UNIVERSITY OF CALIFORNIA
MEDICAL CENTER LIBRARY
SAN FRANCISCO
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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 <J. Spot of Mariotte of an Eye with a Large Angle a 63
47. The Ophthalmophakometer 64
48. The Images of Purkinje Observed with the Ophthalmophakometer 64
49. Position of the Images of Purkinje, the Lamps being Arranged Vertically .... 65
50. Position of the Images of Purkinje, the Lamps being Arranged Horizontally . . 65
51. Defect of Centering ; Alignment of the Images Impossible 66
52. Determining the Position of an Internal Surface of the Eye 68
53. Determining the Position of an Internal Surface of the Eye 69
54. Calculation of the Size of the Circle of Diffusion 73
55. Rules of the Optometer of Young 76
56. Magnification by Means of the Stenopaic Opening 77
57. Retinal Image in Myopia and Hypermetropia 82
58. Principle of Badal 84
59. Size of Retinal Image when the Focus of the Lens Coincides with the Anterior
Focus of the Eye 84
60. Distribution of the Anomalies of Refraction 85
61. Refraction of a Pencil of Parallel Rays by a Spherical Surface 95
62. Spherical Aberration of a Lens 97
63. Deformity of the Shadows of the Needles 98
64. Experiment of Volkmann loo
65. Distribution of the Light of the Circle of Diffusion 101
66. The Aberroscope 102
67. The Rules of the Optometer of Young 102
68. The Appearance Assumed by the Line of the Optometer of Young 103
69. Deformity of the Shadows in an Eye with Strong Spherical Aberration 105
70. Aberration Over-Corrected Towards the Borders 106
71. Aberration Over-Corrected Above 106
72. Aberration Over- Corrected Everywhere 1 06
72*2. Stadfeldt's Instrument for Measuring Aberration of the Crystalline Lens (Dead) 107
73. Achromatic Prism no
74. Prism a vision directe no
75. Chromatic Aberration of the Eye 112
76. Phenomena of Dispersion 113
77. Circles of Diffusion and Focal Lines of a Regularly Astigmatic System 115
78. Focal Lines of a Regularly Astigmatic System 116
79. Construction of the Elliptical Diffusion Spot 117
80. A Torus 119
81. Focal Line of Lens Placed Obliquely 120
82. Astigmatism by Incidence ; Focal Lines 120
83. Explanation of the Difference in Level (denivellation)* 123
84. Keratoscopic Images of a Case of Keratoconus 131
85. Forms Under which a Luminous Point is Seen by a Regular Eye 139
86. In Regular Astigmatism with Spherical Aberration 140
87. Figures of a Luminous Point Obtained by Combining a Spherical with a Cylindri-
cal Lens 140
88. Forms which a Luminous Point Presents to the Author's Right Eye 141
89. To an Eye with Double Obliquity 141
90. Figures of the Left Eye of M. Ree 142
91. Curved Focal Line 142
92. Irregular Eye (Diplopia) 143
93. Aberroscopic Phenomena 145
94. Diagram of Variations of Refraction in the Pupil 145
95. Course of the Rays in the Author's Right Eye 146
96. Specks on the Anterior Surface of the Cornea 148
97. Striae Produced by Winking 148
98. Prismatic Effect of the Layer of Tears 148
99. Speckled Appearance of the Entoptic Field Produced by Rubbing the Cornea . . 149
100. Star Figure of the Crystalline Lens 149
101. Incipient Cataract Seen Entoptically 149
*[This figure 83 does not quite illustrate the actual picture that we obtain by looking at the cornea! images K
and L with the ophthalmometer. For with the Wollaston prism K is not seen any more, but instead of it we
observe K a at the place indicated in the figure, and K a at a distance, K Kj to the left of K in the direction of
doubling ot the prism. The same is the case with L t , only that L 2 is displaced to the right. But to avoid com-
plication the two images K a and L 3 have been omitted.] W.
FIG. PAGE
101 a. The Eatoptoscope 150
102. Parallax of the Entoptic Phenomena 151
103. Determination of the Position of an Entoptic Object 152
104. Entoptic Luminous Image Surrounded by a Shadow 153
105. Entoptic Observation of the Vessels . . 154
106. Entoptic Observation of the Vessels 155
io6a. Entoptic Phenomenon 158
107. Centripetal Movement of the Catoptric Image 164
108. Putting the Eye Under Water 168
109. Ciliary Muscle of Man 169
no. Ciliary Part of the Eye of a Cat 170
111. Change of Aberroscopic Phenomena During Accommodation 171
112. Appearance of the Luminous Point 172
113. Appearance of the Luminous Point 173
1 130. Slciascopic Examination of Accommodation 175
114. Reflection Images of the Eye 176
115. Reflection Images of the Eye 176
116. Reflection Images of the Eye 177
117. Deformity of the Corneal Image of a White Square in a Case of Keratoconus . . 177
118. Refraction by a Parabolic Surface 178
119. Deformity of the Crystalline Surfaces During Accommodation 179
1 20. Accommodative Phenomena of the Eye 180
121. Accommodative Phenomena of the Eye 180
122. Change of the Anterior Chamber During Accommodation 182
122 a. Reflection Images on the Anterior Surfaces of the Dead Crystalline Lens .... 183
122 b. The Dead Crystalline Lens and the Accommodated Crystalline Lens 184
123. Crystalline Lens of the Ox 185
124. Optic System of the Eye of the Ox , . 186
125. Illumination of the Fundus by a Light for which the Eye is Accommodated . . . 190
126. Illumination of the Fundus by a Light for which the Eye is Not Accommodated . 191
127. Principle of the Ophthalmoscope of Helmholtz 192
128. Magnification of the Fundus, both Patient and Observer being Emmetropic . . . 194
129. Line of Image of Papilla if the Fundus of Patient is Placed Free in the Air. . . 195
130. Magnification of Fundus if Patient is Myopic 195
131. Construction of the Ophthalmoscopic Field 196
132. Magnification by the Inverted Image in Emmetropia 201
133. Influence of Refraction of the Examined Eye on the Magnification if Focus of
Lens Coincides with Anterior Focus of Eye 2OI
134. Influence of Refraction of the Examined Eye on the Magnification if Lens is
Nearer to the Eye than in Fig. 133 202
135. Construction of the Ophthalmoscopic Field by the Inverted Image 203
136. Skiascopy. Plane Mirror 205
137. Skiascopy. Concave Mirror 206
138. Boundaries of the Skiascopic Field 207
139. Theory of Leroy 208
140. Theory of Leroy 208
141. Theory of the Paracentral Shadow 209
142. The Advantage of the Position of the Pupil Near the Nodal Point 215
143. Experiment of Helmholtz 2i6
144. Hyperbolic Chessboard of Helmholtz 217
145. Artificial Eye 218
146. Image of a Window in the Artificial Eye 218
146 a. Section of the Retina of a Frog 223
147. Experiment of Bouger 225
148. Curve Showing the Relation between the Light Sense and the Illumination . . . 227
149. Photoptometer of Foerster 228
150. Disc of Masson 229
150 a. Disc of Helmholtz and Disc of Benham 230
151. Spectrum of Refraction; Spectrum of Diffraction 235
152. Table of Colors after Newton 237
153. Experiment of Ragona Scina 239
154. Experiment with Colored Shadows 240
155. Disc of Masson 241
156. Curves of Parinaud to Show the Threshold for Different Rays of the Spectrum . . 246
FIG. PAGR
157. Color Box of Maxwell 248
158. Mixture of Colors by Means of a Glass Plate 249
159. Table of Colors after Newton 250
1 60. Color Table of Maxwell 252
161. "Color Box" of Maxwell 253
162. Color Curves of Maxwell 254
163. Color Table of Maxwell 256
164. Color Table of Helmholtz 260
165. Color Table of Maxwell 265
166. Color Curves of a Dichromatic 267
167. Color Table of a Dichromatic 267
1 68. Chromatoptometer of Chibret 271
169. Experiment of Hooke 278
170. Measurement of the Visual Acuity by a Grating 278
171. Measurement of the Visual Acuity by a Grating 278
172. Experiment of Hooke, the Optics of the Eye being Defective 278
173. Mariotte's Blind Spot 284
174. Phenomenon of Troxler 285
175. Determination of the Center of Rotation of the Eye 288
176. The Two Axes of Rotation Lying in the Horizontal Plane 288
177. Demonstration of the Law of Listing 290
178. Demonstration of the Law of Listing 291
179. Demonstration of the Law of Listing 292
180. Discs of Volkmann 295
181. Modification of the Experiment of Meissner 296
182. Illustration of the Meter Angle : 302
183. Explanation of Binocular Physiologic Diplopia 308
184. Experiment to Find the Center of Projection 310
185. Horopter of Johannes Muller 311
186. Apparent Form of the Sky 315
187. Influence of Parallax for Stereoscopic Vision 316
188. Principle of Stereoscopic Images 318
189. Stereoscope of Wheatstone 320
190. Pseudoscope of Wheatstone 320
191. Telestereoscope of Helmholtz 321
192. Binocular Ophthalmoscope 322
193. Antagonism of the Visual Fields 324
194. Suppression of one of the Images in Stereoscopic Vision 327
195 to 201. Optic Illusions
XVI
PHYSIOLOGIC OPTICS
BOOK I
OCULAR DIOPTRICS
CHAPTER I
OPTIC PRINCIPLES
1. Optic Properties of Bodies. Bodies are of three kinds : transparent
bodies, through which we can see objects, translucent bodies such as
ground glass, through which we perceive light, but cannot distinguish
form, and opaque bodies. No body is absolutely transparent. Pure
water is transparent, but very little light will pass through a great thick-
ness of water. On the contrary very thin layers of opaque substances
Fig. 1. A, luminous source ; B, opaque body ; C, shadow ; D, penumbra.
are more or less translucent, as all know who have examined micro-
scopic preparations.
2. Rectilinear Propagation of Light. In a homogeneous medium
light is propagated along straight lines which are called luminous rays.
SHADOWS. When rays emanating from a luminous point fall upon
an opaque body there is produced behind the latter a shadow which is
conical in shape. We can construct the form of this shadow by drawing
straight lines joining the different points of the border of the body with
2 PHYSIOLOGIC OPTICS
the luminous point. If, instead of a point, the source is a luminous sur-
face the shadow is surrounded by a penumbra, the intensity of which
diminishes more and more towards the periphery. An observer placed
in the shadow C could not see any point of the luminous surface; placed
in the penumbra D he would see a part of that surface, greater in pro-
portion as he approaches the border.
IMAGES PRODUCED BY A SMALL APERTURE. Rays passing through
a small aperture into a dark room form on a screen an inverted image
of exterior objects. By diminishing the aperture the image gains in dis-
tinctness, but loses in luminosity. Photographs may be taken in this
way.
3. Beflection and Absorption. Rays which strike the surface of an
opaque object are partly absorbed and partly reflected. If the surface is
not polished the rays are reflected in a diffuse manner : each point of the
surface sends back light in all directions. It is through the agency of
this irregularly reflected light that objects are visible, and the fact that
they are visible, whatever may be the position of the observer, provided
the rays are not intercepted, proves conclusively that any point whatever
of the surface sends rays in all directions.
4. Regular Reflection. The more polished the surface the less dif-
fuse is the reflection. Thus the surface of a highly polished mirror is but
slightly visible. Polished surfaces reflect rays regularly following a law
which was 'known from remote ages, viz., that the reflected ray is in the
same plane with the incident ray and the normal to the point of incidence,
and that both rays form equal angles with the normal, which is expressed
by saying that the angle of incidence and the angle of reflection are equal.
The effect of this reflection is to produce images of external objects.
The image of a point is the place where the rays which emanated from
that point meet again after reflection or refraction. In order that the
image may be perfect, all the rays employed should meet in a point. Gen-
erally this condition is not quite fulfilled, there being more or less pro-
nounced aberrations. A point and the image of this point we designate
as conjugate points. An image is real when the rays proceeding from
a point meet again in a point ; it is virtual when it is formed not by the
reunion of the rays themselves, but of their prolongations. A real
image can be received on a screen; a virtual image cannot, but it is visi-
ble to the eye which is in the path of the rays because the optic system
OPTIC PRINCIPLES
A'
of the eye forms a real image of it on the retina, exactly as if the virtual
image was an object.
5. Plane Mirrors. Construction of the Image. Let fall from a point
A (fig. 2) of the object a perpendicular AB on the surface, DE, of the
mirror, and mark on its prolongation a point A' so that AB is equal to
A'B. A' is the image of
A, for since AB = A'B,
the two angles are
equal, and consequently
also the two angles i,
each of which is equal
90 a. The image
formed by a plane mirror
is virtual, erect and equal
in size to the object.
To tell whether a mir-
ror is true place the eye
near the surface by way
of observing images un-
der as great an incidence
as possible. If the mir-
ror is not true the images
of external objects are deformed. One can also notice these deformities
very distinctly by placing oneself quite a distance in front of the mirror
and observing the images of distant objects.
6. Concave Spherical Mirrors. The middle of the spherical surface
is called the apex, a straight line passing through the center and the apex
is the axis, and the angular measurement of the mirror is the aperture.
In order that images may be true the aperture must be small (8 to 9 de-
grees). The principal focus of the mirror is the place where incident rays
parallel to the axis meet after reflection. The principal focal distance is.
the distance of the principal focus from the mirror.
IN ALL OPTIC PHENOMENA THE COURSE OF THE RAYS is REVERSI-
BLE. If in figure 2, the ray AC is reflected along CF, an incident ray-
along FC is reflected along CA. It follows that rays coming from the
principal focus of a concave mirror must be parallel after reflection.
The principal focus of a plane mirror is at infinity, because incident
parallel rays are still parallel after reflection.
Fig. 2. Keflection on a plane mirror. A, the object ;
A', its image; DE, the mirror; AC, incident ray; CF,
reflected ray.
PHYSIOLOGIC OPTICS
The principal focus of a concave mirror is situated half way between
v the apex and center. We have, indeed
-> \ * = * (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<f> =
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<i> = 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 <J>;
2. The ray B<J>, 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 <f> 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 <J> 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, <J> 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 <K, is the distance of the second
principal point from the posterior focus; it is equal to the distance of
the anterior focus from the first nodal point, ^ K .
Fig. 17.
It follows that the distance of the first principal point from the first
nodal point is equal to the distance of the second principal point from
the second nodal point and to the difference between the focal distances
F 2 F x . The distance between the two principal points is equal to the
distance between the two nodal points.
The ratio between the focal distances is equal to the ratio between
the indices of the first and last medium Jr a = n.
We call principal planes two planes perpendicular to the axis and pass-
ing through the two principal points. The image of an object situated
in the first principal plane is formed in the second principal plane and
vice versa. It is the same size as the object and its direction is the same
as that of the object.
A ray which, in the first medium, passes through the first nodal point,
passes, after refraction, through the second nodal point, and the direc-
tions of the ray before and after refraction are parallel.
20
PHYSIOLOGIC OPTICS
Knowing the position of the cardinal points, the image of a given point
can be found by construction or calculation in a manner analogous to
that which we have already employed in the case of infinitely thin lenses.
To find the image of the point G (fig. 18) by construction we can choose
two of the three following rays :
i. The ray GA, which is parallel to the axis, must cut the second
principal plane at D, at a distance from the axis equal to Ah it and it must
pass through 4> 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 <t
I would be equal to D. If we knew
the amount of doubling used we r .-- -- %
would thus have measured I ab, ^ ----- ^
and our object would be attained.
When a and b touch we say that we &
have obtained contact. If we use as \ii>~'
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"
<l 10
Visual Iine
Na
Fig. 42. Diagram of corneal refraction after Eriksen. The abscissas indicate the di-
tance of the visual line in degrees, the ordinates, the corneal refraction in dioptrics.
The full curve indicates the refraction of the horizontal meridian of a left cornea measured
in graduations of five degrees. The zero corresponds to the visual line. aa, optic
part of the cornea ; 06, 06, basilar part. The dotted curve cc corresponds to the ellip-
soid calculated according to the three measurements taken at and 25 on the right
and left of the visual line ; dd is the axis of this ellipsoid and the distance of this line
from zero corresponds to the angle which is often called the angle a. We see that the
true form of the cornea differs considerably from the ellipsoid.
The horizontal diameter, as well that of the optic part as that of the
entire cornea, is a little greater than the vertical diameter.
Neither Sulzer nor Eriksen have found an axis of symmetry properly
so called. Nevertheless, most of the diagrams of the latter show a
tendency to symmetry around an axis directed about 5 outwards and
58 PHYSIOLOGIC OPTICS
a little below the visual line. If, therefore, the comparison with an
ellipsoid is persisted in, we must imagine it much more pointed than we
have done up to the present, and we must suppose the summit cut-off
by a section perpendicular to the axis and replaced by a spherical cap.
As far as the optics of the eye are concerned, the obliquity of the
cornea plays only a slightly important role, since the optic part of the
cornea is nearly spherical. This part corresponds to a linear diameter of
about 4 mm. When the pupil is large the basilar part may, therefore,
play a certain part ; according to the little table of Eriksen it would be
especially inwards and above that its influence would be felt. But it is
impossible to know anything of it without having examined each eye
by itself, for the obliquity of the cornea is often compensated for by
the eccentricity of the pupil. The position of the pupil varies much in
different eyes. Sulzer found that on an average the center of the pupil
is 5 outwards from the visual line, and that it is sometimes displaced
upwards, sometimes downwards. This decentering of the pupil may,
therefore, compensate for the obliquity of the cornea, so that it is espe-
cially outwards that we must expect to notice the effect of the peripheral
flattening.
The basilar portion is less regular and much less polished than the
central portion, which partly explains the slight success of optic iridec-
tomies. The catoptric images have frequently a diffuse aspect and the
ophthalmometric measurements leave much to be desired. Eriksen also
has tried to obtain an idea of the variation of the radius of the peripheral
parts by examining the form which the image of a white square assumes
in the horizontal meridian, at different distances from the visual line.
We see on fig. 43 that the image becomes longer and longer until
about 30 from the visual line, where it is two and a half times greater
than at the center. Just at the periphery the image becomes narrower,
Fig. 43. Forms of the image of a white square at different parts of the cornea (horizontal
..^ mer idian, internal half), after Eriksen. The figures at the top of the squares indicate
the distance in degrees from the visual line ; those at the bottom the refraction (in the
horizontal meridian) in dioptrics.
and ends as a rectangle placed upright ; at this place the image is some-
times double; a second image is formed still farther away on the edge
OPHTHALMOMETRY 59
towards the sclera, and this image is inverted in the horizontal direc-
tion, but not in the opposite direction. These latter phenomena indicate
that the curvature increases very considerably towards the border, and
that beyond this place there is, at least in some eyes, a concavity, like
a furrow which separates the cornea from the sclera. We must note
that the images should increase a little in height towards the periphery
at the same time that they increase in width, because the curvature
diminishes also in the vertical, but much less than in the horizontal direc-
tion. This increase is not indicated on the figure.
In a general way we may, therefore, consider the portion of the cornea
which plays a part in the optics of the eye as spherical, so that the angle
, understood in the sense in which we generally accept it, loses its
importance. This is why I have defined the angle as being the
angle between the visual line and the optic axis of the eye, a definition
which others have also given to it.
Note, furthermore, that the normal cornea is slightly astigmatic ; we
reserve a special chapter for this anomaly of refraction.
The radius of the normal cornea does not fall below 7 mm., but in
cases of keratoconus we may meet radii of 6 or 5 mm., or even still
smaller radii, to a point where the arc of the ophthalmometer becomes
too short; we cannot separate the mires sufficiently to obtain contact.
The images of the mires assume in this case, as also when there are
corneal opacities, irregular forms.
By the Sulzer-Eriksen method we determine the radius of curvature
at a given part of the cornea. We obtain by this method a very good
idea of the form of the cornea, but the results are not directly applicable
to ocular dioptrics for the reasons given on page 13. To be able to
calculate the aberration produced by a peripheral flattening of the
cornea, we should know the normal (the part of the perpendicular to
the cornea comprised between the latter and the visual line). To deter-
mine it Brudzewski made certain changes in the ophthalmometer. He
replaced the arc by a larger one, reaching 170. One of the mires is
fixed at the middle of the arc so that its border when prolonged would
pass through the axis of the telescope, while the other mire slides on the
arc so as to be able to obtain contact. The observed person fixes the
middle of the objective during all the measurements. He uses prisms
of different doubling power. He begins, for example, with a prism
doubling I mm. ; and, the arc being placed horizontally, he determines
the position, on the nasal side, which the movable mire must have so
that he may obtain contact. He then makes the same determination
60
PHYSIOLOGIC OPTICS
on the temporal side, after having placed the arc vertically upwards and
downwards. These measurements give the length of the normals to
the cornea at four places, situated at I mm. from the visual line. He
then replaces the prism by another doubling 2 mm., and so forth. Know-
ing the normal he can then directly calculate the aberration produced
by the corresponding part of the cornea (see chapter VII).
We observe, furthermore, that the ophthalmometer lends itself very
well to the examination of the curvature of the surfaces of the dead eye.
Holth thus made a series of measurements in the laboratory of the Sor-
bonne. He placed the eye with the cornea upwards under a mirror at 45
which sent the reflected image in the direction of the ophthalmometer.
The mirror must not be too small, for it must allow us to measure also
the peripheral parts of the surfaces by displacing the instrument. As the
surfaces are generally more or less misty, we are obliged to coat them
Fig. 44. Keratoscopic images of a cornea presenting a considera 1 le astigmatism at the
central part (central ring of figure C), while the remainder of the cornea is nearly
exempt from it. After Javal. C, direct look ; H, upwards look ; B, downwards; D,.
to the right ; G, to the left.
with a very thin layer of oil to make them bright. It was necessary
for the measurement of the cornea to make an injection into the vitreous
body so as to make its tension that of the eye, but it was interesting
to note how much he could change the tension of the eye without
observing any perceptible alteration in the curvature of the cornea.
01*11 TUALMOMETRY
61
To measure the curvature of the posterior surface of the cornea, Holth
injected a solution of gelatine into the anterior chamber; as soon as
the gelatine solidified he removed the cornea and measured the anterior
surface of the cast, made bright with oil. The anterior surface of the
crystalline lens is measured directly, after the cornea and iris have been
removed. To measure the posterior surface he cut the eye in two,
along the equator, and, the vitreous body being removed, the ey;e was
placed with the cornea downwards. Holth gave an account of the results
achieved by him at the Ophthalmological Congress of Utrecht in 1899
(see also page 182).
EXAMINATION WITH THE KERATOSCOPIC Disc. The measurement of
peripheral parts of the cornea takes too much time to be of service in
Fig. 45. Keratoscopic figures of a case analogous to that of figure 44. After Javal.
clinics, but we can obtain information about the peripheral parts of the
cornea by means of the keratoscopic disc, a circular disc, on which are
painted concentric circles of different colors. We can place it on the
telescope of the ophthalmometer by taking out the double refracting
prism, or simply by holding it in the hand and looking through a central
aperture (Placido). Generally the patient looks towards the middle of
the disc ; the images of the circles are then circular in a normal eye, and
elongated along the meridian of least refraction in the astigmatic eye;
62 PHYSIOLOGIC OPTICS
by making the patient look towards the border of the disc it is easy
to establish the peripheral flattening of the cornea.
In cases of irregular astigmatism the circles assume irregular forms ;
and we may often, by studying these forms, obtain important informa-
tion on the anomaly in question. Thus figs. 44 and 45 show the
appearance of the disc in cases in which the central part of the cornea
was affected with a pronounced astigmatism, while the middle zones
were scarcely affected at all; we see, in fact, that the central ring of
Fig. 46. Keratoscopic figures of a case of keratoconus. After Javcd.
figure C, which corresponds to the middle of the cornea, is much
lengthened, while the more peripheral rings are almost circular. In
cases of keratoconus the image of the disc is very small when it is
formed at the summit of the cornea, but the least deviation of the look
causes a change of form by lengthening it in the radial direction (fig. 46).
We have seen (page 36) that the visual line passes through the cornea
perpendicularly or nearly so. When making a keratoscopic examina-
tion the observed person looks into the telescope; the center of the
concentric rings of the image indicates, therefore, the place where the
visual line passes through the cornea, and if, at the same time, we
illuminate the eye moderately we can account for the direction of the
OPHTHALMOMETR7
visual line relatively to the different parts of the eye. It may be useful
to modify the appearance of the disc. Figure 460 shows the keratoscopic
rr appearance of an eye affected
with a high degree of astig-
matism, and of which the
angle has an unusual size;
the small black circle indi-
cates the pupil, the white fig-
ure is the cornea! image of
a large white disc provided
with a black cross, the arms
of which were placed in the
principal meridians; its el-
liptical form is due to the
astigmatism. The visual line
corresponds to the intersec-
tion of the two black lines.
We notice that it is placed
very eccentrically in the pupil so that the four quadrants of the latter
are of very different size. The angle was about 9; the axis of the
crystalline lens was directed 8.8 outwards and 3.8 downwards from
the visual line.
As in every instance in which the angle a has an unusual size, the
cause was to be found in the displacement of the fovea, a displacement
which, in this case, manifests itself also by an increased distance between
the point of fixation and the blind spot (fig. 466). The internal border of
the latter was at 15 instead of 11 or 12.
Fig. 46a. Keratoscopic image of an eye with a
large angle a.
Fig. 466. Spot of Mariotte of an eye with a large angle a, compared with that (dotted)
of a normal eye. a, point of fixation.
31. Measurement of the Angle a. For the following measurements
I use the ophthalmophakometer (fig. 47, see page 44). I designate by A
the cursor which carries only one lamp; by B that which carries two,
placed on the same vertical rod, and by C the third cursor which carries
a rod on which moves a small bright ball which serves as the point of
fixation.
I place the arc horizontally and the cursor B at the zero of the
64
PHYSIOLOGIC OPTICS
graduation of the arc (i) so that its two lamps are in the same vertical
plane as the middle of the objective of the telescope, and I request the
Fig. 47. The ophthalmophakometer.
Fig. 48. The images of Purkinje observed with the ophthalmophakometer. The two
lamps B, figure 47, are in the same vertical plane as the axis of the telescope and the
observed person looks at 5.7 on the nasal side, so as to align the images. The optic
axis of the eye coincides in these circumstances with the axis of the telescope.
(1) The lamp of the cursor A is not used in this experiment.
OPHTHALMOMETRY
observed person to look towards this latter place. It is clear that, if
the surfaces of the eye were centered around the visual line, we should,
in these circumstances, see the six images of reflection on the same
Fig. 49. Position of the images when the observed person looks into the telescope. Th
position of the lamps is the same as in figure 48. At the middle, the corneal images
on the right, those of the anterior surface of the crystalline lens; on the left, those of
the posterior surface of the crystalline lens. The images of the posterior surface of the
cornea are not visible.
Fig. 50. The two lamps are in the same horizontal plane as the axis of the telescope.
The observed person looks into the telescope.
vertical line (fig. 48) (those of the posterior surface of the cornea are
not visible under these conditions). But this has never happened.
66
PHYSIOLOGIC OPTICS
We always see, as in fig. 49, the images of the anterior surface of the
crystalline lens, on the one side, those of the posterior surface of the
crystalline on the other, and the corneal images in the middle. I then
request the observed person to fix the bright ball of the cursor C, and
I displace this cursor until I see the images placed as in fig. 48. The
optic axis of the eye is then in the vertical plane, passing through the
axis of the telescope, and the angular distance of the cursor C from
the telescope indicates how much the visual line deviates from the optic
axis in the horizontal plane. We find that it is necessary to place the
cursor C on the nasal side at a distance from the telescope varying
between 4 and 7 (angle ). This angle can be determined with very
great exactness.
Fig. 51. Defect of centering; it is impossible to align the six images.
I then place the arc vertically so that the two lamps are in a horizontal
plane : generally the six images are not on a horizontal line (fig. 50) ;
by displacing the cursor C, which the observed person fixes, until I see
all the images on a horizontal line, I determine the vertical deviation
of the visual line.
The optic axis is nearly always directed outwards from the visual
line, and most frequently downwards (2 to 3); sometimes we find it,
however, in the same horizontal plane, or deviated a little upwards.
DEFECT OF CENTERING. We sometimes observe that it is not pos-
sible to place the six images on a straight line (fig. 51). We succeed in
aligning two pairs, whichever we want, but the third remains outside. This
OPHTHALMOMETRY 67
takes place when the eye is not exactly centered; that is to say, when
the axis of the crystalline lens does not pass through the center of
curvature of the cornea (the posterior surface of which I neglect). We
can nearly always establish slight defects of this kind, but most fre-
quently they are negligible. When we find more considerable defects,
it is generally because the axis of the crystalline lens passes a little (up
to 0.25 mm.) above the center of curvature of the cornea.
32. Determination of the Position of the Internal Surfaces. To meas-
ure the radii of the surfaces we must determine: i the position (the
distance from the summit of the cornea) of the surfaces ; 2 the position
of the centers. It is true that there exists, as we shall see, a means of
determining the radii directly, but we must not forget that all the sizes
which we are measuring here are apparent sizes, and that, to find the real
values, we must reduce the results by a calculation following the rules
which we have already given (page 41). To make this reduction it is
necessary to know the position of the surfaces, which knowledge is
likewise necessary in order that we may be able to combine the sur-
faces with one another so that we may proceed to calculate the entire
optic system.
I take the anterior surface of the crystalline lens, as an example, and
I suppose that we are making the measurement in the horizontal direc-
tion. It is useful to dilate the pupil.
I place the arc of the instrument horizontally, and I place also, as far
away as possible from the telescope the cursor A, the lamp of which
must be sufficiently brilliant that the image of the surface to be meas-
ured may be quite visible. This done, I place the cursor C, which carries
the mark of fixation, at a place such that the optic axis of the eye may
bisect the angular distance between the telescope and A (i). It is
necessary, therefore, to have previously measured the angle . We
then displace the cursor B, the lamps of which must be very feeble so
that we may see only the corneal images, until the crystalline image of
A is exactly on the same vertical as the corneal images of B. Glancing
at fig. 52, it is easy to see that we now possess the elements necessary
to calculate the distance of the anterior surface of the crystalline lens
from the summit of the cornea, for the angle c is half the angular distance
of A from the telescope, and the angle d is half of the angular distance
(1) If the eye is not centered we must replace the optic axis by the line passing through the center
of curvature of the cornea and the center of the surface which we desire to measure. We find this line
as we found the optic axis in the preceding experiment, by aligning the corneal images with the images
of the surface to be measured.
68 PHYSIOLOGIC OPTICS
(i) of B from the telescope. Supposing that we knew the radius of the
cornea R , which should have been measured previously, the triangle
Fig. 52. Method of determining the position of an internal surface of the eye. S 1} an-
terior surface of the cornea ; C lt its center ; S 2 , anterior surface of the crystalline lens ;
C 2 , its center; Cj, C 2 , optic axis of the eye.
O 2 C P gives us the relation O 2 C x = R 3 -JlJ-f , and we have for the
distance, looked for
r n T? n P P (-( sin d \ TJ sip c sin d
O, O., = K, Oo C/i = K! II : I = K, : .
\ sin c/ sm c
If very great exactness is not desired, the sines can be replaced by
the arcs.
EXAMPLE. Let the radius of the cornea be 7.98 mm., the distance
of A from the telescope 28 nasal, that of B 16.8 nasal; we will have
Oi O 2 = 7-98 (i ?i 8 u' ) = 3.16 mm. The apparent depth of the
anterior chamber would, therefore, be 3.16 mm., whence we find the true
value 3.73 mm. by placing in the formula -^- -f -- = I, the values F x =
23.64, F 2 = 31.61, f x = 3-16.
33. Determination of the Centers of the Internal Surfaces. We place
A above the telescope, and we move C with the mark of fixation as far
as possible from the telescope, but so that the image may not disappear
(1) We can imagine the two lamps of B united into one only, at the level of the lamp of A.
OPHTHALMOMETR7
69
behind the iris ; then we displace B until the corneal images of its two
lamps are on the same vertical line as the crystalline image of A.
Under these conditions, the axis of the telescope is perpendicular to
the apparent anterior surface of the crystalline lens (i). We find the angle
Fig. 53. Method of determining the position of an internal surface of the eye. The
letters signify the eame as in figure 52.
a (fig. 53) by adding (subtracting) the angle x to the angular distance
of C from the telescope. The angle b is half of the distance of B from
the telescope ; we have C 2 Q = R! -|{J-| and the distance sought equal to
sin a -{- sin 6
sin a
EXAMPLE In the same eye as before let = 5.1, the distance of B
from the telescope 12.4 temporal and that of C from the telescope 9.9
nasal. We would then have for the distance sought 7.98 (i + ; " ) =
18.28 mm. and the apparent radius would be 18.28 mm. 3.16 mm. =
(1) If we imagine the lamp placed at the center of the objective, the ray which reaches the observer's
eye would be reflected exactly on itself, which can take place only if it meets perpendicularly the ap-
parent surface.
70 PHYSIOLOGIC OPTICS
15.12 mm. The position of the real center would be 13.78 mm. (i) and
the radius of the real surface 13.78 mm. 3.73 = 10.05 mm -
34. Direct Determination of the Radii. In fig. 49, as well as in figs.
50 and 51, the ratio between the distances separating the two images
of the same kind is equal to the ratio between the apparent radii. We
may, indeed, consider the distance, separating the two lamps as an object,
three images of which are formed on the pupil; these images are pro-
portional to the radii following the formula -J- = -- , since O and / are
the same in the three cases.
We can make sufficiently accurate measurements of the radii if we
make use of two cursors similar to A and two others similar to B. We
place the lamps A in such a position as to be able to observe clearly
the images produced by the anterior surface of the crystalline lens.
Then we displace the cursors B, the lamps of which must be feeble,
until the corneal images of the lamps of each are on the same straight
line as one of the crystalline images of A. We consider the distance
which separates the cursors A as object for the anterior surface of the
crystalline lens, and that separating the cursors B as object for the
cornea. As the images are alike, the radii must be inversely propor-
tional to the objects. Knowing the radius of the cornea, we can, there-
fore, calculate the apparent radius of the anterior surface of the crys-
talline.
To determine the astigmatism of the surface we must repeat all the
measurements in the vertical meridian.
The posterior surface of the crystalline lens is measured exactly like
the anterior surface. As to the posterior surface of the cornea, its
image is not visible at the middle of the pupil. We must, therefore, limit
ourselves to measuring the peripheral parts. The direct determination
of the position of the surface, following the method indicated in para-
graph 32, is not applicable for the same reason, but the position of the
center can be determined after paragraph 33, and the length of the
radius as we have just explained, which gives indirectly the thickness
of the cornea. It is necessary to have previously measured the radius
of the anterior surface of the cornea at the place where we are making
the measurement, for generally this place is so peripheral that the
flattening of the cornea makes itself felt. Besides, the posterior sur-
(1) [Considering that we have again obtained this apparent position with reference to the refraction
of the cornea, -we must therefore in the formula -*X -j- *X =- 1 put FI = 23.64; F 2 = 31.61 and
fl _ _ 18.28, this gives / 2 = 13.78.] W.
OPHTHALMOMETRY 71
face undergoes, towards the periphery, a flattening analogous to that
of the anterior surface, so that the relation between the radii of the
two surfaces seems almost the same everywhere.
35. General Remarks. We can, therefore, thus measure on the living
subject all the optic constants except the indices. But we must not
deceive ourselves as to the exactness of these measurements; except-
ing those of the anterior surface of the cornea, they are not very exact.
In fact, the crystalline images are feeble, and those of the anterior sur-
face of the crystalline lens very diffuse, which causes the measurement
to become less certain; there are also other sources of errors, such as
that made by comparing the surfaces to spherical surfaces. It may
happen also that the observed eye does not fix exactly at the moment
of observation. When we wish to determine, for example, the radius
of the anterior surface of the crystalline lens, we have to depend on
three measurements, that of the radius of the anterior surface of the
cornea, that of the position of the anterior surface of the crystalline,
and that of the position of its center. The errors of these measure-
ments are added in the final result. I do not think, therefore, that we
can guarantee an exactness of more than half a millimeter in the final
result. As far as the optics of the eye are concerned, this want of
exactness does not present any considerable importance. Indeed, it
must not be forgotten that the difference of index of the media which
separate the internal surfaces is very slight, making it unnecessary to
know the radii very exactly ; an error of half a millimeter in the measure-
ment of the anterior surface of the cornea corresponds to about 3 D.,
whilst the same error in the measurement of the anterior surface of the
crystalline lens corresponds only to a third of a dioptry. But, as to
the thickness of the crystalline lens, which is only 4 mm., an error of
half a millimeter presents a vast importance. The much disputed ques-
tion of knowing whether the crystalline lens changes its thickness
during accommodation can with difficulty be decided by the observation
of the crystalline images, for the alleged change (an increase of 0.4 mm.)
does not exceed the limit of error.
Ophthalmometry of the cornea has passed the doors of the labora-
tories, and has been introduced into clinics where it is daily rendering
great service. It might be asked, therefore, whether the measurements
of the internal surfaces could not also find clinical application. Indeed
there often exist between the astigmatism indicated by the ophthal-
mometer and subjective astigmatism, differences the cause of which
72 PHYSIOLOGIC OPTICS
it is very natural to look for in the internal surfaces, and which we
might hope to disclose by these methods. I have made some measure-
ments of this character, but I do not think they have a great future.
They are always very complicated; it would be necessary, in fact, to
measure the radius of each surface at least in two meridians, and as
each radius calls for two measurements (of the surface and the center)
this would involve already 12 measurements ; it would then be necessary
for us to calculate the real values in order to deduct the astigmatism
of each surface and lastly to combine these astigmatisms with that of the
anterior surface of the cornea. This is already sufficiently complicated,
but it becomes more so if, as is probable, the main meridians of the
internal surfaces coincide neither with one another nor with those of
the anterior surface of the cornea. It is true that it would be possible
to simplify the methods for practical application, and to replace the
calculations by approximations, but I do not think the result is worth
the trouble, more especially as it is probable that we frequently woulfl
not find what we look for, the explanation of the differences between
ophthalmometry and subjective astigmatism, for these differences are
probably frequently due to the fact that the peripheral parts of the
cornea have an astigmatism different from that of the central parts,
which we measure with the ophthalmometer.
Bibliography. Aubert (H.). Pfluger's Archiv. Bd. 35, p. 597, 1885. Javal (E.).
Memoires tfophtalmometrie. Paris, 1890. Sulzer (D.). La forme de la cornee humaine et son
influence sur la -vision. Arch, d'opht., 1891. Eriksen. Hornhindemaalinger (Danish). Ara-
hus, 1893. Tscherning (M.). Beitrage zur Dioptrik des Auges (Zeitschrift fur Psychologic
und Physiologie der Sinnesorgane, III, p. 429). Brudzewski (K.). Beitrag zur Dioptrik des
Auges. Arch, fur Augenheilkunde. XL, 3.
CHAPTER V.
CIRCLES OF DIFFUSION ON THE RETINA.
36. Definition. Receiving on a screen the image of a distant lu-
minous point, and moving the screen forwards and backwards, we see
that there is only one position in which there is formed a distinct image
of the point. In every other position we see on the screen a luminous
spot of the same form as the aperture of the lens, which spot is the larger
the farther it is removed from the distinct image. This luminous spot
is called circle of diffusion.
The same thing happens in the eye, with this difference that, not being
able to move the retina backwards or forwards, we move the luminous
point which amounts to the same. The round form of the image of
diffusion is due to the round form of the pupil ; if we look, for example,
through an aperture which is triangular and smaller than the pupil, the
image of diffusion is triangular
and is somewhat improperly
called circle of diffusion.
It is easy to calculate the size
of the circle of diffusion (fig.
54). If the diameter of the pupil
(of exit) be designated by />, 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<x,il in Wecker and Lan-
dolt. Traite complet d'ophtalmologie. Paris, 1883. Boehra (L.). Das Schielen. Berlin, 1845.
Arlt (F.). Die Krankhciten des Auges, I-III. Prag., 1851. Stellwag v. Carion. Die
Ophthalmologie vom nitwwissenschaftlich<n Standpunktc aus. I-II. Erlargen, 1853. Tscher-
ning (M.), Studien iiber die Aetiologie der Myopie. Arch. f. Ophfh., XXIX, I, 1883. Dim-
mer (F.). Zur Glaesercorrection bei Aphakie. Kl. M. f. A. 1891. Ostwalt (F.). Einige
Worte uber Glasercorrection bei Aphakie. Kl. \f. f. A. 1891. Demicheri (L.). Faux knti-
cone. Ann. d'oc. 1895.
CHAPTER VII.
SPHERICAL ABERRATION.
50. Optic Principles. When the aperture of a spherical lens is not
very small, the rays proceeding from a point of the object do not,
after refraction, reunite exactly at a point, as would be essential to form
a good image; the borders of the lens are more refracting than the
center. Thus the test case lens, the center of which has a refraction of
20 D., refracts 25 D. towards the borders. Generally speaking, the same
is true of all refracting and reflecting systems (fig. 61). It is possible,
Fig. 61. Refraction of a pencil of parallel rays by a spherical surface. Spherical aberra-
tion. At A, the rays are condensed towards the border ; at B, towards the axis of th
pencil ; p, q, two needles.
nevertheless, to construct systems of large aperture, which present only
very little aberration (aplanatic lenses), and others in which the aberra-
tion is over-corrected, the borders being less refracting than the center
(lentilles suraplanetisees) .
The degree of aberration increases as the square of the aperture of
the lens and as the cube of its refracting power. It depends, besides, on
the distance of the object and the form of the lens. A plano-convex
lens presents less aberration than a bi-convex lens, if the spherical side
is turned towards the incident rays supposed to be parallel ; it presents
95
96 PHYSIOLOGIC OPTICS
more in the contrary direction. It is for this reason that the objectives
of opera glasses are bulged in front. The best form of simple lens is that
which the English call crossed lens (periscopic), in which the radius of the
posterior surface is about six times greater than that of the anterior
surface. We give here the refracting power, at 15 millimeters from the
axis, of different lenses, all having at the middle a refraction of 20 D.
The incident rays are supposed to be parallel.
Crossed lens. Plano-convex with the Bi-convex. Plano-convex wi*h the
convex surface in frout. plane surface in front.
ifl.l D. 22.3 D. 23.6 D. 23.8 D.
It is evident that, the weaker the aberration of the lens, the more
aperture can be given to it without the aberration interfering with the
distinctness of the image. The crossed lens is little used, because the
plano-convex lens is nearly as good. Besides, for the correction of
chromatic aberration, compound lenses are usually employed (a Hint lens
and a crown lens cemented together). Both glasses can then be cut in
such a way as to neutralize the spherical aberration also, until the total
aberration becomes almost nothing for a given distance of the object.
51. Phenomena Dependent on the Spherical Aberration of Lenses. I am
going to explain some experiments by which the spherical aberration of
lenses may be studied. In order to have very marked phenomena we
must use a strong lens, 20 D. (convex) of the test-case, for example, or,
better still, a strong plano-convex lens (the objective of an opera glass),
the plane side of which is turned towards the luminous source, placed
at a great distance.
a. APPLICATION OF THE PRINCIPLE OF SCHEINER. We place on the
lens an opaque screen in which we have previously made, not two aper-
tures as in the experiment of Scheiner, but four, which are equidistant,
placed on the horizontal diameter of the lens, two central ones, 2 and 3,
and two peripheral, I and 4 (fig. 62). The object being a distant luminous
source, we receive the images on a white screen placed behind the lens.
First, placing the latter beyond the focus, we see (fig. 62 A) four luminous
spots which correspond to the apertures of the screen, but which are
placed in reverse order. The distance between the central spots is less
than that which separates each of the peripheral spots from the neigh-
boring spot. The two central spots reproduce the form of the source
enlarged, while the two peripheral spots are elongated in the horizontal
direction, especially if the aberration is strong. The pencils passing
through the peripheral openings are, indeed, astigmatic by incidence (see
SPHERICAL ABERRATION
97
ch. IX). By moving the screen nearer, the two central spots are blended
into one (fig. 62 B). At this moment the screen is at the focus of the
central part of the lens, while it is still beyond the focus of the peripheral
* K
Fig. 62. Spherical aberration of a lens.
parts. Advancing the screen still more, the spots I and 4 approach and
are blended (fig. 62 E, focus of the peripheral part), while spots 2 and 3
are again separated. Finally we have four spots, as at the beginning
of the experiment ; but they are now arranged in the same order as the
apertures ; the distances separating the two spots on each side are less
than the distance between the central spots. We observe also that the
peripheral spots are now elongated in the vertical direction. If the
lens is very large we can observe all the different phases shown on
fig. 62.
98
PHYSIOLOGIC OPTICS
To determine the degree of aberration, we have only to measure the
distances of the positions E (focus of the peripheral parts) and B (focus
of the central part) from the screen. The difference between these two
distances, expressed in dioptrics, tells the degree of aberration. To have
more accurate measurements it is advisable to cover, each time, the two
apertures we are not using; for the determination of E, we cover the
central apertures, for that of B the peripheral apertures. We can also
cover the two apertures situated on the same side and determine the
focal distance on the other side (the position F, fig. 62), but it is not
necessary in order to determine the course of the rays : we can, indeed,
construct figure 62 by knowing the positions B and E only.
b. EXAMINATION OF THE CIRCLES OF DIFFUSION. Examining the
circle of diffusion, without putting the screen with the openings on
the lens, we see that as long as the white screen is situated beyond the
focus, the light is concentrated at the middle of the circle ; the brightness
diminishes rapidly towards the borders. When it is situated within the
focus, we see, on the contrary, a luminous disc surrounded by a more
brilliant circle. This phenomenon is easy to understand : we see, in fact,
in figure 62, that the rays are condensed towards the border, between
the lens and the focus, while they are concentrated around the axis
beyond the focus.
c. DEFORMITY OF THE SHADOWS. Put the white screen beyond the
focus, and place a knitting needle against the lens. We then see the
shadow of the needle in the circle of diffusion and observe that this
n
in
Fig. 63. Deformation of the shadows of the needles. Successive sections of the pencil
of figure 61. Section I is supposed to be made at C (fig. 61), section II at A, section III
at B, the two latter enlarged ; ab } a needle ; a' V and a" b", its shadows.
shadow is straight only if the needle coincides with a diameter of the
lens; otherwise it is curved, with its convexity towards the center. If
the screen is between the focus and the lens, the shadow is concave
towards the middle, but the curvature is much less pronounced.
SPHERICAL ABERRATION 99
To understand these deformities let us suppose the lens divided into
concentric zones of the same width. A glance at figure 62 shows that
after refraction the corresponding zones of the circle of diffusion
diminish in width towards the periphery, when the screen is situated
between the focus and the lens, while they increase in width towards the
periphery beyond the focus. In figure 63, I shows the lens seen from
the front and divided into concentric circles ; the two straight lines rep-
resent two needles. In figure 63, n represents a circle of diffusion
between the lens and the focus. We see that the zones become narrower
towards the edge, and we understand that the point a' is relatively nearer
the center than the point b', which gives the shadow its curved form.
Knowing the position of the concentric circles of the diffusion spots,
it is easy to construct the form of the shadow, since the shadow of a
point of the needle must be at the same angular distance from the
horizontal diameter as the point itself. In figure 63, in represents a
circle of diffusion beyond the focus.
An over-corrected lens gives all the phenomena here mentioned, but
in the reverse order, while a corrected lens (aplanatic) gives none of
them. The circles of diffusion of an aplanatic lens have the same bright-
ness in their whole extent, and the shadow of the needle remains
straight everywhere. To give a good image a lens must be approx-
imately aplanatic. The preceding experiments can be used as a verifica-
tion of the aplanatism of a lens.
d. APPLICATION OF THE PRINCIPLE OF FOUCAULT. We obtain very
pretty phenomena by using the method by which Foucault studied his
telescopes. We place a luminous point a little beyond the focus of the
lens which we wish to study, so that its image is quite distant (2 to 3
meters). The observer takes his place beyond this image, so that his
eye is in the luminous pencil on the axis of the lens, which he approaches
gradually. Under these circumstances the eye sees luminous the parts
of the lens which send rays to it. If the lens were aplanatic, all the rays
would meet at the focus, and, reaching this point, the observer ought
to see the entire lens luminous. At some distance from the focus, he
would see, on the contrary, only a small central part luminous, the other
rays not entering his eye. If the lens is affected with spherical aberra-
tion, we observe the following phenomena : placed very far off we see
only a quite small central spot, which increases in diameter accordingly
as we approach the focus where it attains its maximum ; but even here it
is far from filling the entire lens. Approaching still nearer we see a
luminous ring become detached and separated from the central part by
100 PHYSIOLOGIC OPTICS
a dark zone. This ring dilates more and more accordingly as we ap-
proach the lens, while the dark zone becomes enlarged. On reaching
a certain point, the ring extends to the borders of the lens and disap-
pears. The phenomena are still clearer if we look through a narrow
diaphragm. It is easy to account for the nature of these phenomena
by glancing at figures 61 and 62. Thus, if we suppose the pupil of the
observer reduced to a point and placed at the intersection E, fig. 62, it
would receive rays I and 4, and the borders of the lens would appear
luminous, while the parts 2 and 3 would be black, the corresponding
rays passing to one side of the pupil. There will always be a small,
luminous spot at the middle, since the axial ray always enters the eye.
The distance, in dioptrics, between the place where the ring appears
and that where it disappears, tells the amount of the aberration. If
the aberration is over-corrected we have the same phenomena in the
reverse order : placed at the focus, we must move away in order to see
the ring; the further away we move the more it increases, until finally
it disappears.
52. Aberration of the Human Eye. Experiments of Volkmann. This
scientist examined the aberration of the eye by repeating the experiment
of Schemer with four openings
located as indicated in figure
64, C. Looking at a pin placed
beyond the far point through
these openings, it is seen
quadrupled (fig. 64, A, a) ; and
by moving closer to it he ob-
* * * served the different phases
c illustrated in figure 64, A, in
the order in which they are
Fig. 64. Experiment of Volkmann. o, corre- , . A1 - . .. .
spends to the most distant position ; e, to the shown in the figure, and which
nearest position of the needle. A phenomena corresponds to the spherical
observed by an eye with strong spherical aber- r
ration ; B, by an eye with over-corrected aber- aberration. It IS easy to ac-
count for this phenomenon by
comparing figure 64 with figure 62. In the position b, the pin is at the
far point of the central parts of the pupil, since the two central images
are reunited ; it is still beyond the focus of the peripheral parts since the
peripheral images are not yet blended. Most of the time, the persons
examined observe the same phenomena in the same order, but some see
them in the reverse order (fig. 64, B), which indicates over-corrected
m
t n i in
SPHERICAL ABERRATION 101
aberration. In the position d (fig. 64, B) the pin is at the far point of the
central parts and within the far point of the peripheral parts. It is
probable that these latter persons used their accommodation, for it is
quite rare to find over-corrected aberration in an eye in a state of repose ;
I have, however, met instances, especially among persons having a large
pupil. On the contrary, during accommodation, it is the rule that the
aberration is over-corrected, as we shall see later on.
53. Experiments of Thomas Young. Long before V 'olkmanri 's time,
Young had already performed a series of experiments much more con-
clusive, but which had been forgotten.
a. A myopic eye sees a distant luminous point as a circle of diffusion,
the brightness of which is concentrated at the middle, if the eye has
I II
Fig. 65. Distribution of the light of the circle of diffusion in an eye with strong aberra-
tion (Antonelli). In I the luminous point is beyond; in II within the focus.
spherical aberration (fig. 65, I). If the aberration is over-corrected, or
if the luminous point is inside the far point, it is the borders that are
the more luminous; an aplanatic eye, or one nearly so, sees the circle
of a uniform brightness. To repeat the experiment, when one is not
myopic, one places in front of the eye a convex lens of 3 to 4 dioptrics.
Many eyes, the optic system of which is irregular, perceive eccentric
concentrations of the light; I shall return to this immediately, (i)
b. Bringing a needle in front of the eye, made myopic, while the ex-
periment a is being performed, we see the shadow of the needle in the
circle of diffusion. If the shadow remains straight everywhere, there is
(1) Young does not mention the experiment under this form, but it is a sequence of other expert
ments which he describes. For the experiment 6, he used the bars separating the four slits of his opto-
meter.
102
PHYSIOLOGIC OPTICS
no perceptible aberration; if it is curved, its concavity towards the pe-
riphery indicates ordinary aberration ; its concavity towards the center
indicates over-corrected aberration. We can perform the experiment in
the different meridians and thus prove that the
aberration is not always the same in the differ-
ent directions.
I have constructed a little instrument, the
aberroscope (fig. 66), consisting of a plano-con-
vex lens which, on its plain side, carries a
micrometer in the form of little squares. We
look at a distant luminous point through the
lens, moving it 10 or 20 centimeters from
Fig. 66. The aberroscope.
Fig. 67. The rules of the optometer of Young.
the eye in order to observe whether the lines then appear curved
or not.
c. THE OPTOMETER OF YOUNG enables us to measure spherical aberra-
tion directly. In the horizontal rule (fig. 67), on the left, are two slits,
very narrow and very close. We look at the line through these slits
and determine the central refraction by observing the intersection of the
two apparent lines, as I have explained in chapter V. Care must be
taken to place the slits so that both the lines appear of the same dis-
tinctness, which takes place when the slits are almost at the middle of
the pupil. This done, we bring the quadrangular aperture in front of
the lens, and gradually lower the vertical rule which has the triangular
SPHERICAL ABERRATION
103
plate, so as to exclude a continually increasing part of the middle of
pupil. We then see two intersecting lines which separate more and
more, until one of them disappears at the moment when the width of
the plate is equal to the diameter of the pupil. We then raise the rule a
little, so as to again see two lines, and measure the refraction. The
difference between this measurement and that made with the two slits
placed at the center indicates the degree of aberration.
00
J II III
Fig. 68. I and II. The appearance assumed by the line f the optometer of Young, seen
through four slits by one eye with strong spherical aberration. O, position of the eye ;
a (a') far point of the peripheral parts ; b (&') far point of the central parts.
III. The appearance of the line, seen in the same circumstances by one eye (left)
with marked obliquity. The external part of the pupillary space is more refracting
than the internal part.
Young made two measurements at once by using four slits of the
horizontal rule. The experiment thus performed is much more elegant
and sure, but it is often difficult to succeed, especially if the pupil is not
dilated. It is easier to succeed if the slits are brought together in pairs,
104 PHYSIOLOGIC OPTICS
leaving a central interval a little greater than that between the pairs.
With the four slits we see four lines (fig. 68, I); if there is spherical
aberration the two central lines intersect farther away (at b) than the
peripheral lines (a). Very frequently the lines partly blend, so as to
give the appearance shown in figure 68, II. Figure 68, III, shows the
appearance which the line assumes to an unsymmetrical eye (left), the
external part of the pupil being more refracting than the internal.
We can also measure with the two slits the refraction at the middle
of the pupil, as we did just before, and then displace the slits successively
towards either border until one of the lines begins to disappear. We
thus determine the refraction near the two borders. This experiment,
by which we determine the position of the point r, figure 68, I, is
analogous to that described on page 98, in which we covered the two
apertures situated on the same side of the lens to measure the refraction
on the other side. The measurements made with the slits placed pe-
ripherally generally differ more from those obtained with the central
slits than do the measurements made with the triangular plate, which is
so also in the case of the lens.
SKIASCOPIC EXAMINATION. While the methods which we have just
mentioned are quite delicate, skiascopy furnishes us with a convenient
means of examining the aberration of the human eye. For this pur-
pose it is necessary to use skiascopy with a luminous point, a method which
has been with good cause recommended by Jackson, and which is nothing
more than an application of the principle of Foucault. We observe the
pupil, while we form a distinct image of a luminous point on the retina.
We surround a flame with an opaque tube pierced with an opening of
one centimeter diameter; it is the image of this opening that we project
on the retina with an ophthalmoscope, and care must be taken in select-
ing the mirror so that this image may be distinct; in other words, so
that the image of the opening formed by the mirror is near the place
for which the observed eye is focused. If the observed person is emme-
tropic, we place the light at 50 centimeters or one meter behind him,
and examine with a plane mirror. If he is myopic, we use, on the con-
trary, a concave mirror which projects the image of the luminous point
near his far point. In all cases it is advisable that the opening of the
mirror be quite small, about 2 mm. The pupil of the observed person
must be dilated.
To examine the aberration, we make the observed person emmetropic,
and, placing ourselves at 50 centimeters distance, we project a light on
the eye. Generally we will see at once the phenomenon of aberration :
SPHERICAL ABERRATION 105
the borders of the pupil are luminous, separated from the central light
by a dark zone. We approach until the ring disappears; if this takes
place at 25 centimeters from the observed person, the aberration is
positive and 4 D. If we do not perceive the ring, we move back as far
as one meter; if it does not yet appear, we try whether the aberration
is over-corrected : we make the observed person myopic 3 D. ; if the
ring appears, we increase the myopia until it disappears. If it disap-
pears with myopia of 4 D., the aberration is 2 D., since we must take
off 2 D., the observer being at 50 centimeters. Brudze^vsk^, who de-
termined the aberration of a certain number of persons in this way,
said that it is rare not to meet with positive aberration in some part of
the pupil. It happens, indeed, quite often that the ring is incomplete,
or even that there remains only a very small section of it. Negative
aberration is met with most frequently inwards or upwards in the pupil
where the corneal flattening begins soonest.
RESULTS. Examined with the aberroscope most people indicate a
certain degree of aberration, which corresponds closely to the nearly
spherical (toric) form of the optic part of the cornea (fig. 69). Since
I II
Fig. 69. Deformity of the shadows in an eye with strong spherical aberration (Anto-
nelli). I, in a state of repose; II, during accommodation. In the latter case the aber-
ration is nearly corrected.
the peripheral parts of a spherical surface are too refracting, we can
correct the defect by flattening it towards the periphery. We also some-
times find people whose aberration is corrected, or even over-corrected,
towards the borders, where the basilar part of the cornea comes into
play (fig. 70). And, if the pupil is placed a little eccentrically, we may
thus find aberration in one direction and over-corrected aberration in
another (fig. 71). Thus the middle of my pupil is slightly myopic and
106
PHYSIOLOGIC OPTICS
the upper part slightly hypermetropic, while the lower marginal part
measures a myopia of three dioptrics, which may even reach four diop-
trics when the pupil is dilated. I have, therefore, spherical aberration
below (and on both sides), over-corrected aberration above. One of
my friends, who is an astronomer, has aberration in the vertical meri-
dian, while the horizontal meridian is corrected.
Some are met with who have slightly over-corrected aberration in
the entire pupillary space (fig. 72). These are probably persons in whom
the spherical part of the cornea is of little extent. The ophthalmo
. 70. Aberration over- Fig. 71. Aberration over- Fig. 72. Aberration over-
corrected towards the borders. corrected above. corrected every where.
metric measurements of Brudzewski, which I have mentioned, page 59,
enable us to calculate directly the degree of the aberration of the cornea.
They show that there exist, in this regard, considerable variations.
Corneal aberration is, as a rule, positive, negative aberration being
rather an exception. Positive aberration is especially pronounced in
cases of corneas of great curvature, which is not surprising, since the
aberration increases in very close proportion to the central refraction.
Negative aberration is met with most frequently on the inner side, some-
times above or below, very rarely outside. The greatest degree of
aberration which Brudzewski found was 4- 4.5 (temporal side), the least
2.2 D. (nasal side). Generally it varied between + 3 and 1.5. The
numbers are calculated for a distance of 4 mm., starting from the axis ;
they correspond, therefore, to a maximum dilation of the pupil ; the
values diminish as we approach the axis.
Stadfeldt measured the aberration of the dead crystalline lens by the
SPHERICAL ABERRATION
107
ID"
method of Foucault. When the crystalline lens was taken from the eye,
in its capsule and with the
zonula, he fixed it in a cork ring
which he then placed in a small
tube filled with serum and closed
in front and behind by plane
parallel plates of glass. He
placed this tube on the support
A (fig. 720), which moved along
the graduated rule E D. The
lens C concentrated the light of
a flame on a very fine opening
pierced in the screen B D. The
crystalline lens was observed
with a telescope, placed at some
distance in the direction K; an
Fig. 72a. StadfeldCs instrument for measur-
ing the aberration of the crystalline lens
(dead).
ocular micrometer permitted the measurement of the diameter of the
aberration ring, corresponding to a given distance between A and the
plate B D. The determination of the focal distance of the central
part is less exact by this method. To have a more exact measurement,
Stadfeldt removed the plate B D, and placed a microscope of slight
magnifying power in the tube K. He then sighted towards an object
placed at a great distance. By displacing the cursor A, leaving the
microscope motionless, he put the latter in focus, first for the image
of the distant object formed by the crystalline lens, and then for the
posterior surface of the crystalline lens itself. The difference between
the two positions of the cursor A enabled him to calculate the focal dis-
tance of the crystalline lens.
By these methods Stadfeldt proved that a central part of the crystal-
line lens (up to a distance of 2 mm. from the axis) may be considered
as aplanatic. This part is surrounded with a zone (up to 3.5 mm. from
the axis), the aberration of which is over-corrected (about 2 D.). Very
close to the borders the aberration changes sign and becomes positive.
The over-correction is due to the diminution of the index towards the
periphery, but very close to the borders the increase of curvature of the
surface is so great that the diminution of the index is not sufficient to
correct the aberration.
Although aberration may sometimes be very pronounced, it does
not seem to hurt the visual acuity much as long as it continues entirely
regular, a remark which Graefe made on the occasion of his celebrated
108 PHYSIOLOGIC OPTICS
case of aniridia. The reason is that patients do not use the part of
the cone of which the diameter is smallest, but another part near B,
figure 61. Placing a screen at this place, the image of a point is pre-
sented as a point surrounded with a slightly luminous halo; if the
brightness of the object is feeble, as is most frequently the case in the
ordinary circumstances of life, this halo is too slight to be perceived,
and the image becomes quite good. We see (fig. 61) that a section of
the caustic (the most luminous part of the cone) has the form of the
head of an arrow. The point of the arrow is directed backwards in eyes
with ordinary aberration and forwards in those with over-corrected
aberration ; it corresponds to the focus of the central rays, and it is this
point which serves for vision; but, as it is very pointed, it follows that
the determination of the refraction cannot be of very great exactness.
The spherical aberration acts, in this regard, as a narrow diaphragm.
If a lens is diaphragmed much it becomes very difficult to determine its
focus exactly. Thanks to this form of the caustic, very regular eyes
can have a very beautiful visual acuity despite a strong aberration ; but,
in most eyes, the refraction is irregular, so that patients have not this
advantage (see chapter X). I think, however, that they generally select
the place where the section of the caustic is smallest, and not that where
the cone has the least diameter.
Bibliography. OSavres de Th. Young, p. 153. Volkmann (A. W.) in Wagner.
Handworterbuch der Physiologic, Art. Sehen, p. 292. Meyer (H.). Ueber die spharischcn
Abweichungen des menschlichen Auges. Poggendorfs Ann. LXXXIX, p. 540. Tscherning
(M.). Diemonochromatischen Abweichungen des menschlichen Auges. Zeitschr.f. Physiol. der Sin-
nesorgane, VI, p. 456. Stadfeldt (A.) and Tscherning (M.). Une nouvelle methode pour
etudier la refraction cristaUinienne, Arch, de physiol., July, 1896. Jackson. Skiascopy. Phila-
delphia, 1896. Stadfeldt (A.). Recherches sur Vindice total du cristaUin humain. Journal de
Physiologic, November, 1899. Brudzewski (K.). Beitrag zur Dioptrik des Auges. Archiv
ur Augcnhcilkunde, XL, 3.
CHAPTER VIII.
CHROMATIC ABERRATION.
54. Optic Principles. By receiving on a screen a pencil of white rays
which, after having passed through a slit, has traversed a prism, we
obtain what is called a spectrum, a luminous band containing the entire
gamut of the colors of the rainbow, arranged in the following order:
red, orange, yellow, green, blue, violet. Each white ray is divided into
colored rays which are refracted differently, the red the least, the violet
the most, which we express by saying that the index of refraction of
the glass is greater for the violet. If we speak of the index of a medium,
without more particular specification, it is generally the index of the
yellow rays (the sodium line) that is meant. The difference between
the index of the violet and that of the red is called the dispersion of the
medium. Instead of receiving the spectrum on a screen, we can observe
it directly by looking at the slit through the prism. For this observa-
tion the prism is frequently combined with an astronomical telescope
(spectroscope).
In order that the spectrum may be really pure we must: i make use
of a very narrow slit ; 2 interpose a lens so that the rays of each color
may be reunited on the screen in a distinct image of the slit. The
spectrum is, therefore, in reality composed of a whole series of images
of the slit; if these images are not distinct they are partly overlapped
and the colors are not pure. To obtain a very great purity of colors,
special precautions must be used: we project the spectrum on a screen
pierced by a slit at the place where the color we desire to examine is
formed. Through this slit an eye situated behind the screen receives
the light of this color, mixed with a little white light, due to diffusion
in the substance of the prism and lens. To eliminate this white light,
we observe the slit through a second prism. It forms a spectrum which
is very weak everywhere, except at the location of the color we desire
to examine (Helmholtz). The length of the spectrum depends on the
size of the angle of the prism and on the degree of dispersion of the
109
110
PHYSIOLOGIC OPTICS
glass: a prism of flint glass produces a spectrum much longer than a
prism of crown glass. Beyond the red there are ultra-red rays, which
are invisible, but which have a greater caloric effect than the visible
rays. Beyond the violet rays there are likewise ultra-violet rays, which,
in ordinary circumstances, are invisible, but which act on photographic
plates. They can be made visible by overlaying the screen with a
"fluorescent" liquid (sulphate of quinine, fluorescence, etc.). Struck by
the ultra-violet rays, these substances send back visible rays, generally
bluish or greenish. With certain precautions we can see directly a part
of the ultra-violet rays, perhaps because the retina itself is fluorescent.
Thus Mascart mentions a physicist who could distinguish the lines of
Fraunhofer in the ultra-violet part of the spectrum as far as the photo-
graphic plate could reproduce them. We cannot make the ultra-red
rays visible because they do not pass through the media of the eye
(Bruecke).
Generally, the media which have a greater index have also a greater
dispersion, (i) but the index and dispersion are not proportional. Thus
Hint glass, for example, gives a dispersion nearly double that of crown
glass, while its index is 1.7 and that of crown 1.5. If we combine a
prism of crown glass with another of flint glass in an inverse manner,
the angle of which is nearly a half less, the dispersion may be neutral-
ized, while there remains a quite considerable part of the refraction of
the crown glass. Such a combination constitutes an achromatic prism
(fig- 73)-
Fig. 73. Achromatic prism.
Fig. 74. Prism d, vision directe.
We can also construct combinations of prisms which give no devia-
tion to the emerging ray, but which have a quite considerable dispersion :
(1) This assertion is true for the glasses which we generally use, but not for the new glasses manu-
factured by Abbe & Schott at Jena since 1886. They succeeded in making one part of crown glass (with
baryta basis) which has scarcely any more dispersion than the ordinary crown glass, but the average
index of which is equal to that of very dense flint, and another part, of crown glass, with low index
and relatively high dispersion. The new glasses are imported for the manufacture of microscopic ob-
jectives (apochromatic systems, see the following page) and also for photographic objectives. Under the
name of isometropic glasses, they have been used for spectacle-making purposes, but, in this respect, they
present no advantage.
CHROMATIC ABERRATION 111
we call these combinations prisms a vision dirccte (fig. 74); they are
much used for the construction of spectroscopes.
By passing through a lens the colored rays are also separated. As
the index is stronger for the blue rays (violet), the blue focus is nearer
the lens than the red focus. This is the reason why the circle of diffusion
of a convex lens is bordered with red inside the focus and with blue
beyond. Lenses may be made achromatic by the same system as
prisms : a convex lens of crown glass is combined with a concave lens,
half as strong, of Hint. The circles of diffusion of such a lens no longer
present red and blue borders, but there still remain traces of other
colors (green and purple). Zeiss at Jena caused these latter to disappear
also by combining several glasses of different kinds, specially manu-
factured for this purpose (apochromatic systems).
55. Chromatic Aberration of the Eye. The eye is not achromatic as
was for a long time believed. The question has played quite a curious
part in the history of optics. Newton thought that the dispersion of a
medium was proportional to its index and that, consequently, the con-
struction' of an achromatic objective was a chimera; this is why, for-
saking astronomical telescopes, he adopted catoptric telescopes. But
Euler concluded that, the eye being achromatic, it must be possible to
construct achromatic lenses, and this remark led Dolknd, the optician,
to construct objectives thus corrected. Later Wollaston demonstrated
that the eye is not achromatic. This is not the only time that useful
results have been arrived at by starting from a false hypothesis.
56. Experiment of Wollaston. A luminous point seen through a
prism gives a linear spectrum. But, making the experiment, we observe
that we cannot see distinctly at once the entire extent of the spectrum.
If the luminous point is at a great distance, the emmetropic eye sees
the red extremity of the spectrum as a distinct line, while the blue ex-
tremity is enlarged and frequently divided into two ("like the tail of a.
swallow"). If we go nearer, taking care not to use our accommodation,
we find a distance at which we are focused for the blue extremity, while
the red extremity is, in turn, diffuse. The observer can, therefore, de-
termine his far point for each extremity of the spectrum ; the difference
gives the degree of chromatic aberration.
Wollaston has likewise directed attention to another phenomenon of
chromatic aberration: the colored borders which are seen along the
lines of the optometer of Young.
11-2 PHYSIOLOGIC OPTICS
EXPERIMENTS WITH THE COBALT GLASS. Placing a luminous point,
such as an opening in an opaque screen, inside the near point, we see a
circle of diffusion bordered with red exactly as when we made the
analogous experiment with the lens ; it is more difficult to see the blue
border which surrounds the point, when it is situated beyond the far
point. The experiment is much more striking when the point is ob-
served through a cobalt glass. These glasses allow only the blue and
red rays to pass; looking at a luminous point situated inside the near
point, through such a glass, we see it blue and surrounded by a red
halo. If the luminous point is situated beyond the far point, we see, on
the contrary, a red point surrounded with blue.
EXPERIMENTS OF FRAUNHOFER. This scientist determined the dis-
tance at which he could see distinctly a spider thread placed sometimes
in the red light, sometimes in the blue light of the spectrum. We thus
obtain very exact results.
57. Results. Young estimated the chromatic aberration of the eye
at 1.3 D., Fraunhofer found 1.5 to 3 D., Helmholts gives 1.8 D. The
number is difficult to determine exactly, since the lowest limit of the
visible spectrum is not well defined. The dispersion of the eye is a
little greater than it would be if the eye were filled with water.
The eye, therefore, is not achromatic, and, as we have seen, it is easy
to convince oneself of it when the object is situated beyond the far point
or within the near point. But when the object is at such a distance that
it can be seen distinctly, we do not see colored borders. The explana-
Violet
Fig. 75. Chromatic aberration of the eye.
tion which is given of this fact is the following: Let A (fig. 75) be a
luminous point which sends the cone ABC into the eye. After refraction,
the white rays are divided into colored rays ; the red rays form the cone
CHROMATIC ABERRATION 113
BrC, the violet rays, which are more refracted, the cone Bz/C, and the
eye accommodates itself in such a way that the retina is between the
two foci, placed so that the red diffusion circle covers the blue one (see
fig- 75)- The intermediary rays of the spectrum, the yellow and the
green, which are the most luminous, are then concentrated at the middle
of the diffusion circle, where they coincide with a part of the red and a
part of the violet, while the peripheral parts of the red and violet form
a purple border all around ; but this border is very narrow, and, as it is
formed by the extreme rays of the spectrum, which are very slightly
luminous, it is too weak to be perceived. When observing a luminous
point with an astronomical telescope, the objective of which is not very
well achromatized, the same phenomena are seen: if the telescope is
focused for a nearer point, the circle appears surrounded with blue ; in
the contrary case it is bordered with red, and, when the point is seen
distinctly, it is surrounded by a very narrow purple border. The same
thing occurs if the point A be replaced by a white object: in the latter
case we do not see colored borders.
58. Phenomena of Dispersion, the Pupil Being Partly Covered. It is
different if a part of the pupil be covered by a screen. Let us fix, for ex-
ample, the sash bar of a window through which we see the sky. Cover-
ing the right half of the pupil with a screen, we see the border aa (fig. 76)
become colored blue, the border bb yellow. In order to explain this fact
let us examine the point a, the last luminous point of the window on the
right, and suppose that the point A in figure 75 is
this point: by covering the half (BO, fig. 75) of the
pupil, instead of a circle of diffusion uniformly illum-
inated by violet and red, we have a circle the right half
of which is violet and the left half red. This latter half
is covered by the circle of diffusion of the following
point of the window on the right, and is not visible ;
there remains, therefore, a blue border (violet) along
the sash bar. Of the point b it is, on the contrary, Fig. 76.
the red half (yellow) of the circle of diffusion which is not covered.
We frequently observe very striking phenomena due to the chromatic
aberration of the eye, by fixing black objects on a white ground, placed
at a distance for which the eye cannot accommodate itself. Looked at
towards the sky, the slits of the optometer of Young present thus very
vivid colorings. The chromatic aberration increases with the diameter
of the pupil. To study it, it is useful, therefore, to make use of
mydriatics.
114 PHYSIOLOGIC OPTICS
59. Correction of the Chromatic Aberration. We could correct the
chromatic aberration of the eye with a concave lens of Hint, exactly as we
can correct the chromatic aberration of a convex lens of crown glass.
The dispersion of flint glass is about three times that of the eye. As
the refracting system of the eye is about sixty dioptrics, a concave flint
lens of about twenty dioptrics would be necessary to correct this aberra-
tion. A myope of twenty dioptrics, who would correct his ametropia
with a flint lens, would have, therefore, at the same time corrected his
chromatic aberration. An emmetrope would be obliged to add to this
lens a convex achromatic lens of twenty dioptrics to remain emmetropic.
The attempts which have been made in this direction (Helmholtz, JavaT)
have not given a very marked improvement of the visual acuity.
Bibliography. (Euvres de Young, p. 154. Wollaston, Phil, trans., 1801, p. 50.
Fraunhofer(J.) Gilberts Ann., LVI, p. 304. v. Bezold (W.). Graefes Arch. f. Ophth.,XlV
2, p. 1.
CHAPTER IX.
REGULAR ASTIGMATISM.
60. Optic Principles. Astigmatism Produced by the Form of the Sur-
faces. To account for the form of the astigmatic pencil, the following
experiment may be made. We combine a convex cylinder, with its axis
horizontal, with a convex spherical lens; the combination of + 3 cyl.
with 4- 6 sph. answers very well. The pencil, which emanates from a
Ooi
O
Fig. 77. Circles of diffusion and focal lines of a regularly astigmatic system. After Fuchs.
(In order that the figure may agree with the text, we must suppose the first focal
line a horizontal, the second 6 vertical.)
distant luminous point and is refracted by the sphero-cylindrical com-
bination, is received on a screen which is gradually moved away from
the lens. Then, instead of a circle of diffusion, the diameter of which
diminishes according as the screen is removed in order to become a
point when the screen is at focus, and to again become circular beyond,
we obtain the forms illustrated on figure 77.
The two straight lines are called focal lines; the distance which sep-
arates them is called interfocal distance, and the meridians of the optic
system to which they correspond are the principal meridians. Together
the rays no longer form a cone in which all the rays pass through a
point, but a more complicated system, characterized by this peculiarity,
that all the rays pass through two short straight lines perpendicular to
each other (the focal lines). The system is known as the conoid of
Sturm.
The first focal line is at the focus of the meridian of greatest refrac-
tion (in our case, the vertical meridian) ; it is parallel to the meridian
115
116
PHYSIOLOGIC OPTICS
of least refraction ; the second focal line is at the focus of the meridian
of least refraction and parallel to the meridian of greatest refraction.
The diffusion spots are everywhere elliptical, except at one point of the
interfocal distance where the luminous spot is circular.
In the principal meridians, refraction takes place as if the lenses were
spherical ; an incident ray parallel to the axis cuts the latter at the focus
of the meridian. The rays which are not situated in the principal meri-
dians do not meet the axis ; their course will be indicated later on.
The length of the focal lines is proportional to the distance of these lines
from the lens. Let F' (fig. 78) (i) be the distance of the first focal line,
F;
Fig. 78. pu horizontal focal line ; p. 2 , vertical focal line.
F" that of the second, P the diameter of the lens, p and p 2 the lengths
of the two focal lines. Then we have
PI
~"
F'
and
^ ; consequently by dividing
The circle of circular diffusion is at a, where the diameters are equal.
It divides the interfocal distance into two parts, which are proportional to
the focal distances. For, designating the diameter at this place by a, and
the two parts of the interfocal distance by x and y we have :
and -
, therefore, by dividing,
y . PL -
x ~ Pl ~ - F'
All the other diffusion spots are ellipses, of which it is easy to calculate
(1) We must suppose that the vertical meridian has been made to rotate 90 around the axis, so as to
be able to draw the two focal lines in the same plane.
REGULAR ASTIGMATISM
117
the axes. Placing a screen at a distance b from the second focal line,
we see (fig. 78) that the axes c and d of the ellipse are found by the
equations -- = l ~ (F f, ~ F and -|- = - , equations which give as the
relation between the axes:
(F" FQ
~F/~~
X
Knowing the axes we can find the ellipse by construction (fig. 79).
We make a circle with half the long axis d (fig. 78) as radius, and draw
therein two diameters, a horizontal BD and a vertical AE, and mark
the points A' and E' so that OA' = OE' = -f . BD and A'E' are then
Fig. 79. Construction of the elliptical diffusion spot.
the two axes of the ellipse, and we can find any point whatever G x , of
the ellipse, by letting fall the perpendicular GH on the long axis, and
marking the point G^ so that %g- = -- .
We can use this construction to find the course of the rays which
are not situated in the principal planes. Suppose, indeed, that one of
these rays passes through a given point of the lens. If the optic system
were spherical and of the power of the meridian of least refraction, we
would have a circle of diffusion of diameter BD, in which it would be
easy to find the point K through which the ray would pass, since the
circle would be only a diminished image of the lens. Having determined
the position of the point K, we find the point K' through which the
ray really passes, by diminishing the distance of K from the long axis
in the proportion -|-.
APPLICATION OF THE PRINCIPLE OF FOUCAULT. Let us place the
luminous point a little beyond the focus of our sphero-cylindrical com-
118 PHYSIOLOGIC OPTICS
bination. The focal lines are then formed at quite a great distance. We
receive the horizontal focal line on a screen which is then removed and
the eye put in its place ; we will then see a vertical luminous band which
passes through the lens, while the parts on the right and left are dark.
As we have already seen (page 99) the eye sees luminous the parts of
the lens which send light to it, and it is easy to see that it receives under
these circumstances all the luminous rays from the vertical meridian,
while it does not receive rays coming from the lateral parts which inter-
sect in other points of the horizontal focal line, to the right and left
of the eye. Placing the eye in the vertical focal line we see a horizontal
band.
61. Defects of the Image. As the image of a point is never exactly
a point, the image of an object can never be really distinct. Outside the
focal lines, the outlines are all more or less dull. If the screen is at p lt
the horizontal lines only are distinct, if it is at p 2 , it is the vertical lines
that are distinct. The image is better at p than at p 2 , since the first
focal line is the shorter.
With a cylinder which is strong compared with the spherical glass,
the image becomes so poor that it is unrecognizable ; with + 6 spherical
combined with + 3 cylindrical of our test case, it is impossible to form
an image on a screen. If, on the contrary, we place this combination
sufficiently far from the eye that the image may be seen inverted, this
image is pretty good, because the pupil of the observer forms a dia-
phragm ; but it is deformed, all the dimensions parallel to the meridian
of greatest refraction being greatly diminished.
2. Astigmatic Surfaces. We have so far obtained astigmatic refrac-
tion by a combination of spherical and cylindrical surfaces, but we can
obtain the same result by refraction through a single refracting sur-
face. If the aperture is very small, this result is obtained with any
surface whatever, (i) For, a small part of any surface always presents
two principal meridians, perpendicular to each other, one of maximum
and the other of minimum curvature. The incident rays, situated in
these planes, remain there after refraction and go to meet the axis after
refraction; the rays which are not situated in these meridians do not
meet the axis, but pass through two focal lines, perpendicular to the
axis and situated in the principal meridians. Among the surfaces for
which this is true, even for quite a large aperture, at least approximately,
(1) We must except the plane, sphere, the part near the axes of the surfaces of revolution, and that
near the points called umbilical of other surfaces, supposing the incidence normal. Otherwise, the re-
fraction is always astigmatic.
REGULAR ASTIGMATISM 119
there are two specially noteworthy: the ellipsoid with three axes and
the tore.
By rotating an ellipse around its long axis, we obtain an ellipsoid of
revolution. And if we suppose that it undergoes a flattening in a direc-
tion perpendicular to the long axis, we obtain an ellipsoid with three axes.
The luminous point must be on the long axis. The two principal
meridians are elliptical (as is every other section of this surface).
The tore is the surface which is obtained by making a circle rotate
around an axis situated in its plane (ab, fig. 80). By cutting a part near
A, we would have an astigmatic surface the principal meridians of which
would be circular ; one would have the same radius as the circle (R t ) ;
the radius of the other (R 2 ) would be equal to the distance of the axis
from the apex of the circle. The luminous point must be on the pro-
longation of AO.
Even with these surfaces a pure astigmatic action is not obtained,
when the aperture is a little large. It is
clear that on account of the spherical
aberration the peripheral parts of the
principal meridians of the tore must have
a greater refraction than the central
parts ; also the astigmatism of a periph-
eral zone becomes greater than that
of the central part, since the refraction
increases more rapidly towards the pe-
riphery in the most curved principal me-
ridian. On account of the flattening
towards the periphery, the aberration is Fi g- 80 - ~ 7 the revolution around
the straight line 06, the circle pro-
less for the ellipsoid ; one of the men- duces a torus,
dians may even be aplanatic for a distant object, but then the other meri-
dian is either over-corrected or under-corrected, so that the astigmatic
effect is never pure.
63. Astigmatism by Incidence. Let us place a spherical lens at some
distance from a luminous point and form the image of this point on a
screen; then make the lens rotate around a vertical axis. The screen
immediately ceases to be at the point ; we must move it nearer the lens,
and we find at the same time that the refracted pencil is astigmatic. The
horizontal focal line is farther from the lens than the vertical focal line.
The refraction has, therefore, increased in both meridians, but more in that
which contains the axis of the lens and the luminous point.
120
PHYSIOLOGIC OPTICS
The focal lines are far from being distinct, especially if we do not
use a small diaphragm. They are rather diffusion spots greatly length-
ened in one or other direction. But the pencil has one true focal line
Fig. 81. Focal line of a lens placed obliquely.
which, in our case, is horizontal ; we find it by making the screen rotate
around a vertical axis, but in a direction the reverse of that of the lens
(fig. 81).
A pencil reflected or refracted obliquely by a spherical surface is also
astigmatic by incidence. It is the same phenomenon which constitutes
spherical aberration.
Let cabd (fig. 82) be an incident pencil parallel to the axis of a refract-
ing spherical surface. Suppose that the pencil is cylindrical, so that ab
Fig. 82.
Astigmatism by incidence. F x , first focal line ; F x/ F //x , second focal line.
is the diameter of the small round spot which represents the aperture
of the surface : ab is then one of the principal meridians and the diameter
perpendicular to ab is the other. On account of the spherical aberra-
tion the ray aF' meets the axis nearer the surface than the ray bF r . The
first focal line, which is perpendicular to the plane of the paper, is at F',
for, if we imagine the entire figure rotating around the axis, F' describes
an arc of a circle, a small part of which may be considered as a straight
REGULAR ASTIGMATISM 121
line, and it is easy to see that all the rays of our pencil must pass through
this straight line (at least approximately). As, on the other hand, the
rays must all meet the axis, F" F"' is the second focal line. Here
again the meridian of greatest refraction is that which contains the axis.
When the incidence is oblique, all the surfaces, the plane surfaces in-
cluded, give astigmatism by refraction.
It is the same in the case of reflection, but then the plane surfaces
are an exception. Ordinary mirrors are not exempt from this defect
on account of the refraction through the thickness of the glass which
is in front of the coating. The best images that we can obtain are those
formed by reflection on a surface of mercury, especially when the layer
is very thin: the pencil is not astigmatic at all. (i)
64. Astigmatism of the Human Eye. Historical. This defect of the
human eye was discovered by Thomas Young in 1801. He never noticed
that his vision was defective, and claimed that he saw as well as most
people. He proved the defect in his own eye by means of his optometer,
and also by observing the forms of the circles of diffusion produced by
a luminous point. He measured its degree by means of the optometer
and expressed it, as we still do, by the difference of refraction of the two
meridians. He had 1.7 D. of astigmatism against the rule. He proved
that his astigmatism was not seated in the cornea, because, by perform-
ing his celebrated experiment of putting the eye under water and sub-
stituting a spherical lens for the cornea (see page 168), he found the
same degree. He attributed the astigmatism to the obliquity of the
crystalline lens, which obliquity he thought much greater than it really
is, and remarked that the defect could be corrected with glasses placed
obliquely in front of the eye.
The astronomer Airy, a professor at Cambridge, was the first who
corrected the defect by a cylindrical glass (1827). He had high com-
pound myopic astigmatism of the left eye, which he studied and meas-
ured by means of a luminous point. Later, Colonel Goulier likewise
studied this defect and prescribed cylindrical glasses to a certain number
of patients.
It was only after the invention of the ophthalmometer by Hclmlwltz
that the measurements of Knapp and Bonders drew attention to this
prevalent anomaly of the human eye. The works of these two investi-
gators appeared almost at the same time, but those of Bonders had
(1) It is claimed, however, that we can still observe a trace of astigmatism, in this case, -with the
telescopes of the greatest magnifying power. This astigmatism might be due to the fact that the sur-
face is not really plane on account of the spherical form of the earth.
122 PHYSIOLOGIC OPTICS
greater influence. He was, in fact, the first to have cylindrical glasses
put in the test case, which greatly contributed to their more general
use. The methods used for the examination of patients were quite de-
fective. The luminous point was especially used to find the meridians,
and the refraction of each meridian was then measured by means of the
stenopaic slit and spherical glasses. A little later Javal introduced
the examination by the star figure and cylindrical glasses.
65. Physiologic Astigmatism. It is rare to find an eye completely
free from astigmatism ; but when the degree is slight, it scarcely affects
the vision. We call this astigmatism physiologic. It is a disputed ques-
tion at what degree we should begin to consider astigmatism pathologic ;
some have placed the limit at 0.5 D. or at 0.75 D., others at I D. or
1.5 D. In certain people we can improve vision with a cylinder of 0.75 ;
others, on the contrary, experience no improvement, although they
may have really the same degree of astigmatism. The aperture of the
pupil, and especially the greater or less regularity of the astigmatic
pencil, here play an important part. One of the best means of disclosing
low degrees of astigmatism consists in observing the form under which
a luminous point appears when placed at different distances. If the
luminous point indicates a trace of astigmatism, we can generally also
verify 'it by the star figure and a weak cylindrical lens, by placing the
latter at first in the correct position and then in the contrary position.
The patient then tells that the former position equalizes the lines better
than the latter.
66. Corneal Astigmatism. The principal seat of astigmatism is in
the anterior surface of the cornea, which is not strange, since it is at this
place that the principal change of index occurs. A deformity of one of
the internal surfaces of the eye, which, at the anterior surface of the
cornea, would produce considerable astigmatism, has only slight effect
on account of the little difference of index of the media. The refraction
is expressed, as we have seen, by (n ~ 10 ' (see page 13), that is to
say, for the cornea, by - and, for one of the internal surface, by
~. The same deformity would, therefore, produce an effect five or
six times less.
We may conceive also that, in the normal eye, astigmatism by in-
cidence could scarcely play any part, since the visual line passes ap-
proximately through the center of curvature of the cornea and through
the middle of the pupil. It is otherwise in cases where there exists a
considerable displacement of the pupil (corectopia), and especially in
REGULAR ASTIGMATISM
123
the case of an artificial pupil. Under ordinary circumstances, there-
fore, it is the form of the anterior surface of the cornea that principally
determines astigmatism; the examination of this surface thus plays an
important part in the search for astigmatism.
67. Measurement of Corneal Astigmatism. There exist different
means of examining whether the cornea is astigmatic and of estimating
the degree of its deformity (disc of Placido, keratoscope of de Wecker
and Massclon, etc.) ; but, to measure it, one can scarcely think of using
any other means than the ophthalmometer of Javal and Schioetz, which
we have already described. The progress which it marks, compared
with old ophthalmometers, consists especially in the facility with which
we find the principal meridians by means of the difference in the level
(denivellatiori). If the arc is in a principal meridian, the images of the
two mires must be on the same level and the black lines which are at
the middle of the mires must be in the prolongation of each other. Out-
side the principal meridians there is a difference in the level (denivellatiori)
greater in proportion as the astigmatism is more pronounced.
Fig. 83. Explanation of the difference in the level (de"nivellation).
To explain this phenomenon, let us examine a spherical cornea after
having removed the doubly refracting prism from the instrument which
124 PHYSIOLOGIC OPTICS
then acts as a simple telescope. We then see only the images of the
two mires, separated by an interval of about 3 millimeters. By rotating
the arc these images describe a circle. Let ABCD, figure 83, be this
circle to which the images of the mires always remain tangents. Let
us replace the prism in position. Then the images are in the same
meridian as the mires themselves, and as the doubling (dedoublemcnt) of
the prism takes place exactly in this meridian there is no difference in
the level. If we replace the spherical cornea by an astigmatic cornea,
the vertical meridian of which is the more curved, the circle ABCD is
replaced by the ellipse AEBF which is constructed as shown on page 117
by reducing the distance of each point from AB in the proportion of
the radii of the two principal meridians. By this construction the dotted
diameter becomes the diameter KL, on which the images now are. The
latter are, therefore, no longer situated in the meridian of the mires,
and as the prism always acts in the direction parallel to this meridian, it
follows that on obtaining contact the two images are not on the same
level. Only when the arc is in one of the principal meridians the mires
and their images are in the same plane and there is no difference in
the level.
We can account for the difference between the image produced by a
spherical cornea and that of an astigmatic cornea, by drawing on a sheet
of paper a circle with two oblique diameters, perpendicular to each
other, and observing the inverted image formed by a strong spherical
lens held at some distance from the eye. The image is identical with
the drawing; but if a convex cylinder with horizontal axis be added,
the circle is replaced by an ellipse with the long axis horizontal, and the
two diameters form between them obtuse angles above and below.
After having placed the ocular in focus for the spider thread, and
then the instrument in focus for the eye, we begin by finding the meri-
dian of least refraction. We place the mires in contact and make the
arc rotate 90. This done, the images of the mires partly overlap, and
the number of gradations overlapped indicates the degree of astig-
matism in dioptrics. If very exact measurements are desired, it is
preferable to find each of the meridians separately, and to obtain contact
in each of them. We read the refraction of each meridian on the arc,
and the difference indicates the astigmatism. We sometimes observe
that the two principal meridians are not exactly perpendicular to each
other; this is due to the relatively great distance between the mires;
for, the principal meridians of a minute part of a surface are always
perpendicular to each other. This is attributable to the fact that the
REGULAR ASTIGMATISM 125
meridians, instead of being plane sections of the cornea, possess a
certain curvature.
68. Regular Corneal Astigmatism. We distinguish between direct
astigmatism or astigmatism with the rule, in which the meridian of
greatest refraction does not differ much from the vertical, and perverse
astigmatism or astigmatism against the rule, in which the horizontal
meridian is that of greatest refraction. If the direction of the meridians
differs much from the horizontal and vertical directions, we say that
the astigmatism is oblique.
Schioets and Nordenson have compiled statistics on the direction of the
corneal astigmatism in school children. Following are the results ob-
tained by Nordenson:
Corneal astigmatism, none 9 per cent.
with the rule 77
against the rule 1
oblique 12
Thirty per cent, had astigmatism of at least I D., 2 per cent, an astig-
matism over 1.5 D. It seems that astigmatism against the rule be-
comes more frequent with age, and that astigmatism with the rule
changes into astigmatism against the rule under the influence of an
increase of tension. Pfalz and G. Martin have thus found astigmatism
against the rule very common in glaucomatous patients, and the ex-
perimental researches of Eissen on rabbits' eyes confirm this result.
Except in post-operative cases, corneal astigmatism only very rarely
exceeds the degree of 5 to 6 D. ; astigmatism against the rule and oblique
astigmatism are never so pronounced. If there is a difference between
the degree of the astigmatism of the two eyes of the same person, we
generally find that the most astigmatic eye has the maximum curvature
greater and the minimum curvature less than those of the other eye,
but the difference is generally greater for the meridian of greatest refrac-
tion (Javal).
69. Relations Between Ophthalmometric and Subjective Astigmatism.
We have said that the first ophthalmometric measurements were made
by Bonders and Knapp. They noticed that there existed a certain differ-
ence between the ophthalmometric and subjective measurements. They
attributed this difference to an astigmatism of the crystalline lens which
would act in a direction contrary to that of the cornea. Since then
much has been said of crystalline astigmatism, but what has been said
126 PHYSIOLOGIC OPTICS
about it is purely hypothetical, for if I except some measurements which
I have made with the ophthalmophakometer, and to which I shall refer
later, I do not think that any one has observed directly astigmatism of
the crystalline lens. Now, the difference between ophthalmometric and
subjective astigmatism may be attributed to many other causes. To
assume nothing as to the nature of this astigmatism I shall call it supple-
mentary astigmatism. According to most investigators the part which
it plays is the following:
i If there is no ophthalmometric astigmatism, we generally find a
slight subjective astigmatism against the rule;
2 If the ophthalmometric astigmatism is against the rule, the sub-
jective astigmatism is generally against the rule and greater;
3 If the ophthalmometric astigmatism is with the rule and of a value
intermediate between I and 3 D., the subjective astigmatism generally
differs only slightly from it;
4 If the ophthalmometer gives an astigmatism with the rule and
greater than 3 D., the subjective astigmatism is also with the rule, fre-
quently greater.
Javal tried to express the relation between subjective astigmatism
(As t ) and ophthalmometric astigmatism (As c ) by the empiric formula:
As t = k + p. A c ,
in which formula k and p are two constants, k = 0.5 D. against the rule
and p = 1.25. This formula would give the following relation:
Against the rule. With the rule.
As. opht. 2 1 12 34- 5 6 dioptrics
As. sub). 3 1.75 0.5 0.75 2 3.25 4.5 5.75 7 dioptries
Against the rule. With the rule.
It is well understood that this permits of many exceptions, for supple-
mentary astigmatism depends on so many factors, that it is very difficult
to give a general expression of its value. Among these factors I shall
state the following:
i The Deformity of the Internal Surfaces. Although these deform-
ities, as I have already remarked, play quite an important part in the
literature, this question has, up to the present, been completely ignored.
To give an idea of the part which they might play, I add the following
table, which gives the results for some eyes I have measured :
REGULAR ASTIGMATISM 127
Mme T. Dr. B. M. V.
Thickness of the cornea I.l5 mm 1.06 mm 1.31 mm
Position of the anterior surface of the crystalline 3.54 mm 4.24 mm 3 66 mm
Thickness of the crystalline - 4.06 mm 3.98 mm 4.25 ram
Anterior surface of the cornea :
Kadius. Horizontal meridian 7.98 mm 7.78 mm 8 29 mm
Vertical meridian 7.60 mm 7.90 mm 8.33 mm
Horizontal refraction 47.24 D. 48.46 D. 45.48 D.
Vertical refraction 49.60 D. 47.72 D. 45.26 D.
Posterior surface of the cornea :
Radius. Horizontal meridian 6.22 mm 5.66 mm 6.17 min
Vertical meridian 5.55 mm 5.11 jnm 5.87 mni
Horizontal refraction 4.73 D. 5.19 D. 4.77 D.
Vertical refraction 5.30 D. 6.76 D. 5.01 D.
Anterior surface of the crystalline lens:
Radius. Horizontal meridian 10.20 mni 12.26 mm 10.42 mn
Vertical meridian 10.10 mm 10.09 mm 9.33 mm
Horizontal refraction 6.13 D. 5.10 D. 6.00 D.
Vertical refraction 6.19 D. 6.19 D. 6.70 D.
Posterior surface of the crystalline lens:
Radius. Horizontal meridian 6.17 mm 6.38 mm 6.73 mm
Vertical meridian 6.24 mm 7.11 mm 8.49 mm
Horizontal refraction 9.63 D. 9.22 D. 8.73 D.
Vertical refraction 9.42 D. 8.27 D. 6.93 D.
Astigmatism in Dioptrics : (1)
Anterior surface of the cornea 2.36 d 0.74 i 0.22 i
Poterior surface of the cornea 0.57 i 0.57 i 0.24 i
Anterior surface of the crystalline lens 0.06 d 1.09 d 0.70 d
Posterior surface of the crystalline lens 0.11 i 0.95 i 1.81 i
Complete system 1.40 d 1.05 i 1.62 i
Although we manifestly cannot draw general conclusions from the
measurements of three eyes, I wish, however, to direct attention to some
of these results. We observe in the first place that the vertical meri-
dian of the posterior surface of the cornea presents a more pronounced
curvature than the horizontal meridian. This condition is repeated in
the three eyes to which I here refer, as well for the first, the anterior sur-
face of which presents astigmatism with the rule, as for the other two
in which it presents astigmatism against the rule. I have also met the
same deformity in other eyes which I have measured, so much so that
there is reason to believe that the condition is general. It is a deformity
analogous to that which, in the case of the anterior surface of the
cornea, produces astigmatism with the rule; but, as the posterior sur-
face acts like a concave lens, this deformity produces astigmatism against
(1) [Here d (direct) stands for astigmatism with the rule and i (indirect) for that against the
rule.] IF.
128 PHYSIOLOGIC OPTICS
the rule. It is probably for this reason that eyes, which have no ophthal-
mometric astigmatism, generally have subjective astigmatism against
the rule. The influence of the posterior surface of the cornea must
correspond partly with the term k of the formula of Javal.
As to the crystalline surfaces, we observe that the anterior surface
presents in the three cases astigmatism with the rule, the posterior
surface astigmatism against the rule. I do not know whether it is a
coincidence or whether it indicates a general rule.
2 The obliquity of the crystalline lens must, after what we have said on
refraction by lenses placed obliquely (page 119), produce astigmatism
against the rule, but very little, at most a half dioptry, and perhaps
less, if the special structure of the crystalline lens results in compensat-
ing the effect of its obliquity as certain authors (Hermann) have sup-
posed.
3 Mention has been made of an astigmatic accommodation of the crystal-
line lens, which would have the effect of correcting the corneal deformity,
and often even over-correcting it. In my opinion this astigmatic accom-
modation is not sufficiently demonstrated ; I shall speak of it forthwith.
4 We must not forget the influence of the distance of the correcting glass
from the eye, in consequence of which the concave correcting glass is
stronger, the convex glass weaker than the true astigmatism. This
influence makes itself felt the more according as the glass is stronger,
and, in order to calculate it, we must take into account not only the
cylindrical glass, but also the spherical glass with which it is combined
(Ostwalt) (i). If certain authors have found that the subjective astigma-
tism with the rule frequently exceeds that found with the ophthalmo-
meter (the factor p of Javal), it is due, perhaps, to the fact that they
generally use concave cylinders.
5 Among the factors which play a part in supplementary astigma-
tism, the most important is probably the variation of the astigmatism
in the different zones of the cornea. The peripheral zones frequently pre-
sent a value, and sometimes also a direction more or less different from
those of the central zones. This, among other things, follows from the
measurements of the peripheral parts of the cornea made by Sulzer;
but it is especially after I began to work with the optometer of Young
that I frequently found considerable differences between the refraction
of different parts of the pupillary space, and that I became convinced
of the importance of these differences. There certainly exist some
regularly constructed eyes, in which the astigmatism is nearly the same
(1) [See also an article by the translator in the Archives oj Ophthalmology, Vol. XXII, No. 1, 1893
where this question is discussed fully.] IF.
REGULAR ASTIGMATISM 129
in the whole pupillary space, but most eyes are more or less irregular.
Entirely regular astigmatism is only imaginary. This explains also
the hesitancy of many patients when tested with different cylindrical
glasses. We have all met cases in which it is almost impossible to
obtain a definite answer from the patient. Sometimes he prefers one
cylinder, sometimes another somewhat different, and, at each new exam-
ination, he manifests a different preference. Most frequently if the
patient hesitates, he has good reasons for doing so. Examination with
the luminous point (see chap. X), which has been much neglected, but
which we have us"ed for some time at the laboratory of Soirbonne, shows
why the patient hesitates and why we frequently do not obtain a very
encouraging result by correction.
70. Astigmatic Accommodation. The question of astigmatic accom-
modation has been much discussed for some years past. It was Dobro-
wolsky who first expressed the idea that astigmatic patients could partly
correct their defect by producing a deformity of the crystalline lens in
a contrary direction, by an irregular contraction of the ciliary muscle.
He thus supposed a latent astigmatism which could be made manifest by
instilling atropine, exactly as in the case of hypermetropia. Later, the
idea was adopted by Javal, and pushed to its extreme conclusions by
G. Martin, Vacher and others, who went so far as to find in this astig-
matic accommodation the origin of a series of diseases: blepharitis,
keratitis, migraine and even, in certain cases, cataract. Some time ago
a reaction set in ; most of the authors in later years, like Eriksen, Sulzer
and especially George Bull, do not admit astigmatic accommodation.
The advocates of astigmatic accommodation based their belief espe-
cially on the change of the astigmatism observed on instilling atropine.
The phenomenon is, in all probability, due to the fact that the astig-
matism of the peripheral parts differs from that of the central part; in
ordinary circumstances these parts are outside the pupil, but in con-
sequence of atropinization the latter is dilated so as to allow the pe-
ripheral parts to come into play. The area of these peripheral parts is
generally greater than that of the central part which corresponds to
the pupil in ordinary circumstances. Suppose, for example, that the
diameter of the pupil may be brought from 4 to 8 millimeters. The
area of a circle being expressed by r 3 *, that of the ordinary pupil is
about 12 square millimeters and that of the dilated pupil about 50 square
millimeters. The pupil has consequently increased by 38 square milli-
meters, or about three times its size. Thus much more light enters
130 PHYSIOLOGIC OPTICS
through these peripheral parts; and it is not surprising that this fact
greatly influences the answers of the patient. All the observations of
a change of astigmatism after instilling atropine prove nothing, there-
fore, in favor of astigmatic accommodation. It has been proposed to
study the question by placing before the eye a diaphragm of the size
of the undilated pupil, but I do not see how we could assure ourselves
whether the position of the diaphragm really corresponded with that of
the undilated pupil. The only observations in favor of astigmatic
accommodation which could lay claim to some value, are those in which
the observer, provided with a weak cylinder, begins by seeing distinctly
one line of the star figure and ends by seeing all with the same distinct-
ness. But the observations of this kind which have been published are
by no means beyond all criticism. If any one desires to again perform
this experiment he had better use a luminous point : after having placed
a weak cylinder before the eye, it would be necessary to observe the
different forms under which the luminous point would be seen at
different distances (see the following chapter) and to repeat this exam-
ination after having worn the cylinder for an hour or two, to see if the
figures had undergone any change.
The alleged astigmatic accommodation was always of a very low de-
gree, i D. to 1.5 D. at most. Frequently, in order to discover it, a very
persistent atropinization was necessary, lasting as much as fifteen days
and even until symptoms of poisoning appeared. I think that frequently
the patient, weary of the struggle, ended by answering all that was
desired.
71. Post-operative Astigmatism. If we examine the cornea eight
days after the extraction of a cataract, we find an enormous astigmatism
against the rule, sometimes reaching 12 or 14 D. The vertical meridian
is flattened, probably in consequence of the interposition of an exuda-
tion between the lips of the wound; the phenomenon is more pro-
nounced if there exists a hernia of the iris. This astigmatism diminishes
gradually; it may disappear altogether, but generally one or two diop-
trics remain. For this reason it is prudent to postpone the selection of
spectacles for two or three months after the extraction, or, if the patient
desires to have them immediately, to warn him that it will be necessary
to change them after two months. Contrary to what we would expect,
the agreement between the subjective astigmatism and the ophthalmo-
metric measurement is less than for the normal eye, which is due partly
to the distance of the correcting glass from the eye (see page 128),
REGULAR ASTIGMATISM
131
partly to the fact that the cornea very frequently retains a certain de-
gree of irregularity after extraction. What we have said of the extrac-
tion of cataract applies also, but in a much less degree, to iridectomy and
other operations performed on the cornea.
72. Keratoconus. Apart from post-operative cases, we meet the
highest degrees of corneal astigmatism in cases of keratoconus. (i) The
apex of the cone does not generally coincide with the visual line, which
gives rise to a strong astigmatism, the direction of which varies, follow-
ing the direction of the apex of the cone. We observe at the same time
that the images of the mires are very irregular. By removing the prism
and placing the keratoscopic disc in its place, we easily find the direction
of the look which brings the apex of the cone into the axis of the
ophthalmometer ; we then see the image of the keratoscopic disc quite
small and frequently regular, round or oval ; in every other position its
Fig. 84. Keratoscopic images of a case of keratoconus.
form is ovoid (fig. 84). The cases which Javal had first described
under the name of decentered eyes, because he thought their deformity
depended on an unusual size of the angle , were affected with a light
degree of keratoconus, as he has since acknowledged. Outside of cases
(1) The expression "keratoconus" is not very happy ; the form of the cornea approaches in these
cases that of a hyperboloid ; we know, indeed, that this body closely resembles a cone with rounded
apex.
132 PHYSIOLOGIC OPTICS
of keratoconus, we quite frequently meet cases in which the images of
the mires or of the keratoscopic disc present more or less pronounced
irregularities, for example, in consequence of old lesions of the cornea.
Frequently, however, we still succeed in making an ophthalmometric
measurement which may give information useful for the choice of a
cylinder.
73. Symptoms of Astigmatism. The most important symptom of
astigmatism is the diminution of visual acuity, which is a consequence
of the want of distinctness of the image. Generally the images are a
little deformed, but astigmatic patients are accustomed to this deformity
and take no notice of it.
ASTHENOPIA OF ASTIGMATIC PATIENTS. On account of their dimin-
ished acuity astigmatic persons are obliged to bring objects near them
for the purpose of obtaining larger retinal images. They are, therefore,
obliged to accommodate more than other persons, which is in itself a
cause of astigmatism. But there are yet other reasons for it.
It may be asked how astigmatic persons see, that is to say, what part
of the interfocal distance is it that they bring preferably on the retina.
Following Sturm it was believed that, in cases in which they have their
choice, they prefer to use the circle of diffusion so as to see all the out-
lines with the same degree of confusion. According to later researches
(Javal) it is the vertical focal line that they use preferably. There are
several reasons for this preference : one is that it is much more import-
ant in reading to see the vertical lines distinctly, the legibility of the
letters depending especially on the distinctness with which the vertical
lines are seen. Another reason is the importance which vertical out-
lines have for binocular vision. If one sees only the horizontal lines,
there is nothing to indicate for what distance the eyes must converge.
For want of being able to use the vertical focal line astigmatic persons
have recourse to the horizontal line, but very rarely to the intermediary
part.
In cases of astigmatism with the rule, the degree of accommodation to
be used depends, therefore, on the meridian of least refraction. Any
one having compound hypermetropic astigmatism, simple hyperme-
tropic astigmatism or mixed astigmatism is, therefore, in the same
situation as a hypermetrope ; he has the same reasons for having accom-
modative asthenopia. Persons having myopic astigmatism with the
rule or against the rule (if it is not combined with hypermetropia) have
Jess cause to suffer from asthenopia and seem, indeed, to suffer less.
REGULAR ASTIGMATISM 133
George Bull especially has laid stress on this explanation of the asthenopia
of astigmatic persons.
74. Examination of Astigmatic Persons. When, on examining the
patient with spherical glasses, we do not find a satisfactory acuity we
suspect astigmatism, unless the explanations of the patient give reason
to suspect an internal disease of the eye. We then submit the patient
to ophthalmometric examination, which, according to the rules that .we
have laid down, gives an approximate idea of the direction and degree
of the subjective astigmatism. If we find a very low degree with the
ophthalmometer we may generally come to the conclusion that the
complaints of the patient need not be attributed to astigmatism. We
then pass to the subjective examination; we make the patient myopic
two or three dioptrics and move the star figure close enough for him
to see one of the lines distinctly. Under these circumstances, the patient sees
distinctly the line which corresponds to the meridian of greatest refraction.
The direction of this line indicates, therefore, the direction of the axis
of a convex cylinder ; a concave cylinder must be placed perpendicularly
to this direction. It is rare to find an appreciable difference between the
direction indicated by the ophthalmometer and that thus found, unless
in the case of a very slight ophthalmometric astigmatism which can have
no bearing, in its position and value, on the total astigmatism. We
may then proceed to find the cylinder which equalizes all the lines, but
the simplest way is to find directly the cylinder which gives the best
visual acuity: we place before the eye the glass which corrects the
spherical ametropia, joining thereto the cylinder indicated by the
ophthalmometer, in the position found by means of the star figure.
After having found how much the visual acuity is thus improved, we
try whether a further improvement is obtained by making the glass
rotate slightly in both directions and adding a + I and I cylinder,
being very careful to place the axis of the glass parallel to that which is
already in the frame. According as the acuity gains by adding a one
dioptry convex or concave cylinder, we replace the glass of the frame
by the following number, and recommence the examination. With
patients who are good observers, or when the astigmatism is slight, we
may sometimes reach a greater degree of accuracy, by using a half-
dioptry cylinder. When we have found the weakest cylinder which gives
the best visual acuity, we verify the spherical glass by adding a + i
spherical which ought to diminish the visual acuity and a I spherical
which ought not to increase it.
134 PHYSIOLOGIC OPTICS
After having made the subjective examination, we examine the patient
with the ophthalmoscope. I will mention farther on the ophthalmo-
scopic signs of astigmatism on which great stress was laid at a time
when there were no other objective signs of this anomaly; they have
become to-day almost mere curiosities, especially since skiascopy has
assumed a merited importance. When we make use of it for verifica-
tion, we place the correcting glass in a frame and examine by skiascopy
whether the correction is complete. We can also use it to find out the
direction of the axis and the value of the astigmatism, if we have no
ophthatmometer.
Skiascopy with a luminous point especially enables us to find very
exactly the direction of the axis by means of the luminous band, men-
tioned on page 118. In order that the phenomenon may be distinct it is
necessary that the eye of the observer be placed in one of the focal lines,
and that the mirror forms the image of the luminous source at the place
of the other focal line. The observer will then see luminous the meri-
dian at the focus of which he is. Thus if the observed eye has a myopia
of 2 D., combined with an astigmatism with the rule of 2 D., he will see
a horizontal luminous band if he is placed at 50 centimeters and illumi-
nates the eye with a concave mirror which projects the image of the
luminous source at 25 centimeters. To see the band vertical he must
place himself at 25 centimeters and examine with a plane mirror. Gen-
erally it is necessary to dilate the pupil.
There are two points in particular on which I would lay great stress.
First, the importance of the subjective examination which must always
have the last word ; it is only in cases in which it is impossible to obtain
information from the patient, that we can attempt to give correcting
glasses according to the data furnished by the objective methods. The
reason is that, in most cases, the correction of the eye by a cylinder
is not a simple optic problem. Most frequently the astigmatism is not
the same in the entire pupillary space; that of the exterior zones differs
more or less from that of the central zones; the best correcting glass
is only a sort of guess, which neither the ophthalmometer nor skiascopy
can assume to indicate exactly. It is well understood that these differ-
ences are usually not great, especially in the case of persons who consent
to the correction, but they suffice, however, to make the subjective
examination indispensable.
The other point which I would emphasize is that the prescribing of
cylinders should not be abused. Since the invention of the ophthalmo-
meter there is too decided a tendency to prescribe cylinders as soon
REGULAR ASTIGMATISM 135
as a diagnosis of astigmatism is made. 'Cylindrical glasses should not,
in my opinion, be prescribed unless they produce a palpable improve-
ment of the visual acuity ; the wearing of glasses is always an annoyance
for the patient, and cylindrical glasses more so than any, as well on
account of the difficulty of wearing them in eye-glasses as on account of
the errors in the direction of the axis which opticians sometimes com-
mit, the difficulty of replacing a broken glass, etc.
If there are several cylinders which give the same acuity it is best to
choose the weakest. If there is astigmatism of only one eye, we may
allow the patient to say whether he will have it corrected or not; gen-
erally he does not gain much by the correction except in cases where
there is a tendency to strabismus.
If we combine two cylinders of the same strength by placing the axes
parallel, they act like a cylinder twice as strong; if we place the axes
perpendicularly to each other, they act like a spherical glass, and if the
axes form an acute angle with each other the effect is the same as that
of a sphero-cylindrical combination, the spherical and cylindrical
strength of which vary with the angle. As we can obtain no other effect
with two cylinders than with one cylinder combined with a spherical
glass, the bi-cylindrical glasses are now abandoned.
The variable cylindrical lens of Stokes was composed of one cylinder
which remained fixed and another which could be rotated ; we thus ob-
tained a variable cylindrical effect, but the instrument had this disad-
vantage that the direction of the axis varied also. Javal remedied this
by making the two cylinders rotate in opposite directions ; but, in spite
of this improvement, the lens of Stokes has never been of any practical
utility, because of the spherical effect which varies at the same time as
the cylindrical, (i)
We can always obtain the effect of a given sphero-cylindrical combina-
tion with the cylinder of contrary sign, by changing the spherical glass.
A + 5 spherical combined with a + 3 cylindrical is thus equivalent to a
H- 8 spherical with a 3 cylindrical. Really, there is need, therefore,
of only one kind of cylinder ; there is also now a tendency to prescribe
only concave cylinders which are combined with convex sphericals to
obtain the effect of convex cylinders. By placing the cylinder on the
side of the eye we thus obtain a slight periscopic effect.
Periscopic glasses, which were invented by Wollaston, are concavo-
(1) [This last defect has been overcome in the optometer of the translator. In this instrument two
spherical lenses are so moved that the spherical effect, produced by the rotation of the two cylinders, is
always neutralized by the contrary spherical effect of the two spherical lenses. Thus a purely cylin-
drical action is obtained. See Annals of Ophthalmology, Vol. Ill, No. 1.] It'.
136 PHYSIOLOGIC OPTICS
convex menisci the concave side of which is next the eye. Their ad-
vantage consists in this that the peripheral parts of the visual field appear
more distinct because the rays pass through the glasses less obliquely
than in the ordinary case. This advantage also exists when the eye is
motionless as regards the peripheral directions of the look. For some
time the attempt has been made to replace cylindrical glasses by toric
glasses, one of the surfaces of which is cut as a tore, the other as a
spherical surface. They have the advantage of being periscopic, but
their manufacture is difficult and up to the present they are not very
popular.
Cases of exact correction of astigmatism are among the most agree-
able which the oculist can meet, and it happens quite frequently that a
normal acuity, or even higher than normal, may be obtained. Frequently
the acuity remains under the normal, and there is a certain number of
cases in which the effect of the glasses is nil or nearly so. Oculists are
not in agreement as to the number of cases in which a good result may
be obtained. Schweigger says that, in a considerable minority of cases
of astigmatism the correction obtained by cylinders is quite satisfac-
tory. Other authorities are less pessimistic.
Bibliography. (Euvres de Young, edited by Tscherning, p. 125. Airy. Transactions
of the Cambridge Phil. Soc., 1827, t. II et 1849, t. VIII. Sturm. Sur la theorie de la vision.
Reports, 1845. Goulier. Sur un defaut assez commun de conformation des yeux et sur les mo-
yens de rendre la vue distincte aux personnes qui en sont atteintes. Reports, 1865. Knapp (H.).
Ueber die Asymmetrie des Auges in seinen verschiedenen Meridiansystemen. Arch.f. Ophth., VIII,
2, p. 185. Donders (F. C.). Astigmatwnus und cylindrische Qldser. Berlin, 1862. Javal
(E.) in de Wecker. Traite des maladies des yeux, II, Paris, 1863. Javal (E.) Sur le ehoix
des verres cylindriques, Ann. d'oc., 1863. Javal (E.). Memoires d j opJitalmometrie. Paris,
1891. Schioetz (H.). Ophtalmometrische und optometrische Untersuchung von 969 Augen.
Arch.f. Augenh., 1885. Nordenson (E. ). Recherches ophtalmometriques sur I'astigmatisme de
la cornee. Ann. d'oc., 1883. Bull (G.). L'asthenopie des astigmates. Bull, de la Soc. fran9.
d'ophtal., 1892, p. 128.
CHAPTER X.
IRREGULAR ASTIGMATISM.
75. General Bemarks. When we do not succeed in obtaining a
normal visual acuity by means of spherical and cylindrical glasses, we
generally attribute the cause of this failure to the retina we diagnose
amblyopia. Sometimes, but, as a rule, quite rarely, the diminution
of visual acuity is attributed to an irregular astigmatism, especially if it
is visible by the deformities of the ophthalmoscopic or skiascopic images.
But it is probable that the more we will study the optics of the eye,
the more the diagnosis of amblyopia will give place to that of irregular
astigmatism, which has served up to the present as the common term
for all optic defects of the eye other than myopia, hypermetropia and
regular astigmatism, that is to say, those which we can correct with
test case lenses. For some time past the majority of works which have
been published on the optics of the eye, have had for their object the
improvement of the methods used to determine these defects as quickly
and as exactly as possible. There is little probability that we can, for
the moment, make progress of any importance in this direction; these
methods are, at present, very well developed ; it even seems to me that
we bid fair to overstep the limit, in this sense that we can perceive a
tendency to desire to determine these defects too exactly. Quarters
of a dioptry are, indeed, superfluous for our test cases, and even half
dioptrics are only rarely indispensable, except for very weak ametropias.
So long as it was supposed that the refraction was the same in the whole
pupillary space, we could imagine the possibility of determining this
refraction with great exactness. But since we know that there are in
nearly all eyes optic differences between the different parts of the pupil-
lary space, and since these differences may reach several dioptrics, the
correcting glass must be regarded as a sort of approximation which
we cannot determine with perfect exactness. It seems that the con-
struction of the eye is such, that the visual acuity is about 2 for a perfect
137
138 , PHYSIOLOGIC OPTICS
optic system; but many eyes have optic irregularities which lower the
acuity to i, to five-sixths, to three-fourths or still lower, and these
irregularities are frequently still more pronounced in astigmatic eyes,
which prevents complete correction.
The study of these irregularities seems, therefore, destined to play
a certain part in future works on the optics of the eye. As I have already
remarked, we can study them with the keratoscopic disc of the Javal
and Schioetz ophthalmometer, and we can measure them with the opto-
meter of Young, which necessitates, however, on the part of the ob-
server a certain amount of work to accustom himself to the instrument.
But the best means of studying these irregularities is the following.
76. Examination of the Eye with a Luminous Point. We have already
seen that the first authors who devoted their attention to the question
of regular astigmatism, used the luminous point to find the meridians
and to judge of the exactness of the correction. Later, the luminous
point was replaced by the star figure, which is in more common use for
finding the meridians, but which gives information only on the astig-
matism which can be corrected by a cylindrical glass. The forms under
which a luminous point is seen furnish, on the contrary, fuller informa-
tion: there is no optic defect of the eye which is not shown in these
figures, sometimes, it is true, under a form which it may be difficult to
interpret. This is why we have undertaken this examination at the
laboratory of Sorbonne. As object we use a very small opening (0.2 mm.
to 0.3 mm.), made in a dark screen, and on which is concentrated the
light of a lamp or daylight. The patient, rendered myopic, gradually
approaches the luminous point while observing the form under which
the latter may appear. We can also place the patient at a fixed distance,
at one meter, for example, and virtually change the distance of the
luminous point by placing concave or convex glasses before the eye;
the patient must avoid as much as possible using his accommodation.
We can thus examine the form of the refracted pencil throughout its
whole extent, for, as far as the question at issue is concerned, it amounts
to the same whether the luminous point be fixed while the retina is dis-
placed, or whether, the retina being fixed, we displace the luminous
point. Most of the time the patient sees circles of diffusion presenting
pretty exactly the form of the pupil, which diminishes according as the
luminous point approaches the focus. But near the latter, in front and
behind, there is a part, the characteristic part of the pencil, where the
circle assumes irregular forms. The round diffusion spots are alike in
IRREGULAR ASTIGMATISM 139
all ; at most we find some slight differences due to the form of the pupil,
to a different distribution of the brightness of the circles, or to entoptic
phenomena which I shall describe in the following chapter. But the
characteristic part of the pencil differs so much in different persons that
I have never met two eyes in which it was alike, except, perhaps, in the
two eyes of the same person.
77. Different Forms of Irregular Astigmatism. We can distinguish
several groups:
i In an ideal eye the characteristic part of the pencil is reduced to a
point. We sometimes meet eyes which do not differ much from this
type, but they are rare, and all have an exceptional visual acuity (fig.
85). (i) It is besides clear that, all things equal, the better the eye the
shorter the characteristic point of the pencil.
Fig. 85. Forms under which a luminous point is seen by a regular eye. After Ree.
2 Eyes regularly astigmatic should see figures similar to those of
figure 77, but eyes so regular scarcely exist. In low degrees of astigma-
tism we scarcely ever have distinct focal lines, and in strong degrees,
where the focal lines are clearer, irregularities appear when the astig-
matism is approximately corrected by a cylinder. The most regular
(1) Figures 85, 86, 87, 89, 90, 91, 92 are borrowed from a work which M. R6e compiled at the laboratory
of the Sorbonne ( Undersoegelse of Oeiet med et lysende Punct, Copenhagen, 1896) and which has the shape
of a small atlas showing the forms under which the eye sees a luminous point. But the question is far
from being exhausted, and it would be desirable that some one should again take it up in a clinic.
With some exceptions, the eyes of the persons examined by M. Ete were what we call normal eyes ;
but it is especially astigmatic persons, whose vision does not improve with cylinders, that should be ex-
amined.
140
PHYSIOLOGIC OPTICS
astigmatic patients frequently see forms analogous to those of figure 86.
The focal lines are thicker at the middle and the interfocal diffusion spot
Fig. 86. Regular astigmatism with spherical aberration. After Ret.
is not circular, but in the form of a lozenge. These forms are due to
the combination of a regular astigmatism with a quite pronounced
Fig. 87. Figures of a luminous point obtained by combining an ordinary strong spherical
lens with a cylindrical lens (astigmatism with spherical aberration). After Ree.
spherical aberration, for we can obtain forms wholly analogous with a
combination of a + 20 sph. with a -f- 6 cyl. of our test cases (fig. 87).
IRREGULAR ASTIGMATISM
141
It is for this reason that one is obliged to use an aplanatic lens to ob-
tain figures of pure astigmatism. In the more irregular eyes we can
a b c d
B
Fig. 88. A, forms which a luminous point presents to my right eye (obliquity in one
meridian, the vertical). B, appearance of the same figures if I cover the lower half
of the pupil. C, appearance of the figures if I cover the upper half of the pupil.
The figures a correspond to a distance of 60 centimeters; the figures b to 1 meter;
the figures c to 1.50 m and the figures d to infinity.
generally find figures which represent more or less perfectly the focal
lines, that is to say, there are two places where the figures are more
Fig. 89. Eye with double obliquity. After Ree.
or less elongated, so that their two long axes are perpendicular to each
other; but these figures are far from being linear.
142
PHYSIOLOGIC OPTICS
Fig. 90. Figures of the left eye of M. Eee (Obliquity in one meridian, the vertical).
Curved focal line.
Fig. 91. Curved focal line. After Eee.
IRREGULAR ASTIGMATISM 143
3 It is not rare for the optic system of the eye to affect a certain
obliquity, so that the figures are symmetrical in relation to a single axis
(and not in relation to two axes, as in regular astigmatism). It is so in
the case of my right eye (fig. 88) and also in that of M. Ree (fig. 90).
These figures are, up to a certain point, analogous to those which are
obtained with a lens placed obliquely.
4 Frequently we discover an obliquity in the two directions per-
pendicular to each other, so that the figures are not symmetrical at all
(fig. 89).
5 An anomaly which is not at all rare consists in a certain curvature
of the focal lines, due probably to the fact that the principal meridians
of the cornea show an analogous curvature (figs. 90, 91).
Fig. 92. Irregular eye (Diplopia). After Ree.
6 We quite frequently meet more irregular figures, those for in-
stance of figure 92, belonging to an eye which has a rather pronounced
diplopia.
78. Rules for Analyzing the Figures of the Luminous Point. The
figures are sometimes quite difficult to analyze. Here are some di-
rections for this analysis:
i We can always decide whether a part of a figure is formed by
crossed rays or not, by covering a part of the pupil. If it is the
144 PHYSIOLOGIC OPTICS
homonymous part of the figure which disappears, this part is formed
by rays which have already crossed the axis before reaching the retina;
if it is the heteronymous part which disappears, the rays have not yet
crossed the axis. Sometimes we can with advantage use cobalt glass
(see page 112) for this analysis.
2 If the luminous point is beyond the punctum remotum, and if the
observer notices a concentric brightness on a part of the diffusion
spot, this part corresponds to a less refracting part than the remainder
of the pupil ; for, the focus of this part is nearer the retina and its rays
are, consequently, less dispersed.
3 If, within the focus, the figures are elongated in one direction,
downwards for example, they are elongated in the same direction beyond
the focus, and the eye is more refracting in this direction. Thus in
figure 95, A, in which the lower part of the surface is supposed to be
more refracting, the part of the cone situated above the axis is every-
where larger. The diffusion spots are seen elongated downward
(fig. 88).
4 The aberroscopic phenomena (page 102) always tell us in what
direction the refraction increases or diminishes, starting from the center
of the pupil.
Finally the optometer of Young permits a more exact analysis of
these irregularities.
Let us take, for example, my right eye (fig. 88), and see how we can
use these rules to analyze the figures. We observe that the upper part
of the figure d, A, seen at infinity, has a greater brightness than the
lower part. On covering the upper half of the pupil, this part disap-
pears, while, if we cover the lower half of the pupil, this part does not
change. We conclude from this, following rule i, that the whole figure
is formed by rays that have crossed the axis, that is to say, that the
whole pupillary space is myopic, and, following rule 2, that the upper
part is much less myopic than the remainder. If I move nearer up to
1.50 m. from the luminous point, I see the figure c which resembles a
luminous T written in a less luminous half circle. If I cover the upper
half of the pupil, the vertical stroke disappears and the horizontal stroke
becomes weaker. We conclude from this, following rule i, that the
vertical stroke is formed by rays which have not yet crossed the axis.
The point situated at 1.50 m. is, therefore, already situated within the
IRREGULAR ASTIGMATISM
145
far point of this part, while it is situated beyond the far point of the
lower part. All the figures are elongated down-
wards, which also shows (following rule 3) that the
pupil is more refracting below. The lines of the
aberroscope are convex towards the middle, below
and towards the two sides, while they are straight
or slightly concave towards the middle above (fig.
93), which shows that the refraction diminishes
towards the periphery above and increases in the Fig 93 _ Aberr08COpic
three other directions. Finally we find, by meas- phenomena of my
uring with the optometer of Young, the refraction
indicated by the diagram (fig. 94, A). The measurements confirm the
other observations, unless it be that they disclose a slight degree of
hypermetropia near the upper border of the pupil, which had escaped
attention in the analysis of the figures. It follows that the course of
Temporally
Nasally Temporally
Nasally
Fig. 94. A, Diagram of the variations of refraction in the pupil (dilated) of my right
eye. B, diagram of the refraction in the pupil of Demicheri : the dotted circle indi-
cates the normal pupil, the full circle the dilated pupil.
the rays must be nearly as I have illustrated them in figure 95 ; A cor-
responds to the vertical meridian, B to the horizontal meridian; the
place marked 2 corresponds to figure 88, c.
As to the means to use for the correction of these defects, they still
remain to be discovered. The only information we can give for the
present is that the forms mentioned under rule 3 could probably some-
times be corrected more or less effectively with glasses placed obliquely.
Contact glasses could evidently correct the greater part of these de-
fects, which reside especially in the cornea. As the cornea scarcely
146
PHYSIOLOGIC OPTICS
tolerates contact Sulzer caused to be cut similar glasses, which are
furnished with a rim by which they are supported on the sclera. Under
this form, contact glasses are easier to wear, but they seem nevertheless
Fig. 95. Course of the rays in my right eye: A, in the vertical meridian (obliquity)
B, in the horizontal meridian (spherical aberration).
to cause a certain annoyance, which will probably prevent their use,
except in special cases.
Bibliography. Tscherning (M.). Die monochromatischen Abweichungen. Zeitschri/t f.
Psych, u. Physiol. der Sinnesorg., IV, p. 456. Ke"e (O. M.). Undersoegdse of Oeiet. med et
lysende Punkt. (Danois). Copenhagen, 1896.
CHAPTER XI.
ENTOPTIC PHENOMENA.
79. Manner of Observing Entoptic Phenomena. When we approach
a luminous point, the circle of diffusion to which it gives rise increases
in size. At the moment when the luminous point is at the anterior focus
of the eye, the rays are parallel after refraction, and the circle of diffu-
sion is the size of the pupil ; on approaching nearer to it, the circle still
increases.
In these circumstances we observe entoptic phenomena, that is to say,
shadows which the corpuscles situated in the refracting media of the
eye project on the retina. If, instead of a point, we use a larger luminous
source, the cone of the shadow becomes too short to reach to the retina,
except the object is very near the latter. Another way of observing
entoptic phenomena consists in placing ourselves at a great distance
and observing the luminous point through a strong convex lens. In
this case the displacements of the shadows take place in the direction
contrary to that which we are going to point out later. Among the
entoptic observations I shall cite the following.
i The luminous spot is limited by the shadow of the border of the
iris ; we can thus study, therefore, the irregularities of the latter. The
pupillary contraction is very well observed on opening or covering the
other eye.
2 We very frequently see small circles the centers of which are
bright, and which have an apparent motion from above downwards,
depending on the winking of the eyelids. They are produced by small
specks on the anterior surface of the cornea, and which move in a con-
trary direction (fig. 96).
3 On winking the eyes we produce transverse striae, due probably to
the wrinkles of the epithelial layer. If we wink for some time, for ex-
ample when keeping one eyelid closed while working with a microscope,
or as artists frequently do in order to obtain a better idea of the entire
147
148
PHYSIOLOGIC OPTICS
impression of a landscape, we can produce striae which last for several
hours and give rise to a very marked diplopia of the horizontal lines
(fig. 97). George Bull especially has studied this question; according to
him the phenomena are specially pronounced after reading for a long
Fig. 96.
After Helmholtz.
Fig. 97. Striae produced by winking
the eyelids. (After George Butt.)
time in the horizontal position, and give rise to a peculiar annoyance
which he has named tarsal asthenopia.
4 On winking the eyelids while looking at a distant luminous point,
we observe long striae which run upwards and downwards from the
point. These striae are due to the layer of tears which is in the con-
junctival sac, and which, near the border of the eyelids, assumes the
form of a prism with a concave surface (fig. 98). This prism deflects
the rays which meet it, and, as its surface is concave, the parts placed
Fig. 98. Prismatic effect of the layer of tears.
near the border of the eyelid act as a stronger prism, which causes
greater deflection of the rays: it is for this reason that we see a stria
and not simply a second image of the luminous point. The upper eyelid
deflects the rays upwards ; it produces, therefore, the striae which we see
directed downwards. In fact, if we lower a screen placed near the eye,
it is the stria directed downwards which disappears first. This phenom-
ENTOPTIC PHENOMENA
149
enon is not, properly speaking, an entoptic phenomenon, but I mention
it here because of its resemblance to those mentioned under No. 3.
5 If we rub the eye, the luminous spot presents a speckled appear-
ance, due to irregularities of the cornea; this appearance soon disap-
pears (fig. 99).
6 We sometimes observe small round discs, sometimes bright and
surrounded with a black border, sometimes dark with a bright border,
proceeding from the crystalline lens. We frequently see also the star
figure of the crystalline lens, sometimes bright (fig. 100), sometimes
Fig. 99. Speckled appearance of the entoptic Fig. 100.
field produced by rubbing the cornea. (After After Helmholtz.
George Bull.)
dark, with somewhat more luminous borders. The crystalline opacities
are outlined in the spot with great distinctness. An intelligent patient
can thus follow step by step the development of his cataract, as we can
see on the drawings which M. Daricr has just published (fig. 101).
7 Nearly every one sees objects situated in the vitreous body; they
become partly visible without further aid by simply looking at the sky,
that is when they are very near the retina.
They are sometimes mobile, sometimes fixed,
but presenting in the latter case an apparent
motion. If, for example, the shadow is seen
a little above the point of fixation, the patient
looks a little higher in order to fix it; but
as the shadow is always seen above the point
of fixation, it continues to direct the visual
line higher and higher; and the shadow
always flees before the look, for which reason
the name muse a volitantcs has been given to
this phenomenon. To make certain whether
Fig. 101. Incipient cata-
ract, seen entoptically.
(After Darier.)
150
PHYSIOLOGIC OPTICS
the motion is apparent or real, we can look at the sky through a window,
on which we select a mark in order to assure fixation; after having
made a rapid movement with the look, we fix this point. If the cor-
puscle is fixed, it should then remain motionless, but most frequently
we see it descend slowly which indicates that the corpuscle really
ascends.
8 We may use entoptic observation to study slight displacements
of the eye as a whole, which it is very difficult to observe otherwise.
To this end I have had constructed a small instrument, the entoptoscope
(fig. ioia). It consists of a small plate of wood which we take between
the teeth; on the plate is fixed a rod
which carries a plate of copper having
the form of the cap of a sphere. In
the middle is pierced a very fine open-
ing (i/io mm.), which is on a level
with the eye. In the concavity of the
cap are stretched two threads, one hor-
izontal and one vertical, placed in the
form of a cross and forming cords with
the cap. When we take the instrument
between the teeth and look towards the
sky we see the entoptic field occupied
by the cross which is greatly enlarged.
We select a point in the cross as a fixa-
tion point. The position of the cross
is thus invariably dependent on that of
the head; if therefore, in given circum-
stances, we observe a displacement of
the cross in the entoptic field, it is
Because it is the latter, that is to say
the e y e > 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 <f Utrecht, 1899. Salomonsohn
(H.). Ueber Lichtbeugung an Hornhaut und Linse. Arch.f. Anal. u. Phys., 1898. Tscherning
(M.) Eine Selbstbeobachtung. XL M. f. A. June, 1898. Tscherning (M.). Compte rendu
du Congres a' Utrecht, 1899.
CHAPTER XII.
ACCOMMODATION.
83. Measurement of the Amplitude of Accommodation. We have de-
fined the amplitude of accommodation as the difference between the
distances of the far point and the near point, measured in dioptrics. It
expresses the value of a convex lens which, added to the eye, would
form an image of the near point at the position of the far point.
For the determination of the near point it is necessary, on account of
the relation between accommodation and convergence, which I shall
discuss later, to close the eye which we are not examining. In order
to reach the highest degrees of accommodation, the patient is some-
times obliged to squint inwards, and, if both eyes are open, the need of
seeing single will prevent him from attaining the limit of his accommo-
dation. In clinics, we generally confine ourselves to determining the
shortest distance at which the patient can read fine print. It is neces-
sary, for this determination, to use very small letters, otherwise the
patient may still read them within the near point, although seeing the
letters only indistinctly. Another method consists in determining the
strongest concave glass through which the patient can see distant ob-
jects distinctly (the table of visual acuity), since the concave glass forms
an image of them so much nearer in proportion as it is stronger. We
can also use optometers, that of Badal or of George Bull (i) for example.
The determination of the near point is always uncertain, because we
can never know whether the patient makes a maximum effort or not.
It succeeds especially poorly in persons of little intelligence, in children,
etc. Anyhow, to determine it exactly is generally of little practical im-
portance ; if we desire an exact measurement, we can instil eserine, but
we thus obtain an amplitude slightly higher than that which the patient
would attain, even when trying his best.
(1) The optometer of Bull resembles externally that of Young, enlarged, but the principle is differ-
ent. We look through a lens of 6 D. without slits, and the line is replaced by a series of small dominoes.
The patient must simply tell the most distant and nearest of these dominoes that he can see distinctly.
160
ACCOMMODATION 161
For scientific researches it may sometimes be important to know
exactly the amplitude of accommodation. We can then determine it
with the optometer of Young, if the observer is master of his accom-
modation, that is to say, if he can make an effort of accommodation
without fixing a near object. If not, the best means is to offer a hair
in a ring, and to see how close we can move it to the eye before it
appears dim. We may with advantage add this ring to the optometer
of Young.
The amplitude of accommodation diminishes in a very regular manner
with age. According to Danders, the diminution begins to make itself
felt at the close of infancy. It is so regular, at least beginning at 25 or
30 years, that we can frequently determine the age of the patient to
almost within one or two years, by means of the optometer of Bull, for
example. At the age of 47 or 48 years this diminution begins to manifest
itself in emmetropes, by the appearance of presbyopia. In hypermetropes
the presbyopia makes its appearance sooner; it appears later in low
myopia, and myopes of a high degree never become presbyopic, although
the amplitude of accommodation diminishes in them as in every one else.
In emmetropes it is very rare to find an exception to the rule laid down
above, unless the pupil is very small. If, therefore, a patient reads
without glasses when over 50 or 55 years old, he must be myopic, if
the pupil is of the ordinary size.
Presbyopes do not suffer from accommodative asthenopia ; when read-
ing they are obliged to hold the book farther away, especially in the
evening; the manner in which they hold the book, far from their eyes
*and near the lamp, is very characteristic.
As to the choice of spectacles, it is clear that if we fix on a distance
for work of 33 centimeters we are never obliged to give to an emme-
trope glasses of a greater strength than 3 dioptrics. But it is frequently
useful, especially when the acuity is diminished, to choose a shorter
distance for work, for example 25 centimeters, corresponding to 4
dioptrics. We frequently notice a tendency to give somewhat stronger
glasses, which, however, cause only slight inconvenience. Thus, the
series
50 55 60 65 years
-f-1 +2 +3 +4 dioptrics
is, perhaps, a little strong, especially for high degrees.
PARALYSIS OF ACCOMMODATION. We meet this disease especially
in children who have had diphtheria. If we learn that the child has not
been able to read for some time past, although it sees perfectly at a
1G2 PEJSIOLOGIC OPTICS
distance, and if we do not find hypermetropia, we may be almost certain
that it has had diphtheria. The diagnosis of paralysis is verified when
the child reads well with the proper convex glasses. Generally there
are no other symptoms of ocular paralysis, among others no mydriasis.
We prescribe convex glasses almost until the recovery, which generally
takes place in a space of two or three months.
The second form of paralysis which we occasionally meet is that which
forms part of a more or less complete paralysis of the third pair. It is
usually accompanied by mydriasis and frequently by paralysis of ex-
ternal muscles. It seems, however, that it may exist without any com-
plication. In glaucoma and cyclitis, the diminution of the amplitude
of accommodation is frequently one of the first symptoms.
SPASM OF ACCOMMODATION. There have been described two forms
of spasm of accommodation. i As we have seen, one has been accus-
tomed to diagnose spasm of accommodation when one found a weaker
refraction after the instillation of atropine. The existence of this sup-
posed spasm, which is always of a very low degree (0.50 to 1.50 D.), is
very doubtful, since the diminution of refraction, after the instillation
of atropine, may often be attributed to the weaker refraction of the
peripheral parts of the optic system of the eye.
2 We sometimes observe in hysterical patients a true spasm of ac-
commodation, extending most frequently to the entire amplitude, and
not to a small part, as in the preceding case. These cases are rare; they
give rise to a transient myopia, which is generally complicated by
monocular diplopia.
84. Mechanism of the Accommodation. Historical, A. Theoretically,
the eye could accommodate itself by one of the following mechanisms :
a. INCREASE OF CURVATURE OF THE CORNEA.
b. INCREASE OF CURVATURE OF THE CRYSTALLINE LENS.
c. ELONGATION OF THE GLOBE.
These three hypotheses have found their adherents, as also have the
two following which are theoretically impossible :
d. ADVANCE OF THE CRYSTALLINE LENS.
e. CONTRACTION OF THE PUPIL.
As to the hypothesis d, we must note that, even if the crystalline lens
would advance so as to touch the cornea, this advance would not suffice
to explain any considerable amplitude of accommodation. The accom-
modative contraction of the pupil was discovered by Schemer. By look-
ing through an opening a little smaller than the pupil, it is easy to con-
9
ACCOMMODATION 163
vince one's self that this contraction is not sufficient to explain accom-
modation.
Apart from these five theories, there have been proposed still others,
much less plausible. Kepler, who was the first to propound the problem
of the mechanism of accommodation, supposed an advance of the crys-
talline lens, whilst Descartes was the first to suppose an increase of
curvature of this organ.
The theory of the change of curvature of the cornea found support in
the measurements of this curvature made by Home and Ramsden towards
the end of the last century. The discussion continued until towards
the middle of the century, and the false hypotheses on the nature of
accommodation have even resulted in two beautiful discoveries. The
theoretical researches of Sturm on the form of the astigmatic pencil
were, indeed, undertaken to prove that accommodation did not exist:
this author thought that distant objects were seen with the posterior
part and near objects with the anterior part of the focal interval. On the
other hand, when Arlt discovered that myopia depended on the elonga-
tion of the globe, he was guided by a false idea on accommodation. He
thought that the action of the external muscles produced an elongation
of the globe, when one is forced to see close at hand; and, as it was
known that myopia was a consequence of near work, he concluded that
myopia must be produced by an elongation of the globe. On making
an autopsy on some excessively myopic eyes, he proved the lengthening
of the globe in these cases, and believed that he had thus confirmed his
hypothesis. We now know that this form of myopia does not depend
on near work, and that accommodation is not obtained by an elongation
of the globe, but by an increase of curvature of the crystalline lens !
The question was decided by the observation of the changes of the
images of Purkinje during accommodation, which prove that accom-
modation is effected by an increase of curvature of the anterior surface
of the crystalline lens. The discovery was made in 1849 by Max Langcn-
beck, but attracted scarcely any attention ; it was only after the beautiful
researches of Cramer (1851-52) that the truth was definitely accepted.
Cramer constructed an instrument which he called ophthalmoscope, with
which he could conveniently observe the catoptric images of the crystal-
line lens, and it was easy for him to show that that of the anterior surface
made, during accommodation, a quite extended centripetal movement.
This fact has been verified by all those who have examined the catoptric
images during accommodation ; it is due to the increase of curvature
of the anterior surface.
164
PHYSIOLOGIC OPTICS
Let ABD (fig. 107) be the surface in a state of repose and C its center,
AjBDi the surface in a state of accommodation and C t its center, O an
object (a lamp placed at a great distance). To find the position of the
image, we draw OC (OQ) (supposing that these are the apparent sur-
faces we need not take into account the corneal refraction). The image
must be on this straight line, at an equal distance between the surface
and center, at I for the surface in repose, at Ij_ for the surface in a state
Eh
Fig. 107. Centripetal movement of the catoptric image of the anterior surface of the
crystalline lens during accommodation. (Discovered by Cramer.)
of accommodation. The observing eye sees the images projected in the
pupillary plane, it sees I at i and I at ^ ; it sees the image, therefore,
make a centripetal movement during accommodation. It is the same,
whatever may be the position of the observing eye; there is only one
point where it does not see motion, viz., when it is on the prolongation
of line II^ in this case the two images I and I overlap, and there
is no apparent displacement. The line II passes through the point B,
the place where the two surfaces touch. This point B, towards which
the apparent movement of the image takes place, whatever may be its
position in the pupil, is usually situated a little outside the center of the
latter; generally it is found almost on the optic axis of the eye.
Recently, Coronat again described the centripetal movement, whence he
erroneously inferred a see-saw movement of the crystalline lens.
The question of knowing by what change the eye accommodates itself
for near vision being solved, it remained to be discovered by what means
the change was effected. Cramer attributed the change to the contrac-
tion of the iris ; he thought that the iris in the state of repose was greatly
swollen in front, and became flattened during accommodation by a
simultaneous contraction of the sphincter and dilatator. He thought that
ACCOMMODATION 165
it thus exerted a pressure on the peripheral parts of the crystalline lens,
and that the ciliary muscle, contracting at the same time, exerted a
traction on the choroid, which pushed the vitreous body forward. In
this way the crystalline lens, subjected to a pressure in its whole extent,
except on the pupillary part, became swollen at this place. Several other
theories, conceived after that of Cramer, also involved the participation
of the iris in the act of accommodation ; they were necessarily abandoned
when Graefe published his celebrated case of complete aniridia, of
traumatic origin, in which the amplitude of accommodation was intact.
A short time after the discovery of Cramer, and without being ac-
quainted with his work, which was published only in the Dutch language,
Hclmholtz made the same observation. He used as his object the dis-
tance between two lamps (or a lamp and its image formed by a mirror).
During accommodation, the distance between the two images diminished
considerably, which is easy to understand, since a sphere forms an image
smaller in proportion as its radius is less.
Hclmholtz confirmed, moreover, the observation made previously by
Hueck, according to which the anterior surface of the crystalline lens
advances a little during accommodation. He measured the thickness
of the crystalline lens, which he found a little greater during accommo-
dation than in a state of repose. He also measured two dead crystalline
lenses, and found their thickness greater than that of the living crystal-
line lens in a state of repose. He further concluded that there was a
slight increase of curvature of the posterior surface of the crystalline
lens during accommodation.
The following are the numbers which he adopted for his schematic
eye, compared with those which he found for the dead eye :
SCHEMATIC EYE DEAD EYE
Repose. Accommodation. A B
Kadiusof the anterior surface.. 10 mm 6 ram 10.16 mm 8.87 mm
posterior surface . 6 mm 5.5 mm 5.86 mm 5.89 mm
Thickness 3.6 mm 4 mm 4.2 mm 431 mm
Focal distance 43.71 mm 33.79 Bim 45.14 mn > 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
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30m-10,'61 (C3941s4)4128