the white, and on the right, going from the white to one of the spectral colors, are the different tints, the purity being greater as we approach the spectral color. If we mix two colors, the mixture will have one of the intermediary hues often bleached with white, and if we mix, in suit- able proportions, two colors situated opposite to each other on the table, 238 PHYSIOLOGIC OPTICS we obtain pure white. Two colors which, when mixed, give white, are called complementary. For this reason red is complementary to green- blue, green to purple, yellow to indigo and orange to blue. It was Newton who first arranged the colors as in this table. We find in it all hues and all degrees of purity. I must add a few words on the sensation of black. First, it must be noted that black produces a real sensation : to see black is not the same thing as to see nothing at all. The most striking example is that of the spot of Mariotte, which corresponds to the papilla. In this spot we see nothing, but we do not see it black. By looking directly in front, one sees a part of the space in which one is; in regard to that which is beyond the limits of the visual field, one does not see it, but it does not appear black. The impression of black is, therefore, a true sensation, which corresponds to the state of repose of the visual organ. There exists no completely black object in nature: even black velvets still reflect a comparatively considerable quantity of light. A black object placed in the direct light of the sun may appear clearer than a white object placed in the shadow. According to some measurements which I have made, the whitest paper which I could find (visiting cards) returns only about a third of the incident light (37 per cent.). The normal white of Kcenig, which is obtained by burning a thread of magnesium and allowing the vapor to be deposited on a sheet of paper, sends back about two-thirds of the light ; its whiteness is nearly that of snow. Ordinary black paper (bristol black) returns nearly 5 per cent, of the incident light (1.5 per cent, of the quantity reflected by the white paper) ; black velvety paper sends back about 5 per 1000 of the incident light (1.5 per 1000 the quantity reflected by white paper). The most absolute black that we can produce is that of an aperture made in the side of a closed box, blackened internally. Compared with this black even the velvety paper appears slightly grayish. Black does not figure on the table of Newton. If we desire to include it in the illustration, we must suppose the colors placed on a body of three dimensions, a pyramid or a cone (Lambert). The table of Newton would form the base of the cone, while the black would form its apex : on the conical surface we would place the colors of little intensity. Thus the brown would be placed between the yellow and the black, etc. 104. Phenomena of Contrast (Simultaneous). Our judgment of colors is always influenced by the colors of surrounding objects. This fact is THE COLOR SENSE 239 well known to painters, whose color sense is generally highly developed, so that they often see colors that inexperienced persons would not per- ceive. But, in special circumstances, this influence makes itself felt in a very striking manner. i EXPERIMENT OF H. MEYER. Placing a small piece of gray paper on a sheet of colored paper and covering the whole with a sheet of tissue paper, the small piece is seen to be of the complementary color. Pfluger had letters, thus arranged, printed for the examination of color-blind- ness. 2 EXPERIMENT OF RAGONA SCINA. Two sheets of white cardboard (BC and BD, fig. 153) are placed so as to form between them a right angle ; on each is a black spot, a, b, and a red glass BE is placed so as to form an angle of 45 degrees with the card- board. The eye A receives from BC the rays which have passed through the red glass and from BD the rays reflected by this glass. The former are red, the latter white, so that the background BC would appear whitish-red. The spot a is seen at a' of a deep red color, because the eye receives at this place only red rays, the white rays which should come from BD being wanting. Corresponding to b the eye receives only white rays coming from BD, and nevertheless, b appears of an intense green by contrast. The ex- periment, which is very pretty, may be performed with other colored glasses. We always see a' and b in complemen- tary colors. Fig. 153. Experiment of Ragona Scina. 3 COLORED SHADOWS. Let A and B (fig. 154) be two candles, of which A may be the brighter ; in front of A we place a red glass ; a and b are the shadows which the stick c forms on a white screen. The screen illuminated by the white light from B and the red light from A, should appear whitish-red, but the red is scarcely perceptible ; b, which is illumi- nated only by the red light from A, appears red, and a, which should appear white, appears green, by contrast. We can also make the ex- periment with daylight and that of a candle, in which case there is no 240 PHYSIOLOGIC OPTICS need of the colored glass, since the colors of the , two lights already differ. We begin by illuminat- ing the screen with daylight; we see the screen ^ white and the shadow black (gray). On lighting the candle the screen still appears white, although / it would seem that it ought to appear yellow, since / it is partly illuminated by the yellow light of the / candle; the shadow, which just now appeared rj B gray, has become yellow by the illumination of Fig. 154. the candle, and the other shadow, which receives Experiment with colored ,, shadows, the daylight, appears blue by contrast. 4 EXPERIMENT OF DOVE. Analogous phenomena with colored shadows are observed when we place a colored glass opposite a mirror. We then see two images of a white object, one by reflection on the an- terior surface of the glass, the other by reflection on the mirror; this latter has the color of the glass, since the rays have passed through the .glass twice. The first, which ought to be white, shows by contrast the complementary color. With a black object on a white ground, the sash of a window for example, we have the phenomena reversed. We observe that the expression "by contrast" scarcely explains these .singular phenomena. In most of these cases it seems that the funda- mental phenomenon lies in the defectiveness of our judgment of white. Thomas Young already directed attention to the fact that a sheet of white paper appears white to us, as well when illuminated by the yellow light of a candle as by the red light of a coal fire. We may say that we con- sider always as white the bodies which return the greatest quantity of light, whatever may be the light used (Javal). This is primarily inde- pendent of the illumination, and this is why a sheet of white paper ap- pears to us white with different illuminations. But the recollection of the illumination by daylight plays, nevertheless, a part, so that, if the real color differs much from it, the paper seems white with a slight colored tone : thus when we look at it through a red glass, in which case the paper returns red rays only, it appears a reddish-white. In the experiment with colored shadows the screen appears to us white when it is illuminated by daylight only, and also when it is illumi- nated by a mixture of daylight and candle light at the same time. But if, under these circumstances, the whitish-yellow light which illuminates the screen appears white to us, it is not strange that the white light which illuminates one of the shadows appears blue, that is to say, less yellow THE COLOR SENSE 241 than the screen. We may regard, so to speak, the zero of the scale of our color sensations (the white) displaced, and with it the entire scale. TRUE SIMULTANEOUS CONTRAST. While the phenomena of which we have just spoken are due to a false judgment of the color white, there are others which are due to a true contrast. By making a disc like that of figure 155, but having a greater number of sectors, rotate we obtain gray rings, and we observe that we cannot see the outer rings which are very pale ; we see only the borders of each ring : the external border, which appears deeper than the rest of the ring, by contrast with Fig. 155. Disc of Masson. the following ring which is paler, and the internal border which appears paler than the rest, by contrast with the neighboring darker ring. By replacing the white and black by yellow and blue, we obtain rings which present different shades of gray; the internal rings are bluish, the ex- ternal rings yellowish. But each ring has an internal border which is yellow, by contrast with the preceding ring which is bluer, and an ex- ternal border which is blue, by contrast with the following ring which is yellower. The phenomenon is very pronounced, but disappears, at least in a great part, if we separate the rings by very fine black circles. The diffuse borders favor considerably the effect of the contrast. 105. After-images (Successive Contrast). When we look at a small colored surface, placed on a white ground, by fixing exactly the same point for a short time, we observe that the color diminishes gradually in brightness: the red becomes brown, etc. We observe at the same time that the object is surrounded by a narrow border of the comple- 242 PHYSIOLOGIC OPTICS mentary color, due to the fact that, in spite of himself, the observer makes slight changes in the direction of the look. We explain the phenomenon by saying that the part of the retina where the image is formed is fatigued for the color in question. If we then transfer the look to a sheet of white paper, we see an image tinted with the comple- mentary color. If the surface be red, the image appears bluish-green. We may suppose the white color as composed of two complementary colors, red and green ; the retina being fatigued for the red color, it is the green color which predominates. If the object we look at is white, the after-image is black; but if we look at a flame or other very bright object, we obtain a colored after-image, the color of which changes before its disappearance. The after-images of the complementary color are called negative: we can also obtain positive images, each part of which has the same color as the original. We close the eyes and cover them with the hand for some minutes, so that no light can enter the eye. We keep in this posi- tion for some time until all prior impressions .on the retina have dis- appeared. This done, we remove the hand and open the eyes for an instant, without, however, changing the direction of the look, shut them immediately and cover them again. If the experiment is very successful, we then see a positive image of exterior objects, of a surprising dis- tinctness. We can scarcely believe that we have really closed our eyes ; the hand seems transparent. If we continue to keep the eyes closed, we see the less illuminated parts of the image disappear, while the more illuminated parts change color, becoming bluish, violet, orange, etc. ; the image disappears and returns again, and so forth. A clear after-image of a chess-board, or other analogous figure, shows phenomena exactly like those which I shall describe later under the heading "Phenomenon of Tro.vler." It now becomes probable that the disappearance and reappearance of the after-images are due to the same causes, likewise unknown, as this phenomenon. The after-images, of which I have just spoken, last for a relatively long time, but there are others which last so short a time that they escape observation in the ordinary distances of life. The simplest way of mak- ing them appear consists in moving the object which is intended to produce them. The secondary image then seems to follow the object because it is formed at the place where the object was a moment before, and because it lasts only an instant. Ordinary after-images form, in these circumstances, a long luminous series. The most striking of these phenomena was described by Purkinje and later, under the name of THE COLOR SENSE 243 "recurrent vision," by Davis. The experiment is very easy to perform : we light a match in darkness, blow out the flame and move the burning wood around. We shall then see the blue after-image, feebly lumin- ous but bright nevertheless, follow the match at some distance, repro- ducing its form exactly. There are two conditions necessary to the success of the experiment : one is that we do not follow the match with the look, for the phenomenon is visible only in indirect vision ; the other is that we use the proper speed, neither too fast nor too slow. With a certain rate of speed the image (called "ghost" by English writers) seems double. According to Bidwell the interval between the match and the after-image corresponds to almost one-fifth of a second. This author sees the space between the match and the remainder of the field blacker, an observation which was confirmed by Agaboban, who repeated the experiment at the Sorbonne, but I have not been able to verify it. By making a black disc with a white sector rotate in full sunlight Charpenticr observed a black sector which formed in the white sector not far from its anterior border, and which was sometimes followed by several others less pronounced. At times the interval between the an- terior border of the white sector and that of the black sector corre- sponded to about -ft- of a second. The observation indicates that when we allow an illumination to act for a very short period on the retina the latter becomes insensible to it after a sixtieth of a second to reacquire its sensibility after the lapse of the same period ; sometimes the phenom- enon is repeated several times (retinal oscillations). The phenomenon must not be confounded with "recurrent vision" for which the interval is much longer. 106. Phenomena Dependent on the Variation of the Brightness of the Colors. The brightnesses of two sources of light of the same color are compared as easily as if there was a question of white light, and we find almost the same value for the fraction of Fechner. If we attempt to compare lights of different color the eye manifests, on the contrary, a very great uncertainty, and besides we encounter a difficulty caused by what is called the phenomenon of Purkinje. Suppose that we have two sources of white light, which we have found of equal brightness. If then we diminish the intensity of both one-half we shall find them again equal. But if we equalize two sources, one of which is blue and the other red, and that then we diminish their brightness one-half, the blue light will appear much brighter than the red light. Let us select two 244 PHYSIOLOGIC OPTICS papers, one red and one blue, which by daylight illumination appear to have the same brightness ; by diminishing the illumination the blue paper will appear brighter than the red paper. With a very feeble illumination the red paper will appear black, the blue paper a pale gray. In order that the experiment may succeed well the papers must be seen under an angle which is not too small, for the phenomenon is but slightly pro- nounced for the macula. In accordance with these observations Mace de Lepinay and Nicati have shown that the visual acuity falls much more quickly on diminishing the illumination when we use red light than when we use blue light : we select a red glass and a blue glass so that we may have, by daylight illumination, the same acuity on looking at the chart through either. If then we close the shutters almost completely so as to greatly diminish the illumination, we observe that the blue glass enables us to still read half of the chart, while with the red glass we cannot, at the first moment, distinguish even the chart; after a little while we can read the large letters, but the acuity for the red always remains lower than the acuity for the blue which is stationary. Kocnig and Brodhun also have shown that the increase of the fraction of Fechner, at the lower limit, begins sooner for the red than for the blue. The following experiment shows in a very striking manner the differ- ence which exists in this regard between the two extremities of the spectrum. We project the spectrum on a screen A, pierced by two apertures, allowing the red rays and the blue and violet rays to pass. Behind the screen A we place a lens which reunites these rays on a second screen B, forming on it an image of the surface of the prism which is turned towards A. This image then shows a pretty, purple color. In front of the screen B we place a stick which forms thereon two shadows, one red, the other blue, and it is easy to so regulate the apertures of the screen A that both shadows may have the same brightness. If we now diminish the width of the slit through which light reaches the prism the purple is diluted more and more with white. The blue shadow becomes grayish, and brighter and brighter compared with the background, while the red shadow retains its color, but becomes darker and darker. Finally it is nearly black and alone visible, the other shadow being gray and having nearly the same brightness as the back- ground. In the spectrum it is the yellow and green rays which have most brightness. The brightness diminishes towards the two extremities of the spectrum, but more towards the blue extremity than towards the red extremity. We must note, however, that if the blue and violet colors THE COLOR SEXSE 245 seem relatively feeble in the prismatic spectrum, this is partly due to the fact that these colors are spread over a much greater space than the others. In the spectrum of diffraction the intensity is greatest in the middle of the spectrum, and diminishes almost alike towards the two extremities. If we lessen the intensity of the luminous source the colors of the spectrum change hue. We first see the yellow and blue colors disappear ; there remain only the red, green and violet, which take the place of the colors which have disappeared. On still further diminishing the bright- ness, the blue changes into a blue-gray, the green into a green-gray, the red becomes brownish and finally all the colors disappear, and we see only gray. The red alone forms an exception; it does not seem to change into gray before disappearing. There exists a very pretty method of showing the change of appear- ance of the spectrum by the diminution of the brightness. It consists in gluing a board of velvety black paper on a white screen so that by projecting on it a horizontal spectrum the upper half is formed on the black paper and the lower half on the white screen. This latter half shows the spectrum as it ordinarily appears, while the upper half has the form of a gray band, with the exception of the part corresponding to the red which appears brown. The colors disappear, therefore, when the brightness of the rays be- comes very feeble. Also when the brightness becomes very strong the impression approaches white. The sun, seen through a red glass, ap- pears a whitish-yellow, although the glass allows only red rays to pass. Concentrating the light of the sun on a sheet of white paper with a lens, after having made it pass through a blue glass, the image of the sun appears white. When we look at the sun through a prism the spectrum presents itself as a colorless strip of a dazzling brightness. Here also it is the red which best maintains its color; in most cases it appears a whitish-yellow. According to Parinaud, these phenomena depend on the adaptation of the eye. The spectrum of feeble brightness, which appears gray to the adapted eye, is invisible to the eye not adapted, and when, the in- tensity increasing, it becomes visible to the non-adapted eye it in turn appears colored. Parinaud determined the threshold for different rays of the spectrum, and found the curves represented by figure 156. The upper curve is that of the adapted eye, the lower curve that of the eye not adapted. The different parts of the spectrum are indicated by the ver- tical lines, prolongations of the lines of Fraunhofer in the diagram of the 246 PHYSIOLOGIC OPTICS spectrum which is above the figure. The numbers on the left indicate the quantities of light necessary in order that these different parts of the spectrum may be perceived. Thus the adapted eye requires a quantity of light equal to I (this quantity being taken as the unit) in order to A B C D E F 100 200 300 Fig. 156. After Parinaud. perceive the green rays near E, while the non-adapted eye requires a quantity equal to 100 in order to perceive the same rays, and a quantity equal to 1500 to perceive the blue rays near G. We see that the eye, by adaptation, gains nothing for the perception of red rays, whilst it gains enormously for the more refrangible rays. But it gains only in luminous sensibility : except the part be, which is common to the two curves, the whole upper curve corresponds to colorless sensations only. According THE COLOR SENSE 247 to Parinaitd, the fovea gains nothing by adaptation ; the rays also appear colored as soon as, with increasing brightness, they become visible to the fovea. The results of Parinaud have been disputed by Charpcntier, and they no longer harmonize well with the experiments mentioned on page 244. According to Charpentier, it is wrong to attribute the colorless sensa- tion which the rays of very feeble brightness call forth to the adaptation of the eye, and, on the other hand, it is certain that if, from full daylight, we enter a relatively dark space, we cannot distinguish right away colors which we observe very well later. Nevertheless, adaptation plays a considerable part in relation to these phenomena as the following observation of Charpentier shows. He covered the plate B of his photoptometer (see page 228) with a black paper, pierced with seven small openings grouped in a space of nine millimeters square. The plate A was illuminated by spectral light of different colors. On opening gradually the diaphragm of the instru- ment, he proved that the first impression which is obtained is that of a diffuse luminous spot, without color; let us designate the aperture of the diaphragm for the moment by a. To distinguish the color it was necessary to give the diaphragm a larger aperture b, and it is only by making the aperture still greater c that we come to distinguish the points. For the eye, adapted to darkness, the apertures b and c remain almost the same as for the non-adapted eye, while the aperture a dimin- ishes enormously especially for the more refrangible colors. It is not strange that there exist differences of opinion on these ques- tions, for there is very little certainty in the determination of the lower limits of the sensations. It must also be noted that the expressions "adapted" and "non-adapted" applied to the eye are vague. If every one is in accord in considering an eye adapted when it remains for half an hour in darkness, or non-adapted when it remains as long in full day- light, the authors do not agree so well in designating the state of the eye when exposed to an intermediary illumination, such as that of the interior of our houses. 107. Methods of Mixing Colors. The fundamental examination of the color sense is made by means of what is called equations of colors: we mix two or three colors in different proportions until the observer declares the mixture similar to a fourth given color, most frequently white. We then examine whether an eye, of which the color sense is normal, recognizes the equation, that is to say, whether the mixture 248 PHYSIOLOGIC OPTICS appears likewise similar to white for this eye. We can mix the two colors in different ways. i Mixtures of Spectral Colors. We form two spectra by means of two prisms, and by allowing these spectra to slide over one another we can mix any two hues from them. Helmholtz accomplished the same end with a single prism, by using a slit in the form of V; each of the branches formed an oblique spectrum, and the two spectra would over- lap to a great extent so that we could obtain all possible mixtures. The apparatus of Maxwell was very ingenious. It consisted of a box, a section of which is shown in figure 157. At E is a narrow slit through which passes light, which is reflected by the mirror e towards the prisms Fig. 157. " Color box " of Maxwell P and P x , through which it passes to meet the concave mirror S. This mirror reflects the light which passes again through the prisms to go to form a spectrum on the far end of the box, AB. At this place are three movable slits x, y and z, which permit spectral light of any hue to leave the box through each of the slits by displacing them. Suppose x cor- responds with the red, y with the green and z with the violet. It must be noted, in consequence of the reversibility of optic processes, that if we illuminate the slit x from the outside by red light, this light will reach an eye placed at E ; but if we illuminate the same slit with green light, this light will not reach an eye at E, but will be projected to one side of E. In order that the green light reach E, it must pass through the slit y. Consequently, illuminating the three slits x, y and z by a white luminous source, an eye placed at E sees the surface of the prism P colored by the mixture of the three colors, which a flame placed at E would project on the slits x, y and z. At the far end of the box is yet another aperture c through which enters white light, which, after having been reflected by the mirror M and concentrated by the lens L, meets a plate of ground glass blackened on the back M x . Xhe eye placed at E sees this plate at the side of the prism, and can thus compare the brightness and color of the mixture with that of the white light, ad- THE COLOR SENSE 249 mitted through c. By properly placing and opening the slits, we can thus obtain a mixture which is not distinguishable from the white light reflected by M ly either as to color or brightness. The latest researches on the mixtures of colors (Kcenig and his pupils) have been made with a large spectral instrument, which was constructed for the laboratory of Berlin, and a description of which is found in the second edition of Helmholtz's work on Physiologic Optics (page 355). 2 Max^vell also studied the mixtures of colors by placing, on the disc of Masson, sectors of different colors (see page 260). 3 We can mix colors by means of a plate of glass ab (fig. 158), which Yellow Blue Fig. 158. Mixture of colors by means of a glass plate. is held so that it may reflect rays of one color at the same time that it allows rays of another color to pass (Lambert). 4 Looking at two colors placed side by side through a double refract- ing prism, we see them separated by a strip the coloration of which is that of the mixture. 5 Placing two glasses of different colors before the two openings in the experiment of Scheincr and looking at the sky, we see the common part of the circles of diffusion in the color of the mixture. 6 Painters frequently use mixtures of coloring matter, but the results which are thus obtained are frequently not in accord with those which are obtained by the other methods. The best known example is the mixture of yellow and blue. Painters thus obtain green, while with a revolving disc we obtain a gray-white (Lambert). Hclmliolts gave the following explanation of this difference: mixing the colors of yellow and blue pigment the superficial molecules send back yellow light and blue light. Together these rays produce the impression of white, as on the revolving disc. The blue molecules situated deeper also send back 250 PHYSIOLOGIC OPTICS blue light, but it must be noted that this blue light, as also that of the superficial molecules, is not pure: by the spectroscope we find that it contains green, blue and violet rays. The yellow molecules send back red, yellow and green rays. Generally the molecules allow to pass rays of the same color as those which they send back. Among the rays re- flected by the deep yellow molecules, only green rays, therefore, can pass through the superficial blue molecules, and, among those reflected by the deep blue molecules, likewise only the green rays can pass through the superficial yellow molecules. The result, therefore, becomes a green color, mixed with the white reflected by the surface. 108. Results of the Mixtures of Colors. Newton devised his table to give a graphic illustration of the results which are obtained by mixing colors. The principle of this table is that all the colors we can produce by mixing two given colors are placed on the straight line which joins these two colors, and so much nearer to that one of the two colors which Green Yellowish-Green Bluish-Green Yellow Blue Indigo Red Purple Fig. 159. Table of colors after Newton. enters most into the mixture. The quantity of the color of the mixture is expressed by the sum of the quantities of the component colors. Sup- pose, for example, that we want the result of the mixture of three parts of green with one part of red and two parts of blue. We begin by THE COLOR SENSE 251 joining the green and red by a straight line which is divided into two by the point p (fig. 159), so that the distance of p from the green may be a third of its distance from the red ; p is then the place of the mixture of the green and red, the mixture being represented by the number 4, the sum of the two component colors. We then join the point p with the blue by a second straight line which is divided into two by the point q, so tjiat the distance pq is to the distance of q from the blue, in the proportion of 2 to 4 ; q is the place of the mixture of the three colors, and the quantity of this mixture is expressed by the number 6. Drawing the line oq and prolongating it until it cuts the spectral curve, we see that the color of the mixture is a bluish-green strongly diluted with white. There enters into this illustration of Newton an expression which is not defined, that of the quantity of the colors. While it is easy to tell what must be expected from equal quantities of the same color, it is not easy to define the expression of equal quantities of two different colors, the result of which is that the form of the curve becomes, up to a certain point, arbitrary. With Newton, we must consider as equal the quantities of two complementary colors, which, when mixed, give white, since the white, on his table, is situated at an equal distance from both. If we take two other complementary colors, we must also consider as equal the quantities of these colors which, mixed, give white, but on condition that this white be of the same brightness as the former. As we shall see, Maxwell and Helmholtz used other definitions. The table of Newton shows that, with the exception of purple, we can- not produce new colors by mixing spectral colors, for we can always, after having found the position of the mixture, draw a straight line passing through the center and this point. Prolonged, this straight line will meet a spectral color, and the mixture is equal to this color diluted with white. The table of Newton indicates also another peculiarity of the normal color sense, namely the fact that we can reproduce all existing hues by mixing, two by two, three colors properly chosen. Let us select, for example, red, green and blue, and draw on the table (fig. 159) straight lines which join these colors. If, then, we select any spectral color, we can always join it to the center of the table by a straight line; this straight line must necessarily cut one of the sides of the red-green-blue triangle and at the place of intersection is found the mixture which is similar, in hue, to the spectral color. On account of this peculiarity the normal eye is called trichromatic. Observe particularly that I have said 252 PHYSIOLOGIC OPTICS that the two colors are alike as to hue. Generally they are not alike as to purity, the color of the mixture being diluted with white. The table of Newton also requires that ,the spectral color must always have greater purity, for, if we could, by mixing two spectral colors, reproduce a third color exactly, these three colors should be placed on a straight line, and the spectral curve could not be circular. But this last condition of the table is not fulfilled. Bluish-Green Yellow Orangi 6lV Fig. 160. Color table of Maxudl. The accuracy of the illustration of Newton has, indeed, been verified by the admirable works of Maxwell. This author found that Newton's table gives a very exact illustration of the results of the mixtures of colors, but that the spectral colors cannot be arranged in a circle, be- cause there are quite extended parts on the spectrum, the colors of which can be reproduced exactly, or nearly exactly, by the mixture of two given colors, and which, consequently, must be placed on straight lines. Figure 160 shows the spectral curve of Maxwell. While the curve of Newton must be considered merely as a conception of the mind, Maxivcll THE COLOR SENSE 253 determined his experimentally with the instrument described in the pre- ceding chapter (fig. 161). To use it he placed it in such a position that the slits .r, y, z and c were turned towards a sheet of white paper illumi- nated by the sun. As a starting point he selected the three following colors (standard colors) : Wave length : Red (R) 0.630/i Green (G) 0.528 n Blue (Bl) 0.457 p He placed the slits x, y and z so as to give access to these colors, and, by regulating the width of the slits, he produced a mixture which differed neither in tint nor brightness from white introduced through the slit c. Fig. 161." Color box " of Maxwell. By measuring the slits he found for x a width of 2.36 mm., for y 3.99 mm. and for z 3.87 mm., and by designating the white, which remained constant through all the experiments, by W, he had thus the equation 2.36 R -f 3.99 G + 3.87 Bl = W He then displaced the slit x so as to give access to orange light ; by regulating the slits he again produced a mixture similar to white which gave him the equation 2.04 Or -f- 3.25 G -f 3.88 Bl = W As white was the same in both cases, we can combine the two equa- tions, which gives or or 2.04 Or -f 3.25 G + 3.88 Bl = 2.36 R -f 3.99 G + 3.87 Bl 2.04 Or = 2.36 R 4- 0.74 G 0.01 Bl 1 Or = 1.155 R + 0.362 G O.f 06 Bl He then repeated the measurement for the other colors, by always combining two of the standard colors with the color in question to pro- duce white. He thus succeeded in expressing all the colors of the spec- 254 PHYSIOLOGIC OPTICS trum by three colors. The following table shows the results of these measurements : COLOR. & "* BLUE p UNITY p j . 5.63 (663) = 2.36 + 0.05 h 0.36 2.77 2.032 2.36 (630) = 2.36 -f 0.00 h o.oo 2.36 1 2.04 (606) = 2.36 + 0.74 - - 0.01 3.09 0.662 Yellow . . . . ! 2.79 (583) = 2.36 + 2.45 - 3 20 (562) 1 55 4- 3 99 - - 0.01 - 0.10 4.80 5.43 0.582 0.589 3 30 (544) = 0.42 4- 3.99 - 0.03 4.38 0.754 f 3.99 (528) = 0.00 -\- 3.99 f 0.00 399 I Green ) i Blue ! 5.26 (513) = 0.33 4- 3.99 - 787 (500) = 0.43 4- 3.99 - 7.83 (488) = 0.39 4- 2.67 514 (477) 024 4- 0.98 - {- 0.44 f 2.22 f 3.87 f 3 87 4.10 5.77 6.15 4.61 . 282 1.363 1.275 1.116 4.28 (467) = 0.14 4- 0.14 f 3.87 3.87 1.105 f 3.87 (457) = 0.00 4- 0.00 f 3.87 3.87 1 Violet 4.10 (449) = 0.08 4~ 0.03 - 5.59 (441) = 014 + 0.09 - 8.09 (434) = 0.04 0.23 3.87 f 3.87 f 3.87 3 98 4.10 3.68 J A'oZ 1.362 2.197 By dividing each equation by the coefficient on the left, we obtain the expression corresponding to the width of the slit of I millimeter. 60 :8 56 St- 52 50 O> Y G Bl Fig. 162. Color-curves of Maxwell. THE COLOR SENSE 255 Under this form the result is found expressed on figure 162. The three curves, designated by R, G, B, correspond to the three standard colors; the numbers underneath are the wave lengths of the different colors of the spectrum, and the position of the three points in which the curves cut the vertical line corresponding to each of the colors, indicates the quantities of the three standard colors needed to produce the mixture. The negative sign of the blue, in the equation of the orange, is found again for the greater number of the colors added to one or other of the standard colors. Its significance is easy to grasp. In fact, if we write the equation of the orange thus : 2.04 Or + 0.01 Bl = 2.36 K + 0.74 G it indicates that we cannot, with the three standard colors, produce a mix- ture exactly like orange, but must, on the contrary, add a little blue to the orange so that it may be like the mixture of red and green. It should be noted that, up to the present, I have simply expressed the quantity of a color by the width in millimeters of the slit giving access to this color. To construct the table of colors we do the same for the three standard colors; but for other colors we will be obliged to select the units in another manner. I have said, indeed, that with Newton the quantity of a mixture is considered as equal to the sum of the quan- tities of the component colors. The sum of the three component colors of the orange was 2.36 + 0.74 0.01 = 3.09 while the width of the slit was 2.04 mm. According to Newton, the quantity of orange passing through the slit of 2.04 mm. is, therefore, 3.09, that is to say, the unit of the orange corresponds to a width of the slit of |;JJ = 0.662 mm. If we wish to use the table to solve questions of mixtures of colors we must, therefore, multiply the quantities found by the table by the figures indicating the units, in order to obtain a result expressed by the width of the slit in millimeters. The units are in the last column of the table. They are obtained by dividing the coefficients on the left by the figures in the column before the last, which indicate the sum of the component colors. To construct the spectral curve, we begin by drawing the dotted equi- lateral triangle of figure 163. We suppose the three standard colors placed at the three angles, an arrangement which was proposed by Young. To find the position of the orange, we begin by dividing the red-green 256 PHYSIOLOGIC OPTICS side into two parts, in the proportion of 0.74 : 2.36. Let P be the point of division: join this point to the blue angle by a straight line, of which we measure the length a. The color at P can be considered either as a mixture of 2.36 R with 0.74 G, or as a mixture of 3.09 Or with o.oi Bl. It follows that the orange must be placed on the prolongation of a, beyond the point P, and by designating its distance from P by x we should have x =JS a- This distance is, for the orange, so small that it Green 50 Bluish-Green Yellow // ft Fig. 163. Color table of Maxwell. is scarcely visible on the figure, the curve coinciding at this position almost with the dotted line. We observe that, on account of the pres- ence of the negative coefficient, the color in question must be placed outside of the triangle. A color which is situated in the interior of the triangle may be reproduced exactly by a mixture of the three standard colors; this is not possible for a color situated outside of the triangle: THE COLOR SENSE 257 it is necessary, on the contrary, to mix it with one of the standard colors, in order that it may seem equal to the mixture of the two others. On the table of Maxwell the greater part of the spectrum (from 0.63 M in the orange-red to 0.53 /* in the green, and from 0.5 I/A in the green to 0.47 ,a in the blue) is arranged on the two sides of a triangle of which the green, between 0.53 v and 0.51 /*, forms a rounded angle, while the extremities of the spectrum form two other somewhat irregular angles. We must imagine the third side of the triangle occupied by the purple colors, which are obtained by mixing red with blue. As nearly all the spectral colors have one of the coefficients negative, almost the entire curve is situated outside of the triangle of the standard colors, which in- dicates that the mixture colors have nearly all a little less purity than the spectral colors. The part situated between the red and the green coincides, however, very nearly with the corresponding side. By select- ing another standard color, green, we could make the part of the curve situated between 0.51 ^ and 0.47 P coincide with the other side of the triangle, but it is easy to see that we cannot select the green color so as to make the two sides coincide with the curve at once. We cannot, therefore, select three spectral colors such that we can reproduce all the other spectral colors exactly by their mixtures; we can reproduce all the hues, but some of > the mixture colors always continue to have less purity than the corresponding spectral colors, whatever may be the standard colors we have chosen. By means of the table of Maxwell we can construct the result of ^nix- tures of any colors. If we mix two colors placed on the same side of the approximately triangular curve, we obtain a mixture color which has as much purity as the spectral color, while if we mix two colors situated each on a different side, we obtain a mixture strongly diluted with white. The three colors which Maxwell selected as standard colors, the red, green and blue, have, therefore, this peculiarity that they cannot be reproduced by mixing other spectral colors, the mixture being always strongly diluted with white. The approximately triangular form of the curve, with the three colors, red, green and blue, placed at the angles, does not depend on the choice of the standard colors. By means of the equations of Maxwell, we can, by a simple calculation, express all the spectral colors by three colors other than his standard colors, for example by orange, blue-green and blue. The curve even then retains its approx- imately triangular form, having the red, green and blue at the angles, but it differs considerably from the equilateral triangle formed by the straight lines joining the three new standard colors, which indicates that 258 PHYSIOLOGIC OPTICS the mixture colors have, in this case, very little purity. Maxwell selected red, green and blue, so that the curve would come as near the triangle in form as possible. Contrary to what has taken place in the case of these three colors, those which are placed on each of the two sides of the triangular curve, may be reproduced exactly by mixing other spectral colors. They are, in this regard, analogous to the purple colors which are obtained by mixing the red and spectral blue, and which appear to the eye as pure as the pure spectral colors. The most interesting phenomenon among the great number of facts which are expressed by the table of Maxwell, is certainly this, that we can produce a perfect sensation of yellow by mixing red and green. The fact was already known to Young, and formed the principal basis of his theory of colors, which I shall mention later on. Lord Raleigh had constructed a special instrument for determining the quantities of spec- tral red and spectral green necessary to produce a complete equality with spectral yellow. In his numerous examinations he could always obtain a perfect equality, but in the matter of the quantities required of the component colors, he found quite unexpected individual differences (see page 262). We can also mix the light of the lithium and thallium flames so as to obtain a light which cannot be distinguished from that of the sodium flame. Another method, also pointed out by Lord Raleigh, consists in looking through a liquid which allows only red and green rays to pass (a mixture of bichromate of potash and blue aniline dis- solved in water). By observing through this liquid an object of a bright white, a cloud illuminated by the sun for example, it appears of a pure yellow, although all the yellow rays are completely absorbed. The liquid is, besides, very sensitive to tints of white light ; the light of the blue sky, which contains too little red, appears greenish, while the light of an arc lamp appears reddish. The yellow occupies a special position among the colors. An observer completely ignorant of the results of the mixtures, as well those of the physicists who obtain yellow by mixing spectral red and green, as those of the painters who, with their pigments, obtain green by mixing yellow with blue, would probably be tempted to class the yellow among the three standard colors of Maxwell, so as to reckon four principal colors in the spectrum: red, yellow, green and blue. As we have seen, the yellow is distinguished from the three others in that it can be reproduced by a mixture of other colors. In this respect it is analogous to the colors which are placed on the other sides of the THE COLOR SENSE 259 triangle, the purple and the blue-green, and it is distinguished from the latter in this that the eye may not perceive any trace of red or green in the yellow, while no one would hesitate to declare that he saw blue and red in the purple, or green and blue in the blue-green. The yellow, in this regard, resembles white in which the eye no longer distinguishes any trace of the component colors. The yellow is also that one of the spectral colors, which, to the eye, seems to offer most resemblance to white. Another peculiarity of the yellow, on which Herschel laid stress, is the considerable change which this color undergoes when its brightness diminishes. A dark blue still seems blue, while a dark yellow appears brown, a color which the observer not prejudiced would con- sider rather as a special color. We can obtain the impression of white in many different ways. The celebrated experiment by which Newton combined by means of a lens all the colored rays of the spectrum in a white image shows, in the first place, that all the colors of the spectrum, when mixed, give white. The equa- tions of Maxwell furnish a long series of examples of the possibility of forming white by mixing three colors. Lastly the table indicates a great number of pairs of complementary colors, that is to say, colors which, mixed two by two in the proper proportions, give white. To find the color complementary to a given color, we have only to prolong the line which joins it to the white, until it meets the curve again. The point of intersection is the place of the complementary color, and the quantities to take of both colors are inversely proportional to their distances from the white. We must recollect, however, that if we wish to express the quantity by the width of the slit in millimeters, we must reduce the numbers, as already pointed out. A glance at the table shows that the green colors (greenish) from 57 to 49.5 have no complementary colors in the spectrum. Their com- plementaries are the purple colors. The complementaries of the red extremity, up to 61, are situated very near one another (from 49.5 to 49.2), those of the blue extremity are condensed near 57. The hue varies, therefore, very slowly towards the extremities of the spectrum, while the variation reaches its greatest rapidity in the blue-green, where the divisions are separated by very marked intervals. Maxwell did not determine the extreme parts of the spectrum; one might think, therefore, that the curve ought to be really more extended ; but, according to the researches of Koenig and Dieterici, this is not the case. These authors made a long series of very minute researches, like those of Maxwell, with their large spectral instrument. Their results 260 PHYSIOLOGIC OPTICS seemed to agree well with those of the latter author; however, they could not verify the bend which the curve of Maxwell makes in the red. According to these authors, the hue does not vary in the spectrum beyond 67 and 43, so that the divisions beyond these limits must on the table coincide with these limits. Maxwell, indeed, himself calls the form of the extremities of the curve somewhat doubtful. If we compare the complementary quantities of red and blue-green, we notice that the red appears darker than the green. To illustrate facts of this kind on the table, Helmholtz supposed as equal quantities of two different colors quantities appearing to have the same brilliancy. He thus obtained the spectral curve illustrated in figure 164. The small circle indicates the position of the white. Since the red complementary Yellow Violet Purple Fig. 164. Color table of Helmholtz. to the blue-green appears darker than the latter, we consider its quantity as smaller and place it consequently farther from the white. Indeed, such a comparison of the brightness of two different colors is not easy, as Helmholtz himself remarked, and the result depends besides on the phenomenon of Purkinje. If, for example, a certain quantity A of yellow light appears to have the same brightness as the quantity B of blue light, we find that the quantity ~ of yellow light will appear darker than the quantity -|- of blue light. The form of the curve would vary, therefore, according to the brightness used. Maxwell showed how, without the help of a spectral instrument, we can make determinations analogous to his own by means of the revolv- ing disc of Masson. It is necessary to have paper discs (colored, whites and blacks) of two different sizes, so as to be able to make two mixtures at once, by covering the central part of the large disc with the small ones. We cut the discs along a radius, in order to be able to combine them so as to obtain colored sectors of any angle. We select three standard colors, the red, green and blue, and we combine three large discs so as to have a sector of each color. In the middle we place two small discs combined so as to have a black and a white sector. Making the whole THE COLOR SENSE 261 rotate, we obtain in the middle a gray circle, surrounded with a ring tinted with the mixture of three standard colors. By regulating the angles of the sectors we make the two tints alike, and write the equation as thus : 165 R -f 122 G + 73 Bl = 100 W -f 260 B (Aubert) W denotes the white, B the black, and the numbers indicate the angles of the sectors. Neglecting the little light reflected by the black, we may write : 165 R 4- 122 G + 73 Bl = 100 W To express any other color, the yellow for example, by the standard colors we replace the red sector by a sector of this color. Regulating the size of the sectors, we find for example : 146 Y + 17 G 4- 197 Bl = 159 W + 201 B or, by dividing by 1.59, 92 Y + 11 G 4- 124 Bl = 100 W We then combine this equation with that of the standard colors^ which gives 92 Y + 11 G + 124 Bl = 165 R 4- 122 G + 73 Bl or 1 Y = 1.97 R 4- 1.21 G 0.55 Bl With these equations we can construct graphic illustrations of the same kind as figures 160 and 162, and, by always working with the same kind of papers, we may thus study and compare the color sense of differ- ent eyes; but the spectral method always remains superior. 109. Abnormal Trichromasia. If we examine a certain number of persons by the method of Maxwell, on constructing the color table of each person, we often find small differences : a mixture which one ob- server declares like white, seems to another colored. It is probable that these differences are due, at least in part, to the fact that a portion of the rays is absorbed by the media of the eye, and that this absorption is more pronounced in some persons than in others. Thus the yellowish color of the crystalline lens of old persons indicates that it must absorb a part of the blue rays. A mixture of yellow and blue, which, to a normal person, appears equal to the white, must appear yellowish to the old person, whose crystalline lens absorbs relatively more of the light of the mixture than of the white light. After extraction of a cataract, the patient often, at the first moment, affects to see all blue, almost as U62 PHYSIOLOGIC OPTICS everything appears tinted with the complementary color when we have looked for a little while through a colored glass and then remove it suddenly. Maxwell attributed some of the phenomena in question to the absorption of the green-blue rays by the yellow pigment of the macula. Looking at a bright line through a prism, he observed a dark spot corresponding to the fovea, which moved up and down with the look, as long as the latter remained in the blue part of the spectrum, but which disappeared as soon as the look left the blue. He recom- mended also, in order to observe the phenomenon, fixing a yellow paper for a little while, and then transferring the look to a blue paper. The spot then appears for some moments. Taking two equal whites, one made of ordinary white light and the other of a mixture composed in great part of green-blue rays, the latter, seen in indirect vision, seemed greenish and more luminous than the former. We have seen (page 198) that the existence of the yellow pigment of the macula may appear doubtful, but the fact that the macula is less sensitive to blue than the remainder of the retina is unquestionable. I do not see the scotoma in the blue part of the spectrum, but another observation which I have made is equally convincing. There exist in commerce transparent sheets of colored gelatine which may often with advantage replace the colored glasses in many experiments. I have such a sheet, tinted probably with an aniline color, which allows the red and blue rays to pass. When, looking at the sky, I put this sheet before my eye, I see at the point fixed a somewhat diffuse red spot, almost the size of the moon or a little larger. After an instant it dis- appears; if then I remove the sheet without changing the direction of the look, I see the after-image of the spot, very slightly greenish and clearer than the surrounding parts. The color table of Maxwell himself differs somewhat from that of Mrs. Maxwell, illustrated in figure 160, differences which could very well be due to the fact that inferiority of the macula for the blue was more pronounced in him than in her. Neglecting these slight differences, an equation of color which is true for a normal eye, remains true for all eyes as weU for normal yes as for dichromatic eyes. This latter assertion was considered entirely general, until Lord Rayleigh, in 1880, discovered a class of eyes for which it is not true. After having produced a mixture of spectral red and spectral green which appeared to him identical with spectral yellow, he asked a certain number of people to compare the two hues. Most of them found the hues identical, but some, amongst whom were his three brothers-in-law, THE COLOR SENSE 263 declared that they saw scarcely any resemblance ; the pure color ap- peared yellow to them, while the compound color seemed to them nearly as red as sealing wax. To see the hues alike, these persons had to add so much green to the mixture that it appeared nearly pure green to a normal eye. The mixture of Lord Rayleigh was 3.13 R + i.oo G; that of his brother-in-law 1.5 R + i.o G. (i) The persons in question presented no other anomalies of the chro- matic system ; they were by no means dichromatics (daltonists). Later re- searches (Bonders, Kcenig and Dieterici) confirmed the opinion of Lord Rayleigh that these people formed a group by themselves: no inter- mediary forms have been found between their anomaly, which Kcenig called abnormal trichromasia, and the normal chromatic system. The anomaly seems almost as frequent as dichromatism ; Kcenig and Dieterici found three cases of it among seventy persons examined, but no case is known in which the anomaly was discovered by the person himself who was affected. 110. Color-Blindness or Dichromasia (Daltonism). The most preva- lent form of dyschromatopsia is called daltonism after the celebrated English chemist, Dalton, who was affected with it, and who gave the first fairly exact description of it. It is calculated that about 4 per cent, of men are affected with this anomaly ; it is much rarer in women, especially in its complete form. For the daltonists, there is in the spectrum a place, in the green-blue, the color of which resembles white (gray). We call this place the neutral point. Instead of the great variation which the normal eye perceives in the spectrum, the daltonists see only two colors: one which they most frequently call yellow, and which fills the entire part situated between the neutral point and the red extremity, and the other which they call blue, and which extends from the neutral point to the violet extremity. In no part belonging to either of the colors does the hue change ; there are differences of purity and brightness only. The color called yellow seems to them pure in the red, orange, yellow and green, until about 0.54 P. or 0.53 \L near the line E. In all this part there are differences of brightness only ; we can make one of these colors like any other color by changing the brightness. The red and orange of the spectrum are often so feeble that they are not perceived unless the spectrum is very clear. Starting from the line E, the color becomes more and more grayish, and (1) The numbers are not comparable with those of Maxwell, Lord Rayleigh having probably used colors different from the standard colors. Otherwise Maxwell and Mrs. Maxwell would both have be- longed to the category of abnormal trichromasia, which is not at all probable. 264 PHYSIOLOGIC OPTICS at the neutral point in the neighborhood of 0.50 />- (see fig. 165) the color is like gray. The brightness diminishes at the same time ; generally, the daltonists tell you that the parts situated near the neutral point are darker than those situated at some distance away from it. It is possible that this diminution of brightness is due to the fact that the neutral point is situated in the green-blue part of the spectrum, the rays of which are most affected by the influence of absorption in the yellow pigment of the macula, a phenomenon which often seems very pronounced in the dichromatics. Starting from the neutral point the other color called blue begins to make itself felt: gaining in purity, it becomes pure at about 0.46 /*, and, starting from this point, presents differences of brightness only ; the maximum is near the place where the color becomes pure. The dichromatics see, therefore, in the spectrum only two colors, but it is difficult to tell which. If we designate the colors as yellow and blue, it is not a sure sign that the spectral colors give them the same impres- sions as those which we obtain by yellow and blue. Generally speaking, it is impossible to communicate to any one the nature of a sensation which we experience otherwise than by a comparison. If, for example, one man told another that an object had a sugary taste, he only means to convey that the object gives him a sensation similar to that which sugar would give him. The other can then verify this if he also finds that the taste of the object is similar to that of sugar, and if he finds it so he will say that the former has a normal taste; but it is impossible to tell whether the object has the same taste for both. As we cannot know how the daltonists see colors, Donders proposed to replace in their case the expressions of yellow and blue colors by those of warm and cold colors, terms which are in use among painters. We must observe, however, that while in all other known cases the daltonism was bilateral, there exists in literature a unique case of uni- ocular daltonism ; it is clear that such a patient would be well qualified to give information on the question of knowing how the daltonists see the colors. The case was very well investigated by Hippel. The left eye was normal, while the right eye, which squinted, but which had been operated on and presented no ophthalmoscopic lesion, showed an anomaly wholly analogous to ordinary daltonism. The neutral point (situated at 0.512 /*) divided the spectrum into a yellow part and a blue part. The red and green of the spectrum were, in hue, similar to the yellow, but appeared a little less bright. Now, looking at the yellow sodium line, first with one eye and then with the other, the subject de- clared that the appearance was the same for both eyes, apart from a THE COLOR SENSE 265 slight diminution of brightness for the dichromic eye. It was the same for the blue indium ray as for the white. If, therefore, we can consider the case of Hippel as a case of true daltonism the difficulty seems solved. The sensations which the daltonists designate as yellow and blue would be identical with those of normal persons. As color-blind persons recognize the equation of the normal eyes, the colors which are complementary for normal eyes are also complementary for them. It follows that the color complementary to the neutral point Green Bluish-Green Yellow Fig. 165. Color table of Maxwell must also appear gray to them (or be invisible), as well as all the colors situated on the diameter of the table which joins them. As the colors next to the neutral point appear strongly mixed with white, their com- plementaries, as long as they are in the spectrum, must appear of very little brightness, since they must neutralize only the little chromatic value which is in these grayish colors. 26G PHYSIOLOGIC OPTICS While an equation of colors, which is true for a normal eye, is so also for the color-blind, the reverse is not true : color-blind persons recognize as similar, mixtures which are by no means so for a normal eye. For a daltonist, we can reproduce the impression of any color of the spectrum, as well as that of white, by mixtures of two colors. On account of this peculiarity, the anomaly in question is also termed dichromasia. Maxwell used two of his standard colors, green and blue. He thus found, for a dichromatic student, the equation 4.28 G + 4.20 Bl = W. The position of this mixture color is marked on the table (fig. 165) by the letter k; the letter K indicates the corresponding spectral color, which is the neutral point. As the daltonists recognize the equations of the normal eyes, we can combine this equation with that of the normal eye (page 253) 2.36 R + 3.99 G + 3.87 Bl = W. We have, therefore, for the daltonist 2.36 K + 3.99 G -f 3.87 Bl = 4.28 G -f 4.20 Bl, an equation which we can also write L = 2.36 K 0.29 G 0.33 Bl = 0. This latter color would not, therefore, produce any impression on the dichromatic eye and would represent, up to a certain point, the element which is wanting in it. Its place is marked by the letter L on the table (fig. 165). As L is situated outside the spectral curve, it is a fictitious color which really does not exist, but which we must suppose still purer than the corresponding spectral color which is marked /, since it is situated farther from the white than the latter. Compared with L, / is to be considered as a mixture of white. Nor is it wholly invisible, but very feeble. For his daltonist, Maxwell succeeded in reproducing all the colors of the spectrum by mixtures of his two standard colors. The results are represented by the curves in figure 166. Moreover, it would be simpler to select two colors which appear pure to the daltonists, as van der Weyde and latterly Kcenig and Dieterici have done. The green color of Maxwell seemed to the daltonists slightly mixed with gray, as the curves show. On the table of colors the whole chromatic system of the daltonists is reduced to a straight line (fig. 167), since all the colors which we can produce by mixing two given colors must be placed on the straight line THE COLOR SENSE 267 which joins them. The line, too, corresponds only to the part of the spectrum in which the colors are seen mixed with white, because all the parts where the colors seem pure, must come together in the two points which form the extremities of the line. Examining a series of daltonists, we observe that the position of the neutral point is not exactly the same in all. It varies in different persons between 0.492^ and 0.502 //. In figure 165 these two points are marked 0,8 62 60 . 68 56 5* St -Sfl %8 * ** ^ A V Or. Y G Bl I Fig. 166. Color curves of a dichromatic, after Maxwell. R and S ; it is, therefore, between R and S that the position of the neutral point may vary, and consequently, the direction of the neutral diameter would vary between RT and SQ. There results a certain difference between daltonists whose neutral point is situated nearer R, and those in whom it is situated nearer S. In the former, the neutral diameter passes through the green-blue and the red (i), and the spectrum seems shortened, because the red extremity contains the colors complementary (338 51 Fig. 167. Color table of a dichromatic, after the measurements of Koenig and Dieterici. to the grayish colors and must, consequently, as we have seen, appear very dark. In the others, the neutral point corresponds to a color situ- ated nearer the green, the complementary of which is purple, and not (1) In order not to depart from the terminology which is generally used, I hare designated the colors from 0.62 to 0.63 ^ as reds, but it must be noted that with the division of the spectrum which I have adopted in figure 151, and which was proposed by Listing, these colors are already in the orange. On the other hand, Chibret found with his instrument that the colon which the daltonists confound most frequently are the orange and blue. 268 PHYSIOLOGIC OPTICS found in the spectrum. As the colors complementary to the gray parts of the spectrum do not correspond to the red extremity, the latter pre- serves its ordinary intensity and the spectrum is not seen shortened. Guided especially by theoretical considerations (see page 273), it has been proposed to distinguish between these two forms by designating the former as anerythropsia (Rothblindheit), the latter as achloropsia (Griin- blindheit). It was Seebeck who first distinguished between these two forms ; but although he has been followed by a great number of scientists, among others by Hclmholtz, Holmgren, Leber and Kccnig, this distinction does not yet seem completely justified. If the neutral diameter had always either the direction SQ or the direction RT, it would be reason- able to distinguish between the two forms, but there seem to exist inter- mediary forms. The position of the neutral point is, moreover, not constant, even for the same individual : it is displaced a little towards the blue when we increase the brightness of the spectrum (Preyer). There have been described some very rare cases of anomalies of color vision, which are usually classified under the name of akyanopsia (Blau- blindheit). In these cases the neutral point would be found in the yellow- green, and the spectrum would be seen shortened at its blue extremity. But the existence of this form is far from being established. In cases of poisoning with santonine, we meet anomalies of color vision which are somewhat in accord with these observations, but these phenomena seem rather to be attributed to a slight transient coloration of the vitreous body. In consequence of the deficiency of their chromatic system, the dal- tonists are often exposed to errors, which are especially striking when they confound red with green. This is why Dalton used to walk in the street with the scarlet cloak of the Oxford doctors, thinking that it was black or gray. Cherries seem to them of the same color as the leaves of the cherry tree, etc. To understand these errors we must recollect that the colors of objects are never pure; they always contain white, and this is why red objects appear gray and not almost black like the red of the spectrum. In spite of these errors it is often astonishing to see how the daltonists know how to overcome their defect by making use of the differences which the colors present to them. Comparing, for example, red with yellow, they can frequently give their true names to these colors. The hue for both is the same, but the red appears to them less pure than the yellow, and they know that this less pure yellow is what is generally called red. They generally seem more sensitive to differences of brightness than normal persons do, and they can some- THE COLOR 8EN8E 269 times see traces of color which the normal eye does not discover. Thus Mauthncr relates a case, in which the daltonist claimed that he saw yellow on a sheet of black paper. On examining the paper it was found that it really did reflect a little of the yellow light, which had escaped the normal observer. 111. Monochromasia. There exists yet another anomaly of the color sense, which is very rare, but seemingly well-established, namely mono- chromasia. While color-blindness implies no other abnormality, mono- chromatic eyes manifest all other signs of weakness : photophobia, albin- ism, diminution of the visual acuity, etc. For these people differences of color do not exist; the only differences they perceive are differences of brightness, almost as on an engraving. The whole color table is narrowed to a point. The spectrum seems to them simply a luminous band, the brightness of which reaches its maximum, not in the yellow as is the case with the normal eye, but in the green (at about 0.52^). Bering emphasized the analogy which exists between the manner in which monochromatics see the spectrum, and the appearance which it presents to the normal eye when its brightness is very feeble. 112. Clinical Examination of the Color Sense. The method of mixing colors forms the fundamental examination of the color sense, and we can scarcely pass it over if we desire to form an exact idea of the chro- matic system of the person whom we observe; but the method is too complicated for clinical use, and it is, besides, completely dependent on the good faith of the person whom we examine. For the clinician it is important to be able to decide quickly and surely whether his client is a dichromatic or not. With this object in view different methods have been invented. It must first be noted that we obtain only little useful information by asking a color-blind person how he would term the color of such and such an object. If we present red to him, for example, it may not un- likely happen that he will designate this color as red, although he does not see it different from certain greens. The method most used is the test with colored yarns (Holmgren). We present to the subject the green shade of least purity and we request him to find the shades which resemble the latter, adding that they may be a little more or a little less pronounced. Besides green shades, the dal- tonist matches yellow grays, brown grays, red grays and pure grays. We then present to him pure purple. It is here that the alleged differ- 270 PHYSIOLOGIC OPTICS ence between the two kinds of daltonists becomes apparent. A person affected with anerythropsia would find that the blue and violet hues resemble pure purple, while a person affected with achloropsia would select the green and gray shades. Individuals who have only an incomplete color-blindness would stand the latter test, but not the former. Krenchel, Daae and others arranged colored yarns in the form of charts; Cohn used colored powders: Seebeck, who invented the method, used colored papers. On the tables of Stilling are arranged a great number of spots of two colors, selected so as to be seen alike by the daltonist. There are, for example, on one sheet complementary spots, red and green ; the .reds are arranged between the greens so as to form numbers visible to the normal eye, but invisible to the dichromatic eye, which sees all the spots of the same color. The tables of Stilling do not seem very good; it appears that there are daltonists who read them, and normal eyes which do not read them. The tables of Pfluger, which I have already men- tioned, are preferable; they are based on a phenomenon of contrast. The patient looks at a purple sheet on which are printed gray letters ; the whole is covered with tissue paper. A normal eye sees the purple ground through the tissue paper, and easily reads the letters which appear by contrast in the complementary color. The daltonist sees the ground gray like the letters, so that he cannot distinguish the latter. We can prove that the anomaly is not feigned by making the patient look through a colored glass. If the patient confounds green and red he should no longer confound them when looking through a red glass, for, as the green rays do not pass through this glass, the green must appear to him much darker than the red. Daltonists who need to be able to distinguish colors, chemists for example, may sometimes use with advantage a colored glass, which puts them in a position to dis- tinguish between two colors which they otherwise confound. Polarization instruments have been used to discover color-blindness ; Rose constructed the first instrument of this character ; the leucoscope of Kcenig is founded on the same principle. The best of these instruments is the chromatoptometer of Chibret. If we place a plate of quartz cut parallel to the axis between two Nicols, parallel to each other and form- ing an angle of 45 with the axis of the quartz, we see the plate tinted a certain color which depends on the thickness of the quartz. Making the Nicol nearest the eye (the analyzer) rotate around the axis of the tube, the color becomes less and less pure. At 45 the field is white, and if we continue to rotate the Nicol we obtain the complementary color, THE COLOR SENSE 271 which increases the purity, up to 90, when it attains its highest point. Replacing the analyzer by a double refracting crystal, a plate of spar, for example, which acts like two Nicols, perpendicular to each other, the field is seen double and one of the images of the field has the color complementary to that of the other. Rotating the spar, the colors be- come less and less pure, and at 45 the two fields are white. The hues of the two complementary colors depend on the thickness of the plate of quartz. In the instrument of Chibret, by placing the plate more or less obliquely, we can use a greater or less thickness, and thus obtain the whole gamut of colors. The instrument thus presents a very great number of hues and degrees of purity. The patient looks towards a window through the instrument. We place the index of purity ES (fig. 168), which regulates the position of the doubly refracting crystal, at 5, which gives colors strongly mixed with white, and after having put the index of the hues E G, which regu- lates the inclination of the quartz on the orange, at zero, we ask the patient if the fields are alike. If they are not, we rotate the index of the ESL Fig. 168. Chromatoptometer of Chibret. hues slowly towards the red, yellow and violet. If the patient always sees the two fields different we repeat the experiment after having placed the index of purity at zero, which makes the two fields white. He ought now to see them alike. If the patient stands these tests, he is not color- blind. If, on the contrary, in the first experiment he sees the two fields alike for a certain hue, he is color-blind. We then increase more and more the purity of these hues. If we thus succeed in producing a differ- ence between the two fields the daltonism is incomplete ; in the contrary case, it is complete. If there is question of persons who desire a certificate to be em- 272 PHYSIOLOGIC OPTICS ployed on railroads, or as sailors, etc., it may, in addition, be useful to examine whether they can distinguish signals. An aperture of 3 milli- meters diameter in a screen, covered with white paper, and illuminated from behind by a lamp, suffices for this examination. We place the person to be examined at 5 or 6 meters distance, and we see whether he commits errors when we place glasses of different colors before the aperture. 113. Hypotheses on the Mechanism of Color Vision. To explain the mechanism of color vision different hypotheses have been tried : the old ones were without any anatomical basis; the more recent have been more or less inspired by the discovery of the retinal purple. None of these hypotheses are satisfactory in character, and the facts known up to the present do not seem yet sufficient to explain the mechanism of color vision. Let us mention briefly these hypotheses. THEORY OF YOUNG. The following is how Young explained his hypothesis : "It is certain that we can produce a perfect sensation of yellow and blue by a mixture of green and red light and of green and violet light. There are reasons for supposing that these sensations are always composed of a combination of separate sensations. This sup- position at least simplifies the theory of colors ; we may, therefore, accept it with advantage until such time as we shall find it incompatible with some phenomenon. We shall proceed, therefore, to consider white light as composed of a mixture of three colors only, red, green and violet." According to this hypothesis, we suppose each nervous fibre of the retina composed of three fibres of the second order ; each of these three fibres would be provided with a special terminal organ (a photo-chemical substance) and also with a special central organ. An irritation of the first fibre would produce a red sensation, an irritation of the second fibre a green sensation and an irritation of the third a violet sensation. These three colors are termed principal colors. An irritation of the first two fibres would produce yellow, etc. An irritation at once of the three fibres produces white, and if none of the fibres is irritated, we have the sensation of black. The red rays irritate the first fibre, the green rays the second, the violet rays the third; the yellow rays irritate the first and second, and so forth. Young explained color-blindness by sup- posing that one of the fibres was wanting. One of the advantages of this hypothesis is that we can suppose the action identical in the three fibres. The action in the terminal organs must necessarily be different, but the one in which the impression is conducted to the brain may be THE COLOR SENSE 273 the same in the three cases. The difference between the three sensa- tions would be produced by the different reaction of the central organs. In this form the theory is very attractive, but does not accord with observations on color vision. It requires, indeed, that we can select three spectral colors so as to be able to reproduce all existing hues and degrees of purity by mixing them. But we have seen that this is not possible; there always remain some of the spectral colors which are purer than the mixtures. According to Young the color table must have an exactly triangular form, but the observations of Maxwell have shown that this is not the case. We cannot use, for example, the standard colors of Maxwell as principal colors, because we cannot reproduce with them the colors situated outside of the triangle. MODIFICATION OF THE THEORY OF YOUNG BY HELMHOLTZ. We must, therefore, suppose that the sensations corresponding to the prin- cipal colors are still purer than the spectral colors, for then their mix- tures could have the same purity as the latter. On the table the principal colors would then be placed farther from the center than the spectral colors, so that the triangle, which we would obtain by joining them, would complete the entire curve. Helmholtz supposed that each spectral color irritated the three fibres at once, but in a different degree. Thus the red rays would irritate the first fibre strongly, the other two feebly. The impression produced by the spectral red would already contain white. Helmholtz remarked, in this regard, that this impression is not the purest sensation of red that we can have. If we first produce an after-image of an object of the complementary color, before looking at the spectral red, the impression becomes much more vivid, because we would thus have fatigued the two other fibres. Helmholtz at first tried to explain color-blindness, as Young did, by the absence of one of the fibres. He supposed, therefore, three kinds of color-blindness : anerythropsia, achkropsia and akyanopsia. As we have seen, the last form is very doubtful, and the first two seem to become blended into one. But, there are yet other difficulties. Persons who are color-blind declare that they see yellow or blue in the spectrum, while, according to Helmholtz, they should see green and violet or red and violet. The hypothesis was saved by saying that it was not possible to know what they meant to convey by blue and yellow, but as this explana- tion became very doubtful, after the observation of Hippel, the hypothesis was modified once more by supposing that color-blind persons possess three fibres, but that in them the colors act equally on two of the fibres. 274 PHYSIOLOGIC OPTICS If, for example, the red rays act as much on the first as on the second fibre, they must produce a yellow sensation. It is the same for green rays. Taking the blue as the third principal color, we could thus ex- plain the manner in which color-blind people see the colors ; but all these modifications do not add to the plausibility of the hypothesis. THEORY OF HERING. This scientist assumes a "visual substance" which is a mixture of three others : one, which determines the sensation of black and white, another, which determines that of red and green, and a third, which determines that of yellow and blue. The red light acts on the red-green substance, causing a katobolic change (disassimilation) which produces the sensation of red. The green light, on the contrary, would cause an anabolic change in this substance by its action (assimila- tion) which would produce the sensation of green. The same takes place in the case of the yellow and blue rays in relation to the yellow-blue substance. The intermediary rays act on the two substances alike. But all the rays act on the whitish-black substance, which Bering expresses by saying that these rays have besides their color value (Vaknz), a white value (Vaknz) also. It is not only the white light, but also the colored rays, which disassimilate this substance. If the two other substances did not exist, all the rays would produce a white sensation, but of differ- ent brightness. This is what takes place in the case of monochromatics (achromatics). If only one of the two substances is wanting we have the dichromatic system. Hering supposes, therefore, four principal colors: red and green, yellow and blue, and he thinks that we have a direct impression of the fact that these four colors are pure, and that the others, perceived by an action on the two substances together, are compound. The rivalry between these two theories, the first of which was inspired by observations on mixtures of colors, whilst the second seems to be derived especially from the study of after images, has formed the sub- ject of a great number of works ; the pupils of Helmholtz tried to prove that the hypothesis of Hering was false, and vice versa. It seems to me that both theories have suffered by it. The theory of Hering seems rather to give a statement of known facts, than to explain them. It is based on the fact, which it seems to me difficult to deny, that the human eye does not see any resemblance between the four principal colors of the spectrum, red, yellow, green and blue, while each of the interme- diary colors resembles two of the principal colors. But it must be noted that the red of Hering ought to be complementary to the green ; it does not correspond, therefore, to the spectral red, which, according to THE COLOR SENSE 275 tiering, already contains yellow, but to a purple color which we cannot readily claim to give the direct impression of a pure color, (i) It seems to me also that a theory which renders no account of the special situa- tion of the yellow among the colors, is necessarily insufficient. OTHER THEORIES. Among the more recent theories, we may cite that of Ebbinghaus, who supposes the existence, in the cones, of a green substance, the decomposition of which would produce the sensation of red and green, while the purple, by its decomposition, would produce the sensation of yellow and blue. Parinaud supposes that stimulation of the rods produces a sensation of non-colored light, while stimulation of the cones may produce all possible sensations, the sensation of colors and the sensation of white. The retina would have two systems sensi- tive to light, one monochromatic, the other trichromatic. The ideas of v. Kries almost agree with those of Parinaud. Arthur Kcenig exploited a theory which may be considered as a devel- opment of the theory of Young-Helmholtz. He supposes the red, green and blue as principal colors. According to Kcenig, the decomposition of the retinal purple into yellow produces the weak sensation of gray, which causes any color when it is sufficiently weak. Further decompo- sition produces the sensation of blue. Perception of the two other principal colors, green and red, is effected by the agency of the pigment cells, while the cones must be considered as dioptric instruments in- tended to concentrate the light on the epithelial layer. I have already mentioned that H. Miiller measured the distance of the retinal vessels from the sensitive layer by means of the parallax of the vessels, seen entoptically (see page 153). In collaboration with Zumft, Kcenig re- peated these experiments with spectral light. He found that the distance increases according as we approach the red end of the spectrum. The layer sensitive to green light, and especially that sensitive to red light, would, therefore, be situated behind the layer sensitive ta blue. The distance of these two layers exceeded even the retinal thickness, which led Kcenig to suppose that the perception of these two colors takes place in the epithelial layer. These experiments still need to be verified; Koster repeated them without success. Bibliography. In spite of the great number of works on color vision, this question still seems imperfectly elucidated. In the preface to his treatise on light which appeared a few years before Newton's works on optics, Huyghens said he would not speak of colors, " a question in which, up to the present, no one can pride himself on his success." It seems (1) Towards the periphery of the visual field there exists a dichromatic zone, in which we see only yellow and blue colon. A red object seems yellow at this place, while a purple color appears blue : it is the intermediary tint which corresponds to the red of Hering. 276 PHYSIOLOGIC OPTICS to me that this phrase, which was true at the time of Huyghens as to the physics of colors, may be applied to-day to their physiology. This subject has not yet found its Newton. Newton (I.). Optics. London, 1704. Lambert. Farbenpyramide. Augsburg, 1772. Dalton, Edinburgh. Philos. Journal. Vol. VI. CEuvres de Young, edited by Tscherning, p. 217-232. Purkinje. Zwr Physiologie der Sinne. II, p. 109, 1825. Seebeck. Ueber den bei manchen Personen vorkommenden Mangel an Farbensinn. Pogg. Ann., 1837, p. 177. Helmholtz (H.). Ueber die Theorie der zusammengesetzten Farben. Pogg. Ann., 1852, p. 45. Helmholtz (H.). Ueber die Zusammensetzung der Spectralfarben. Pogg. Ann., 1855, p. 1. Helmholtz (H.). Ueber die Empjindlichkeit der menschlichen Netzhaut fur die brechbarsten Strahlen des Sonnenlichts. Pogg. Ann., 1855, p. 205. Maxwell (C.). Experiments on Colors as Perceived by the Eye with Remarks on Color Blindness. Transact, of the Roy. Soc. ofEdinb. , XXI, 1855. Maxwell (C.). On the Theorie of Compound Colors and the Relations of the Colors of the Spectrum. Phil, trans., I860. Maxwell (C.). On the Unequal Sensibility of the Foramen Centrale to Light of Different Colors. Edinb. Journ., 1856, IV, p. 337. Hering (E.). in Lotos Prag. 1880-82-85-87. Rayleigh. Nature. Vol. XXV, p. 64, 1881. Mac de Lepinay and Nicati. Ann. de chimie et de physique. Ser. 5, t. 24, p. 289, 1881 et t. 30, p. 145, 1883. - Uhthoff ( W.). Ueber das Abhdngigkeitsverhdltniss der Sehschdrfe von der Beleuchtungsintensitdt. Grafes Arch. XXXII, 1886. Uhthoff (W.). Weitere Untersuchungen uber die Abhdngigkeit der Sahscharfe von der Intensitdt sowie von der Wellenldnge im Spektrum. Grafes Arch. XXXVI, 1890. Kriess (I. v.). Die Gesichtsempfindungen und ihre Analyse. Leipzig, 1882. v. Hip- pel. Grafes Archiv. XXVII, 3, p. 47. 1881. Krenchel ( W.). Ueber die Bypothesen von Grundfarben. Grafes Arch. XXVI, p. 91, 1880. Kcenig u. Brodhun. Experimented Untersuchungen uber die psychophysische Fundamentalformel in Bezug auf den Gesichlssinn. Acad. of Berlin, July 26, 1888, and June 27, 1889. Kcenig (A.) and Dieterici (C.). Die Grundempjindungen in normalen und anomalen Farbensystemen und ihre Intensitdtsvertheilung im Specfrum. Zeitschrift fur Psychol., IV., p. 241, 1892. Kcenig (A.) et Zumft (I.). Ueber die lichtempfindliche Schicht in der Netzhaut des menschlichen Auges. Acad. of Berlin, 1894, May 24. Kcenig (A.). Ueber den menschlichen Sehpurpur und seine Bedeutung fur das Sehen. Acad. of Berlin, 1894, June 21. Chibret. Chromatoptometre. Bulletin de la Soc. fr. d'opht., 1836, p. 336. Ebbinghaus (H.). Theorie des Farbensehens. Hamburg, 1893. Parinaud (H.). La sensibUite de Vceil nux couleurs spectrales; fonctions des elements retiniens et du pourpre visuel. Ann. d'oc. t. CXII, p. 228, 1894. Koster (W.). Ueber die percipirende Schicht der Netzhaut beim Menschen. Grafes Arch., LXI, 1, p. 1, 1895. CHAPTER XVIII. THE FORM SENSE 114. Central Visual Acuity. The power of distinguishing forms is a very complex faculty, which is in great part connected with the ocular movements. To judge of the form of objects we grope for them, so to speak, with the look. Nevertheless, indirect vision furnishes an idea of the form of objects. According to empiric ideas (page 219) it would be the observations made during the displacements of the look that would have taught us the meaning of the impressions obtained in indirect vision. The lowest angle under which two points can be distinguished from each other has been taken as the measure of the form sense. Astron- omers for a long time devoted attention to this question. Hooke, for instance, said that in order that a double star can be recognized as such by the eye, the interval must correspond to one minute, and moreover, that good eyes would be necessary to see two stars under these condi- tions. Later, the physiologists took up the question, generally by work- ing with a small grating the bars and intervals of which were of the same size. We place the grating towards the sky and try how far we can move away from it before the bars become confused. Care must be taken that the image formed on the retina is distinct, by correcting defects of refraction, if there are any. In accord with most observers Helmholtz found nearly the same angle as Hooke, that is to say, one minute, but it must be observed that it is neither the width of a bar nor that of the interval, but the sum of the two, which corresponds to this angle. Considering the anatomical structure of the retina, we would expect that the angle of least distinction would correspond to the size of a cone. In the experiment of Hooke we may suppose, indeed, that we can distinguish two stars if, between the two cones on which their images are formed, there is found a third, which does not receive any 277 278 PHYSIOLOGIC OPTICS impression (fig. 169). We may, therefore, conclude that the angular size of a cone must be smaller than the angular distance separating the two stars. In the experiment of Helmholtz, on the contrary, we cannot conclude that the size of the cone must be smaller than the angular size of the black bar ; for we can very well imagine a larger cone, the central part of which may be occupied by the image of the black bar, while the lateral parts would be occupied by a part of the images of the intervals, but which would receive, however, less light than the neigh- Fig. 169. Experiment of Hooke. The images of two stars (e, e) are formed on two cones separated by a third. Fig. 170. Measurement of the visual acuity by a grating, aa, Images of the bars separated by those of the intervals, bb. Fig. 171. Measurement of the visual acuity with a grating. Limit. All the cones receive the same impres- sion. boring cones (fig. 170). But we can conclude that the cone must be smaller than the angular distance separating the centers of the two neighboring luminous intervals (or, which amounts to the same thing, smaller than the sum of the black bar and a luminous interval), for if the size of the cones were equal to this distance, all the cones would Fig. 172. Experiment of Hooke, the optics of the eye being defective. Instead of distinct images the stars form diffusion spots ee, ee. receive the same quantity of light (fig. 171), and the bars would be con- fused. Thus the result obtained by Helmholtz is in agreement with that of Hooke. Placing the distance of the nodal point of the eye from the retina at 15 mm. the angular size of a minute corresponds to 6( yL 36 Q = 0.004 mm - In the fovea the size of the cones is about 0.002 mm. The visual acuity does not seem, therefore, to altogether reach the degree which we THE FORM SENSE 279 would expect according to the structure of the retina, probably on account of optic irregularities. It seems rare, indeed, that a luminous point forms its image on a single cone, and if it extends over several cones, it is not strange that the angle of least distinction is larger than the angular size of a cone (fig. 172). One might think that the least angle of visibility may serve as a measure of the form sense, that is to say, that we can measure it by determining what is the smallest visual angle under which an object may be seen; but it is evident that this angle depends solely on the luminous intensity of the object, for, in spite of their minimum angular size, we see fixed stars very well when they are sufficiently luminous. If the eye were optically perfect, so that the image of the star could be formed on the surface of a single cone, it is easy to see that the luminous impression which this cone may receive, if it be sufficiently strong, would suffice to make the object visible, even if the image did not occupy the entire surface of the cone. But, as a rule, the optic properties of the eye are not so good. Most people do not see the stars as points, but as small surfaces so much greater in proportion as the star is brighter; the image of the star is, indeed, a circle of diffusion composed of more or less luminous parts : when the light is feeble these latter parts disappear so that the star appears smaller. As long as the star is luminous the image, therefore, generally covers several cones; if the light diminishes the image may be formed on a single cone, but the visibility always depends on the brightness only. A comparison with the preceding experiment shows also that we cannot use the visibility of a single star as a measure of visual acuity ; the experiment would be identical with that of the grating, if we imagine two infinitely large bars separated by an interval corresponding to the star. We have seen that we may conclude that the angular size of the cone is smaller than the angular size of a bar plus an interval ; but this, in the present case, has no application. In clinics we use, for the measurement of visual acuity, the charts of Snellen or others constructed on the same principle. The letters are arranged so as to be seen under an angle of 5 minutes ; the lines which form the letters, as well as most of the intervals which separate them, are seen under an angle of i minute. We see that the normal acuity of Snellen corresponds to half of that which Helmholtz found, with his grating, in which each bar and each interval corresponded to a half minute. We have found also that the best eyes have a visual acuity which approaches 2 (\ or -}-) and we can be almost certain that if, with a good 280 PHYSIOLOGIC OPTICS illumination, the acuity is only equal to I, the eye presents defects suffi- ciently pronounced to be easily established. We have said that the angle under which the letters are seen cor- responds to 5 minutes. The angle being equal to the linear size of the letter divided by the distance at which it is seen, it is clear that the letters which are intended to be seen at a distance of 12, meters must have double the linear size of those which are seen at 6 meters. If the former are seen at a distance of 6 meters only, we say that the visual acuity is equal to ~ = ^ . Different authors, Javal among others, have observed that this way of designating the visual acuity is not very logical, and that we should, in this case, say that the acuity is equal to J, since the surface of the letter in question is 4 times greater than that which corresponds to the acuity I. In spite of the theoretical objections which may be made to it, the chart of Snelkn is, however, very practical. It is certain indeed, that some of the letters are much more easily read than others on the same line. The legibility of a letter is, indeed, a very complex affair, which is far from depending altogether on the size of the intervals separating the different lines. Attempts have been made to remedy this, some- times by making larger the letters which are read with difficulty, some- times by selecting only letters which are easily legible. These improve- ments are not widely employed, for they are without much utility; by using the chart we learn, in fact, very quickly the degree of legibility which each letter has for a normal eye. A more serious inconvenience is the small number of large letters, which frequently renders the deter- mination of refraction difficult in cases in which the acuity is not so good, because the patients learn the letters by heart. To have a con- stant illumination, it is well to place the chart in a dark place and to illuminate it with a gas jet provided with a reflector, which protects the eyes of the patient. The chart of Javal is transparent and placed by the side of the patient, who looks at it in a looking-glass. We thus achieve this result, that the letters, being opaque, are always seen perfectly black, and that the distance is double by reflection. The size of the letters increases in geometrical progression, which had already been proposed by Green. Burchardt had printed series of groups of dots of different sizes arranged after the principle of Snellen. The patient must be able to count the number of dots which compose a group. Many oculists followed the example of Snellen and constructed charts on the same principle. We still use the reading test types of Jaeger, the first fairly complete THE FORM SENSE 281 collection of characters of different sizes which had been used. The advantage which the chart of Snellen presents is that it has written upon it the distance at which the patient ought to be able to see each line, which enables oculists to examine the sight of all patients at a like dis- tance. This principle had already been applied by Stellwag. In 1891, Guillery proposed to measure the visual acuity simply by the distance at which we can distinguish a black point on a white ground. By comparisons with the letters of Snellen, he found that a black point seen under an angle of 50 seconds corresponds to the normal acuity ; at 5 meters it should have a diameter of 1.2 mm. This point is designated as No. i. No. 2 has the surface twice as large as No. i, and the patient who sees only No. 2 at 5 meters distance, has an acuity of J, etc. Each point is on a white square, sometimes in the center, sometimes below, sometimes in an angle, etc., and there are on the same line several tests side by side in which the point has the same size. The patient must tell at what part of the square he sees the point. It seems that we measure the visual acuity quite as well in this way as by the principle of Snellen y which is quite interesting, and shows that we cannot identify the exam- inations with the luminous point on a black ground with that made by means of a black point on a white ground. Javal constructed a small portable scale on the same principle: it is composed of small black squares, such that the side of a square is also equal to the diagonal of the preceding one. If the side is equal to I, the diagonal is V l2 + l2 = V 2 > which is the side of the following square; the diagonal of this latter is then 2, and so forth. In this manner the area of a square is always double that of the preceding square. RELATIONS BETWEEN VISUAL ACUITY AND ILLUMINATION. The visual acuity depends directly on the illumination of the chart, but it is quite difficult to determine the relation in a general way, because there are many different factors which affect it. Thus the relation must de- pend on the pupillary size, on the manner in which the pupil contracts under the influence of light, on the degree of optic perfection and espe- cially on the adaptation of the eye to darkness. Druault has made some researches on this question, by moving a candle (of stearine of 22 mm. diameter) towards the visual acuity chart, and noting the distance at which this light would allow each line to be read; the eye was in a degree of medium adaptation. In order to obtain high degrees of illum- ination, he replaced the candle by a lamp equivalent to fifty-four candles. The following table shows his results, taking as unit the illumination obtained by placing a candle at a distance of one meter. 282 PHYSIOLOGIC OPTICS Illumination. Acuity. 0.016 meter candles ............................. -^L = 0.075 .200 0.020 " " ........... ................. _yL = 0.15 J.UU 0.028 " " ............................. -J5- =0.21 0.047 " " ............................. -15- = 0.30 ou 0.12 " " ............................. -15- = 0.37 0.25 " " 30 ' 0.67 " " -||- = 0.75 1.50 " " -41- = 1.00 10 16.7 " " -15- = 1.25 5400 " " -15- = 1.50 We note that the acuity increases rapidly at first, then slowly, with the illumination, and finally there is need of an enormous increase of illumination in order to make the acuity rise from 1.25 to 1.50. Still increasing the illumination, the acuity would probably still increase, but very little, so that the curve indicating the visual acuity for the different illuminations would be a flattened curve much elongated and more or less like the curve of the light sense (fig. 148). I have already observed that the relation between the visual acuity and the illumination depends, furthermore, on the color of the light used (page 244). The theory according to which the layer of the cones and rods would be the sensitive layer, explains sufficiently well the acuity which we obtain with a good illumination, but it gives by no means a satisfactory explanation of the manner in which the acuity falls when the illumina- tion diminishes. 115. Peripheral Acuity. We determine the limits of the visual field with a perimeter or campimeter, by allowing the person examined to fix the center, and finding up to what limit the patient can still see the object in indirect vision. The distance of the eye from the plane of the campimeter, or from the arc of the perimeter, varies slightly for differ- ent instruments. The object is generally a white square (or a colored THE FORM SENSE 283 one), the side of which is about I centimeter. With the white object we thus find the absolute limits of the field; taking larger or brighter objects we scarcely obtain any more extended limits. It is otherwise for the examination with colors. It seems, indeed, that by taking sufficiently large and bright objects we obtain larger limits than by ordinary exam- ination. In clinics, we examine generally with the white, blue, red and green, and we find, as a rule, the field less extended in the order in which I have named the colors. If one finds different limits for the red and green, this is probably due to the fact that colors which are not com- plementary or which have a different brightness are used. Otherwise we ought to find the same limits. The visual acuity falls greatly as soon as the image is moved away from the fovea. If, for example, we fix the border of the chart of Snellen the acuity falls in consequence to J or -^-. Attempts have been made to determine the peripheral acuity according to the principle of Snellen, but the method is very difficult to use clinically, whilst another method introduced by Bjerrum seems to give good results. He simply repeats the perimetric examination with smaller and smaller objects. He uses a distance of 2 meters, placing the patient in front of a large black cur- tain; the objects used are small ivory discs of different sizes, fixed on black rods of i meter in length. The observer must wear black gloves. By thus examining, Bjerrum found as the limits of the normal field : Outside. Inside. Below. Above. Withadiskof 3 mm 35 30 30 25 - 6 mm 50 40 40 35 Normal limits 90 60 70 60 By this method we can frequently establish defects which we could not otherwise find. We thus meet cases of atrophy of the optic nerves, in which the field examined in the ordinary manner is normal, whilst the method of Bjerrum reveals considerable contractions. In glaucoma Bjerrum has, by his method, discovered scotomata scattered in the field, but which are generally connected with a spot of Mariotte by a lacuna in the form of a bridge. The paracentral scotoma is thus connected with the papilla by a lacuna which surrounds the upper or lower half of the macula. Its form indicates directly the course of the nerves. Sometimes it may be useful to repeat the examination with diminished illumination. More recently, Groenotuw has made analogous measurements with a black point on a white ground. He designates as isopters the lines drawn in the visual field through the points where the visual acuity is the same. 284 PHYSIOLOGIC OPTICS These methods are founded on the same principle which was used by Guillery for the measurement of central acuity. Their theory is still to be formulated. In the normal field there is only one interruption, namely, the blind spot which corresponds to the papilla. It was discovered by Mariotte, whose name it bears, and created at the time a very great sensation. From his discovery Mariotte drew this conclusion, that it is the choroid which is the sensitive layer of the eye, since it was absent in this place, and this idea was for a long time accepted. We can determine the form of the blind spot by the ordinary methods with the perimeter, and still better by placing ourselves at a distance of one or two meters. The spot has an elliptical form ; generally we succeed, on examining with a Fig. 173. Mariotte' s blind spot in my right eye, drawn by Holth. very small object, in following the big vessels a little outside of the papilla (fig. 173). If we do not succeed in following them farther, it is due to the lack of stability of the fixation. According to the researches of Dr. Holth, who drew figure 173, it is almost impossible to maintain an almost exact fixation for more than 5 or 6 seconds ; after this time the look makes involuntary deviations which may reach a third or half a degree, and after 20 or 30 seconds we frequently observe deviations which often exceed one degree. We can control fixation by using as the object of fixation a point marked on a small colored surface on a white ground. After a very short time we see the surface surrounded with a THE FOKM SENSE 285 border of the complementary color. The internal border of the spot of Mariotte is about 12 degrees from the point of fixation, and the diameter corresponds to about 6 degrees, or 12 times the diameter of the moon. PHENOMENON OF TROXLER. If we draw several black spots on a sheet of paper and fix one of them for some time, we see sometimes one, sometimes another of the surrounding spots disappear, to reappear a little while after, generally at the moment of winking or of making a slight movement of the eye. This singular phenomenon which was described at the beginning of this century by Troxler, has recently been Fig. 174. studied by Dr. Holth. The color of the background, as well as that of the spots, plays no part ; during the disappearance of these latter we see in their place the background only; the scotoma is, therefore, filled almost like the spot of Mariotte. Even the spot fixed may disappear after a long period of fixation. In order to study the phenomenon we can observe a regular diagram as in figure 174. For my eye the phe- nomenon begins after having fixed the middle for 8 or 9 seconds, that is to say, at the moment when the fixation begins to be less steady. From this moment the figure shows continuous changes: sometimes 286 PHYSIOLOGIC OPTICS one part of the figure disappears, sometimes another. An interesting fact is that most frequently the scotomata are not absolute : sometimes it is the horizontal lines which disappear at one place, while the vertical lines persist, sometimes the contrary takes place. These phenomena recall forcibly that which has been described under the name of antag- onism of the visual fields and which we observe, for example, when pre- senting in a stereoscope horizontal lines to one eye and vertical lines to the other. If we fix the center of a figure composed of concentric circles and radii, we see sometimes the latter, sometimes the circles. On a chess-board we see sometimes one, sometimes another of the squares disappear, and so forth. Holth even caused luminous objects to disappear, the moon for example; according to him small objects dis- appear even if we give them a slow motion. There is reason, therefore, to be on the guard against this source of error, if we wish to perform perimetry with precision. Bibliography. Hooke v. Smith, Robert. Court complet d'optique, translated by Peze- nas. Paris, 1767, p. 44. Troxler. Ueber das Verschwinden gesehener Gegenstdnde innerhalb unseres Gesichtskreiscs. Himly u. Schmidt. Ophthalm. BibllotJielc., 1802, II, p. 1. CEuvres dt Young, edited by Tscherning, p. 78. Stellwag T. Carion. Die Accommodationsfehler des Auges. Wien, 1855. Guillery. Em Vorschlag zur Vereinfachung der Sehproben. Arch. f. Augenheilk., XXIII, p. 323, 1891. Grcenouw. Ueber die Sehschdfe der Nelzhautperipherie und eine neue Untersuchungsmethode derselben. Arch. f. Augenheilk. , XXVI, p. 85, 1893. Bjerrum. Undersoegelsen of Synet. Copenhagen, 1894. S. Holth. Om det normale Synsor- gans Stirreblindhed. Norsk Magaeinfor Laegevidenskaben. August, 1895. BOOK III THE OCULAR MOVEMENTS AND BINOCULAR VISION CHAPTER XIX. THE LAW OF LISTING 116. Center and Axes of Rotation of the Eye. The movements of the eye are made freely in all directions; the extent of the field of fixation is about 55 in all directions. It is easy to prove that the soft parts which fill the orbit are incompressible : if we try to push the eye backwards, we meet with considerable resistance ; the movements of the eye are limited, therefore, to its rotations. These rotations are made, at least approximately, around a center which, according to the determinations of Bonders, is situated about 10 mm. in front of the posterior surface of the sclera, or 14 mm. behind the summit of the cornea. It coincides with the center of the posterior surface of the globe, supposed to be spherical. It is not certain that the center of rotation is exactly the same for movements in different di- rections. Danders, in collaboration with Dojer, determined the position of the center of rotation of the eye in the following manner. He first measured the diameter of the cornea with the ophthalmometer of Helmholts, and then placed a hair (a, fig. 175) stretched vertically in a ring, in front of the middle of the cornea. He then examined the angular size of the 287 2SS PHYSIOLOGIC OPTICS lateral movements of the look, which the observed person had to make, in order that the hair would be seen successively in coincidence with the left and right borders of the cornea. Let ACD (fig. 175) be one of these movements, p half the diameter of the cornea, and x the distance CE. Then we have p = xtg ACD, from which we can calculate x. Adding to Fig. 175. this distance the height of the cornea, we find the distance of the center of rotation from the cornea. Fig. 176. The six motor muscles form, as we know, three pairs, (i) which cause the eye to turn around three axes passing through the center of rota- (1) [This statement is only approximately true, as according to the careful measurements of Volk- mann, each of the six muscles of the eye seems to rotate the latter around its own axis. See paper by the translator in the Archives of Ophthalmology, Vol. XXVII, No. 1, 1898 : Are our present ideas about the mechanism of the eye-movements correct?] W. THE LAW OF LltiTINtt 289 tion of the eye. The axis of the external and internal recti is vertical. The axes of the two other pairs are situated in the horizontal plane. The nasal extremity of the axis of the superior and inferior recti, BA (fig. 176) is situated a little in front, so as to form an angle of about 70 with the visual line. The temporal extremity of the axis of the oblique muscles CD (fig. 176) is directed very much forwards; it forms an angle of about 35 with the visual line. The internal and external recti turn the eye, therefore, directly in- wards and outwards. The superior and inferior recti direct the look upwards and downwards, but at the same time a little inwards. The inferior and superior oblique direct the look either downwards or up- wards but at the same time outwards. The look is directed straight upwards by the combined action of the superior rectus and the inferior oblique, and the direction downwards is obtained by the combined action of the inferior rectus and superior oblique. The muscles make possible the rotation of the globe around any axis. This is all that it is of importance to know for the physiology of the eye. We must not think that the eye turns oftener around the axes which we have just described, than around the intermediary axes. It seems, indeed, that all six muscles are concerned each time the eye makes any motion; the axis around which the eye turns is, therefore, always different from the three which we have just mentioned. 117. The Law of Listing. Supposing the head to be motionless, the position of the eye is determined for a given point of fixation. This is far from being evident a priori, for the eye could still perform rota- tions around the visual line. Each time that the look returns to the same point, no matter in what way, the eye always reassumes the same posi- tion (Bonders). If, by fixing a colored ribbon stretched horizontally, we produce an after image, and then project the latter on a wall, keeping the head motionless, the image assumes a position which is not always horizontal, but which is always the same every time that the look returns to a given point. This position is determined by the law of Listing. There exists a certain direction of the visual line in relation to the head, which we call primary direction; the corresponding position of the eye is named primary position, and every other position (direction) is called secondary. The primary direction generally corresponds to the direction which the visual line assumes when we look at the horizon, giving to the head the position which seems most natural ; but it happens quite frequently, however, that one is, under these circumstances, 290 PHYSIOLOGIC OPTICS obliged to lower the look slightly, in order to put the eye in the primary position. In this case, one is obliged to lean the head slightly backwards in order to make the primary direction horizontal. We must suppose this direction invariably connected with the head, in all the movements of which it partakes. According to the law of Listing, the eye may be brought from the primary position to any secondary position by a rotation around an axis perpendicular to the two successive directions of the visual line. This defines for us at the same time the primary position. The axes of Listing are all contained in a plane perpendicular to the primary direction and pass through the center of rotation of the eye. This plane is, therefore, as invariably, connected with a head. To demonstrate the law of Listing, we place ourselves at a distance of one or two meters from a wall on which is placed a fixation mark A (fig. 177), on a level with the eyes. It is necessary to make the position of the head secure. If we do not wish to make verv exact measurements, Fig. 177. a head-rest, like that of the ophthalmometer of Javal and Schioetz, suf- fices. If, on the contrary, we desire a very great exactness, we use the little mouth-board (planchette) of Helmholtz, the border of which is cov- ered with sealing wax. We squeeze the planchette between the teeth while the sealing wax is still warm, so that the latter may receive the imprint of the teeth. We then fix the planchette on a stand, so as to THE LAW OF LISTING 291 be able to turn it to the right or to the left or to incline it any number of degrees fixed upon (Hering). We place on the wall, at A, a rectangular cross so that its arms may be horizontal and vertical. The cross ought to contrast boldly with the background, so as to permit us to obtain a very pronounced after image by fixing it for a little while. We take the planchette between the teeth and, inclining the head (with the planchette) a little forward or back- ward, or inclining it a little to the right or to the left, we find a position such that on moving the look along the prolongation of each of the arms of the cross, the after image of this arm glides all the time on itself (fig. 177). We then observe that there exists only one position of the .head for which this is possible; for every other position of the head the after image of the cross turns around during the dis- placement of the look. When we have found this position of the head, we fix the planchette, so as to be able to again find the position every time that we take the planchette between the teeth. Then, when we fix the point A, the eye is in the primary position. Suppose, indeed, that XXX x --) c X X X "X Fig. 178. we fix a second point B, situated on a prolongation of the horizontal arm: since the meridian which was horizontal when fixing A, is also horizontal when fixing B, it is clear that the look may be brought from A to B by a motion around a vertical axis, that is to say, around an axis perpendicular to the two directions of the visual line. It is the same for displacement in the vertical direction. In order to demonstrate that this is also the case for the oblique displacements, we tilt the cross (fig. 202 PHYSIOLOGIC OPTICS 178). It is then easy to prove that the after image of one of the arms of the cross glides all the time on its prolongation, when the look follows this prolongation, and that, consequently, the eye turns around an axis perpendicular to this meridian. The law of Listing is thus verified. If, in these experiments, the look does not follow the prolongation of one of the arms of the cross, we observe phenomena which might seem in contradiction with the law of Listing. Thus fixing the point C (fig. 177) we observe that the after image of the vertical arm of the cross is no longer vertical ; it has undergone a rotation, and the upper extremity is carried to the right. A little reflection shows that this is simply a con- sequence of the law of Listing, and that the meridian which was vertical when fixing A, cannot remain vertical when the eye turns around an axis perpendicular to the direction AC. Bonders, who first described this phenomenon, attributed it to a rotary movement (Raddrehung) of the eye, that is to say, a rotation around the visual line, but it is clear that such a rotation cannot take place since the axis of Listing is per- Fig. 179. pendicular to the visual line. The horizontal arm of the cross seems to have suffered a rotation in a contrary direction, but this is merely the result of the projection of the after image on a plane which is not perpendicular to the visual line, (i) If we project the image on the con- (1) [How much these after images ought to be inclined towards the horizontal and vertical lines of the wall has been explained by the translator in a paper entitled "The Law of Listing and Some Dis- puted Points about Its Proof." Archives of Ophthalmology, Vol. XXVIII, March, 1899. The relation between these angles and the angles of Helmholtz is elucidated in a paper by Dr. O. Hay in the Journal of the Boston Society of Medical Sciences, in Oct., 1899, and in a paper by Professor L. Hermann, in Pfliiger's Archiv der Physiologic, Nov., 1899.] W. THE LAW OF LISTING 293 cave surface of a hollow hemisphere, in the center of which is the eye, the cross remains rectangular and seems to have suffered a complete rotation to the right (fig. 179). In these experiments, the position of the two eyes is exactly the same: we can cover sometimes one eye, sometimes the other, and the position of the after image does not change. It must be noted that the eye may be transferred from the primary position to a secondary position, by rotating around the axis of Listing. I do not say that it really makes this movement, for the law of Listing defines solely the position of the eye in the state of repose. We know nothing, or almost nothing, of the manner in which the eye makes its movements. There is no reason to assert that it turns around the axes of Listing, nor even to suppose that the look always follows the same way to go from one point to another. The best method of studying this question would probably be to bring the look quickly from one point to another, leaving the eye exposed to a pretty intense light. The after image of the luminous source then assumes the form of a line which permits some conclusion as to the nature of the movement. What we have said suffices to determine any position of the eye. If the look passes from one secondary direction to another, the position of the eye is nevertheless determined by the law of Listing, since, having reached its new secondary position, it must have the same position as if it had reached there, starting from the primary position. Note that the look cannot be brought from one secondary position to another by turning around an axis perpendicular to the two directions in the visual line. For, if the look goes from B to C (fig. 177), following the pro- longation of the vertical arm, we observe that the after image of this arm starts from the prolongation and rotates more and more so as to attain the position which it should have when the look will have arrived at C. In making this movement of the look, the eye does not rotate, therefore, around an axis perpendicular to the visual line, and we can in this case speak of a true rotary movement. If we displace the look so that the after image moves always on itself, the point of fixation de- scribes a curve the convexity of which is turned towards the point A. It is the same for the horizontal arm : if we bring the look from C to E, so that its after image moves on itself, we obtain a curve with its con- vexity downwards. The following illusion, described by Hclmholts, re- sults from this fact. If, after having fixed the point A in the primary position, we raise the eyes and survey quickly with the look a horizontal straight line 294 PHYSIOLOGIC OPTICS situated higher up, it appears concave towards the floor (compare page 217). This is due to the fact that oblique directions of the look are very rare. Generally, we take care when we desire to look at any object, to turn the head in such a way that the eyes are nearly in their primary position, and that the horizontal lines are drawn on the retinal horizon (the meridian of the retina which is horizontal in the primary position: in the experiment fig. 177, the retinal horizon is marked by the after image of the horizontal arm of the cross). On account of this custom we have a tendency to consider the direction of the retinal horizon as horizontal, even when it is not. Looking upwards and to the left, the retinal horizon inclines its right extremity downwards, and, if we con- sider this direction as horizontal, it follows that the straight line which we observe must appear inclined to the left; when the look reaches the other extremity, this latter will seem inclined to the right; thus it is that the line assumes its curved aspect, but we must survey it quickly, otherwise it seems rather to lean sometimes to the right, sometimes to the left. ANOTHER METHOD OF DEMONSTRATING THE LAW OF LISTING. As the retinal horizon passes through the papilla, we can use the position of the spot of Mariotte to account for its direction. Pick drew, on a card- board movable around a point O, a black spot just large enough to dis- appear in the spot of Mariotte, when he fixed the point O in the primary position. Turning the head to the right or to the left and inclining it at the same time, while he continued to fix the point O, the spot reappeared and he then measured how much it was necessary to turn the cardboard to make it disappear again. Proceeding thus, we find, as by the pre- ceding method, that the eyes follow pretty exactly the law of Listing, at least while the visual lines remain parallel. 118. Experiments of Meissner. Apparently vertical meridian. There exists another method which has been described by Meissner, and which enables us to verify the law of Listing in a very exact manner. But before explaining this method, I must mention a singular phenom- enon which we meet when we wish to judge whether a line is vertical or not. We hold a plumb-line in front of a wall painted uniformly and we fix a point situated a little in front of this line (i) : we then see the latter in double homonymous images, and we would expect to see two vertical (1) We must not place ourselves too near the line, in order that the influence of convergence, of which I shall speak immediately, may not interfere. TEE LAW OF LISTING 295 and parallel lines; but the two lines seem to converge upwards: seen with the right eye, the upper extremity of the line seems to lean to the left. If we fix a point situated behind the line, the images are crossed and seem to converge downwards. A vertical line seen with one eye only does not, therefore, appear vertical, but its upper extremity seems to lean to the left or to the right, according as it is the right eye or the left eye which looks at it. Looking at a rectangular cross, one of the arms of which is horizontal and the other vertical, the two angles, the upper right and lower left, will appear, for the right eye, larger than the other two, while the contrary takes place for the left eye. Since, for the right eye, a vertical line appears to lean to the left, there must exist a line leaning to the right, which seems vertical. We can determine the direction of this line by observing a white disc movable around its center and on which we draw one diameter. Along the border is a scale graduated in degrees, the zero of which corresponds to the vertical line, and which must be placed so as not to be visible. The observer tries to turn the disc so as to place the diameter vertically. With the right eye he places nearly always the upper extremity some degrees too far to the right, with the left eye some degrees too far to the left. For the horizontal meridian, the phenomenon is less pro- nounced. It is necessary to arrange the experiment in such a manner that the observer cannot be guided by the view of the surrounding objects. Another method of determining the angle between the apparently vertical meridians of the two eyes has been described by Volkmann (fig. 1 80). He placed two small revolving discs on a vertical wall so that the distance separating their centers would be equal to the distance between the eyes. On each disc was shown one radius. He observed the discs as with the stereoscope, the right eye fixing the disc on Fig. 180. Discs of Volhnann. the right, the left eye that on the left. He placed one of the radii ver- tically, and then tried to place the other so that the two radii would 29G PHYSIOLOGIC OPTICS appear to form a single straight line ; it was necessary that they should form an angle of about two degrees. Among the stereoscopic tests which are given in Javal's manual on strabismus, several show small discs like those of Volkmann, on which the two radii are exactly parallel. On overlapping the two discs they form only one, but the diameter appears broken; the two radii seem to form an obtuse angle. If we pre- sent to the right eye the figure which was intended for the left eye, the angle seems turned in the opposite direction. It is probable that these phenomena are due to the more important part played by the downward look in everyday life : we look downwards when reading, and when walking the look most frequently follows the ground, etc. By repeating the experiment of Meissner, we will find that the two images appear parallel if we bring the lower extremity of the plumb-line towards the observer, until, in relation to the line of the look, it has almost the inclination which a book has when we hold it in the ordinary position of reading. If we draw a straight line on a sheet of paper placed on a table so that this line is in the median plane of the observer, we see, on placing ourselves in the position which we ordi- narily assume in order to read or write, making the visual lines parallel, that the two images of the line appear parallel. Glancing at figure 181, in which the eyes are shown projected on the table, it is easy to see that the extremity A of the line which is nearest the observer forms its image on more peripheral parts of the retina than the extremity B. The two meridians of the retinge which receive the images, converge therefore downwards, since the extremity A forms its image higher and more towards the periphery than the extremity B. We have formed our judgment according to this experiment, and when, under other circum- stances, a line comes to form its image upon this meridian, we consider it as situated in the median plane. According to Javal, the experi- ments establishing binocular vision in persons affected with strabismus, confirm absolutely the preceding explanations. Fig. 181. One can understand how these methods may be used, if not to directly verify the law of Listing, at least to compare the position of the two eyes. Working in the primary position, and with the two visual lines parallel, Volkmann found that it was necessary to THE LAW OF LISTING 297 give to the radii of his discs directions converging about two degrees downwards, in order that they would appear to form an unbroken line. Leaving the visual lines parallel, he found the same angle for all sec- ondary directions, and the law of Listing was thus verified. It is other- wise when we converge. After having placed the eyes in the primary position, Volkmann converged for a point situated at 30 cm. in the same horizontal plane. Since, under these circumstances, the eyes pass from the primary position to an internal position, the law of Listing would have demanded that the directions of the two radii would continue to form an angle of two degrees ; but Volkmann found that it was necessary to increase their inclination to four degrees, in order that the resulting line would be seen unbroken. Converging, each eye had, therefore, made a rotary movement of one degree, which it would not have made by taking the same position, if the visual lines were parallel. The eyes do not, therefore, follow exactly the law of Listing when the visual lines are not parallel. The following experiment is very easy to perform. We place two candles, one meter from each other, and we observe them at one or two meters distance, taking care to put the eye nearly in the primary posi- tion. We then try to converge as if to fuse the two candles. We will then observe that they appear slightly inclined towards each other ; the nearer to each other we bring the candles, the greater the inclination ; the angle between the two candles may reach 15 or more. The image of the left eye is inclined, the upper extremity to the right and vice versa. Bering, and later Landolt, have made exact measurements of these devia- tions from the law of Listing. 119. Historical. The question of knowing whether the eye per- forms rotary movements around the visual line has been much disputed. Hneck thought that he observed that the eye undergoes a rotation in a reverse direction when the head is leant towards the shoulder so that the meridian of the retina, which is vertical in the ordinary circumstances of life, remains vertical. He attributed this rotation to the contraction of the oblique muscles, and his ideas were shared by all scientists until Ruete demonstrated the error of Hneck by means of the examination with the after images, and gave a correct explanation of the action of the oblique muscles. Bonders took up the question, and enunciated a law which bears his name, according to which the position of the after image is always the same for the same direction of the eye ; but the question was stated clearly only by the enunciation of the law of Listing, which 20S PHYSIOLOGIC OPTICS is found for the first time in the treatise of Ruete of 1853. Listing did not publish it himself. Meissner was the first who verified this law by experiments. After the experiments of Ruete and Bonders everybody supposed the rotary movements of Hueck did not exist, when Javal demonstrated that the eye performs, nevertheless, a very slight rotation in this direction. He had observed, indeed, that when he leant his head to the right or to the left the direction of the axis of his cylindrical glasses no longer coin- cided with that of his astigmatism. This is, perhaps, the most exact test to see whether glasses are properly placed. Helmholtz verified the fact by placing on a level with his eyes a small colored band on a frame fixed on his planchette. By leaning the head with the planchette, the secondary image turned a little in the opposite direction, so as no longer to coincide with the ribbon. Bibliography. GEnvres de Young, edited by Tscherning, p. 145. Hueck. Die Ach- sendrehung des Auyes. Dorpat, 1838. Donders (F. C.). Hollandische Beitrage, 1848. Ruete. Lehrbuch der Ophthalmologie, 1853. Fick (A.). Die Bewegungen des menschlichen Augapfels. Zeitschrift fur rat. Medizin, IV, 1854. Meissner (G.). Die Bewegungen des Auges. Arch. f. Ophth., II, 1, 1855. v. Helmholtz. Ueber die normalen Bewegungen des menschlichen Auges. Arch.f. Ophth., IX, 2, 1863. Volkraann (A. W.). Physiologische Un- ersuchungen im Gebiete der Optik. II. Leipzig, 1864. Donders and Doyer in Donders. Anomalies of the Refraction of the Eye. London, 1864, p. 180. Javal (E.). in de Wecker. Traite des maladies des yeux. I, p. 815. Paris, 1866. Tscherning (M.). La loi de Listing. Paris, 1887. CHAPTER XX. THE OCULAR MOVEMENTS. 120. Jerking Movements of the Eyes. It seems as if the eye should foe kept motionless in order to obtain an impression, at least an impres- sion which can be perceived with some distinctness. If, in a railroad train which is going quite fast, we fix a point on the window, the land- scape appears confused, the images of its different parts succeeding one another too quickly on the retinae to be perceived distinctly. Observ- ing the eyes of any one who is looking at the landscape, we see that -they move by jerks. The eyes of the person observed make alternately a rapid movement in the direction of the train to catch the object, and a slower movement in the opposite direction to keep the image of the object on the fovca. Then they again make a rapid movement with the train to catch a new object, and so forth. The eye cannot fix the same point for even a little while, without the formation of after images which annoy the vision, and without the phe- nomenon of Troxler interfering. The eyes are, therefore, in perpetual motion which is made by jerks: they fix a point, make a movement, fix another point, and so forth. While reading, the eyes move also by jerks, four or five for each line of an ordinary book. Lamare constructed a small instrument, formed by a point which is supported on the eye across the upper eyelid, and which is fastened to the ears of the observer by rubber tubes. With this instrument each movement of the eye causes a sound to be heard. We hear four or five slight sounds during the reading of one line, and a louder sound when we begin to read a new line. 121. Relative Movements of the two Eyes. The relative movements of the two eyes are governed by the necessity of seeing the object single. It is necessary for this purpose that an image of the object fixed be formed on each fovea. When, after having looked at an object at a certain distance, we look at another situated at the same distance, the 299 300 PHYSIOLOGIC OPTICS two eyes make associated movements : both turn to the right, or both to the left, upwards or downwards, etc., and one as much as the other. If the objects are both in the median plane, but at different distances, it is necessary, in order to bring the look from the more distant to the nearer, that the eyes make a movement of convergence: both turn in- wards to the same extent; finally, if the two objects are in different directions, the second nearer than the first, the eyes perform a com- bination of an associated movement and a movement of convergence. If the second object is situated farther away than the first, the eyes make a movement of divergence (negative convergence). It is impossible to cause a movement to be made with one eye without the other moving also, or at least without its having a tendency to move. A very simple experiment would seem to indicate the contrary. Sup- pose that the two eyes fix a point a, and that we place in the visual line of the right eye an object b. If we ask the observed person to fix b, the left eye is directed towards this point, while the right eye remains mo- tionless. But, if we observe closely, we shall see that this eye makes really two slight changes of position, for instead of receiving no innerva- tion, as one would think, its muscles receive two, one which would cause it to make an associated movement (to the right), and another which would cause it to make a movement of convergence (to the left) ; the results of these two innervations neutralize so that the eye remains motionless. It was Hcring who described this experiment, which is of great importance for the understanding of the relation between the movements of the two eyes. The two kinds of movements of which we have spoken are the only ones which the eyes have usually to make in the interest of fusion, and they are the only ones which they can make. It is possible, however, to make them diverge a little. I mean absolute divergence and not relative divergence, which is only a less degree of convergence. We can make this divergence necessary for fusion by placing before one eye a prism with its apex turned outwards ; but the angle of the prism which the eyes can thus overcome does not much exceed five degrees. We are unable to raise the look of one eye while leaving the other motion- less ; but by placing before one eye a very weak prism, apex upwards, this eye deviates a little, however, in the interest of fusion. The prism which we may thus overcome generally does not exceed two or three degrees. These peculiarities of the ocular movements are evidently not due to the muscular apparatus. There is, indeed, nothing to prevent the right THE OCULAR MOVEMENTS 301 eye from making a movement to the right, but it cannot make it while the left eye makes a movement to the left. If we cannot perform two movements at once, this is due to the fact that we cannot give the neces- sary innervation for this movement. And we cannot give this innerva- tion because we are not accustomed to give it, since, far from being useful, it would be harmful, on account of the diplopia to which it would necessarily give rise. The impulse which guides the ocular movements is, up to a certain point, analogous to that which makes us keep our eyes open and the head erect, with this difference, however, that the in- nervation which guides the movement of the eyes is much more rigor- ous ; we can lower the head or close the eyes if we desire to do so, but we cannot put the eyes in divergence. The innervation in question dis- appears during sleep. When struggling against sleep, we observe diplopia, and the two images affect relative positions which they never have in a state of wakefulness. The homonymous images which we obtain by squinting voluntarily are always parallel, if I except the phe- nomena mentioned in the preceding chapter, and they are at the same height (if the head be kept erect). The images which we obtain when sleep comes upon us have, on the contrary, wholly irregular positions : sometimes one is higher than the other, sometimes they undergo rota- tions, etc. At the same time the eyelids have a tendency to close and the head to fall. 122. Measurement of Convergence. - - This measurement is made pre- ferably with the rotary prism of Cretes. As we know, this instru- ment is composed of two superimposed prisms of the same strength. A special mechanism allows them to be turned in opposite directions. When the apices have the same direction, the effect is double that of each of the prisms.' If we cause them to rotate the deviation always takes place in the same direction, but it gradually diminishes and dis- appears when the apices are directed in different directions. The instru- ment replaces, therefore, a whole series of prisms of different strength. We place the prism with the apex outwards while the patient looks at a distant flame, and we increase the strength of the prism until the subject sees two images of the flame. We thus find abduction; for healthy eyes, it is five to seven degrees of prism. We then turn the prism apex inwards and increase its strength until diplopia is produced. Adduc- tion is much stronger than abduction ; it may reach 20 or 30 degrees of prism, or more. We can also measure adduction and abduction for a nearer point. Adduction often exceeds the maximum value of the prism 302 PHYSIOLOGIC OPTICS of Cretes, and on the other hand, it quite frequently happens that it is- greater than we find it at that moment, because the observed person: does not do his best to fuse the images. It would also be better to measure the adduction simply by trying how near we could approach an object without its appearing double (ophthalmodynamometer of Landolt). We sometimes meet rare cases of defect of convergence, where the adduction is greatly diminished, while the abduction is normal. In other cases both are diminished: the patient can fuse well two- images which are formed on the two maculae, but he experiences no need of fusion; even when the double images are very near each other,, the eyes do not make the slight motion necessary to fuse them. We have seen (page u) that the deviation produced by a prism cor- responds nearly to half its angle. If we can overcome a prism of six degrees, apex outwards, it is equivalent to saying that we can make the visual line diverge three degrees. This manner of indicating the degree of deviation is the simplest, and that which is most frequently used. It has been attempted to introduce another notation first described by Javal, and afterwards adopted by Nagel. This author names meter angle the deviation which one of the visual lines under- goes when, after having fixed a point at infinity, we look at a point situated at one meter distance on the visual line of the other eye. a> (fig. 182) is r therefore, a meter angle, if A is situated at a dis- tance of one meter; two meter angles, if A is at 50 centimeters, and so forth. The system was in- vented to measure the convergence in a manner analogous to the measurement in dioptrics which we use for refraction (accommodation). The meter angle corresponds to about three degrees and a half. This system seems to offer scarcely any advantages, and it has this quite serious disad- vantage, that the value of a meter angle is not the same for different persons. It varies with the base line. We call by this name the distance between the centers of rotation of the two eyes ; it varies between 66 mm. and 58 mm., or still less. We can measure it by sighting a distant object, a lightning rod for example, along the surface of a planchette held horizontally. We close one eye and fix a needle in the planchette, so that it may appear to coincide with the lightning rod. The needle must not be placed too near the eye Fig. 182. THE OCULAR MOVEMENTS 303 in order that its images may not be too diffuse. Then we repeat the experiment with the other eye without displacing the head ; opening the two eyes, we should see the two needles blended into one, which coin- cides with the lightning rod. The distance between the needles is equal to the base line. We find also very great variations, especially if we examine children, whose base line is manifestly very short. Now it is clear that the deviation which the eye must undergo, in order to pass from infinity to one meter distance, is so much more con- siderable in proportion as the base line is greater. A meter angle cor- responds to 34o' for a person who has a base line of 64 mm., to 32o' if the base line is 58 mm. To do well, therefore, it would be necessary each time we measure the convergence in meter angles, to tell also the length of the base line. Prentice proposed to number prisms according to the linear deviation which they produce at a given distance, observing that at a distance of one meter the deviation produced by a prism of one degree is about one centimeter. 123. Relations between Accommodation and Convergence. In the interest of single and distinct vision, it is necessary that there be formed on each favea a distinct image of the object fixed. In order that the images be formed on the two foveas, it is necessary that the individual make his eyes converge towards the observed object, and in order that the images be distinct, it is necessary that each accommodate exactly for the object. There is thus formed a relation between accommodation and convergence, so that we cannot easily converge towards an object without also accommodating for this object. The rule, however, is not absolute; we can, if it is necessary for distinctness of vision, change within certain limits the degree of accommodation without changing the degree of convergence. This play of the accommodation, which is possible while the convergence remains the same, has the name relative amplitude of accommodation (Bonders). We can measure this amplitude by placing convex and concave glasses before the eyes until the object appears double or diffuse. Bibliography. Javal (E.). In de Wecker. Trait $ des maladies des yeux. Paris, 1866. Donders. Anomalies of tie Refraction of the Eye. London, 1864. Nagel (A.). Ueber die Seziehungen dioptriscker Werthe und der Betrage symmetrischer Convergenzbeu'egungen nach mc- trisc.hen Einhciten. Mittheilunr/en aus der opktalmiatrischen Klinik in Tubingen. Tubingen, 1880. Lamare. Les mouvemenfs des yeux dans la lecture. Evil, de la Soc.fr. d'opht. 1882, p. 354. Prentice (Ch. F.). Ein metrisches System zur Bezeichnung IL. Bestimmwng v. Prismen. Archir. /. Augenheilk. XXII, p. 215. CHAPTER XXI. THE PROJECTION OF VISUAL IMPRESSIONS. 124. Projection Outwards in TJniocular Vision. In order to be able to form a correct idea of the position of an exterior object, it is neces- sary to be informed as to the direction and distance of this object. Judg- ment of the direction is formed as well, or better, with a single eye; the superiority of binocular vision is apparent in the judgment of dis- tance, but at the same time, in the matter of direction, it causes certain illusions from which persons blind of one eye are exempt. We shall first discuss the vision of these latter. GENERAL LAW OF PROJECTION. An impression of any point of the retina is projected outwards into the visual field, following the line of direction; that is to say, following a straight line passing through the retinal point and the nodal point of the eye. We have seen that in- versely, an exterior point for which the eye is focused forms its image at the point of intersection of the line of direction with the retina. As long as there is question only of objects seen distinctly, the law of pro- jection is equivalent to saying that we see exterior objects in the direc- tion in which they really are. The law of projection does not apply merely to the ordinary phenomena of vision : all the retinal impressions, the phosphenes, after images, entoptic phenomena, circles of diffusion, etc., are projected according to this law, which is entirely general. As exceptions we can cite only the deformities of objects seen indi- rectly, which seem to show that the law is not followed very exactly for very peripheral parts of the retina, and perhaps for some of the illu- sions which I shall mention later. 125. Projection of the Visual Field. The law which we have just announced regulates the manner in which we localize objects in the 304 THE PROJECTION OF VISUAL IMPRESSIONS 305 visual field, but it does not regulate the projection of the visual field in its entirety. The latter depends on the manner in which we judge the position of the eye, or rather the direction of the visual line. If in uniocular vision, we judge correctly the direction of the visual line, the entire visual field is projected in a correct manner. We shall, therefore, proceed to discuss the means by which we form this judgment. Supposing that we fix a point A, and that we desire to fix another point B. As long as we fix A, B is seen in indirect vision, and the dis- tance between the images enables us to judge of the degree of innerva- tion necessary to bring the look towards B ; generally this judgment is quite exact so that we bring the look towards B almost without hesita- tion. From innervation results the contraction of the muscles, the change of position of the eye and the change of the retinal image until B forms its image on the fovea. One might think that the sensation of the moie or less considerable contraction of the muscles, the gliding of the eye between the lids, etc., could furnish us with information on the direction of the visual line, but this is not so; we judge this direc- tion solely by the degree of innervation which we have used to bring the look into this direction. This fact is well established by the observation of patients affected with ocular paralysis. If, for example, we tell a patient affected with paralysis of the right external rectus to close his left eye and look to the right, he furnishes the innervation necessary; the eye remains motionless on account of the paralysis, but the patient thinks he has moved it to the right, so that there results a false projection; if we tell the patient to move his finger rapidly towards an object situated to the right, not having time to guide himself by the sight of the finger, he constantly moves it too far to the right. A healthy person can make the experiment by looking to one side, while he exerts a traction in the opposite direction on a fold of the skin, near the external canthus. The traction is communicated by the conjunctiva to the globe, and on account of the resistance which it exerts, one is obliged to use a stronger innervation to bring the look to the opposite side; we conclude from this that the look is carried farther in this direction than it really is, which causes projection of the visual field in a false manner. Judgment of the degree of innervation used is very exact, because it is always corrected by the result obtained, as the following experiment shows. One looks directly in front after having put a prism of ten de- grees, apex to the left, before each eye. Seen through the prisms, an object situated at ten degrees to the right, appears five degrees from the 3C6 PHYSIOLOGIC OPTICS visual line, and we need only an innervation corresponding to five de- grees to fix it ; we think, therefore, that it is situated at five degrees to the right, and, if we wish to grasp it, we do not bring the hand far enough to the right. But it suffices to repeat the experiment only a few times in order to be no longer deceived : we learn very quickly to reckon with prisms. If then we repeat the experiment after having removed them, we bring the hand too far to the right. When we judge correctly the direction of the visual line there is in monocular vision no possible illusion as to the direction in which objects are. In mathematics we often determine the position of a point by means of what are called polar coordinates. Being given a fixed point, named center of coordinates, the position of any other point is determined by the direction and length of the radius vector, that is to say, of the line which joins the two points. In uniocular vision, the center of coordi- nates is represented by the eye, or, more exactly, by its nodal point ; the law of projection gives the direction of the radius vector. To know the exact position of the exterior point, there is wanting, therefore, only the length of the radius vector, but this the eye does not give, at least not in a direct manner. It is easy, indeed, to convince oneself that while the eye informs us very exactly on the direction in which the light comes, it gives us no information as to the distance whence it comes. The information which the greater or less degree of accommodation used could furnish is too in- definite. In the tenth chapter I laid stress on the importance which the study of the form under which a distant luminous point is seen may have in the matter of exact knowledge on the optics of the eye. One might think that one can replace the distant luminous point by a near luminous point placed at the focus of a strong lens. If the eye would inform us on the distance whence the light comes to it, the result of the two ex- periments ought to be the same, since the rays reaching the eye are parallel in both cases. But this is not so. Other information tells us, in fact, that, in the latter case, the luminous point is very near, which makes us see the figure of diffusion extremely small, and makes this form of experiment not to be recommended. We know also that the after images appear to us large or small, according as we project them on a distant or near surface, which shows clearly that the eye does not accord to them a real distance. If we do not present to them a surface on which they can be projected, for example by closing the eyes, they generally seem to have the same apparent size as the object of which they are the image; we accord to them the distance of this object, a THE PROJECTION OF VISUAL IMPRESSIONS 307 distance which is not told by a direct sensation, but which we judge by an unconscious reasoning, as we shall see in the following chapter. 126. Projection in Binocular Vision. The impressions of the two macula arc projected towards the same place. When the eyes perform their functions correctly, both of them always fix the same object, so that under these circumstances the fact stated is not surprising. But it is the same when they do not fix the same object, as is evident among others from stereoscopic experiments. The following experiment seems to me to demonstrate this fact in a very striking manner, but it is neces- sary to be able to squint in order to repeat it. It is quite easy to learn to squint inwards; in order to squint outwards we take hold of a fold of the skin near the outer canthus of one eye, while we look towards the opposite side. To perform the experiment, we close one eye and look at the flame with the other, so as to produce an after image. We then open the closed eye and select a point which we fix with this eye while we are endeavoring to squint. We then see the after image place itself on the point of fixation, although the visual line of the eye to which it belongs is not at all directed towards this point. We can squint more or less considerably, placing the visual line in divergence or in con- vergence : as long as the other eye fixes the point of fixation, the after image is located there also. PHYSIOLOGIC BINOCULAR DIPLOPIA. Let A, figure 183, be an ob- ject which both eyes fix, B another nearer object. If we close the right eye, the point B is seen five degrees to the right of A ; if we close the left eye, it is seen five degrees to the left of A. Opening both eyes, A is seen single at the place where it really is; we see two images of B, one five degrees to the left, the other five degrees to the right of A. We therefore see B in double crossed images; if we fix B, A is pre- sented in double homonymous images. We can perform the experi- ment with two candles, and, if necessary, we can make the diplopia more striking by placing a red glass in front of one eye. This singular phenomenon, which had already been described by Alhasen, is known as physiologic binocular diplopia. CENTER OF PROJECTIONS. We observe that the correct information which the eyes furnish to us gives rise to a false interpretation, for it is evident that, when an object is seen double, there is at least one of the images which does not coincide with the object. When we close one eye, 308 PHYSIOLOGIC OPTICS the corresponding image disappears, "*"'? while the other image does not change position. The false judgment must, therefore, persist also in this case, at least for one of the eyes. The sight of normal persons does not, therefore, necessarily become similar to that of a one-eyed person. The physiologic diplopia is due to the fact that we do not take into con- sideration the different position of the two eyes; without a special examina- tion we cannot tell whether an image belongs to one eye or the other. We refer every visual impression, from whatever eye it may come, to a common and single center, which, in my case, coincides pretty exactly with the right eye. Recall- ing the mathematical terms which we have used in the preceding chapter, we may say that it is the center of the coordinates the position of which we judge imperfectly. If we took into account the different position of the two eyes, we would have two centers of coordinates, and the idea of the direction of the object would suffice to fully determine its position. In the experiment (fig. 183) we would thus reason as follows: Since we see with the right eye an object five degrees to the left of A, with the left eye the same object five degrees to the right of A, the object must be in the midjile plane and nearer than A; we would therefore see B single and in its right place. Instead of this we refer the impressions, as in uniocular vision, to a single center, and we inform ourselves that the object must be double, since it is seen at once to the right and the left. DIRECTING EYE. (i) In my case this center of coordinates coincides almost exactly with the right eye, probably because, having used it so much separately, I have acquired the faculty of judging exactly with this eye the position of exterior objects, or, in other words, because there is developed a kind of uniocular vision in addition to binocular Fig. 183. (1) According to a communication from Javal, the binocular vision of Vallee was like mine. He de- scribed this condition as general (in a communication to the Academy of Sciences, about 1830), and gave the name directing eye to the eye which controls projection outwards. H. Kaiser has also described the same condition for his eyes. TEE PROJECTION OF VISUAL IMPRESSIONS 309 vision. I must add, however, that this condition was not developed as a result of my labors on physiologic optics, because the phenomena were the same when, twelve years ago, I began to devote my attention to this subject. According to Hering the center is often at an equal dis- tance between the two eyes, and this would, in fact, be the true type of binocular vision, in which neither of the eyes plays a dominant part. The reasons why I say that in my case the center of projections coin- cides with the right eye, are as follows : i When on looking at a distant object I see a near object in double crossed images, and when I try to touch this object by a quick motion, I grasp it correctly if I sight the image with the right eye, while I bring the hand far from the object if I sight the image with the left eye. It is the same if I close one eye. With the right eye I judge accurately the position of objects seen indirectly, as a one-eyed person would do; with the left eye I judge falsely. Thus, in the experiment figure 183, closing the right eye, I see B five degrees to the right of A, as I ought to, but I refer the impression to my right eye, and, thinking that the object B is five degrees to the right of the visual line of my right eye, in order to reach it I bring my hand towards B x . I have also noticed, especially when I observe the double images of near objects, accidentally and with- out trying to, that one of them, that of the right eye, presents a more material appearance, while the other rather resembles a kind of shadow ; Dr. Knapp, Jr., made the same remark to me. It must be noted that my eyes are practically equal, as to acuity and refraction. 2 I fix a mark P (fig. 184), not too bright, placed on a dark and uni- form background. Interposing a stick between my eyes and the back- ground, on the visual line of the right eye, I see it in double images; the image of the right eye (d) coincides with the mark of fixation, while the image of the left eye is seen more to the right (g) (fig. 184 A). If now I fix the stick, it is the image g of the left eye which is brought towards that of the right eye d, in order to coincide with it, while the latter remains motionless. One might think that this is due to the fact that I placed the stick on the visual line of the right eye, but this is not so; if I place the stick on the visual line of the left eye (fig. 184, B) so that the image of the right eye d is seen to the left, it is still the latter which remains motionless, while that of the left eye makes a great move- ment to join itself to it when I fix the stick. This apparent movement exists also when I close the right eye, although, under these circum- stances, the left eye does not make any movement. Under this latter form the experiment was described by Hering. 310 PHYSIOLOGIC OPTICS 3 This author furthermore described the following experiment: we fix binocularly an object placed at some distance in the median plane, and we try, by a quick movement, to place a stick quite near the face in the direction in which we see the object; it is better to conceal the movement of the hand with a screen. Making this experiment, I bring the stick pretty exactly on the visual line of the right eye. The experi- ment is easy to repeat even with persons who are not accustomed to study such questions, and we can control by placing ourselves in front of the observed person and sighting with one eye along the mark of fixation and the space between the eye-brows (glabella) of the observed Fi?. 184. person. I have observed several persons in this way. Most of them show a marked tendency to prefer one or other eye, which seems to indicate a tendency to a development of a uniocular vision in addition to the binocular vision like that which I have described for my eyes. Per- sons enjoying pure binocular vision must place the stick in the median plane; as the center of projection does not coincide with either of the eyes, these people cannot project correctly objects seen indirectly. This type of vision, therefore, seems inferior to the other, as far as orienta- tion is concerned. HOROPTER. All the points outside the point fixed are not seen double; the point C (fig. 183), for example, is seen ten degrees to the right of A, as well with the right eye as with the left eye ; it is therefore seen single. The entirety of the points seen single while we fix a given THE PROJECTION OF VISUAL IMPRESSIONS 311 point, is called horopter. The study of the horopter is quite a compli- cated mathematical problem, and without much interest, since the di- plopia is only very slightly indicated when the object is a little distant from the point of fixation. It may be solved when we know the posi- tion of the corresponding points (see the following chapter) and the law which regulates the position of the eyes (law of Listing). When the point of fixation is in the plane which contains the primary position of the visual lines, we see single all the points which are on a circle passing through the point of fixation and the nodal points (horopter of Johannes Fig. 185. Horopter of Johannes Miiller. Mutter, fig. 185). It is easy to see that on fixing A, B is seen single, because the two angles designated by a are equal, since both correspond to the arc AB. If we fix a point on the floor, situated in the median plane, the horopter corresponds almost to the plane of the floor. SUPPRESSION OF DOUBLE IMAGES. As one sees some exterior objects double, and some single, one might think that it would re- sult in great confusion. It does not : most people have never observed double physiologic images before making the experiment described above. Under ordinary circumstances the attention is always brought to bear on the object fixed, and the look never remains for any length of time on the same object, so that we have not much time to perceive 312 PHYSIOLOGIC OPTICS double images. It must also be observed that the objects, not fixed, form their images on the peripheral parts of the retina, where the per- ception is less distinct than at the macula. It is scarcely possible to sup- pose a serviceable binocular vision if the entire retina had an acuity like that of the fovea. But we also make important use of the phenomenon known under the name of neutralization of images, and which has been given special prominence by the works of Javal on the vision of persons affected with strabismus (see chapter XXIII). In addition to the fact that most of the time an object seems to be at two different places, binocular vision gives rise to yet another con- tradiction. Making the experiment with the two candles before the screen DE (fig. 183), we have seen that the right eye sees the candle B at five degrees to the left of A ; in this direction the left eye sees a part of the screen; and as we do not take into consideration the different position of the two eyes, but refer our impressions to a common center, the result is that we seem to see two objects in the same direction. Interposing a stick between the eyes and a book (controlled reading of Javal) we can read without interruption only when both eyes are open ; if we close one eye, the stick covers some of the characters. We here meet the same contradiction; we see the stick in the same direction as the characters which it conceals, and as, on the other hand, we know that it is nearer than the book it appears transparent. But, in cases in which such an interpretation is not possible, for example when we present to both eyes wholly different images, in a stereoscope, we observe what is called antagonism of the visual fields. It is sometimes the images of one eye that predominate, sometimes those of the other, and as long as we see in a part of the visual field images of one eye, those of the other are completely suppressed. It seems that this suppression of the images of one eye plays a great part in binocular vision, and that it is this which generally causes us not to observe double physiologic images. It is not easy to know which of the two images is suppressed, for as soon as we pay attention to this question both appear. Generally it is the more eccentric image, or, in other cases, the image which, on account of the perspective, occu- pies the smallest retinal surface (Javal) which disappears. But, in most persons, there seems, as I have already stated, to be developed a certain superiority of the eye which is most frequently used separately, and then it is always the image of the other eye which is suppressed. Bibliography. M uller (Johannes). Beitrage zur vergleicJienden Physiologic des Gesichis- sinnes. Leipzig, 1826. Hering (E.). Beitrage zur Physiologic. Leipzig, 1861. Kaiser (H.). Compendium der physiologischen Optik. Wiesbaden, 1872, p. 298. CHAPTER XXII. MONOCULAR PERCEPTION OF DEPTH 127. Influence of Accommodation. I have already said that the eye gives us no direct information as to the distance from which light comes to it. We might think that the degree of accommodation used in order to see the object distinctly would inform us as to its distance. When the eye is accommodated for distant objects, near objects do not appear dis- tinct, and an experienced observer might use this circumstance to judge of the distance of an object. Young said that painters must take care to show near objects vaguely under penalty of obtaining a hard and dis- agreeable effect. But the importance of accommodation for the judg- ment of distance is but small, because, generally, we are dealing with such long distances that the difference of accommodation is insignificant. For all distances exceeding one meter, the variation of accommodation does not reach one dioptry. 128. Indirect Judgment of Distance. In the absence of direct in- formation, a whole series of circumstances enable us to judge of the distance of an object, generally by an unconscious judgment. a. The knowledge of the nature of objects often furnishes us with a means of knowing their distances. Thus, if we know the size of an ob- ject, we can judge its distance from its angular size. It is the size of man especially which enables us to make this judgment. Generally we judge directly of distance. When we see a man very far off, he does not appear to us small, because we know what size he ought to be, but we conclude that he must be very far away, since the angular size is small, and this, without this latter fact directly striking our consciousness. This observation is quite characteristic of the manner in which un- conscious judgments are formed, and it must be noted that this way of judging is something to be learned. I recall very well that the first time I saw a man climb the mast of a ship, he appeared to me like a doll, 313 314 PHYSIOLOGIC OPTICS and Helmholtz reports a similar observation. If we look at distant objects through a telescope they are enlarged; but as long as we have to do only with objects of known size, such as men, houses, etc., they seem to preserve their natural size, but appear near. We must open the other eye to convince ourselves that they are really enlarged. b. A means which is often used to judge whether one object is nearer than another, is to observe whether it conceals a part of the other. If one hill conceals the lower part of another hill it must be nearer. c. If we are acquainted with the object at which we are looking, or if there is a certain regularity, we easily come to know what part is nearest. On the photograph of a house, we easily judge the distance at which the different parts ought to be, while photographs of rocks, landscapes, etc., are frequently more difficult to interpret. d. The shadows thrown are often important for the judgment of dis- tance. If a surface is illuminated, the luminous source must be in front of it, and if an object casts a shadow on this surface, it must be nearer the observer than the surface. It is for this reason that we obtain a much better idea of the reality by adding shading to a drawing. e. Finally, aerial perspective sometimes influences the idea which we form of distance. We comprise under this term the darkening and change of color which distant objects undergo on account of the in- complete transparency of the layers of air which separate them from the observer. The vapors of water which are in the atmosphere reflect the blue rays, and allow the red rays to pass. Comparing the spectra of a blue sky and a cloudy sky, Lord Rayleigh thus found that the brightness of the latter diminishes greatly towards the blue extremity. When the spectra had the same brightness in the red, the green of the cloudy sky was already less strong than that of the blue sky. It is for this reason that the setting sun appears red, and distant mountains blue. When there is much water vapor in the atmosphere, we see distant objects, such as forests and hills, more distant and consequently larger than they really are. In the mountains the air is, as a rule, very pure, which causes us to often judge the distance and height of the summits much smaller than they really are. We know that the sun and moon appear larger when they are near the horizon, which is merely an illusion. If we measure their angular size, we find it exactly the same in both cases. Likewise, if we try to divide the distance between the zenith and the horizon into two equal parts, we are greatly deceived ; the lower part is always too small. Since MONOCULAR PERCEPTION OF DEPTH 315 the moon, near the horizon, appears larger than near the zenith, although it has the same angular size, it is equivalent to saying that we judge it to be farther away. The illusion is due to the aerial perspective. The moon is seen through a much thicker layer of the terrestrial atmosphere when it is near the horizon than when it is at the zenith. It seems, how- ever, that the comparison with terrestrial objects also plays a part in this judgment (fig. 186). These different means enable us to judge more or less exactly of the distance of an object. They are especially useful to us when we have Fig. 186. After Young. The curve indicates the apparent form of the sky. The sun, although teen under the same angle, seems of variable size. to do with long distances, on which the parallax, of which I am about to speak, cannot give any information. 129. Influence of the Parallax. The idea which we obtain of the relief, by displacements of the head, is well known to all who use the ophthalmoscope. We thus obtain a very distinct idea of the depth of an excavation, etc. We often use this means, without knowing it, to study an object difficult to interpret, and it is the principal means by which one-eyed people account for the relief. The observer often sees thus, without his perceiving that he does so, the relative movements of exterior objects, and he uses them to account for their position. If, for example, while the eye is displaced from a to b (fig. 187) the observer sees the object A displaced to the right relatively to the object B, A must be nearer than B ; to draw this conclusion, we need not look dur- ing the displacement. If, after having observed the objects in the posi- tion a, we close the eye to open it again only in the position b, we ob- serve, nevertheless, that A has changed place relatively to B, which suf- fices to judge of its distance. The judgment is here based on the comparison of the successive retinal images ; images change for each new position of the eye. But, 316 PHYSIOLOGIC OPTICS xB as all comparison by memory is defective, we obtain a much more distinct idea of the differ- ence between the images, and consequently of the relief, by comparing the images simultane- ously with the two eyes, and it is for this rea- AX > son that we always judge distances better with two eyes than with one. It is easy to convince ourselves that this is so by trying to reach a stick placed at some distance with the finger coming from the side. Looking with one eye only we are deceived much more frequently than when we open both eyes. ^^ ^ When we look with the two eyes, each eye ( j + ( j receives a perspective image of the objects situ- ji ^7 a ted in front of us; as the two eyes are not at tig. 187. th e same place, there result between the images differences which are the more pronounced the smaller the distance of the object. If, on the contrary, we look at a plane image with both eyes, the retinal images are identical. This, therefore, is a sign by which the appearance of an object of three dimensions is distinguished from a plane image. It is only for near objects that this difference exists: if the objects are at a great distance, the retinal images are alike; thus a land- scape presents almost the same appearance whether we close one eye or whether we open both. Bibliography. (Euvres de Young, edited by Tsclierning, p. 244. CHAPTER XXIII. BINOCULAR PERCEPTION OF DEPTH. 130. Influence of Convergence. -- The most important information on the distance of an object is furnished us by the degree of convergence which it is necessary to use to fix it binocularly. Just as for the judg- ment of the direction of the visual line in uniocular vision (see ch. XXI), it is the degree of innervation used which guides us, and not at all the sensation of the position of the eyes, which is always very vague. It is solely for differences of convergence that we have a very exact sensa- tion; we can judge with very great exactness whether one object is nearer or farther away than another; the judgment of absolute distance is very uncertain. When we fix a distant object, a near object appears in double crossed images. Although we may not often perceive these images, they give us, nevertheless, a vague idea of the distance of the object, for they suffice to give a pretty accurate impulse to convergence, since, guided by them, we converge for the object without much effort. But it is only after having accomplished convergence and having seen that the innervation given has attained its object, that we have an accu- rate idea of the distance. The difference between the two judgments is almost analogous to that which we find when we wish to measure the distance between two points. Suppose that we wish to measure this distance with a compass, provided with a scale graduated in millimeters, telling the distance between the two points. We can readily, at first sight, give to the compass approximately the aperture which is neces- sary, but we obtain a more exact and distinct idea of the distance when we make the measurement and see how much must be added to or taken away from the estimated distance. 131. The Stereoscope. -- The advantage of binocular vision was made clear only by the invention of the stereoscope by Wheatstme (1833). With this instrument we obtain an impression of depth much superior to that which any other representation can give of it. 317 318 PHYSIOLOGIC OPTICS Each of the images of the stereoscopic representation is drawn in such a way as to form in the eye a retinal image like that which the object would form there. Distant objects are, therefore, represented by images which are identical, while the images of near objects are different. STEREOSCOPIC PARALLAX. In order to account for the manner in which objects are represented on stereoscopic images, we may suppose two transparent plates (MM, fig. 188), placed in front of the eyes at the Fig. 188. place which the stereoscopic image will occupy later. From all the ex- terior points we suppose straight lines directed towards the eyes. There start thus from each exterior point two of these lines, and the point at which each of these straight lines cuts the corresponding plate is the reproduction of the exterior point. If the latter is at infinity the two straight lines are parallel, and the distance BB^ between the two points, is equal to the base line. If we place the two transparent stereoscopic figures one over the other, so that the two reproductions of the same point situated at infinity overlap, we can make the reproductions of all the points situated at infinity coincide two by two. If, on the con- trary, the exterior point (C, fig. 188) is not at infinity, the distance between the two reproductions is less than that of the eyes. We des- ignate the difference by the name stereoscopic parallax. The parallax of the point C is BD + E I D 1 E. Designating the distance between the two eyes by b, that of the object from the eyes by AO = d, and the distance of the plate from the eyes by g, we have BINOCULAR PERCEPTION OF DEPTH 319 b E b E bg - = - r = - or E = -f- . d g d y d The parallax increases, therefore, with the distance between the two eyes, and it is the greater as the object is nearer the observer. METHODS OF OBSERVING THE STEREOSCOPIC IMAGES. a. Making the visual lines parallel, we can without further trouble blend the two images into one, which appears in relief. We then see three images, the middle one of which gives the relief; for each eye sees not only the image which is intended for it, and which is blended with that of the other eye, but also the image which is intended for the other eye ; we can eliminate the two useless images by placing the hand as a partition between the eyes. It may be difficult to make the visual lines parallel while accommodating for a quite short distance, but if we succeed in doing so, the illusion is as perfect as with the stereoscope. Frequently we do not succeed with the ordinary stereoscopic images because, be- ing intended for the stereoscope of Brewster, they are calculated for too long a base line, which obliges us to make the visual lines diverge in order to fuse them. We can also look at the images by directing the right eye towards the image of the left, and vice versa, so that the visual lines intersect at a point situated in front of the image. It is then necessary to place on the left the image intended for the right eye, under penalty of seeing the relief reversed, if the supposed object lends itself to such an interpreta- tion. The fused image appears diminished and situated in front of the plane of the drawing, at the point of intersection of the visual lines. b. The stereoscope of Wheat stone, the first which was constructed, is composed of two plane mirrors (bd and bdj, forming a right angle (fig. 189); the eye O L looks into the mirror on the right at the image of the drawing Bj D 1} which it sees at ff^ ; the eye O sees the image of BD at the same place ; the two images are fused into a single one presenting relief. In order not to have the relief reversed or pseudoscopic, it is necessary to present to the left eye the image intended for the right eye, since the mirrors reverse the images. c. The stereoscope most used is that of Brcwster: each eye looks through a prism with convex surfaces, the apex of which is turned towards the nose. The glasses produce a certain magnification, and their prismatic effect renders it unnecessary to make the visual lines parallel. We can replace the glasses of the stereoscope of Brewster by ordinary convex lenses, by decentering them ; that is to say, by placing them so 320 PHYSIOLOGIC OPTICS that the distance between the centers of the two glasses is greater than the distance between the eyes. Fig. 189. Stereoscope of Wheatstone. d. When the image represents an object which is symmetrical in rela- tion to the median plane, the two drawings are symmetrical. We can, therefore, in this case obtain a stere- oscopic effect by looking with one eye at an ordinary drawing, with the other at its image by reflection, since the reflection produces a symmetrical image of it. The most convenient way is to look through a prism with total reflection. e. Placing a prism with total reflec- tion in front of each eye, we obtain pseudoscopic relief when we look at any object, providing such an inter- pretation is possible. A cigar is thus presented as a hollow leaf of tobacco, etc. Wheatstone had constructed an instrument of this kind named pseudoscope (fig. 190). f. The telestereoscope of Helmholtz is composed of four mirrors ar- ranged as we see in figure 191. The rays ab, a'b', coming from a landscape, are reflected by the large mirrors towards the small ones, and by the latter towards the eyes. We obtain the same effect as if the eyes A and B were in the position of their images (A B x ) produced by the double reflection. We have seen that binocular relief is due to the dis- Fig. 190. Pseudoscope of Wheatstone. BINOCULAR PERCEPTION OF DEPTH 321 tance which separates the two eyes. The greater this distance is the more pronounced is the relief. The instrument gives relief to objects which, under ordinary circumstances, are too distant to give this per- Fig. 191. Telestereoscope of Helmholtz. ception; at the same time it makes them appear nearer and smaller, almost as if we looked at a diminished model of them. g. The iconoscope of Javal resembles somewhat an inverted telestere- oscope, the eyes having taken the place of the object (a and aj, and the object that of the eyes (in the direction of AB). The instrument acts as if the eyes were very near each other, at c and q. Looking at objects through this instrument, the relief disap- pears : the object appears flat, as in a painting. On the contrary, if we observe an engraving through the instrument, it presents a more pro- nounced relief than under ordinary circumstances. For, the binocular vision then ceases to make us observe that the different parts of the image are in the same plane, which destroys the illusion. Looking through the iconoscope the relief is more marked than when simply closing one eye. h. The binocular ophthalmoscope of Giraud-Teulon is analogous to the iconoscope. The mirrors are replaced by two glass rhombohedra, each of which covers half of the opening of the ophthalmoscope. As 322 PHYSIOLOGIC OPTICS in the preceding case, the rays reach the eye after a double reflection on the small surfaces of the rhombohedron. The instrument acts as if the eyes were at cc (fig. 192). i. We draw the two figures, over each other, one with red lines, the other with blue lines. Looking through a red glass we do not see the red lines, and vice versa. If we look at these anaglyphs, placing a red Fig. 192. Binocular ophthalmoscope of Giraud-Teulon. glass in front of one eye and a blue glass in front of the other, we ob- tain a stereoscopic effect. Changing the glasses the relief is reversed, if the nature of the object permits such an interpretation (d* Almeida). 132. The effect of the stereoscope is to give an idea of the third dimen- sion, such as no other representation can give of it. Its use has become especially popular since stereoscopic photographs have been made, for though we can make stereoscopic drawings of stereometric figures, etc., it is impossible to make them of a landscape so that the reproduction may be exact. Dove used the stereoscope to see whether a bank note was false, by placing it in one of the fields and putting a genuine note in the other. If it was false he saw some of the letters leave the plane of the paper, for it is impossible to make an entirely exact counterfeit of an engraving, and the least difference in the distance of the letters produces relief. STEREOSCOPIC LUSTRE. Under ordinary circumstances there are usually formed only in one eye images of the same objects as in the BINOCULAR PERCEPTION OF DEPTH 323 other ; as long as we place in the stereoscope images of real objects only, we simply see the relief. I have already said that, in the case of the controlled reading of Javal, we see at the same place the stick and the letters which it should conceal. The observer gets over the difficulty by supposing the stick transparent. Another interpretation of the same kind is known as stereoscopic lustre (Dove). If we draw one of the stereo- scopic figures with black lines on a white ground, the other with white lines on a black ground, we observe that the fused image presents a certain brightness, almost as if it was covered with a layer of plumbago. Replacing the black surfaces by colored surfaces, we sometimes obtain the metallic lustre. Every bright body, in fact, sends back two kinds of light : regularly reflected white light and diffuse light which has the color of the body itself. When, in the stereoscope, we see at the same place white light and colored light, the contradiction is explained by supposing that the object we look at is bright. ANTAGONISM OF THE VISUAL FIELDS. When the images placed in the two fields are so different that they cannot be fused, as, for example, if we present to one eye horizontal lines and to the other vertical lines,' we observe the phenomenon known as antagonism of the visual fields: it is sometimes one, sometimes the other field which predominates, and while one predominates the other is suppressed ; we do not see it at all. It is not the field of the same eye which predominates everywhere ; the common field is composed of parts belonging to either eye. When one of the fields has predominated at one place for some time, the appear- ance changes, the other field getting the upper hand. The change often takes place under an external influence; a winking of the eyelids or a change in the direction of the look sometimes suffices to bring it about. Furthermore, the phenomena vary much according to the objects. If we present to each eye outline pictures which do not correspond to each other, drawn on a uniform ground, but different for both eyes, we observe that the ground of each field predominates near the picture which belongs to it. The following experiment demonstrates this fact in a quite striking manner. We draw in one of the fields a large black vertical bar, in the other, another similar but horizontal bar: on blend- ing the fields the bars form a cross (fig. 193), the middle of which, situated at the point where the two bars cross, is black ; the parts next to the middle are whitish, because the outline picture makes the white ground predominate. The extremities of the arms appear, on the con- trary, almost as black as the middle, in spite of the superimposing of the white on the other field. 324 PHYSIOLOGIC OPTICS Fig. 193. After Hdmholtz. In making this experiment, we experience a difficulty in fixing the images on each other : the vertical arm glides on the horizontal arm. This is due to the fact that there are no com- mon vertical lines which can guide us for the degree of convergence. On account of their importance for con- vergence we designate the vertical lines as the dominating outlines. To prevent the two figures from gliding on each other, we place at the middle of each line a small white cross. The tendency to fuse these small crosses suffices to fix the vertical bar at the middle of the horizontal bar. When the two fields have not the same color, we generally observe antagonism of the visual fields. I have thus arranged the experiment ,with colored shadows (page 240) so as to have one of the shadows in each field of the stereoscope. On blending them it was sometimes one, sometimes the other color which predominated. I repeated the experi- ment with several of my pupils, none of whom succeeded in seeing the gray shadow. There are authors, however, who claim to have ob- tained the color of the mixture ; the phenomenon is then, perhaps, of the same order as stereoscopic lustre. 133. Identical Points of the Retinae. We say that one point of a retina is corresponding to, or identical with, a point of the other one, when the images of the same exterior point falling on these two retinal points are blended into a single image. If, in the second eye, the image is formed on any other point, it is not blended with that of the first eye : the point is seen double. It is evident that the two foveas are corresponding points, since the object fixed is always single. To find the other identical points, Johannes Muller has given the following rule. We suppose the retina divided into quadrants by a horizontal meridian and a vertical meridian, both passing through the fovea. The position of each point is then deter- mined, as on a terrestrial globe, by its longitude and latitude in rela- tion to these two meridians. Two points having the same longitude and latitude are identical. The rule of Muller agrees with that which we have laid down in chapter XXI, according to which an object is seen BINOCULAR PERCEPTION OF DEPTH 325 single when the two eyes see it in the same direction in relation to the point fixed. The researches of Volkmann have shown that the law of Miiller is not wholly exact, and that it is necessary to replace the vertical meridians by apparently vertical meridians, which, for a person standing upright and looking towards the horizon, converge about two degrees in the downward direction, so as to almost meet at the ground (see page 295). We then suppose the retina divided by circles parallel to this meridian as well as to the horizontal meridian, and the law of Miiller is applic- able. Placing in each field a really vertical line, these lines appear to converge upwards and must, consequently, cross if we try to blend them. In order that the experiment may succeed it is necessary, how- ever, to arrange them so that one line may be white on a black ground, the other black on a white ground. Otherwise the lines are blended nevertheless. THEORIES ON THE NATURE OF IDENTITY. The question of knowing why two points are corresponding while two others are not, has been much discussed. Most of the advocates of the theory of identity suppose that there exists an anatomical relation between the two corresponding points. They suppose that the nerves conducting the impressions of two corresponding points unite, on their way to the chiasma, into one which conducts the impression to the brain. This idea was already expressed by Galien, and has been confirmed by Newton, Wollaston and others. The so-called theory of projections is expressed almost as we have described it in chapter XXI: a point on the left retina, situated 10 degrees to the left of the fovea, localizes its impression at 10 degrees to the right of the point of fixation ; the point situated at 10 degrees to the left of the right fovea localizes its impression in the same direction ; and as the two impressions are localized in the same direction, they are blended into one. The identity of the two foveas might be a result acquired by experience. This theory has been upheld by Kepler, Porter- Held and, under an erroneous form, by Giraud-Teulon. Immediately after the invention of the stereoscope and the studies of the production of relief to which this invention gave rise, there was an inclination to abandon the idea of corresponding points, for the stereoscopic experiments seem opposed to what we have said on these points. Indeed, let us look in the stereoscope at a representation of the two points A and B, both situated in the median plane, and fix the more distant A. The images of B are not formed on two correspond- ing points, since in one eye its image is to the right, in the other to the 326 PHYSIOLOGIC OPTICS left of the fovca. Nevertheless, we see it single and in relief ; that is to say, nearer than A. On account of this apparent contradiction, Wheatstone inclined towards the theory of projections. In despair of a better explanation, the advocates of the theory of identity supposed that a point of one of the retinae does not correspond to a point, but to a small surface of the other (Panum). An image falling on the point of the first retina could then become blended, either without relief, with an image formed at the middle of the small surface of the other, or with relief, with an image formed on a more peripheral point of the small surface. But, under this form, the theory of identity was not tenable ; it would be necessary, indeed, to suppose that the same two points could be sometimes corresponding, sometimes not corresponding, which is scarcely admissible. The question was cleared up only by the labors of I aval. THEORY OF JAVAL ON THE PRODUCTION OF RELIEF. This theory calls especially for two factors, the neutralization (partial suppression of one of the images) and the influence of the ocular movements, on which Brucke had already insisted. In chapter XXI reference was made to the suppres- sion of one of the images, which takes place when different images are formed on two corresponding parts of the retinae. We then see, some- times the image of one eye, sometimes that of the other, and while we see the image of one eye, the corresponding part of the image of the other disappears absolutely. In normal persons the suppression espe- cially manifests itself alternately for both eyes, under the form of an- tagonism of the visual fields; in strabismic patients, on the contrary, we often have occasion to observe the constant neutralization of a great part of the visual field of one eye. Brucke was the first who insisted on the great importance of the ocular movements for the perception of relief. Anyhow, it is certain that without them we could have only a very vague notion of it. Look- ing into a stereoscope, especially if the images are difficult to fuse, it is only after I have permitted my look to wander for some time on the figures, fusing sometimes the images of the distant objects, sometimes those of the near objects, that relief appears to me. As long as the sensation of relief is not produced I see double, sometimes the near objects, sometimes the distant ones; but at the moment when relief appears, I see all of them single. Certain authors claim that they have observed relief by illuminating the stereoscopic images with an electric spark, the duration of which light is so short that all ocular motion is necessarily excluded. This would certainly be impossible in my case. BINOCULAR PERCEPTION OF DEPTH 327 for there always elapses a certain time before the real illusion, which does not prevent me from being able to form all at once a vague notion of relief. According to Javal, it is necessary, indeed, to distinguish between the idea of relief, which is produced by the fact that we see near objects in double crossed images, and the measurement of relief, which depends on the sensation of the degree of innervation necessary to converge towards the near object. To account for the manner in which we come to obtain the sensation of relief, it is preferable to use images which are quite difficult to blend, the stereoscopic parallax of the objects represented being quite strong. We immediately fuse the images of distant objects, and all the others appear in double images. We then allow the look to stray on the figure, which forces convergence more or less, according as the object is represented more or less distant. After having con- tinued thus for some time, relief manifests itself almost in the same way as we can with closed eyes obtain a very distinct idea of the form of an object by feeling it with the fingers. At the same time that relief appears, the double images disappear ; the image of one or other eye is suppressed. If one of the eyes plays the part of the directing eye (see page 308) it is usually the images of the other eye which are suppressed, unless the image of the pre- ponderating eye is much more peripheral than that of the other. In cases in which this preponderance is not developed, the double images seem to appear following the law of Javal: we suppress that one of the images which occupies the smallest retinal surface. We can account for the manner in which we suppress the images by looking at a rule which is held obliquely before the eyes, so that it presents a greater surface to one eye than to the other. Whether it occupies the position AA (fig. 194), or the position BB, it seems to me, seen binocularly, to have the same appearance as when I close the left eye. Persons in whom the preponderance of one eye is not developed see the rule binocularly, as it is presented to the left eye, if it occupies the position AA. In the position BB they see it, on the contrary, as it presents itself to the right eye. Fig. 194. 328 PHYSIOLOGIC OPTICS The discussion of the two theories of binocular vision, that of identity and that of projections, has not yet closed. The explanation of Javal is applicable in reality as well to one as to the other. We can imagine the projection learned by experience; and even the fact of always project- ing the images of the two foveas at the same place, the foundation stone of binocular vision, may be something learned. It is, perhaps, the superiority of the fovea, as to visual acuity, which causes us to always bring the images of the object which interests us to form themselves on both foveas, and we may thus have been led to always localize the impression of the two foveas at the same place. On the other hand, the advocates of the theory of identity take their stand on the anatomical observations of the semi-decussation in the chiasma, and especially on comparative anatomy, which shows that in many animals fish, for example whose eyes are placed so as not to have a common visual field, the optic nerves cross completely. Clinical observations in hemi- anopsia, especially those of partial hemianopsia, are a further argument in favor of this theory. The study of the vision of strabismic patients, which is perhaps the best means of deciding the question finally, shows, as we shall see in the following chapter, that, in consequence of a false position of the eyes, there may be developed a kind of correspondence between two retinal points which, under ordinary circumstances, are not corresponding; but this relation never assumes the character of true binocular vision with fusion, and it sometimes suffices, in a person who has squinted since childhood, to place the eyes in an approximately correct position, in order that, in the course of a fortnight, correct pro- jection may gain the upper hand. Bibliography. Wheatstone (C. ) . Contributions to the Physiology of Vision. On some Re- markable and hitherto Unobserved Phenomena of Binocular Vision. Phil, trans., 1838, II, p. 371- 394. Wheatstone (C.). Contributions to the Physiology of Vision, II. Phil. Mag., 4, III, p. 149-152, and p. 504-523. - Brewster (D.). The stereoscope. London, 1858. Helmholtz (H.). Das Telestereoskop. Pogg. Ann., CI, p. 494-CII, p. 167. Javal (E.). Sur un instru- ment nomme Iconoscope, destine d, donner du relief aux images planes examinees avec les deux yeux. Report, LXIII, 927. Javal (E.). De la neutralisation dans Facte de la vision. Ann. d'oc., LIV, p. 5. Miiller (Johannes). Beitrage zur vergleichende Physiologic des Gesitchtssinnes. Leipzig, 1826, p. 191. Volkmann (A. W.). Physiologische Untersuchungen im Gebiete der Optik, II. Leipzig, 1864. Newton (J.). Opticks, 1717, p. 320. Panum (P. L.). Phi/si- ologische Untersuchung uber das Sehen mit zwei Augen. Kiel, 1858. Briicke. Ueber die stereoscopische Erscheinungen. Miiller' s Archiv fur Anat. u. PhysioL, 1841, p. 459. Nagel (A.). -Dos Sehen mit zwei Augen und die Lehrevonden identischen Netzhautstellen. Leipzig, 1861. Javal (E.). Manuel du strabisme. Paris, Masson, 1896. CHAPTER XXIV. STRABISMUS. 134. Different Forms of Strabismus. We say that there is strabismus when the two visual lines do not intersect at the point fixed. The image of the point fixed is not, therefore, formed on the two foveas, and since the two foveas are always corresponding points, there is no binocular vision. One might, therefore, define strabismus as the con- dition in which binocular vision is wanting, at least at certain moments or for certain directions of the look. It must be observed, however, that we may meet with cases in which the visual lines have the proper direction, at least apparently, but in which binocular vision is, never- theless, wanting; this case often presents itself in persons affected with strabismus, who have undergone a successful operation. It is also customary to speak of strabismus when one eye deviates, even if it is completely blind. The study of strabismic patients is very important for different questions of physiologic optics. We distinguish two forms of strabismus : paralytic strabismus, due to a paralysis of one or more muscles, and concomitant strabismus, which, in the great majority of cases, is due to the defect of innervation (Hanscn- Grut). The symptoms by which we make the differential diagnosis between these two forms of strabismus are well known. They have passed from the classic memoir of Graefe into all treatises of ophthal- mology. In cases of paralytic strabismus the excursion of the eye is less on the side of the paralyzed muscle, and the secondary deviation is greater than the primary. Patients present diplopia, either spontane- ously, or more especially if we examine them with a candle and a colored glass. The distance between the two images increases when the look is directed towards the side of the diseased muscle, and it is the image of the diseased eye which is farthest away in this direction. When the patient closes the healthy eye and looks towards an object situated on the side of the diseased muscle, the projection is false; for, 329 330 PHYSIOLOGIC OPTICS as it is necessary, on account of the paresis, to use a stronger innerva- tion to bring the eye to fix the object, the patient thinks that this object is situated more to one side than it really is, and when he wants to grasp it quickly he brings the hand too far to that side. I have already observed (page 305) the importance of this observation to demonstrate that we judge the direction of the look above all by the degree of in- nervation used to bring it into this direction. CONCOMITANT STRABISMUS. When we speak of strabismus with- out other qualification it is generally this form that we mean. In this strabismus the deviation is almost the same for all directions of the look, except that generally the convergence is more pronounced for the downward than for the upward look. The secondary deviation is equal to the primary deviation. The patient does not complain of diplopia, but we may always bring it about by the means which I shall describe forthwith. The distance between the two images is the same everywhere, to whichever side the patient looks. The simplest means of diagnosing strabismus is to make the patient fix an object, the finger of the observer, for example. If one of the eyes seems to deviate, we cover the other, and if the former then makes a movement to fix, it was deviated : strabismus is, therefore, proved. This examination must be repeated for a distant object. If we do not discover strabismus by this means, it may, nevertheless, happen that the patient has it, but in a very slight degree, or, in other words, that he has no binocular vision ; we may, in this case, place a prism, apex inwards, in front of the eye. If there is binocular vision the eye makes a movement of convergence to neutralize the effect of the prism (Graefe). If the strabismus is periodic we can sometimes discover it by making the patient fix a very small object, a word printed in very small type, for example; the patient is obliged to accommodate to distinguish the word, and the effort of accommodation may then cause strabismus. LATENT STRABISMUS. In order to see whether there is latent stra- bismus, we make the patient fix the finger of the observer ; we cover one eye and examine, on uncovering it, whether the eye deviated under the hand and whether it straightened itself in order to fix. If the deviating eye does not straighten itself, the strabismus has become manifest ; if it does straighten itself, it is latent. According to Graefe, we make the patient observe a long vertical line which has at the middle a black spot, or, which is preferable, a candle, while we place in front of one of his eyes a prism, apex upwards. If there is latent strabismus, the patient sees two objects placed exactly one above the other (if the apex of the prism STRABISMUS 331 forms a horizontal line). If not, there is latent strabismus, and we can then measure the degree of it by placing the prism of Cretes before the other eye and finding the degree of this prism which makes one image appear above the other. We can also use the Maddox test, etc. Javal placed a ground glass lens before one of the eyes of the patient; this glass prevents the eye which it covers from distinguishing anything, while the observing eye sees the covered eye sufficiently well to judge of its position. Making the examination in this way, we find, in many people, a slight degree of latent divergent strabismus for near vision. This condition is often designated as insufficiency of the internal recti. This expression is ill-chosen and should be discontinued. The internal recti are not weaker than in the normal eyes, as Hansen-Grut has shown, for, other- wise this weakness ought to manifest itself also for the associated move- ments. If the right internal rectus were really weaker than in the normal state, we should, when looking to the left, see the phenomena appear which characterize paresis of the right internal rectus, which is by no means the case. It is not in the muscles, it is in the innervation of convergence that we must search for the cause of this deviation. We might, therefore, speak of an insufficiency of convergence, but this also would be a bad expression, for many patients affected with this defi- ciency can converge as well as normal persons ; it is only the stimulus of convergence that is wanting, (i) 135. Measurement of Strabismus. i We cover the good eye; the strabismic eye straightens itself, and we value, in millimeters, the extent of the displacement of the cornea. 2 Javal has proposed to measure the deviation in degrees by means of the perimeter. He places the patient so that the strabismic eye is in front of the point of fixation of the perimeter. The patient fixes this point with his good eye. The observer then moves a candle along the arc of the perimeter, sighting in the direction of this candle towards the strabismic angle. He finds the position in which the corneal image is at the middle of the pupil, which indicates approximately the direction of the visual line of the strabismic eye. In the keratoscopic arc of de Wecker, the candle is replaced by a white mire, and at the point of fixa- tion is a small mirror in which is reflected a distant object which serves as the point of fixation. (1) [In this country Stevens' nomenclature has been generally accepted. According to him this con dltion is called exoph&ria.]W. 332 PHYSIOLOGIC OPTICS 3 We can use the distance of the two images as a measure of the strabismus if there is diplopia. We can measure this distance with the prism of Cretes, or by projecting the images on a wall provided with a graduation in degrees (Hirschberg, Landolf) or on a Prentice scale. The deviation often varies much with the distance of the object fixed. It may also be useful to determine the deviation at different distances, at 4 meters and at 25 centimeters, for example, as Schioetz has proposed. 136. The etiology of concomitant strabismus is a quite complex ques- tion on which opinions are still divided. Boehm discovered the relation which exists between hypermetropia and convergent strabismus, and Bonders, in a general way, announced the part that the anomalies of re-fraction play in the etiology of strabismus. This influence cannot be denied, and it is especially striking for convergent strabismus. In my extensive compilation of statistics of young conscripts (see page 84) there were 42 cases of convergent strabismus, of whom 31 were hyper- metropes, 7 emmetropes and 4 myopes ; that is to say, that about 70 per cent, of the persons squinting inwards were hypermetropes. But, on the other hand, there were in all 301 hypermetropes (of 2 dioptrics or more) ; only a very small minority of the hypermetropes squint, there- fore. The manner in which Bonders explained the relation between con- vergent strabismus and hypermetropia is well known. When an emme- trope fixes a near object, it is above all the necessity of seeing it single which regulates the position of his eyes. But, if we cover one of the eyes, this need no longer exists, and, nevertheless, the observed person generally continues to converge towards the point fixed; this is due to the relationship which exists between accommodation and converg- ence. Even if the observed person is sufficiently myopic to make it un- necessary for him to accommodate for the object, the covered eye con- verges, nevertheless, pretty exactly for the object. This is due to what Hansen-Grut termed sensation of the distance; knowing that the object is at a short distance away, the patient converges because he is accustomed to do so in the interest of binocular vision, even in a case in which this interest no longer exists. These three factors regulate the degree of convergence to be used. Under ordinary circumstances, it is the first factor which is of most importance ; but, in cases of hypermetropia, it may happen that, in order to sustain his accommodation, the patient converges more than is neces- sary for fusion. He then sacrifices his binocular vision to obtain distinct vision with one eye only, and this happens with special ease when the STRABISMUS 333 vision of the other eye is diminished for one reason or another (opacities of the cornea, astigmatism, etc.). In a certain number of cases we find vision greatly diminished without any perceptible reason. We cannot yet say whether this diminution is a consequence of strabismus (ambly- opia ex anopsid), or whether it is not rather a cause of strabismus, due to a congenital anomaly. If we thus explain why a hypermetrope may become strabismic, we cannot well understand why the great majority of hypermetropes do not squint. They often seem to have quite as much reason to squint as strabismic patients. Javal supposes that strabismus has developed under the influence of paresis of the accommodation which is cured later. The existence of such paresis is certainly hypothetical, but it would very well explain the origin of strabismus ; the parents of strabismic children are quite frequently affected with convulsions, intestinal worms, which might have produced nervous troubles, etc. According to de Wecker, a certain number of cases of convergent strabismus might be due to a paralysis of one of the external recti acquired during infancy. Paralytic strabismus would be transformed later into concomitant strabismus. Myopia plays, in the production of divergent strabismus, a less im- portant role than hypermetropia in the production of convergent stra- bismus. As the myope does not accommodate at all, or only slightly for near objects, one of the factors which sustains convergence is want- ing. If the eyes are very unequal, there may readily follow a divergent strabismus relative to near objects. On the other hand, distant vision is so diffuse for the more imperfect eye that binocular vision is of little usefulness, and this eye then easily deviates outwards. Generally speak- ing, every eye, the vision of which is destroyed or greatly diminished, has a tendency to deviate outwards. In very rare cases we meet in myopes a special form of convergent strabismus. The ideas on the nature of strabismus are much divided. Most authors find the cause of strabismus in the muscles, for instance, v. Graefe ("ex- cess of average contraction"), Schweigger ("excess of elasticity of the muscles"), etc. Others, Alfred Graefe and Javal, for instance, attribute periodic strabismus and the variable part of permanent strabismus to innervation, while they suppose that the permanent part is dua to con- secutive muscular alterations. The theories which attribute the vast majority of cases of strabismus to a defect of innervation are beginning to gain ground. They have been advocated by Stellwag, Rdhlmann, Hansen-Grut and Parinaud. The theory of Hansen-Grut seems to me to adapt itself best to the phenomena. 334 PHYSIOLOGIC OPTICS According to this author, the whole muscular theory collapses before the following observation. Suppose a left convergent strabismus of 6 mm. : if this strabismus had a muscular origin, it would be necessary that the limit of excursion outwards of the left eye would be displaced inwards 6 mm. But we never find anything of the kind. If the limit is sometimes displaced a little inwards, this is due to a lack of habit, since we never have occasion to make so great a motion with the stra- bismic eye. Hansen-Grut distinguishes between the position of anatomic equilibrium and the position of functional equilibrium of the eyes. The former is the position which the eyes assume apart from all nervous influence. When the eyes are in this position (during sleep, after death, etc.), the visual lines diverge in nearly all patients. The position of functional equilibrium is the position which the eyes assume when we look at a distant object with one eye covered. In this position the visual lines are parallel in normal persons. The convergent strabismus is due to the fact that there is developed an unusual position of functional equilibrium ; the divergent strabismus, on the contrary, is due to the fact that such a position is not developed at all, so that the eyes are placed in the posi- tion of anatomic equilibrium. 137. Vision of Strabismic Patients. Except in cases of convergent strabismus of myopes, strabismic patients do not generally complain of diplopia; they suppress the image of the deviated eye, so that the stra- bismic eye serves only to slightly increase the visual field. We may, however, always cause diplopia by holding a red glass in front of the good eye, by keeping this eye closed for some days, etc. ; but then we often meet with the singular phenomenon termed paradoxical diplopia. This diplopia was discovered by v. Graefe. Examining persons affected with convergent strabismus, in whom he had performed a tenotomy which partly corrected the defect, he found crossed diplopia, although the visual lines were still convergent, and the patients, according to the ordinary rule, should have indicated homonymous diplopia. Javal was the first to study this phenomenon on patients not operated on. The ex- planation of this fact is that there is developed what has been very im- properly named a vicarious fovea. The patient has first cultivated the habit of suppressing the image of the strabismic eye ; then there is gradu- ally formed an idea of the false position of the strabismic eye ; he has learned that an object which forms its image on the fovea of the good eye, forms its image at a point (b) inwards from the fovea of the strabismic STRABISMUS 335 eye, and he has learned to localize this image at the place where the ob- ject to which it belongs is situated. If we place a prism, apex down, in front of the good eye, the patient sometimes says that he sees only the image of this eye, but generally we succeed in making him see also the image of the strabismic eye ; the patients localize it almost on the same vertical line as the image of the good eye, instead of indicating widely separate homonymous images. It is, therefore, as if there was developed a correspondence between the point b and the fovea of the good eye. But the localization of the image is always very uncertain ; the patient some- times says that he sees both images well, but that it is impossible to tell which is the image of the strabismic eye. If we perform a tenotomy which does not completely correct the deviation, the image of the point fixed is no longer formed either on the true fovea or the vicarious fovea, but between the two. Patients first project the image according to the vicarious fovea: as it is formed on a part of the retina situated outside of the latter, the patient sees the object in crossed images. Later, especially if we make systematic exer- cises in order to reach it, the true fovea comes to exert its preponderat- ing influence : the patient sees the object in homonymous images. Fol- lowing the development of the change of vision of the patient, we some- times succeed in finding a time when the patient projects the image of the strabismic eye according to both foveas at once: he sees with the strabismic eye, at the same time, one image to the right and another to the left of the object. This singular form of vision has been described by Javal under the name binocular triplopia. I have had occasion to study a case of this character. 138. Treatment of Strabismus. If we confine ourselves to the treat- ment by operation, it is prudent not to completely correct convergent strabismus, for the strabismic eye has a tendency to put itself in diverg- ence, a tendency which sometimes suffices by itself to finally cause the convergent strabismus to disappear. On the contrary, when it is our in- tention to reestablish binocular vision, we must try to make the position of the eyes as correct as possible. This reestablishment is often a very long and difficult matter ; the task is less arduous in cases in which there still exists binocular vision in a part of the field. In certain cases, such as the periodical divergent strabismus and the convergent stra- bismus of myopes, we succeed by means of some exercises, or even by the simple operative treatment. According to Javal, who especially de- voted his attention to this question, the course of the treatment is as follows : 336 PHYSIOLOGIC OPTICS a. Reestablishment of diplopia and, if possible, of the vision of the stra- bismic eye. We keep the good eye covered by means of a blind patch ; if the vision of the other eye is very bad, in order to less annoy the patient, we allow him to wear the patch on the bad eye during several hours of the day; but it is necessary, during this period of treatment, never to allow the two eyes to be uncovered at the same time, under penalty of never seeing the neutralization disappear or of seeing the strabismus increase; for, as the diplopia annoys so much less as the images are more distant from each other, the patient tries to squint more strongly in order to separate the images. b. Reestablishment of the approximately correct position of the eyes by way of operation. c. Stereoscopic exercises. We begin by placing in each field, on each visual line, a round spot. If the patient fuses them, we move them farther or nearer, in order to develop in him the necessity of seeing single. The stereoscope of Javal, an imitation of that of Wheatstone (fig. 189), but with a variable angle between the mirrors, lends itself very well to this exercise. As soon as the patient sees double, we begin. When the patient has succeeded, we make him fuse letters by giving him smaller and smaller characters. For all these tests it is necessary to add to each figure numerous small marks, different ones for each eye, in order to make certain that the patient really fuses. He ought to see the figure with both series of marks ; otherwise, he neutralizes one of the figures, instead of fusing both. When beginning these exercises, we often encounter the phenomenon which v. Graefe designated under the name of antipathy to single vision. When we place the round spots in positions corresponding to the visual lines, the patient converges or diverges in order not to fuse them; if we try, in this new position of the eyes, he makes his convergence change again, and so forth. Javal invented a very ingenious card to surmount this difficulty, which is often very great. d. Exercises without the stereoscope. There often exists a part of the field in which the patient sees single; then we make him exercise in order to increase this part, for example, by placing a candle in the part of the field in which the patient fuses and bringing it towards the other part; when the patient sees double, we begin again. e. If the patient stands these different tests, we begin to make him do controlled reading. We interpose a pencil between the eyes and the book ; reading can then take place without interruptions only by using both eyes. This exercise must be continued for months. It is only a STRABISMUS 337 long while after the reestablishment of binocular vision that the patient can see relief. Bibliography. Bohm. Das Schielen. Berlin, 1845. v. Grafe (A.). Ueber Dop- peltxehen nach Schieloperationen und Incongruenz derNetzhaiite. Arch. f. Ophth., I, 1, p. 82. v. Grafe (A.). Ueber eigenthiimliche zur Zeit nock unerkldrliche Anomalien in der Projection der Netzhautbilder. Arch. f. Ophth., II, 1, p. 284. v. Grafe (A.). Symptomenlehre der Augen- muskettahmungen. Berlin, 1867. Donders (F. C.). Anomalies of the Refraction and Accommo- dation of the Eye. London, 1864. Hansen-Grut (E. ). Pathogeny of concomitant squinting (Bow- man lecture). Transactions of the Ophthalmolog-ical Society of the United Kingdom^ Vol. X, 1890. Javal (E.). Manuel du strabisme. Paris, Masson, 1896. CHAPTER XXV. OPTIC ILLUSIONS. 139. We designate by the above name cases in which the visual impressions give rise to a false judgment on the nature of the object. Illustrations, paintings and, generally, all representations of an object have the effect of producing these illusions; and all optic instruments act in a like manner. In the former part of the book I have mentioned several times illusions of a more special character ; I shall here describe briefly some others, the explanation of which, in most cases, is quite obscure. a. A first series of illusions is based on the fact that a line or space seems larger when it is divided than when it is not. This is the reason Fig. 195. why the two parts ab and be of the line (fig. 195) have the same length, but that still the part be appears longer, because it has divisions. The Fig. 196. two illustrations of figure 196 are square, but the illustration a seems wider and the illustration b higher, on account of the divisions. For 338 OPTIC ILLUSIONS 339 the same reason, a space filled with furniture appears larger than when it is empty. b. Very small angles are estimated to be larger than they are in reality. The following illusions may be considered as examples of this rule. The lines ab and cd of figure 197 are situated in the prolongation of each other, but cd seems displaced upwards. The illusion increases if we move the figure farther away. We may conceive that if we judge the acute angle to be too large, the line cd ought to seem to have undergone a rotation around the point c, the line ab around the point b, which would produce the illusion in question. The same error of judgment seems to take place in the illusion produced by the designs of figure 198 (Hering) and figure 199 (Zollner). In figure 198 the long lines are straight and parallel, but seem curved ; in the upper part of the figure they appear to have their concave sides turned towards each other; in the lower part the contrary takes place. 197. Fig. 198. In the figure of Zollner, the long straight lines, which are parallel, seem to converge or diverge upwards, following the direction of the small oblique lines. We can conceive that these illusions would be produced if the judgment attributes a too large size to the acute angles. Accord- ing to Helmholtz, the movements of the look play a great part in the production of these illusions; they appear much more pronounced if we keep the look quiet. If we bring a point slowly from right to left 340 PHYSIOLOGIC OPTICS in front of the figure of Zollner, while fixing it with the look, the lines seem to move; those which appear to incline their upper extremity to 1 m K * > J5 ;> Z s/ \i Fig. 199. the right seem to ascend, while the others seem to descend, and the in- clination seems at the same time more pronounced. If we bring the /K \x Fig. 200. point from left to right, the lines affect a reverse movement. The ex- periment is not very easy to perform, but we can obtain the same effect more easily by keeping the point which we fix motionless and moving the drawing. OPTIC ILLUSIONS 341 c. The two long straight lines of figure 200 have the same length, but b appears smaller than a. d. We frequently estimate cylinders too large. If we place a large bottle on a sheet of paper, and trace its circumference, we can with difficulty conceive, after having taken away the bottle, that we are not deceived, so small is the circle. Another error of judgment is well known: we present a tall hat to some one, asking him to indicate on the wall its height, starting from the ground. Generally the height pointed out is about half too large. e. I have already mentioned the reverse of relief which we observe when we change the stereoscopic images sideways, and which is known under the name of pscudoscopia. We sometimes observe the same phe- nomenon under other circumstances. If, for example, we fix with one eye the posterior part of the upper border of a lamp chimney, we obtain quite easily the illusion that this part is in front, and the glass seems Fig. 201. at the same time to lean towards the observer. Observing with one eye the cast of a medal, it may be difficult to tell whether the figure is hollow or in relief. Analogous phenomena often present themselves in cases in which a drawing may be interpreted in two different ways. Thus figure 201 342 PHYSIOLOGIC OPTICS seems composed of cubes, the illuminated side of which is turned some- times to the right, sometimes to the left. When one interpretation has predominated for a certain time, the other suddenly presents itself. We can instigate the change by quickly imagining the contrary relief. f. We mention, finally, the illusions of movements of exterior ob- jects, which often present themselves in consequence of the false judg- ment of the movements which we ourselves make. One of the best- known examples is that of the apparent movements of objects when we are traveling by rail; the traveler does not take into account his own change of position and attributes the movement to the exterior objects. The reverse illusion often presents itself when one train stops alongside of another ; if the latter is put in motion, we often attribute the movement to our own train. Waltzers see exterior objects rotate around them in a direction contrary to their own rotation. The move- ment seems to continue for some time after stopping, on account of the persistence of the jerking movements of the eyes (page 299). Generally, exterior objects do not appear to be displaced during the movements of the look, but if we bring the look quickly from one of the limits of the field to the other, exterior objects seem to move in the contrary direction. Aubert has described the following illusion, which is due to a like reason. In the shutter of a completely dark room we make a vertical slit, which is then the only object visible. Leaning the head towards one of the shoulders, the slit seems to undergo a rotation in the reverse direction ; it no longer appears vertical. We judge the inclination of the head to be less than what it is, almost in the same manner as the move- ments which we cause the eyes to make while keeping the lids closed, always seem less than they really are. The experiment also succeeds outside of the dark room, especially if we place ourselves in such a way as not to see any other lines, the direction of which we know to be vertical. Bibliography. Zollner. Ueber eine neue Art von Pseudoscopie. Pogg. Ann., CX, p. 500. Hering (E.). Bdtrage zur Physiologic. Leipzig, 1861, I, p. 65. Aubert (H.). Physiologic der Netzhaut. Breslau, 1865. TREATISES TO CONSULT. GEuvres ophtalmologiques of THOMAS YOUNG, translated and annotated by M. TSCHER- NING. Copenhagen, Hoest, 1894. The memoires of Young were published at the beginning of the century in the Transactions of the Royal Society of London and reprinted in his Lec- tures (London, 1807). A later reprint in Peacock Works of Thomas Young, London, 1855, is not to be recommended, the reproduction therein of the pretty illustrations of Young being quite defective. The works of Young are often of a very difficult reading, but many of the modern ideas on ocular dioptrics and on the vision of colors dated from him. On account of the great importance of the works of Young, I have published a French edition of them which I have tried to make of an easier reading by explanatory notes. v. HELMHOLTZ (H.). Handbuch der physiologischen Optik. Leipzig, 1867. This monu- mental work is indispensable to all those who desire to make a profound study of physiologic optics, but it is not a very easy study. The book contains nearly all that was known on the subject of physiologic optics at the time of its appearance and a complete bibliography. In 1885, the author began a new edition of it (Leop. Voss, Hamburg), which was continued after his death by A. KCENIG. The only difference between it and the former consists of a number of intercalations, which, however, are not of very great importance, if we except those of the second part which contain the results of the researches on the vision of colors of Kcenig, Dieterici, Brodhun, Uhtho/, etc. The latter portion of the work contains, from the hand of K&nig, a complete bibliography, which will be very useful to the investigators of the future. The work of HELMHOLTZ was translated into French by E. JAVAL and N. T. KLEIN (Masson, 1867), but this translated edition is exhausted. The student of physiologic optics must not dispense with reading the original memoirs of this great scholar. HERMANN (L.). Handbuch der Physiologie der Sinnesorgane. 2vol. Leipzig, 1879. The part which has to do with vision has been treated by FICK (A.) (Dioptrics), KUEHNE (Chemistry of the Retina] and HERINO (E.) (Movement of the Eyes, Binocular Vision). Less important works and of an easier reading : FICK (A.). Lehrbuch der Anatomie und Physiologie der Sinnesorgane. Lahr, 1864. KATSER(H.). Compendium der physiologischen Optik. Wiesbaden, 1872. Apart from some parts which the author has treated in an original manner, this work is an extract from v. HELMHOLTZ. AUBERT (H.). Physiologische Optik, in Handbuch der gesammten Augenheilkunde von A. ORAEFE und TH. SAEMISCH. Leipzig, 1876. The most original part is an extract from : AUBERT (H.). Physiologie der Netzhaut. Breslau, 1865, a book which contains a great number of very elaborate researches on the retinal functions. LE CONTE (JOSEPH). Sight. London, 1881. In spite of some errors this work is very instructive on account of its originality. From the time prior to v. HELMHOLTZ dates MACKENZIE ( W. ). The Physiology of Vision. London, 1841, being based especially on the works of YOUNO and WHEATSTONE. 343 844 PHYSIOLOGIC OPTICS What was known on the subject of physiologic optics in the last century is found in : PORTERFIELD (WILLIAM). A Treatise on the Eye. 2 vol. Edinburgh, 1759, and in: JUBIN (JACQUES). Essai sur la vision distincte et indistincte in the great treatise on optics of EGBERT SMITH ( A Complet System of Opticks). London, 1738. In French Cours complet tfoptique of EGBERT SMITH, translated by PEZENAS. Paris, 1767. The work of JURIN on indistinct vision is still the best on this somewhat neglected question. Of the works on more or less important branches of physiologic optics we may cite : BONDERS (F. C.). On the Anomalies of Accommodation and Refraction of the Eye. London, 1864. In German by O. BECKER. Wien, 1866. In French by E. JAVAL, in DE WECKER. Traite des maladies des yeux. Paris, 1866. On account of its remarkable clearness BONDERS is of a very easy reading, and may be recommended to every young medical student who desires to begin the study of this branch of ophthalmology. The same subject has been treated in : NAGEL (A.). Die Anomalien der Refraction und Accommodation des Auges in Grafe und Sdmisch. Handbuch der Augenheilkunde. Leipzig, 1880. LANDOI/T (E.), in DE WECKER and LANDOI/T. Traite complet d'ophtalmologie, 1884. MAUTHNER (L.). Vorlesungen iiber die optischen Fehler des Auges. Wien, 1876. MAUTHNER (L.). Farbenlehre. Second edition. Wiesbaden, 1894. The books of Mauth- ner are written in a very clear style and bear the impress of great learning. Memoires d'ophtalmometrie, annotated and preceded by an introduction by E. JAVAI,. Paris, Masson, 1890. This work contains a great number of notes on ophthalmometry by different authors. E. JAVAL. Manuel de Strabisme. Paris, Masson, 1896. This work is important for the study of binocular vision. INDEX Abduction, 301 Aberration, chromatic, 80, 100, 109, in, 114 produced by accommodation, 175 spherical, 80, 95, 104 Aberroscope, the, 102 Aberroscopic phenomena, 144, 145, 171 Absorption of light, 2 Accommodation, 38 amplitude of, 81, 160 astigmatic, 129 author's theory of, 167 central and peripheral, 173 Cramer's theory of, 164 Helmholtz theory of, 165 H. Muller's theory of, 166 influence of, 313 mechanism of, 162, 163, 165, 167 paralysis of, 161 relative amplitude of, 303 skiascopic examination of, 174 spasm of, 162 Young's theory of, 167 Accommodation and convergence, relation between, 303 Achloropsia, 268 Acuity, visual, 278 peripheral, 282 Adduction, 301 Aerial images, 34 perspective, 314 After-images, 241 positive, 242 negative, 242 Akyanopsia, 268 Amblyopia exanopsia, 333 Ametropia, 8 Anaglyphs, 322 Anerythropsia, 268 Angle alpha, 36, 63 critical, 9 meter, 302 of convergence, 10 of deviation, 10 of incidence, 2 of refraction, 2 of visibility, 279 Aniridia, 165 Antagonism of the visual fields, 323 Aperture of an optic system, 34 Aphakia, 80, 92 Asthenopia, accommodative, 91, 161 of astigmatic patients, 132 tarsal, 148 Astigmatic persons, examination of, 133 surfaces, 62 Astigmatism, 115, 137 against the rule, 125 by incidence, 96, 119 crystalline, 125 corneal, 122, 123, 125, 128 irregular 80, 137, 139 latent, 129 oblique, 125 of the human eye, 121 physiologic, 122 post-operative, 130 produced by the form of the surfaces, 115 regular, 80, 115, 118 ophthalmometric and subjective, 125 supplementary, 126 symptoms of, 132 with spherical aberration, 140 with the rule, 125, 132 Arteries, pulsation of, 199 Atropine, 212 Auto ophthalmoscope, 200 Base line, 302 Binocular ophthalmoscope, 321 Binocular vision, 287 projection in, 307 theories of, 325, 326, 328 Black, sensation of, 238 absolute, 238 Brightness, 236 Brushes of Haidinger, 157 Cardinal points, 19 methods of finding, 20, 21 of the crystalline lens, 24 of the human eye, 32 Cataract, 168, 233 Cat's eye, amaurotic, 190, 191 Centering, defect of, 66 345 Characteristic part of a pencil of light, 139 Chess-board of Helmholtz, 216 Chromatic aberration, 80, loo, 109, in, 114 correction of, 1 14 Chromatoptometer of Chibret, 270, 271 Ciliary corona, 157 Ciliary muscle, discovery of. 169 structure of, 170, 186, 187 Cocaine, 212 Color blindness, 263 Color-box of Maxwell, 248, 253 Color curves of Maxwell, 254 of a dichromatic. 267 Color phenomena of contrast, 238, 241 Colors, complementary, 238 equation of, 247 methods of mixing 247 results of mixtures of, 250 sensations of, 237 spectral, 248 the principal, 272 the standard, 253 Color sense, 234 clinical examination of, 269 Color table of Helmholtz, 260 of Maxwell, 252, 256, 265 of Newton, 237, 250 Color vision, mechanism of, 272 Ebbinghaus's theory, 275 Helmholtz theory, 273 Hering's theory, 274 Koenig's theory, 275 Parinaud's theory, 275 Young's theory, 272 Concave spherical mirrors, 3 aperture of, 3 apex of, 3 axis of, 3 principal focus of, 3 principal focal distance of, 3, 6 reflection on, 4 Conjugate points, 2, 5 Conoid of Sturm, 115 Contact glasses, 145 Contact of corneal images, 48 Controlled reading, 336 Convergence, defect of, 302 measurement of, 301 negative, 300 Convex mirrors, 6 Co-ordinates, center of, 306 polar, 306 Cornea, basilar part of, 56 conical, 54 examination of peripheral parts of, 56 increase in curvature of, 162 in keratoconus, 59, 60, 6l optic part of, 56 refracting power of, 31, 57 results of measurements of, 54 utilized part of. 53 Crystalline lens, 28 accommodative layer of, 184 advance of, 162 astigmatic accommodation of, 128 Crystalline lens, catoptric images of, 163,164 change in thickness of, 182 contents of, 184 cortical portion of, 30 deformity of, during accommodation, 179 increase in curvature of, 162 measuring aberration of. 107 measuring surfaces of, 67, 68, 69, 70 luxation of, 80 nucleus of, 30, 184 obliquity of, 128 refracting power of, 31 total index of, 30 Cylindrical glasses, 121, 134 Czermak, experiment of, 75 Daltonism, 263 bilateral, 264 monolateral, 264 Decentered eyes, 131 Deformity of internal surfaces in astigma- tism, 126 Descartes, law of, 8, 20 Dichromasia, 263, 266 Dichromatopsia, 263 Diffraction in the eye 157 Diffusion circles, 73 98, 172 size of, 73 examination of, 98 Diplopia. physiologic binocular, 307 paradoxical, 334 Disc keratoscopic, 61 of Benham, 230 of Helmholtz, 230 of Masson, 229 of Placido, 6 1 ofVoIkmann, 295 Dispersion, 109, 113 Distance, indirect judgment of, 313 sensation of, 332 Doubling, methods of in ophthalmometry,48 Dove, experiment of, 240 Empiric theories, 217 Entoptic phenomena, 147 analysis of, 151 manner of observing, 147 parallax of, 151 Entoptic object, determination of position of, 152 examination of refraction of, 152 Entoptic observation of vessels of retina, 153 Entoptoscope, the, 150 Eye, an artificial, 218 aperture of the optic system of the, 34 color of fundus of the, 198 center and axes of rotation of, 287 directing, 308 emmetropic, 8l methods of illuminating fundus of the, 190 muscles of, 289 340 Eye, optic axis of the, 37 optic constants of the, 27 optic system of the, 27, 31 schematic, of Helmholtz, 28 the simplified, 26 Eyes, associated movements of the, 300 jerking movements of the, 299 relative movements of the two, 299 rotary movements of, 297 Erect image, examination by, 193, 197 Eserine, 212 Exophoria, 331 Far point, 8 1 Fixation, point of, 36 Fechner, law of, 224 explanation of the, 224 verification of the, 225, 226, 227 Focal distance, anterior, 19 of a convex mirror, 6 of a concave mirror, 7 posterior, II, 19 principal, 3 Focal interval of Sturm, 163 lines, 115, 116, 143 Focus, anterior, 19 posterior, 19 principal, 3, 4 Form sense, the 277 measure of the, 277, 279 Foucault, principle of, 99 Fovea, 36, 79, 198, 221, 232 Fraunhofer, experiments of, 112 lines of, no, 235, 245 Gauss, theory of, 18, 34 Glabella, 310 Globe, elongation of, 162, 168 H Hemeralopia, 232 Hess and Heine, observations of, 181, 188 Homatropine, 212 Hooke, experiments of, 277, 278 Horopter, 310 Hue, of color, 236 changes of, 236 Hypermetropia, 80, 82, 90 absolute, 90 axial, 79 correction of, 82 latent, 90, 194 Hypoconchia, 86 Iconoscope of Javal, 321 Identical points of the retina, 324 Identity, theories on the nature of, 325 Image, 2 defects of the, 118 erect, examination by, 193, 197 inverted, examination by, 200 of mirrors, 3, 4 of lenses, 15 of any optic system, 20 produced by a small aperture, 2 real, 2 useful, 37 virtual, 2 Images, displacement of in accommodation, 180, 181. manner of observing the, 42, 45 of Purkinje, 28, 29, 40, 42, 64, 65 of the eye, false, 39 of the second order, false, 44 suppression of double, 311 Innervation, judgment of, 305 Intensity, 236 Inter-focal distance, 115, 116 Internal surfaces, position of, 67 centers of, 69 deformity of, 126 Interval of an optic system, 22, 25 Inverted image, examination by, 200 Iris, 164 apparent, 34 Iridodonesis, 213 Isopters, 283 Jaeger, test-types of, 280 Javal, test chart of, 280 Judgment, unconscious, 313 K Keratoconus, 80, 131, 176, 177 Keratoscope of de Wecker and Massilon, 1 76 Keratoscopic disc, 6l image, 60, 61, 62, 63 Lens, 14 achromatic, ill aplanatic, 95 axis of, 14 concave, 16 crossed, 96 crown, 96 flint, 96 focal distance of a, 14, 17 infinitely thin, 14, 23 measuring focal distance of, 17 optic center of, 14 over-corrected, 95 phenomena dependent on spherical ab- erration of, 96 refracting power of, 18 Lenticonus, 80 false, 80 34: Leucotna, central, 233 Leucoscope, the, 270 Light, harmful, 39 lost, 39 monochromatic, 157, 234 quantity reflected, 8 rectilinear propagation of, I useful, 39 Light sense, the, 224 measurement of, 228 Lithium flame, 234 Listing, axes of, 293 law of, 217, 218, 289, 290, 292, 294, 296, 297 Luminous point, analysis of the, 143 figures of, 143 Luminous rays, I incident, 3 reflected, 3 M Macula, 198, 233, 262 Maddox test, 331 Meissner, experiments of, 294 Menisci, 16 Meridian, apparently vertical, 294 Meter angle, 302 Meyer, H., experiment of, 239 Micrometer, 197 Microphthalmia, 55 Mile, experiment of, 75 Mires, 47 Mirrors, concave spherical, 3 plane, 3 portion of used, 7 Monochromasia, 269 Musca- volitantes, 149, 155 Mydriatics and myotics, 212 Myopia, 80, 84, 89, 163 atropine treatment of, 89 axial, 79 correction of, 81 dangerous, 84 treatment of, 89 N Nativistic theories, 219 Near point, 8 1 determination of, 160 Neutral point in the spectrum of color-blind, 263 Nicol prism, 157 Nodal points, 19, 32 Normal, of a surface, 14 Nyctalopia, 233 Oblique illumination, 213 Ocular movements, 287, 299 muscles, action of, 289 Opaque bodies, I Ophthalmometer, 48, 49, 50 of Brudzewski, 59 of Helmholtz, 49, 56 of Javal and Schioetz, 51, 56 Ophthalmometry, 47 Ophthalmodynamometer of Landolt, 302 Ophthalmophakometer, 44, 64, 175, 179 Ophthalmoscope, 190 binocular, 321 of Coccius, 7 of Cramer, 163, 189 of Helmholtz, 192 principle of, 192 Ophthalmoscopic examination of refracting media, 204 field, 196, 202 magnification, by erect image, 194 magnification by inverted image, 200 Ophthalmoscopy, 190 Optic axis, 36 constants of the eye, 27 illusions, 338 properties of bodies, I Optic system of the cornea, 31 of the crystalline lens, 31 of the eye, 31 aperture of the eye, 34 obliquity of the eye, 143 Optogram, 221 Optometer, 83 of Badal, 160 of George Bull, 160 of Mile, 75 ofScheiner, 75 ofWeiland, 135 of Young, 75, 144, 173 Papillary excavations, 197, 199 Papilla, 197, 198, 238 scleral border of, 199 Paracentesis, 189 Paracentral shadow, 209 theory of, 209 explanation of, 209 Parallax, influence of the binocular, 317 Penumbra, 2 Perception of depth, monocular, 313 binocular, 317 Periscopic glasses, 96, 135 Phosphene of Czermak, 156 Phosphorescence, 190 Photoptometer of Charpentier, 228, 247 of Foerster, 228 Placido, disc of, 61 Plates of Helmholtz, 204 Point of fixation, 36 Position of anatomic equilibrium, 334 of cardinal points, 25 of the centers, 67 of the surfaces, 67 of functional equilibrium of eye, 334 348 Presbyopia, 161 Primary direction of eye, 289 position, 289 Principal focus, 3, 4 focal distance, 3 meridians, 115 planes, 19 points, 19 Prism, achromatic, no, in a vision directt, no, in Nicol, 157 refraction by a, IO with total reflection, 9 Wollaston, 50 Projection in binocular vision, 307 Projections, center of, 307 general laws of, 304 theory of, 325 Pseudoscope, the, 320 Pseudoscopia, 341 Punctura proximum, 76, 8 1 remotum, 76, 8l Pupil, 211 apparent, 34, 21 1 contraction and dilatation of, 21 1 in accommodation, 213 influence of light on, 212 movements of, 212 nerve control of, 21 1 of albinos, 191 of entrance, 35 of exit, 35 real, 34 variations of refraction in, 145 Purity of color, 236 Radii, direct determination of, 70 Radius vector, 306 Ragona Scina, experiment of, 239 Reflection, 2 images of the eye, 176, 177 regular, 2 total, 8 on a concave mirror, 4 on a plane mirror, 3 Refracting surface, power of, 13 simple, 23 Refraction, 8 anomalies of, 79 by a parabolic surface, 178 by a prism, lo by a spherical surface, II, 12 by plane parallel plates, 10 by a surface of revolution of the second degree, 13 index of, 8 in the pupil, 145 ophthalmoscopic and subjective, 197 Relief, idea of, 327 measurement of, 327 theory of, 326 Retina, 219, 221 Retina, changes of, 221 detachment of, 232 functions of, 221 pigment of, 222 Retina of frog, section of, 223 Retina seen by the ophthalmometer, 199 Retina's own light, 226 Retinal horizon, 294 Retinal purple, 198, 221 discovery of, 222 Retinal oscillations, 243 Saturation of color, 236 Scheiner, experiment of, 75, 96, 249 Scopolamine, 212 Secondary direction, 289 Shade of color, 236 Shadows, I colored, 239 deformity of the, 98 experiments with, 240 Sight, line of, 74 Skiascopic examination for astigmatism, 134 206 field, 20 examination of optic anomalies, 210 Skiascopy, 205 application of, 205 with concave mirror, 205 with plane mirror, 205 Snellen, charts of, 279 Sodium flame, 234 Spectacles, choice of, 87, 161 Spectroscope, 234 Spectrum, 234 colors of, 236 of diffraction, 235 of refraction, 236 Spot of Mariotte, 63, 238, 284 Spherical aberration, 80, 95, 104 Spherometer, 17 Staphyloma, 197 Stenopaic opening, 77 Stereoscope, 317 effect of, 322 of Helmholtz, 320 of Wheatstone, 320 Stereoscopic exercises, 336 images, methods of observing, 319 lustre, 322 parallax, 318 photographs, 322 Strabismic patients, vision of, 334 Strabismus, 329 cause of, 333 concomitant, 329, 330, 332 convergent, of myopes, 334 latent, 330 measurement of, 331 nature of, 333 paralytic, 329 relation between convergent and hyper- metropia, 332 349 Strabismus, relation between divergent and myopia, 333 treatment of, 335 Strontium flame, 237 Synchisis scintillans, 204 Syringe of Pravaz, 189, 214 Tapetum, 190 Telescopic system, 22 Telestereoscope of Helmholtz, 321 Thallium flame, 234 Threshold, the, 227 determination of 231 Tint, 236 Tore, 119, 136 Translucent bodies, I Transparent bodies, I Trichromasia, abnormal, 261 Triplopia, binocular, 335 Troxler, phenomenon of, 242, 285 Veins, pulsation of, 199 Vision, "recurrent," 243 single, antipathy to, 336 Visual acuity, 278 central, 277 measurement of, 278, 279 peripheral, 282 Visual acuity and illumination, relation b&. tween, 281 Visual field, projection of the, 304 Visual fields, antagonism of the, 312, 323, Visual impressions, projection of, 304 Visual line, 36 Volkmann, disc of, 295 experiments of, loo W White, normal, of Koenig 238 Wollaston, experiment of, ill prism of, 50 LIST OF AUTHORS Abbe, 26, 28. 35. Agabobon, 243. Airy, 121. Almeida (d'), 322. Argyll Robertson, 213. Arlt, 86, 94, 163, 171, 187, 213, 214, 220. Aubert, 56, 72, 261, 342, 343. Babbage, 193. Badal, 83, 84, 160, 202. Becker, 46, 344. Beer, 190. Bellarminoff, 191, 210. Benham, 230 v. Bezold, 114. Bidwell, 243. Bitzos, 209, 210. Bjerrum, 202, 210, 231, 233, 283, 286. Blix, 46. Boehm, 91, 94, 332, 337. Boll, 222, 223. Bouguer, 225, 228, 233. Bourgeois, 55. Bouty, 26. Bowman, 169, 189. Brewster, 151, 152, 159, 319, 328. Brodhun, 244, 276. Brown-Sequard, 211. Brudzewski, 59, 72, 105, 106, 108. Bruecke, no, 169, 189, 190, 193, 210, 326, 328. Bull (George), 129, 133, 136, 148, 149, 160, 161, 220. Burkhardt, 280. Burow, 153. Charpentier, 228, 233, 243, 247. Chibret, 270, 271, 276. Coccius, 46, 50, 83, 166, 187, 189, 210. Cohn, 86, 213, 270. Coronat, 164. Cramer, 163, 164, 165, 179, 181, 182, 186, 189. Cretes, 301, 302, 332. Crzellitzer, 159, 186, 189. Cuignet, 205, 210. Gumming, 190, 193, 2 to. Czermak, 75, 156, 166. Daae, 270. Dalton, 263, 268, 276. Darier, 149, 159. Darwin, 219. Davis, 243. Demicberi, 30, 43, 80, 94, 145, 178, 184, 204, 210. Descartes, 8, 20, 163 Dieterici, 236, 259, 263, 266, 267, 276. Dimmer, 93, 94. Dobrowolsky, 129. Dojer, 287. Dollond, in. Doncan, 151, 152, 159. Donders, 50, 54, 83, 86, 88, 89, 90, 91, 92, 94, 121, 125, 136, 151, 152, 158, 161, 169, 197, 219, 263, 264, 287, 289, 292, 297. 2 98, 33, 33 2 , 337. 344- Dove, 240, 322, 323. Druault, 157, 158, 159, 281. Dubois (Raphael), 49 Dubois-Reymond, 213, 220, 223. Ebbinghaus, 275, 276. Eissen, 125. Erikstn, 56, 57, 58, 59, 72, 120. Euler, ill. Fechner, 224, 225, 226, 227, 228, 230, 231, 232, 233, 243. 244. Fick, 294, 298, 343. Foerster, 170, 189, 228, 233. Fontana, 170. Fraunhofer, no, 1 12, 114, 235, 245. Fukala, 89. Galien, 325. Gariel, 26. Gauss, 18, 19, 26, 27, 34. v. Genderen Stort, 222, 223. Giraud-Teulon, 321, 322, 325. Goulier, 12 1, 136. v. Graefe, 83, 107, 189, 200, 329, 333, 334, 336, 337- Graefe (Alfred), 165, 189, 333, 337. Green, 280. Groenouw, 283, 286. Guillery, 281, 284, 286. Haidinger, 157, 159. Hamer, 54- Hansen Grut, 232, 329, 331, 332, 333, 334, 337- Hay, 292. Heath, 26. Heine, 181, 188, 189. v. Helmholtz, 5, 26. 28, 30, 47, 49, 50, 54, 56, 79, 109, 112, 114, 121, 149, 165, 166, 167, 169, 170, 171, 181, 182, 183, 184, 187, 188, 189, 190, 192, 193, 196, 204, 210, 213, 216, 217, 218, 219, 230, 248, 249, 251, 260, 268, 273, 274, 275, 276, 277, 278, 279, 287, 290, 293, 298, 314, 320, 321, 324, 328, 339, 343. Hencke, 166. Henle, 36. Hensen, 166, 187. Hering, 219, 269, 274, 275, 276, 291, 297, 300, 309, 312, 339, 342, 343- Hermann, 128, 292, 343. Herschel, 26. Hess, 181, 188, 189. Ileuse, 46. v. Hippel, 264, 265, 273. Hirschberg, 83, 332. Hocquard, 185. Holmgren, 268, 269. Holth, 60, 61, 184, 284, 285, 286. Home, 163. Hooke, 277, 278, 286. Hueck, 165, 181, 189, 213, 297, 298. Huyghens, 276. Iwanoff, 187. Jackson, 104, 108, 174, 210. Jaeger, 200, 280. Jamin, 26. Javal, 36, 40, 50, 51, 52, 55, 56, 60, 62, 72, 83, 89, 114, 122, 123, 125, 126, 128, 131, 132, 135, 138, 186, 231, 240, 280, 281, 290, 296, 298, 302, 303, 308, 312, 321, 323, 326, 327, 328, 331, 333, 334, 335, 33 6 , 337, 343. 344- Johnsson, 76. Jurin, 78, 344. Kagenaar, 50. Kaiser, 308, 312, 343. Kepler, 38, 163, 325. Klein, 233, 343. Knapp (H.)t I2I I2 5, 136. Knapp, Jr., 309. Kcenig, 236, 238, 244, 249, 259, 263, 266, 267, 268, 270, 275, 276. Koster, 172, 176, 182, 275, 276. Krause, 183, 189. Krenchel, 232, 233, 270, 276. v. Kries, 275, 276. Kuehne, 222, 223, 343. Laiblin, 156. Lambert, 225, 233, 238, 249, 276. Lamare, 299, 303. Landolt, 94, 297, 302, 332, 344. Langenbeck, 163, 189. Leber, 268. Le Conte, 343. Leonardo da Vinci, 37. Leroy, 197, 208, 209, 210. Listing, 30, 38, 151, 159, 217, 218, 289, 290, 292, 293, 294, 296, 297, 298, 311. Lorenz, 26. Mace de Lepinay, 244, 276. Mackenzie, 343. Maddox, 331. Mannhardt, 170, 189. Mariotte, 238, 283, 284, 285, 294. Martin, 125, 129. Mascart, 79, no. Masselon, 123, 176, 177. Masson, 229, 230, 231, 233, 241, 249, 260. Matthiessen, 28, 30, 38, 56. 352 Mauthner, 50, 94, 166, 269, 344. Maxwell, 248, 249, 251, 252, 253, 254, 256, 257, 258, 259, 260, 261, 262, 266, 267, 273, 276. Meissner, 294, 296, 298. Meyer (H.), 108, 239. Mile, 75, 78. Miiller (H.), 153, ! 54. *59, I 66 , l6 9, 1 7, 189, 221, 275. Muller (Joannes), 311, 312, 324, 325, 328. Nagel, 302, 303, 328, 344. Newton, 5, 81, in, 237, 238, 250, 251, 252, 255, 2 59, 276, 325, 328. Nicati, 244, 276. Nordenson, 125, 136. Ostwalt, 93, 94, 128. Panum, 326, 328. Parent, 205, 208, 210. Parinaud, 232, 245, 246, 247, 275, 276,333. Petit (Jean Louis), 183, 189. Pfalz, 125. Pfluger, 93, 239, 270. Placido, 61, 123. Porta, 37. Porterfield, 325, 344, Pouillet- Muller, 26. Pravaz, 189, 214. Preyer, 268. Prentice, 303, 332. Purkinje, 40, 41, 42, 44, 46, 64, 80, 153, I 5 6 *59i l6 3, l66 i *89, 200, 213, 242, 243, 260, 276. Raehlmann, 333. Ragona Scina, 239. Ramsden, 163. Rayleigh, 258, 262, 263, 276, 314. Ree, 139, 140, 141, 142, 143, 146. Risley, 87. Rochon Duvignaud, 189. Rose, 270. Ruete, 200, 210, 297, 298. Salomonsohn, 157, 159. Scheiner, 38, 75, 76, 78, 96, 100, 162, 249. Scbioetz, 40, 50, 51, 52, 56, 123, 125, 136, 138, 57, 158, 159, '86, 290, 332. Schlemm, 169. Schmidt- Rimpler, 204. Schweigger, 136, 333. Seebeck, 268, 270, 276. Smith (Robert), 286, 344. Snellen, 84, 279, 280, 281. Snellius, 8. Sous, 83. Stadfeldt, 33, 38, 93, 106, 107, 108, 168, 1 86, 189, 214. Steiger, 55. Stellwag, 91, 94, 281, 286, 333. Stilling, 86, 270. Stokes, 135. Sturm, 115, 132, 136, 163. Sulzer, 55, 56, 57, 58, 59, 72, 128, 129, 146. Troxler, 242, 285, 299. Tscherning, 38, 46, 50, 72, 78, 94, 108, 114, 136, 146, 159, 189, 220, 276, 286, 298. Turk, 199. Uhthoff, 276. Vacher, 129. Verdet, 26. Vierordt, 156. Vcelkers, 166, 187. Volkmann, 100, 101, 108, 288, 295, 296, 297, 298, 325, 328. Wecker (de), 88, 123, 176, 204, 331, 333. Werlein, 75. Weyde (v. d.), 266. Wheatstone, 317, 319, 320, 326, 328, 336, 343- Wollaston, 50, ill, 114, 135, 325. Wullner, 26. Young, 30, 38, 47, 75, 77, 101, 102, 103, in, 112, 113, 121, 138, 144, 145, 156, 157, 160, 161, 167, 168, 169, 173, 174, 197, 220, 240, 255, 272, 273, 275, 298, 3^3, 315, 3^6, 343- Zeiss, ill. Zinn, 185. Zoellner, 339, 340, 342. Zumft, 275, 276. 353 THE PRINCIPLES OF REFRACTION in the Human Eye, Based on the Laws of Conjugate Foci BY SWAN M. BURNETT, M. D., PH. D. Professor of Ophthalmology and Otology in the Georgetown University Medical School Director of the Eye and Ear Clinic, Central Dispensary and Emergency Hospital ; Ophthalmologist to the Children's Hospital and to Providence Hospital, etc., Washington, D. C. In this treatise the student is given a condensed but thor- ough grounding in the principles of refraction according to a method which is both easy and fundamental. The few laws governing the conjugate foci lie at the basis of whatever pertains to the relations of the object and its image. To bring all the phenomena manifest in the refraction of the human eye consecutively under a common explanation by these simple laws is, we believe, here undertaken for the first time. The comprehension of much which has hitherto seemed difficult to the average student has thus been rendered much easier. This is especially true of the theory of Skiascopy, which is here eluci- dated in a manner much more simple and direct than by any method hitherto offered. The authorship is sufficient assurance of the thoroughness of the work. Dr. Burnett is recognized as one of the greatest authorities on eye refraction, and this treatise may be described as the crystallization of his life-work in this field. The text is elucidated by 24 original diagrams, which were executed by Chas. F. Prentice, M. E. , whose pre-eminence in mathematical optics is recognized by all ophthalmologists. Bound in Silk Cloth. Sent postpaid to any part of the world on receipt of price, $I.OO (4s. 2d.) published by THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL, TRADES, I9TH AND BROWN STS., PHILADELPHIA, U.S.A. THE OPTICIAN'S MANUAL VOL. I. BY C. H. BROWN, M. D. Graduate University of Pennsylvania ; Professor of Optics and Refraction ; formerly Physician in Philadelphia Hospital ; Member of Philadelphia County, Pennsylvania State and American Medical Societies. The Optician's Manual, Vol. I., has proved to be the most popular work on practical refraction ever published. The knowledge it contains has been more effective in building up the optical profes- sion than any other educational factor. A study of it is essential to an intelligent appreciation of Vol. II., for it lays the foundation structure of all optical knowl- edge, as the titles of its ten chapters show : Chapter I. Introductory Remarks. Chapter II. The Eye Anatomically. Chapter III. The Eye Optically ; or, The Physiology of Vision. Chapter IV. Optics. Chapter V. Lenses. Chapter VI. Numbering of Lenses. Chapter VII. The Use and Value of Glasses. Chapter VIII. Outfit Required. Chapter IX. Method of Examination. Chapter X. Presbyopia. The Optician's Manual, Vol. I., is complete in itself, and has been the entire optical education of many successful opti- cians. For student and teacher it is the best treatise of its kind, being simple in style, accurate in statement and comprehensive in its treatment of refractive procedure and problems. It merits the place of honor beside Vol. II. in every optical library. Bound in Cloth 422 pages colored plates and Illustrations. Sent postpaid on receipt of $1.5O (6s. 3d.) published by THE KEYSTONE, THE ORGAN OP THE JEWELRY AND OPTICAL. TRADES, I9TH & BROWN Sxs., PHILADELPHIA, U. S. A. THE OPTICIAN'S MANUAL VOL. II. BY C. H. BROWN, M. D. Graduate University of Pennsylvania ; Professor of Optics and Refraction ; formerly Physician in Philadelphia Hospital ; Member of Philadelphia County, Pennsylvania State and American Medical Societies. TICIANS The Optician's Manual, Vol. II., is a direct continuation of The Optician' a Manual, Vol. I. , being a much more advanced and comprehensive treatise. It covers in minutest detail the four great subdivisions of practical eye refrac- tion, viz : Myopia. Hypermetropia. Astigmatism. Muscular Anomalies. It contains the most authoritative and complete researches up to date on these subjects, treated by the master hand of an eminent oculist and optical teacher. It is thoroughly prac- tical, explicit in statement and accurate as to fact. All refrac- tive errors and complications are clearly explained, and the methods of correction thoroughly elucidated. This book fills the last great want in higher refractive optics, and the knowledge contained in it marks the standard of professionalism. Bound in Cloth 408 pages with illustrations. Sent postpaid on receipt of SI.5O (6s. 3d.) published by THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL. TRADES, I9TH & BROWN STS., PHILADELPHIA, U. S. A. OPHTHALMIC LENSES Dioptric Formulae for Combined Cylindrical Lenses, The Prism-Dioptry and Other Original Papers BY CHARLES F. PRENTICE, M. E. A new and revised edition of all the original papers of this noted author, combined in one volume. In this revised form, with the addition of recent research, these standard papers are of increased value. Com- bined for the first time in one volume, they are the greatest compilation on the subject of lenses extant. This book of over 200 pages contains the following papers : Ophthalmic Lenses. Dioptric Formulas for Combined Cylindrical Lenses. The Prism=Dioptry. A Metric System of Numbering and Measuring Prisms. The Relation of the Prism-Dioptry to the Meter Angle. The Relation of the Prism-Dioptry to the Lens Dioptry. The Perfected Prismometer. The Prismometric Scale. On the Practical Execution of Ophthalmic Prescriptions involving Prisms. A Problem in Cemented Bifocal Lenses, Solved by the Prism=Dioptry. Why Strong Contra=(ieneric Lenses of Equal Power Fail to Neutralize Each Other. The Advantages of the Sphero=Toric Lens. The Iris, as Diaphragm and Photostat. The Typoscope. The Correction of Depleted Dynamic Refraction (Presbyopia). Press Notices on the Original Edition : OPHTHALMIC LENSES. " The work stands alone, in its present form, a compendium of the various laws of physics relative to this subject that are so difficult of access in scattered treatises." New England Medical Gazette. " It is the most complete and best illus- trated book on this special subject ever pub- lished." Horological Review \ New York. " Of all the simple treatises on the prop- erties of lenses that we have seen, this is in- comparably the best. . . . The teacher of the average medical student will hail this little work as a great boon " Archives oj Ophthalmology, edited byH.Knapp, M.D. DIOPTRIC FORMULA FOR COMBINED CYLINDRICAL LENSES. *' This little brochure solves the problem of combined cylinders in all its aspects, and in a manner simple enough for the compre- hension of the average student of ophthal- mology. The author is to be congratulated upon the success that has crowned his labors, for nowhere is there to be found so simple and yet so complete an explanation as is con- tained in these pages." Archives of Oph- thalmology, edited by H. Knapp, M.D. "This exhaustive work of Mr. Prentice is a solution of one of the most difficult prob- lems in ophthalmological optics. Thanks are due to Mr. Prentice for the excellent manner in which he has elucidated a sub- ject which has not hitherto been satisfactor- ily explained." The Ophthalmic Review, London. The book contains HO Original Diagrams. Bound in cloth. Price, $I.5O (6s. 3d.) published by THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, I9TH & BROWN STS., PHILADELPHIA, U. S. A. SKIASCOPY AND THE USE OF THE RETINOSCOPE A Treatise on the Shadow Test in its Practical Application to the Work of Refraction, with an Ex- planation in Detail of the Optical Principles on which the Science is Based. This new work, the sale of which has already necessitated a second edition, far excels all previous treatises on the subject in comprehensiveness and practical value to the refractionist. It not only explains the test, but expounds fully and explicitly the principles underlying it not only the phenomena revealed by the test, but the why and wherefore of such phenomena. It contains a full description of skiascopic apparatus, including the latest and most approved instruments. In depth of research, wealth of illustration and scientific completeness this work is unique. Bound in cloth; contains 231 pages and 73 illustrations and colored plates. Sent postpaid to any part of the world on receipt of $I.OO (4s. 2d.) published by THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, IQTH AND BROWN STS., PHILADELPHIA, U.S.A. OPTOMETRIC RECORD BOOK A record book, wherein to record optometric examinations, is an indispensable adjunct of an optician's outfit. The Keystone Optometric Record Book was specially pre- pared for this purpose. It excels all others in being not only a record book, but an invaluable guide in examination. The book contains two hundred record forms with printed headings, suggesting, in the proper order, the course of examina- tion that should be pursued to obtain most accurate results. Each book has an index, which enables the optician to refer instantly to the case of any particular patient. The Keystone Record Book diminishes the time and labor required for examinations, obviates possible oversights from carelessness and assures a systematic and thorough examination of the eye, as well as furnishes a permanent record of all exam- inations. Sent postpaid on receipt of $1 .OO (4s. 2d.) published by THE KEYSTONE, THE; ORGAN OF THE; JEWELRY AND OPTICAL TRADES, i9TH & BROWN STS., PHILADELPHIA, U.S.A. ttfafofrel THE LIBRARY UNIVERSITY OF CALIFORNIA San Francisco Medical Center THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW Books not returned on time are subject to fines according to the Library Lending Code. Books not in demand may be renewed if application is made before expiration of loan period. 30m-10,'61 (C3941s4)4128