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 THE NATURE 
 
 AND THE 
 
 CONSEQUENCES OF ANOMALIES 
 
 OF 
 
 REFRACTION
 
 AN ESSAY 
 
 ON 
 
 THE NATURE 
 
 AND THE 
 
 CONSEQUENCES OF ANOMALIES 
 
 OK 
 
 REFRACTION 
 
 BY 
 
 F. C. DONDERS, M.D. 
 
 LATE PKOFESSOK OF PHYSIOLOGY AND OPHTHALMOLOGY IN THE UNIVERSITY 
 OF UTRECHT 
 
 ( Translated under the supervision of the Kirschbaum School of Languages 
 and Bureau of Translation of Philadel/ihia.) 
 
 REVISED AND EDITED BY 
 
 CHARLES A. OLIVER, A.M., M.D. (Univ. Pa.) 
 
 ONE OF THE ATTENDING SURGEONS TO THE WILLS' EYE HOSPITAL; ONE OF THE 
 OPHTHALMIC SURGEONS TO THE PHILADELPHIA HOSPITAL, ETC. 
 
 •JKHitb portrait anO ©tbcr ITllustrations 
 
 PHILADELPHIA 
 P. BLAKISTON'S SON & CO. 
 
 IOI2 WALNUT STREET 
 1899
 
 Copyright, 1899, by P. Blakiston's Son & Co. 
 
 PRESS OF WM. F. FELL & CO., 
 
 1220-24 SANS1M STREET. 
 
 PHILADELPHIA.
 
 3. 
 
 Ki^i,' 
 
 TO 
 
 HERMAN SNELLEN, M.D., 
 
 PROFESSOR OF OPHTHALMOLOGY IN THE UNIVERSITY 
 OF UTRECHT, 
 
 THIS ENGLISH TRANSLATION OF THE WORK OF HIS TEACHER 
 
 AND PRKUECESSOR IS " IN TESTIMONY OF THE 
 
 WARMEST FRIENDSHIP AND OF 
 
 THE HIGHEST ESTEEM" 
 
 De&icateD 
 
 BY THE EDITOR.
 
 EDITOR'S PREFACE. 
 
 In his duties, the Editor has not attempted in 
 any way to draw a comparison between the 
 Author's and his own thoughts and beHefs on 
 the subjects treated in this volume. It has been 
 his sole desire to give a great man greater 
 honor and to offer such a man's works an in- 
 creased amount of usefulness. In this spirit, 
 and as a result of this thouo-ht, he has oriven 
 each aphorism exactly as it appeared in the 
 original work, thus enabling him to show to 
 the present ophthalmic world, in spite of in- 
 numerable controversies, to what slight extents 
 the fundamental principles laid down by the 
 talented Author in the pages of his almost 
 unique brochure have suffered correction, alter- 
 ation, and conversion during the thirty pro- 
 gressive years that have followed its publication. 
 
 Indeed, it is remarkable, considering the many 
 ways in which the finger of science has in the 
 past three decades since the work was laid away 
 in a comparatively infrequently used language, 
 been guiding medical empiricism by means of 
 skilled observation and laboratory research into
 
 viii EDITOR'S PREFACE. 
 
 the now fast approaching domain of rational 
 scientific medicine, that this man's work should 
 have so much of the real truth in it, and that 
 his deductions should be so certain of applica- 
 tion to newly acquired facts that were unknown 
 at the time he gave his results to the physio- 
 logic world. Here, in this branch of medicine 
 — in the study of dioptrics — it may be truly 
 said that the proper application of precise and 
 well-grounded sciences by one who was in- 
 timately acquainted with them in their every 
 detail, to the uncertainties of new and never- 
 before-tried work, gave the Author answers 
 that were far ahead of those that were known 
 to the medical men of his day. 
 
 To disturb such results, when given in trust, 
 as it were, in a posthumous publication, would 
 be desecration. To give the original conceptions 
 of such monumental and beneficial labor, has 
 been a task of veneration and love. 
 
 Charles A. Oliver. 
 
 Philadelphia, U. S. A., 1899.
 
 TABLE OF CONTENTS. 
 
 PAGE 
 
 Section I. Emmetropia and Ametropia, lo 
 
 Section II. Amplitude of Accommodation (Absolute, 
 Relative, and Binocular) in Emmetropia 
 and Ametropia, 19 
 
 Section III. Visual Acuteness and Projection in Emme- 
 tropia and Ametropia, 30 
 
 Section IV. Line of Direction, Center of Rotation, and 
 Movements of the Eye in Emmetropia 
 and Ametropia 39 
 
 Section V. Acuteness of Vision and Amplitude of 
 
 Accommodation, Modified by Age, . . 44 
 
 Section VI. Consequences of M and of H, 57 
 
 Section VII. Regular Astigmatism, 69
 
 ABBREVIATIONS. 
 
 The following 
 E, . 
 M, 
 H, 
 Hm, 
 HI, 
 Ht, 
 As, 
 Pr, 
 
 /, • 
 r, . 
 
 P, . 
 
 R, 
 
 A:, 
 A„ 
 /o, 
 /i. 
 A. 
 
 Pi. 
 P2. 
 
 Ri, 
 R2, 
 
 c, 
 
 I, .' 
 /^ ■ 
 >, 
 <, 
 
 R-P, 
 11 
 P R' 
 
 ; abbreviations are adopted in this work : 
 
 Emmetropia. 
 
 Myopia. 
 
 Hypermetropia. 
 
 " , Manifest. 
 
 " , Latent. 
 
 , Total. 
 Astigmatism. 
 Presbyopia. 
 
 Punctum proximuni (nearest point of distinct vision). 
 Punctum remotissimiitn (farthest point of distinct vision). 
 
 . Distance from / to k' : In M 
 
 diopter. 
 
 Distance from r to /■'' .• In M = — diopter. 
 
 Infinity. 
 
 Absolute range of accommodation = diopter. 
 
 Relative range of accommodation. 
 
 Binocular " " <' 
 
 Radius of curvature of cornea in the visual line. 
 
 Relative nearest point. 
 
 Binocular " " 
 
 Relative farthest point. 
 
 Binocular " " 
 
 Distance from p-^ to k''. 
 
 " " r^ " k^. 
 
 Point of convergence of visual lines. 
 
 Anterior nodal point. 
 
 Posterior " " 
 
 Anterior focal point. 
 
 Posterior " " 
 
 Distance of focal point of a glass lens. 
 
 " " " " " an auxiliary lens of the eye. 
 Greater than. 
 Less than. 
 Region of accommodation. 
 
 Amplitude of "
 
 A SUMMARY OF THE NATURE OF 
 ANOMALIES OF REFRACTION AND 
 THEIR CONSEQUENCES. 
 
 In various places^ I have written on tlie 
 chanores that are found in the refraction of the 
 eye, with their symptoms and consequences. 
 These writings contain a portion of the results 
 of a series of examinations, extending over 
 many thousands of eyes, that were commenced 
 six years ago, and have been continued with 
 the collaboration of several of my students. 
 
 This study gave the subject a wider scope 
 and, at the same time, by bringing into view the 
 connection between cause and effect, rendered 
 the knowledge of the subject-matter more 
 thorough and its general review much easier. 
 In fact, everything pertaining to anomalies of 
 refraction can, at the present time, be united 
 into an easily understood system. 
 
 Of that system, a summary is hereby offered 
 to the reader. Examination will show that it 
 not only contains what has been previously 
 said on the subject, but that it sums up in 
 
 1 See Bibliography. 
 2 9
 
 lo ANOMALIES OF REFRACTION. 
 
 advance that which will, in the future, find a 
 more extended and more comprehensive con- 
 sideration. I hope, therefore, that it may not 
 be unwelcome as a guide to some, as an intro- 
 d^iction for further study to others, and as a 
 general review to those who may have read and 
 heard of the subject before. 
 
 I. EMMETROPIA AND AMETROPIA. 
 
 I. Eyes are distinguished into emmetropic 
 and ametropic ones. In emmetropia, E ^ the 
 posterior focal point, <f", of the dioptric system, 
 in a condition of accommodative rest, lies ex- 
 actly within the retina ; in ametropia, cp" lies 
 either in front of the retina (myopia, M), or is 
 situated behind it (hypermetropia, H). 
 
 II. E, therefore, has its most remote point of 
 distinct vision r situated at co , M at a finite dis- 
 tance in front of the retina, and H at a finite 
 distance behind the retina. The distance from 
 the eye (more exactly that from the anterior 
 nodal point k') to r is R. In M, R is positive, 
 in H it is negative, and in E it is infinite. 
 
 The nem^est point of distinct vision is p ; its 
 distance to k' is P. The ran^e of accommo- 
 dation may be expressed in the number of 
 
 1 See List of Abbreviations following List of Contents.
 
 EMMETROPIA AND AMETROPIA. ii 
 
 diopters ^ of the lens, which, during relaxa- 
 tion of the muscle of accommodation and 
 under the conditions stated in Paragraph IX, is 
 required to throw a sharp and a clear image on 
 the retina. The range of accommodation is 
 
 designated p — r ^^ a* 
 
 III. The point r is to be determined by par- 
 allel visual lines — i. e., by estimating the artificial 
 lenses which are required to see luminous 
 points or fine streaks distinctly at a practically 
 infinite distance. To determine the point /, 
 fine threads, or very small luminous points, 
 which are to be brought nearer and nearer to 
 the naked eye until their images become indis- 
 tinct, are to be used as test-objects. The de- 
 termination should be made during the greatest 
 amount of convergence of the visual lines that 
 is obtainable ; so that consequently, in cases of 
 H, and frequently in those of E, it becomes 
 necessary to do this by means of convex lenses, 
 the distances of the points obtained being re- 
 duced in accordance with the method of pro- 
 cedure. 
 
 IV. The measurement of the radius of curv- 
 ature, /o, of two hundred corneae of eyes that 
 were partly emmetropic and partly markedly 
 
 ^ Vide Paragraph X.
 
 12 ANOMALIES OF REFRACTION. 
 
 ametropic, by means of Helmholtz's ophthal- 
 mometer, has shown that the radius of corneal 
 curvature in the line of vision in both conditions 
 is nearly the same. 
 
 The average condition found was : 
 
 Males. Females. 
 
 Emmetropia ^^^=7.785 mm. ; 7.719 mm. : 
 
 Myopia /^=n 7.874 " ; 7.867 " : 
 
 Hypermetropia/^, = 7.96 " ; 7-767 " 
 
 V. In the myopic eye, the crystalline lens 
 lies relatively deeper, and therefore the dis- 
 tance of the focal point of the dioptric system 
 of such an eye is correspondingly somewhat 
 greater. That the distance of the focal point 
 of the crystalline lens itself should be smaller 
 has not as yet been made apparent. In the 
 hypermetropic eye, the crystalline lens lies 
 closer to the cornea, and, consequently, the 
 distance of the focal point of the dioptric sys- 
 tem of this form of eye is somewhat shorter. 
 
 VI. From Paragraphs IV and V, the con- 
 clusion follows, per exclusionem, that the axis of 
 vision in the myopic eye is the longer, and that 
 in the hypermetropic eye it is the shorter. This 
 has been directly proved, a, by determining the 
 actual shape of the eyeball during life, which is 
 at times made possible by having the subject 
 direct the visual line as far outward as possi-
 
 EMMETROPIA AND AMETROPIA. 13 
 
 ble ; b, by measurements made after death in 
 numerous cases of M, and in some cases of H ; 
 c, by determination of the focal distance of the 
 cornea (estimated from its radius of curvature 
 p^ of an eye that had had its crystaUine lens 
 removed (aphakia), and of that of the artificial 
 lens that was necessary to cause the focal point 
 to fall on the retina, — and this for eyes in which 
 the ametropia, previous to the extraction of the 
 crystalline lens, could have been determined. 
 It is possible, however, that H is sometimes 
 also caused, partly, by a greater focal distance 
 of a flatter crystalline lens. 
 
 VII. Through disease alone, the cornea be- 
 comes the cause of M ; sometimes also of H. 
 Usually, however, its refraction is then at the 
 same time very irregular. In all the following 
 observations, these relatively rare cases of M 
 and H are excluded. 
 
 VIII. The individual differences of emme- 
 tropic eyes are so slight that it becomes wholly 
 warrantable in taking, after the example of 
 Listing, a schematic eye as the basis for most 
 calculations. In M and H, in which only the 
 length of the axis of vision deviates essentially, 
 the same position of the cardinal points may be 
 admitted.
 
 14 ANOMALIES OF REFRACTION. 
 
 IX. The degree of H and M is expressed by 
 the amount of refractive power of an artificial 
 lens that is required for correction — that is, to 
 cause the focal point to fall on the retina ; or, 
 in other words, to allow the subject to see 
 clearly at an infinite distance. This artificial 
 lens is supposed to be infinitely thin, to stand 
 in the air, and to coincide with k'. 
 
 X. The degree of refractive power of an 
 artificial lens is expressed by a definite number 
 
 of diopters, which is equal to distance of the focal point' 
 
 this distance beino^ estimated in meters. Arti- 
 ficial lenses of plus five diopters' and of minus 
 four diopters' strengths are equivalent to one- 
 fifth of a meter of positive and to one-fourth of 
 a meter of negative distance of focal point. 
 
 M = 7,00 signifies a M, in which an artificial 
 lens of seven diopters' strength, and H = 3- 50, 
 a H, in which an artificial lens of three and a 
 half diopters' strength is required for correction 
 under the conditions that are noted in Para- 
 graph IX. 
 
 XI. About the fiftieth year of age, E grad- 
 ually makes place for H. Even at the greatest 
 age, however, the acquired H rarely reaches 
 more than one and three-quarters diopters. 
 This is not dependent upon any increasing flat-
 
 EMMETROPIA AND AMETROPIA. 
 
 15 
 
 teninor of the cornea whose radius of curvature 
 rather sHghtly decreases in aged persons. I have 
 found personally — 
 
 In 79 
 
 men .... 
 
 . . 
 
 . . . on an average /q 
 
 = 
 
 7 
 
 858 
 
 " 20 
 
 " under 20 years of age •' " " " 
 
 ^ 
 
 7 
 
 932 
 
 '•'51 
 
 " " 40' 
 
 ( ( 
 
 (((( i i i i a i I 
 
 =: 
 
 7 
 
 882 
 
 " 28 
 
 " over 40 
 
 i e 
 
 an an a n 
 
 = 
 
 7 
 
 819 
 
 " II 
 
 " " 60 
 
 i i 
 
 an ( i a a a 
 
 = 
 
 7 
 
 809 
 
 "38 
 " 6 
 
 women, . . . 
 
 
 
 
 
 7 
 7 
 
 798 
 720 
 
 " under 20 j 
 
 ears 
 
 ofage " " " " 
 
 z= 
 
 " 22 
 
 " " 40 
 
 i i 
 
 an i i i i a ( < 
 
 = 
 
 7 
 
 799 
 
 " 16 
 
 " over 40 
 
 " 
 
 4<<( i I i i a ii 
 
 ^ 
 
 7 
 
 799 
 
 " 2 
 
 " " 60 
 
 t ( 
 
 an a ic a a 
 
 = 
 
 7 
 
 607 
 
 An increase of the focal distance of the crys- 
 talline lens, partly as a consequence of flatten- 
 ing, and partly as the result of hardening with 
 an increasing' refractive coefficient of the ozUer 
 layers, combined, in very old age, with a short- 
 ening of the axis of vision, are to be considered 
 as the causes of acquired H. 
 
 XII. M is often hereditary ; almost always 
 either in reality or as disposition that is inborn. 
 It increases during the years of development, 
 and, notwithstanding the subsequently increas- 
 ing distance of the focal point of the crystalline 
 lens (XI), it remains progressive when it exists 
 in a high degree (seven diopters or more) all 
 throuorh life. As such, and also in still lower 
 degrees, it is a disease of the eye that is based 
 upon an increasing morbid expansion of the
 
 l6 ANOMALIES OF REFRACTION. 
 
 ocular membranes, coupled with ophthalmo- 
 scopically noticeable atrophy, and is often asso- 
 ciated with inflammatory signs that are visible 
 in the bottom of the eye ; a condition involving 
 various kinds of disturbances that are more or 
 less necessary, 
 
 XIII. M occurs in all orrades from zero 
 (the emmetropic eye) to twenty-eight diopters. 
 Grades of seven, nine, twelve, and even of four- 
 teen diopters are not unusual. All distinctions 
 between high and low degrees are arbitrary. 
 In zero, or emmetropia, the axis of vision has 
 a length of twenty-two to twenty-three milli- 
 meters ; in M of twenty-eight diopters it has a 
 length of about thirty-one millimeters. In high 
 degrees of M, as proved by ophthalmoscopic 
 examination, M is present in a higher degree 
 for direct vision (that is, in the yellow spot), 
 than it is for indirect vision ; the expansion of 
 the ocular membranes beinor the greatest at the 
 posterior pole of the eye, 
 
 XIV. H is usually hereditary ; then it is 
 always congenital. It increases slightly, espe- 
 cially after the fiftieth year of life, at which age, 
 in case that E originally existed, H begins to 
 develop (compare Paragraph XI). The lower 
 grades occur the most frequently ; grades of 
 six diopters are already very rare ; while those
 
 EMMETROPIA AND AMETROPIA. 17 
 
 of nine and twelve diopters or higher are only 
 found by the way of exception. 
 
 XV. In the first place, H is to be separated 
 into inanifest (Hm) and latent (HI). Only in 
 Hm can the subject see more clearly at a dis- 
 tance with positive lenses ; in HI such lenses 
 are rejected. In HI, H is suppressed in conse- 
 quence of an inherent exertion of accommoda- 
 tion which is controlled by habit and can not be 
 arbitrarily nullified. 
 
 XVI. The QT-reater -r is, the higher are the 
 
 decrees of H that are rendered latent. Mod- 
 erate degrees are also in measure made mani- 
 fest, not only permanently so in consequence 
 
 of a decrease of ^ (with the advance of 
 
 years), but also temporarily, even in youth, 
 through fatigue following exertion. 
 
 XVII. Paralysis of accommodation, tempor- 
 arily caused by instillations of sulphate of atro- 
 pine (strength, i : 1 20 — that is, one part of the 
 drug to one hundred and twenty parts of dis- 
 tilled water), renders H entirely manifest after 
 
 one or two hours' time. If ^ should be very 
 
 great, Hm may, through the cycloplegic action 
 of the atropine, rise from zero to four and a 
 half diopters, and even to six diopters ; from
 
 i8 ANOMALIES OF REFRACTION. 
 
 two and a quarter to seven diopters, etc. In E 
 and in M, paralysis of accommodation causes 
 the refraction to diminish barely one-half of a 
 diopter in amount. 
 
 XVIII. Hm is further subdivided into absolute, 
 in which, notwithstanding the strongest effort 
 of accommodation, ^p" lies behind the retina ; 
 into relative, in which a sharply recognized 
 point p' is more greatly removed from the eye 
 than the point of convergence of the visual line 
 C ; mto facultative, in which, although the con- 
 dition may be suppressed by accommodation, 
 yet weak positive lenses are not rejected for 
 distant vision. With the decrease of A, H, 
 which is facultative in youth, soon becomes 
 relative, and subsequently absolute. 
 
 XIX. H was observed and correctly charac- 
 terized by Ware in 1813. Later, it remained 
 unmentioned until 1854, when it was imperfectly 
 described by Ruete, this being followed by the 
 better explanations of Stellwag von Carion, 
 and VON Graefe. Based upon the results of 
 the author's examinations, it has been shown 
 that low and moderate degrees of H are very 
 common ; that they prevail more frequently 
 than M ; that they are sometimes entirely lat- 
 ent ; and that they occasionally, even in the 
 latent form, are the underlying cause of two
 
 EMMETROPIA AND AMETROPIA. 19 
 
 important anomalies which thus far have not 
 been well understood, convergent squi7it and 
 asthenopia or hebetude (fatigue produced by 
 exertion in gazing at objects that are situated 
 close to the eye). 
 
 XX. The reason why H, although generally 
 prevailing, remained so long unrecognized, 
 seems to be found in the fact that in very high 
 degrees of H small objects — for instance, type 
 of an average size (partly because of a more 
 rapid increase of the visual angle than of the 
 circles of dispersion (von Graefe) and partly 
 on account of a oradual reduction of the 
 size of the pupil) — can be seen better near the 
 eye than at some distance from it, thus causing 
 the condition to be regarded as M with weak- 
 ness of sight. Moreover, the minor degrees 
 of H are latent in youth, and when exposed in 
 later life, are confounded with presbyopia. 
 
 2. AMPLITUDE OF ACCOMMODATION (ABSO- 
 LUTE, RELATIVE, AND BINOCULAR) IN 
 EMMETROPIA AND AMETROPIA. 
 
 XXI. The faculty of accommodation being 
 dependent upon the crystalline lens growing 
 more convex, was assumed on eood orrounds 
 by Young. This was demonstrated by Lang- 
 ENBECK, and especially by Cramer, directly for
 
 20 ANOMALIES OF REFRACTION. 
 
 the anterior surface of the lens from the 
 changes of the images of reflection. Later, 
 these, as well as those for the posterior surface 
 of the lens (in a slighter degree), were proved 
 by Helmholtz, who made further measure- 
 ments and found the results so uniform and 
 certain that he concluded that the ordinary 
 limits of accommodation could approximatively 
 be explained therefrom. 
 
 XXII. An alteration in the shape of the 
 cornea does not take place in accommodation. 
 The theory of elongation of the visual axis 
 was long ago refuted by Thomas Young. It 
 appears, therefore, that the act of accommoda- 
 tion rests exclusively on changes that take 
 place in the shape of the crystalline lens. 
 Knapp, who in four eyes found alterations in 
 the shape of the crystalline lens, carefully 
 measured them, and proved that they corre- 
 sponded tolerably well with the A as deter- 
 mined at the same time according to my 
 methods of visual tests. 
 
 XXIII. Formerly, a certain degree of ac- 
 commodation was assumed in cases in which 
 there was an absence of the crystalline lens 
 (aphakia). I have shown, even in youthful sub- 
 jects, that not the slightest trace of accommo- 
 dation remains in this condition. In efforts
 
 AMPLITUDE OF ACCOMMODATION. 21 
 
 for accommodation, connected with increased 
 convergence, made exclusively by the inward 
 rotation of one (covered) eye with a narrowing 
 of the pupils of both eyes, a remote bright 
 point, sharply seen through the requisite lens, 
 retained as perfectly its form as it did when 
 looked at with parallel visual lines, notwith- 
 standing that lenses of +0.125 D. strength 
 (obtained by a combination of +0.75 D. with 
 — 0.625 D. — =% — or inverted) were suffi- 
 cient to produce a distinct change of form in 
 the crystalline lens. 
 
 Herein lies a positive proof that accommoda- 
 tion depends wholly upon changes in the shape 
 of the crystalline lens. 
 
 XXIV. A = P— R (compare Paragraph III) 
 signifies the dioptric power of a positive lens 
 which the eye adds to itself by the act of accom- 
 modation. This manner of expressing the 
 amplitude of accommodation is in conformity 
 with the actual change that may be supposed to 
 be taking place by the addition of an auxiliary 
 positive meniscus lens to the anterior surface of 
 the crystalline lens. 
 
 XXV. This helping lens /' (/' denoting the 
 distance of the focal point) is, however, not ex- 
 actly equal to A = P — R. From the powers of 
 P and R and of/' (computed from the form of
 
 22 ANOMALIES OF REFRACTION. 
 
 the crystalline lens of the same person, measured 
 during life, and during accommodation for dis- 
 tant and near vision), it has been shown that in 
 
 the emmetropic eye ^ • j, 
 
 I . I 
 
 9 ' lo 
 
 XXVI. It is further found that /' : A slighdy 
 differs in M and H. If the supposition be made 
 that the cardinal points have the same situation, 
 it will be realized that an equal change of form 
 of the crystalline lens represents a slightly 
 greater amplitude of accommodation in the 
 myopic eye, and a somewhat smaller one in 
 the hypermetropic eye than that which is pres- 
 ent in the emmetropic organ. (In high grades 
 of H, and — as might be expected, by reason of 
 the diseased stretchino- of the ocular tunics — 
 in hieh deofrees of M, much smaller values are 
 generally given to both /' and A.) 
 
 XXVII. A difference in the value of A in M 
 and H of moderate degrees is, however, not 
 shown empirically. It is possible that the value 
 of /' in myopia is in reality smaller. 
 
 XXVIII. When P and R are modified by the 
 employment of convex or concave lenses, they 
 are designated as P^ and R^. By the use of 
 negative lenses. P., and R^ become more greatly 
 removed than P and R ;' while by the employ- 
 ment of positive ones they become less removed.
 
 AMPLITUDE OF ACCOMMODATION. 23 
 
 Further, P^ — R^ is not equivalent to P — R, but 
 becomes increased by the use of concave lenses, 
 and diminished by the employment of convex 
 lenses, these results being the more pronounced 
 the further the lenses are made to stand in front 
 of the eye. 
 
 Through magnifying lenses A is more greatly 
 diminished. How little remains during the em- 
 ployment of microscopes, spy-glasses, and tele- 
 scopes, can be readily determined when the 
 following ratios are obtained : A. 
 
 F', the focal distance of the objective ; 
 
 F", the focal distance of the ocular ; 
 
 X, the distance from the objective to the ocular; and 
 
 y, the distance from the ocular to /''. 
 
 XXIX. The various grades of M and of H in 
 their relation to A are represented graphically 
 by the table on the following page. 
 
 The numbers i8 to o (Fig. i) give the dis- 
 tances of the points of distinct vision that are 
 situated in front of k\ while those below o, run- 
 ning from o to 9, designate similar distances 
 that are positioned behind k' . Each of the lines 
 
 a, b, c, and d, uniting p and r, shows the ampli- 
 tudes of accommodation, these being "propor- 
 tional to the lengrths of the lines themselves. 
 The line a represents E, with A ^ 9 ; the line 
 
 b, likewise, shows E, with A = 1.50 (presby- 
 opia) ; the line c designates M = 3, with A =
 
 24 
 
 ANOMALIES OF REFRACTION. 
 
 1 2 — 3 = 9 ; and the line d, on the contrary, 
 exhibits H = 3, with A = 3 + 3 = 6. 
 
 XXX. The amplitude of accommodation A 
 is the absolute one. For any amount of posi- 
 tive convergence of the visual lines, p^ and rj, 
 together with Pj and Rj, as their distances to k', 
 are employed. The symbols A^ = Pj — R^ are 
 
 t8 
 
 
 IP 
 
 P 
 
 Q 
 
 P 
 
 
 (; 
 
 
 
 
 3 
 
 
 
 P 
 
 
 ^ 
 
 r 
 
 
 
 
 
 
 1 
 
 
 
 
 
 r 
 
 r 
 
 
 
 
 3 
 
 
 
 
 
 
 
 
 
 r 
 
 5 
 
 
 
 
 
 9 
 
 
 
 a 
 
 b 
 
 C 
 
 d 
 
 
 
 Fig. 
 
 I. 
 
 
 
 , 
 
 used for the relative amplitudes of accommoda- 
 tion ill any given convergence. The farthest and 
 the nearest points seen simultaneously by both 
 eyes are characterized as p^ and r^ ; their dis- 
 tances to k\ as P2 and R^ respectively ; and the 
 binocular amplitude of accommodation, as P2 
 — R, = A,. 
 
 XXXI. Fig. 2 represents the positions of the
 
 AMPLITUDE OF ACCOMMODATION. 
 
 25 
 
 nearest points, p„ p^, and p, and of the farthest 
 ones r, fj, and r^ at differing divergences, as 
 studied in an emmetropic eye of good accommo- 
 dative power in an intelligent individual of fifteen 
 years of age (compare Paragraph XXXIV). The 
 numeration on the table has the same meaning 
 as that given above. The degree-marks placed 
 
 1 M 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 Y 
 
 
 
 
 
 
 
 
 
 
 ^ . 
 
 ^ 
 
 
 
 ^ 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 / 
 
 
 
 '■^ 
 
 ^ 
 
 X 
 
 
 
 
 V 
 
 
 / 
 
 
 
 /^ 
 
 y 
 
 
 
 
 / 
 
 / 
 
 
 / 
 
 
 y 
 
 / 
 
 
 
 
 
 
 / 
 
 
 / 
 
 
 / 
 
 
 
 
 
 
 
 
 
 / 
 
 
 / 
 
 
 
 
 
 
 
 
 
 / 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 ii°.2i' 22°.5o' 34°.32' 46°.38 59°. 20' 7i°.5o' 
 
 Fig. 2. 
 
 below the figure, represent the angles made at 
 the point of convergence of the visual lines that 
 have been calculated for a distance of sixty-four 
 and a half millimeters between the parallel 
 visual lines of the two eyes. On the diagonal 
 K K', the vertical lines, expressing the degrees 
 of convergence, intersect the horizontal ones 
 3
 
 26 ANOMALIES OF REFRACTION. 
 
 which represent the distances in fractions of one 
 meter each that correspond with these degrees. 
 The sio-nification of the remaining- letters in the 
 figure can be understood by reference to the 
 previous paragraphs. 
 
 XXXII. With the knowledge of the meaning 
 of the lines p„ p^, and p, and r, i\, and r^, in 
 their relation to the degrees of convergence, 
 everything that relates to accommodation be- 
 comes understandable. Thus, from Fig. 2 the 
 following may be inferred: 
 
 E 
 
 A = 9.75 diopters. 
 
 A3 = 9.25 
 
 Aj — for ii°2i' =: 6.00 diopters, etc. 
 
 XXXIII. Figure 2, moreover, teaches that, 
 as far as p^, a portion of A lies above and 
 another part is situated below K K'. The former 
 is the positive, and the latter is the negative 
 portion, of the relative amplitude of accommo- 
 dation. Accommodative action can only be 
 continued for a distance in which the positive 
 part of A is not too small in comparison with 
 the negative portion. 
 
 XXXIV. To find the lines j^^j,/^' and/* and;-, 
 r„ and i\, it becomes necessary, in addition to 
 obtaining p and r, to determine p^^ and i\ with
 
 AMPLITUDE OF ACCOMMODATION. 27 
 
 various convex and concave lenses ; care being 
 taken to take note of every corresponding de- 
 gree of convergence. Further, by reduction of 
 pf^ and ^0, according to the focal distances of the 
 lenses used,and their distances from the eye, it is 
 obligatory to compute p^ and r^ in exact corre- 
 spondence with the different degrees of con- 
 vergence. The black dots in figures 2 and 3 
 show the points that have been gotten in this 
 manner. 
 
 XXXV. For the determination of these 
 measurements, I employed an optometer, in 
 which the lenses, which were laterally separated 
 from one another by a distance that was equal 
 to that of the parallel visual axes of the two 
 eyes, were placed at 0^.5 from k' . These lenses 
 were moved in grooves which were so con- 
 structed as to describe arcs from the turning 
 points of the eyes, in such a way that the dis- 
 tances of the lenses to k' always remained the 
 same, and, at every angle of convergence, the 
 visual axes coincided with the axes of the lenses 
 that were employed. 
 
 XXXVI. The variation in the forms of the 
 lines /j, p^, and /, and r, i\, and r^ in M and in 
 H (Fig. 3, M and H) is remarkable. 
 
 It is apparent that with slight convergence, 
 myopes can not accommodate so much by far.
 
 28 
 
 ANOMALIES OF REFRACTION. 
 
 and that hypermetropes can and must accom- 
 modate more greatly than emmetropes (com- 
 pare Fig. 2). With hypermetropes, only after 
 ciliary paralysis has been obtained (vide Para- 
 graph XVII), can the point r be determined as 
 r^, — the farthest point of total H, as indicated 
 
 tVM. 
 
 1 
 
 T5 
 
 T5 
 
 2 
 5T 
 
 1 
 5 
 
 2 
 T5 
 
 
 
 
 
 
 
 
 
 
 ^/ 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 / 
 
 r 
 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 r. 
 
 
 
 
 
 
 
 
 > 
 
 ^ 
 
 / 
 
 1 
 
 
 
 
 
 
 
 / 
 
 
 
 / 
 
 / 
 
 
 
 
 
 ^ 
 
 Et- 
 
 
 
 J 
 
 
 '/ 
 
 
 J 
 
 
 
 
 
 
 
 
 
 /. 
 
 y 
 
 y 
 
 
 
 
 
 r 
 
 -^ 
 
 Tt 
 
 
 / 
 
 h 
 
 
 
 
 
 
 
 
 
 P: 
 
 A 
 
 
 
 
 
 
 ,p 
 
 
 
 / 
 
 '^ 
 
 / 
 
 
 
 
 r^ 
 
 s^^ 
 
 ^ 
 
 
 
 
 y- 
 
 / 
 
 
 Vifl 
 
 
 
 ^. 
 
 
 
 
 
 
 y 
 
 
 ^ 
 
 
 
 ,'' 
 
 
 
 
 
 
 
 
 ^ 
 
 
 ,' 
 
 nt 
 
 
 
 
 
 
 
 
 rm 
 
 
 
 
 
 
 
 
 
 
 
 
 ,' 
 
 '' 
 
 
 
 
 
 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 i 
 
 
 
 Fig. 3. 
 
 in figure 3. The points r {i\„^ in the figure) are 
 situated higher than would be the case if H 
 were not to so o-reat a degfree latent, beine 
 therefore noted in the figure as r,,„ (that is, f\ in 
 manifest H). The latent portion, with parallel 
 visual lines, is shown by the vertical distance
 
 AMPLITUDE OF ACCOMMODATK3N. 29 
 
 between r,„ and r^, which Is here equal to 3.50 D., 
 while the total hypermetropia, H or Ht, is equiv- 
 alent to 4.75 D. 
 
 XXXVII. Dissimilarity in the conformation 
 of the lines is the consequence of practice. 
 Myopes habituate themselves to accommodate 
 but feebly with slight degrees of convergence, 
 whereas hypermetropes, under similar circum- 
 stances, accommodate very forcibly. By the 
 continual employment of correctional spectacles, 
 the shapes of the lines more nearly approach 
 those of emmetropes: in a like manner, even a 
 brief use of spectacles will have a similar influ- 
 ence. 
 
 XXXVIII. The form of the lines /„ /,, and 
 p, and r, 1\ and r^, in ametropia, proves that 
 the neutralization of the ametropic condition by 
 concave or convex lenses, has not rendered the 
 eye similar to an emmetropic organ. 
 
 XXXIX. This makes manifest why each ame- 
 tropic case should not be at once entirely neu- 
 tralized. In order to understand this clearly, r 
 in ametropia (Fig. 3) should be brought to co 
 and the lines reduced in accordance. However, 
 the condition gotten, does not accurately repre- 
 sent that which is really obtained by the neutrali-
 
 30 ANOMALIES OF REFRACTION. 
 
 zation of the ametropia (compare Paragraph 
 XXXVIII). 
 
 3. VISUAL ACUTENESS AND PROJECTION IN 
 EMMETROPIA AND AMETROPIA. 
 
 XL. The acuteness of vision, V, of different 
 individuals is obtained and compared by deter- 
 mining the smallest angle under which they are 
 able to recognize objects of known form in an 
 illumination of average intensity. Square capi- 
 tal letters may serve as objects (vide Snellen's 
 test-type), by which control in reference to cer- 
 tainty of recognition is vouchsafed by the fact 
 that they must be named. With a normal eye, 
 the subject is able to recognize such letters 
 under an angle of five minutes' opening (Snel- 
 len). Some subjects have the ability to seethe 
 test-objects under a smaller angle. 
 
 Snellen's test-letters are numbered in accord- 
 ance with the distance D, at which they can be 
 properly seen under an angle of five minutes. 
 If, therefore, the distance d, at which the letters 
 can be recognized, is ascertained, the degree of 
 
 visual acuteness will be equivalent to V = j^- In 
 normal acuity of vision, it will be found that 
 d == D and V = I. 
 
 XLI. V in M is often imperfect. In M>6 
 diopters, it is nearly always so unless the re-
 
 VISUAL ACUTENESS. 31 
 
 fractive condition is congenital and the subject 
 is quite young. In M>7 diopters, imperfect 
 visual acuity is the ride, while in M>9 diopters, 
 it will always be found to be below normal. 
 
 XLII. On account of the o^reater distance 
 from k" to the retina in M, retinal images for 
 equal angles under which objects can be seen, 
 are larger. In opposition, as it were, the retina, 
 in consequence of stretching, is greater in ex- 
 tent, and, therefore, contains a fewer number of 
 percipient elements in any given area of surface. 
 With a complete compensation of both of these 
 factors, the projected retinal images would re- 
 tain an equal size, and V in each case remain 
 the same. The fact that V in high degrees of 
 M is generally lessened in the position of the 
 visual line, is — not considering diseased altera- 
 tions — explained by the stretching of the ocular 
 membranes, which has been ascertained ana- 
 tomically to be relatively greater in the region 
 of the yellow spot. 
 
 XLIII. In the estimation of V with concave 
 lenses that neutralize the myopic condition, it 
 will be found that the visual acuity is lower than 
 normal. This is so because the second nodal 
 point k" (including the artificial lens in the 
 dioptric system of the eye) is situated closer to 
 the retina, causing the retinal images to become
 
 32 ANOMALIES OF REFRACTION. 
 
 smaller. The closer the correcting lenses are 
 placed to k", the more readily do they neu- 
 tralize the myopia, the further removed is k" 
 from the retinal plane, and, in consequence, the 
 less influence do they exert on V. 
 
 XLIV. In minor degrees of H that are over- 
 come by constant exercise of the power of 
 accommodation, V is not infrequently normal. 
 In addition, by reason of the actually shorter 
 distance of k" to the retina, the retinal images 
 are not so large as those that are found in an 
 emmetropic eye. The retina of H, however, 
 offers a smaller surface, so that, notwithstanding 
 the fact that the total number of percipient ele- 
 ments be equally great, they must necessarily 
 stand much closer to one another. Whether 
 such be really the case, especially in the region 
 of the fovea centralis, is well worthy of further 
 examination. 
 
 XLV. In the hiofher o;rades of H, V is not 
 seldom found to be imperfect. In the highest 
 degrees, it is usually the case. Various causes 
 for these results are brought into play by the 
 existent conditions : a, the retinal images are 
 smaller ; b, there often exists an abnormal sym- 
 metry of the refracting surfaces of the eye ; and 
 c, in the highest grades of H, the entire eye is
 
 VISUAL ACUTENESS. 33 
 
 imperfectly developed, die nerve taking share 
 in this faulty development. 
 
 XLVI. When in H, clear images are obtained 
 on the retinal plane, not by undue exertion of 
 the power of accommodation, but through the 
 employment of bi-convex lenses placed in front 
 of the eye, then such retinal images (because 
 k" is moved forward) are probably as large or 
 possibly larger than those that are found in the 
 emmetropic eye : consequently, V increases. 
 In moderate degrees, V corrected in a similar 
 manner, is sometimes >i ; in other cases, it = 
 I. In hicrh decrees, however, V remains often 
 <i, this generally resulting from the causes that 
 are mentioned in Paragraph XLV, under d 
 and c. 
 
 XLVII. In young subjects who have been 
 successfully operated on for congenital cataract, 
 and as a result,^have a refraction of about H = 
 14.5 to 12 diopters, H, when properly corrected 
 by a bi-convex lens, often gives V> i . The causes 
 of this are the increased size of the retinal image, 
 and the forward displacement of /c" by the sub- 
 stitution of an artificial lens that is placed in 
 front of the cornea for the crystalline lens which 
 was situated behind the cornea. 
 
 XLVIII. In the correction of H, the focal dis-
 
 34 ANOMALIES OF REFRACTION. 
 
 tance of the lens that is used must be as many 
 inches (milhmeters) greater as the lens is re- 
 moved from the eye. As a result of this, the 
 images of the retina become successively larger 
 and larger in size ; an act that may be compared 
 to that of the working of a Galilean telescope, 
 in which the objective corresponds with the con- 
 vex lens before the eye, and the concave lens 
 of the ocular, in association with the eye, may 
 be considered to belong to a hypermetropic 
 eye. As calculation teaches, the magnification 
 is quite marked. In cases of H = 14.5 diop- 
 ters, a lens of 12 diopters' strength, held at one 
 and a half centimeters' distance in front of the 
 eye, produces a lineal magnification (relatively 
 to an emmetropic eye before operation) of 1.322 
 times; while a lens of 2.25 diopters' strength, 
 held at ten centimeters' distance in front of the 
 eye, gives a magnification of more than seven 
 times the true size. 
 
 In higher degrees of H without aphakia, simi- 
 lar use may be made of a relatively weak con- 
 vex lens as a Galilean telescope. 
 
 XLIX. Lenses that magnify or minify, alter 
 the relation between the dimension of the 
 imaofe of the retina and the movement of the 
 head that is required to survey an object which 
 is situated in the line of vision without moving 
 the eyeball. Therefore, should the head be
 
 VISUAL ACUTENESS. 35 
 
 moved under such circumstances, it will appear 
 as if all objects that are seen magnified are 
 advancing toward the eyes, and that all ob- 
 jects that are apparently diminished in size 
 are receding from the eyes. Such, however, 
 is not the case when the eyes are moved, as 
 the disturbed relationship is practically com- 
 pensated for by the incorrect direction in which 
 an object that is seen obliquely through the lens 
 is supposed to lie. 
 
 As a rule, the various visual directions are 
 obtained in measure by coetaneous movements 
 of the head, and in part by rotatory motions of 
 the eyeball. In such cases, the apparent move- 
 ment of objects takes place, though only to a 
 slight degree, by the employment of magnifying 
 or minifying lenses. 
 
 L, Magnifying lenses have the effect that 
 measurements made with them on a surface 
 that is perpendicular to the visual line are pro- 
 jected larger when one eye is used than with- 
 out a lens ; whereas, on the contrary, estima- 
 tions of depth (differences of distance) made 
 under similar circumstances are projected 
 smaller. Diminishing lenses oive results that 
 are the opposite. The key thereto is essentially 
 this : Eqitiform objects or surfaces, some angles 
 of which are commonly known as right angles, 
 produce, when placed at similar distances and
 
 36 ANOMALIES OF REFRACTION. 
 
 under equal inclination, dissimilar perspective 
 retinal images that are the direct results of 
 differences of size. Consequently, uniform 
 retinal images, with a difference in size, cause 
 them to be projected as unlike objects. Lenses 
 change merely the size, and not the form, of 
 retinal images. Therefore, their employment 
 gives rise to a projection of other forms ; that is, 
 such, by which, retinal images that are of relative 
 size, would be produced. A study of their con- 
 struction teaches that these are less deep the 
 larofer the retinal imao-e becomes, and vice 
 versa. 
 
 LI. Likewise, the stereoscopic parallax for two 
 eyes is decreased by magnifying lenses, and is 
 increased by diminishing ones. The explana- 
 tion thereof lies enclosed in this : that from 
 slightly remote objects, the angle under which a 
 surface shows itself perpendicular to the visual 
 axis is inversely proportionate to the distance ; 
 while, on the contrary, the parallactic angle for 
 the two eyes is about proportionate to the 
 squares of the distances. 
 
 LII. In high grades of myopia the retina is 
 stretched. The retinal image is therefore pro- 
 jected smaller than it was. before the distention 
 took- place. With a disproportionately great 
 amount of stretching at the posterior pole of
 
 VISUAL ACUTENESS. 37 
 
 the eye, an object that is seen directly is pro- 
 iected smaller than it was before the stretchinof ; 
 in fact, it is projected smaller than it is in 
 emmetropia (compare Paragraph XLII), Not- 
 withstanding this, in fixing an object, its size is 
 exactly determined and its boundaries are pre- 
 cisely indicated with the finger. In directing 
 the line of vision successively upon the object's 
 diametrically opposed boundaries, the modified 
 connection between the quantity of the neces- 
 sary contraction of the muscles and the pro- 
 jected size of the images is not indicated by 
 any apparent movement of the object. 
 
 Thus, a point of the retina is, in consequence 
 of a slowly progressive displacement by stretch- 
 ing, projected outwardly in a direction which 
 is unlike that of the original. If the line of 
 projection for a selfsame percipient element of 
 the retina can, in spite of displacement, change 
 so as to retain its connection with other means 
 of perception, it is admissible to assume that 
 the direction is not original, but has been 
 brought into existence by an association with 
 some other means of perception. 
 
 « 
 
 LIII. In a similar manner, the projection of 
 the entire visual field, equally with all its points, 
 can, under abnormal conditions, be modified. 
 With any fixed state of equilibrium of the mus- 
 cles of the eye, an object that is seen directly,
 
 38 ANOMALIES OF REFRACTION. 
 
 apparently lies straight before the eye. If the 
 position is changed while the subject believes 
 that the same equilibrium has remained, — in 
 paralysis, for instance, or after section of the 
 internal or the external rectus muscle, etc., — he 
 will still project that which is seen centrally, 
 directly in front of his eyes, although the object 
 is situated to one side ; the visual field then 
 being improperly projected. Studied in con- 
 nection with the other eye, it will be found that 
 double images are one of the consequences 
 thereof — they being homonymous in character 
 when the eye has turned towards the nasal 
 side, and heteronymous in type when it has 
 deviated towards the temporal side. If, how- 
 ever, the deviated eye is constantly used alter- 
 nately with its fellow, — which occurs especially 
 in deviations toward the temporal side, — it learns 
 to localize and duly distinguish its impressions 
 from those of the other eye. The projection is 
 then made with much exactness, and thus, the 
 situation of the two objects, which have their 
 respective images placed in the foveae centrales 
 of the yellow spots are shown as quite different. 
 Both yellow spots are thus no longer projected 
 towards the same points in space. In like man- 
 ner, with such deviation, with or without the 
 employment of weak prismatic glasses, homony- 
 mous double images are seen of an object 
 whose retinal images fall to the outer side of
 
 VISUAL ACUTENESS. 39 
 
 the fovea centralis of the rio-ht as well as of the 
 left eye. The reverse condition may appear 
 after a long-continued or a congenital deviation 
 of one eye to the nasal side. 
 
 LIV. Herein lies the proof that, in abnormal 
 position of the visual axes, each eye by itself 
 can learn to project its field of vision in the cor- 
 rect direction, and that, therefore, the ordinary 
 projection of the two fields of vision upon each 
 other can also be learned as a consequence of 
 the subject seeking for corresponding retinal 
 images for the two keenly percipient yellow 
 spots. Accordingly, through projection of their 
 impressions, with slight allowances to be made 
 for one another, other retinal points also acquire 
 the value of very closely corresponding points, 
 which signification, not being dependent on 
 any fundamental anatomic condition, they may 
 also lose aeain. 
 
 4. LINE OF DIRECTION, CENTER OF ROTATION, 
 AND MOVEMENTS OF THE EYE IN EM- 
 METROPIA AND IN AMETROPIA. 
 
 LV. The long axis {g a, Fig. 4) of the corneal 
 ellipsoid cuts the cornea almost exactly at its 
 middle (Helmholtz, Knapp). The same ap- 
 plies to ametropic eyes [g a, of Fig, 5, showing 
 a myopic eye, and ^ ^ of Fig. 6, showing a
 
 4° 
 
 ANOMALIES OF REFRACTION. 
 
 i 
 
 hypermetropic one). The visual Hne //' is the 
 line of direction which, extending through the 
 nodal point, unites the fixed point of the object 
 
 Fig. 4. 
 
 i 
 
 ^ 
 
 ^ W \i 
 
 
 \ 
 
 Fig. 5. 
 
 < 
 
 Fig. 6. 
 
 with its retinal image, which — as examination 
 with the ophthalmoscope has taught me — lies in 
 the fovea centralis of the yellow spot. 
 
 The visual line cuts the cornea at the nasal
 
 LINE OF DIRECTION, ETC. 41 
 
 side and generally slightly above the middle 
 (Senff, Helmholtz, Knapp). If the refracting 
 surfaces are centered, as is almost always the 
 case, the axis of the cornea practically becomes 
 at the same time the visual axis, and is crossed 
 at k by the visual line under an angle that is 
 shown hy I k g. This angle is designated by 
 the symbol a. 
 
 LVI. The angle a differs in the emmetropic 
 and in the ametropic eye. In fifteen emmetropic 
 eyes, we (Donders and Doijer) found 7° as the 
 maximum and 3°5' as the minimum, with an aver- 
 age of 5° .082' ; in twelve hypermetropic eyes, 
 9° was the maximum, 6° was the minimum, and 
 7° 55' was the average; in ten myopic eyes, 
 the maximum equalled 5° 25' and the minimum 
 equalled 1° 5' (that is, 1° 5' to the temporal 
 side of the axis of the cornea, as can be seen 
 in Figure 5), with an average of 2°. 
 
 LVII. The result of the various values of the 
 angle a is that, with parallel visual lines, the 
 corneal axes of hypermetropes diverge more 
 than those of emmetropes, while those of myopes, 
 on the contrary, diverge less, or even converge. 
 With similarly directed visual lines, therefore, 
 myopes show an apparent convergent squint, 
 while hypermetropes exhibit an evident diver- 
 gent strabismus. 
 4
 
 42 ANOMALIES OF REFRACTION. 
 
 LVIII. The cause of the various values of 
 the angle a is, as regards myopia, to be found 
 in the stretching of all of the ocular mem- 
 branes, mostly at the outer posterior portion of 
 the eyeball, so that the yellow spot is moved 
 towards the nasal side. In hypermetropia, the 
 greater value of the angle a is due in measure 
 to the shorter distance between k" and the 
 retina, and in part to a congenitally more ex- 
 ternal situation of the yellow spot. 
 
 LIX. The angle a was obtained by determin- 
 ing the angle formed between the visual line 
 and the axis of an ophthalmometer that was re- 
 quired to have a flame placed in this axis, re- 
 flected exactly in the middle of the cornea ; 
 the reflectinor imaee beincr situated in the 
 middle, when each of its double images corre- 
 sponded precisely with the border of the oppo- 
 site double image. 
 
 LX. In the said position of the double 
 images, the designated angle of the ophthal- 
 mometer-plates simultaneously indicated the 
 half-breadth of the cornea, or rather its half- 
 chord ; the situation of the turning point behind 
 this chord being determined by calculating how 
 great the angles of rotation (equal on both 
 sides) must be in order to cause the extremi- 
 ties of the chord to alternately come together
 
 LINE OF DIRECTION. 
 
 43 
 
 with the same point in space. The probable 
 fault in this calculation amounted to less than 
 one per cent. 
 
 LXI. To the distance between the corneal 
 base and the turning- point was added two and 
 six-tenths millimeters as the height of the seg- 
 ment of the cornea. In this manner was found 
 column "b" of the followino- table: 
 
 
 
 • Position of the Turning Point: 
 
 
 a 
 
 b 
 
 c 
 
 d 
 
 e 
 
 f 
 
 
 Length of 
 
 behind 
 
 in front of 
 
 Percentage 
 
 behind 
 
 Angle be- 
 
 
 the optic 
 
 the 
 
 the posterior 
 
 proportion. 
 
 the middle 
 
 tween the 
 
 
 axis. 
 
 cornea. 
 
 surface of the 
 sclerotic. 
 
 
 of the 
 optic axis. 
 
 axis of 
 cornea and 
 the line of 
 
 vision. 
 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 
 E 
 
 23-53 
 
 13-54 : 
 
 9.99 = 57.32 : 42.48 
 
 1.77 
 
 5°. 082 
 
 M 
 
 25-55 
 
 14.52 : 
 
 11.03 = 56-83 : 43-17 
 
 1-75 
 
 2° 
 
 H 
 
 22. lO 
 
 13.22 : 
 
 8.88 = 59.8 : 40.2 
 
 2.17 
 
 7°-55 
 
 Column "a " was computed from the ametro- 
 pia, in which it was supposed that the cardinal 
 points corresponded with those of the sche- 
 matic eye. 
 
 LXII. The table demonstrates that the turn- 
 ing point lies rather considerably behind the
 
 44 ANOMALIES OF REP"RACTION, 
 
 middle of the visual axis with which it was 
 formerly considered to almost meet. For the 
 hypermetropic eye, this result is particularly 
 true, though perhaps the crystalline lens in 
 such an eye is less convex than it is in the em- 
 metropic organ, in which the computed visual 
 axis (column "a") would be too short, and con- 
 sequently, the turning point of the eye would 
 lie relatively more anteriorly. 
 
 LXIII. The position found for the turning 
 point of the eye is advantageous for the move- 
 ments of the organ. The nearer the point of 
 rotation is situated to the posterior extremity 
 of the visual axis, the less are the movements 
 restricted by the optic nerve. As a rule, the 
 larger eyeball is generally the cause of the re- 
 strained movement of the highly myopic eye ; 
 at least the distance between the turning point 
 of the eye and the laterally displaced optic 
 nerve is relatively not greatly increased. 
 
 5. ACUTENESS OF VISION AND AMPLITUDE OF 
 ACCOMMODATION, MODIFIED BY AGE. 
 
 LXIV. Figure 7, herewith given, has been 
 copied from an article by Dr. Vroesom de 
 Haan, entitled " Investigations on the Influence 
 of Age on Acuteness of Vision," which was 
 published at Utrecht in 1862. The studies
 
 V AND A AS MODIFIED BY AGE. 
 
 45 
 
 were made on two hundred and eighty-one 
 subjects, one or both of whose eyes were nor- 
 mal, without any opacities, and free from dis- 
 turbing astigmatism. M > 0.75 diopters, and 
 manifest H of 0.5 diopters, except in advanced 
 age when H = 1.25 diopters was still allowed, 
 
 Z6M 
 
 
 24.20 
 
 
 22:20 
 
 
 
 
 
 
 ^ 
 
 1 
 
 ?0?0 
 
 
 
 
 "~^^ 
 
 K 
 
 m?o 
 
 
 
 
 
 \ 
 
 /6?n 
 
 
 
 
 
 
 \ 
 
 1470 
 
 
 
 
 
 
 \ 
 
 h^ 
 
 n?o 
 
 
 
 
 
 
 
 
 r\ 
 
 lo?n 
 
 
 
 
 
 
 
 
 V 
 
 
 8.26 
 6-20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 420 
 
 
 
 
 
 
 
 
 
 
 220 
 
 
 
 
 
 
 
 
 
 
 0:20 
 
 
 
 
 
 
 
 
 
 
 40 so 
 
 Fig. 7. 
 
 60 
 
 80 Age. 
 
 were excluded. During the examination, care 
 was taken to correct all ametropia. 
 
 LXV. In the figure, the age is given in the 
 abscissas. The ordinates show V, which is ex- 
 pressed by the number of feet, d, at which D 
 = XX, is recognized. In his investigation, de 
 Haan required only the recognition of the letters
 
 46 ANOMALIES OF REFRACllON. 
 
 U, A, C, and L. As a result, the equation that 
 he found for V was too large. An examination 
 has taught us that on account of this error, a 
 reduction of one-sixth was necessary ; which 
 decrease has been introduced in the ficrure. 
 
 LXVI. The figure teaches that in the emme- 
 tropic eye, up to about the age of twenty-seven 
 years, V remains almost unchanged. From 
 this age it slowly decreases until it falls below 
 V = o.5 in advanced life. 
 
 LXVII. It further appears that to the age of 
 forty-two years, V is, as a rule, >i. There 
 exists, however, quite pronounced individual 
 differences. In cases in which V = i, no cause 
 can be properly assumed as to the presence of 
 any anomaly ; this is the signification of what 
 has been adopted by Snellen as V = i. De 
 Haan found as his maximum that V = 1.7. 
 
 LXVIII. The studies were all made under 
 adequate illumination. A series of personal 
 tests, made in each instance by de Haan, taught 
 him, however, that on account of differences 
 in illumination under which the examinations 
 were made on various days, there appeared 
 oscillations of V = 22.5 ; 20, and V = 19.5 : 
 20. These variations were, nevertheless, fairly 
 equally distributed over all ages. Conse-
 
 V AND A AS MODIFIED BY AGE. 47 
 
 quently, the line of curvature practically under- 
 went but slight change when all of the exam- 
 inations were noted as being made during equal 
 degrees of illumination. 
 
 LXIX. The cause of lessening acuteness of 
 vision increasing with agfe must be looked for 
 in the ocular media, as well as in the optic 
 nerve. 
 
 LXX. The remarkable clearness with which 
 the fundus oculi of young subjects can be seen 
 ophthalmoscopically, confirms the belief that the 
 transparency and the uniformity of structure of 
 the ocular media decrease in advancing age. 
 The crystalline lens reflects a greater amount 
 of light, its tint grows more yellow, and by 
 oblique illumination, the lines of separation of 
 its sectors become more distinct. Irregular 
 astigmatism increases. Monocular polyopia, 
 with imperfect accommodation, in spite of the 
 ever-decreasing pupillary area, becomes more 
 pronounced and more disturbing. The vitreous 
 humor g^rows more turbid and becomes richer 
 in membranes, corpuscles, and filaments, which, 
 as microscopic examinations and entoptic studies 
 have taught me, are the causes for so-called 
 mouches volantes. In these changes, the cornea 
 is the least affected, particularly, at all events, 
 in its middle zone.
 
 48 ANOMALIES OF REFRACTION. 
 
 LXXL Among the most prominent altera- 
 tions seen in the eye-ground of advanced age, 
 are maculated thickenings of the membrana 
 vitrea of the chorioid — knots, as it were, that 
 penetrate into the retina, appearing as protuber- 
 ances which displace and disturb areas of its 
 outer percipient layer. 
 
 LXXII. In high degrees of myopia, acuteness 
 of vision, especially, diminishes much more 
 quickly during advancing age than it does in E. 
 In M = 9 or I 2 diopters, V at the age of sixty 
 years is usually </^. 
 
 LXXIII. The cause thereof is, increasing 
 atrophy of the ocular membranes through 
 stretching ; this often being coupled with a 
 chronic, low-grade inflammation combined with 
 a slight translucency of vitreous humor. These 
 conditions may be seen with the ophthalmo- 
 scope. 
 
 LXXIV. As a rule, the amount of atrophy is 
 in direct relation with the degree of M, though 
 in equivalent grades of M it is found to be pro- 
 portionately most marked in older subjects. 
 
 LXXV. In H, the decrease of V which is 
 dependent upon increase of years, pursues a 
 similar course to that which is seen in E.
 
 V AND A AS MODIFIED BY AGE. 
 
 49 
 
 LXXVI. The amplitude of accommodation, 
 I : A, diminishes even somewhat in early life 
 (from the tenth year or before), and decreases 
 quite regularly so as to about = O at the age 
 of sixty or seventy years. In addition, in the 
 
 M. 
 
 lO /5 20 25 30 35 40 45 SO SS 60 65 70 75 80 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \p 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 S, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 N, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \s 
 
 ">». 
 
 
 
 
 r 
 
 
 
 
 
 
 
 
 
 —1 
 
 
 ^r^: 
 
 p' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "V 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 8. 
 
 emmetropic eye, there is coetaneously formed 
 a slight degree of H. Figure 8, herewith given, 
 illustrates this quite well, pp' is the line of cur- 
 vature of the nearest points, and rr' is that of 
 the farthest points, expressive of the function-
 
 50 ANOMALIES OF REFRACTION. 
 
 ing power of the age (from ten to eighty years). 
 After the sixty-fifth year of age, the determina- 
 tions oi p become less accurate, this being so 
 on account of a lessening of V and by reason of 
 the small diffusion circles that are associated 
 with a narrow pupil. 
 
 LXXVII. The cause of the early decrease of 
 ^ while the muscular mechanism of accommo- 
 dation is still undoubtedly undisturbed, is to be 
 sought in the early increasing density of the 
 crystalline lens, whereby its capacity for change 
 of form is decreased. At a greater age, there 
 is superadded to this an actual diminution of 
 the anatomical constituents of the muscular 
 mechanism. 
 
 LXXVIII. The decrease of ^^ in E gives 
 rise to presbyopia, Pr. The point at which Pr 
 commences is merely empirical. Especially 
 fine near-work can not be done properly during 
 the use of artificial light in the evening when 
 P2>2 2 cm. With P2>2 2 cm. I have therefore 
 proposed to let Pr commence. This happens 
 in cases of E almost without exception between 
 the years of forty and forty-two. We find the 
 degree of Pr to be 4.5 — p. 
 
 LXXIX. As Pr advances, the lines p^, p^ and 
 p, and r, r^, and r^, in cases of E, increasingly
 
 V AND A AS MODIFIED BY AGE. 
 
 51 
 
 assume the shape which is primarily character- 
 istic of H. Figure 9, exhibiting the accommo- 
 dation of a forty-three-year-old subject, furnishes 
 the proof thereof. (Compare this with figure 2 
 in Paragraph XXXV!.) 
 
 LXXX. In M, the decrease of ^ pursues 
 
 J. M. 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 r- 
 
 '/ 
 
 
 
 
 
 
 
 ^ 
 
 
 
 / 
 
 -/ 
 
 
 ^ 
 
 
 
 r, 
 
 
 
 
 
 "> 
 
 V 
 
 / 
 
 r, 
 
 
 
 
 
 
 
 
 
 z 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 r- 
 
 
 
 
 
 
 
 
 
 
 
 
 22'.50' J'f'J?' 4$°3d' SS^ZO' 72'SO 
 
 Fig. 9. 
 
 almost a similar course to that which is seen in 
 E. Solely in very high degrees, ^ decreases 
 more quickly ; otherwise the progress of p is 
 altered by the variation to which r, and conse- 
 quently M, are subjected. 
 
 During the years of development, M is, with- 
 out exception, progressional, the rule being that
 
 52 
 
 ANOMALIES OF REFRACTION. 
 
 this is the more pronounced the higher is the 
 grade of the M. High degrees of M remain 
 progressive for long periods of time, while the 
 highest grades of the condition are continually 
 advancing. • 
 
 LXXXI. From the results of a great number 
 of examinations continued over a period of many 
 years, and in accordance with a comparative 
 study of the spectacle lenses that have been em- 
 ployed for many years past, and those that are 
 still used, I have projected the following schemas : 
 
 M 
 
 10 15 20 25 30 J5 40 45 50 55 60 65 70 75 
 
 
 Fig. io. 
 
 Figure lo represents the course of M as 
 found in a slight and almost stationary degree 
 of the condition.
 
 V AND A AS MODIFIED BY AGE. 
 
 53 
 
 Figure 1 1 illustrates the directions that are 
 assumed in a high-grade, temporarily progres- 
 sive M. 
 
 Figure 12 shows the course that is found in 
 a very high, permanently progressive degree, 
 
 LXXXII. From this, it can be seen that it is 
 
 T 
 
 2 
 35 
 
 JL 
 15 
 
 'ii 
 
 1 
 T^ 
 
 2 
 
 ^T 
 
 1 
 
 ■5 
 
 1 
 
 M. 
 
 /O 15 20 Z5 30 S5 40 4S 50 55 60 65 70 75 80 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -^ 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 N, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "v. 
 
 
 ^ 
 
 -^ 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 r' 
 
 
 V 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 T^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. II. 
 
 an error to suppose that M, as a rule, lessens 
 with an increase of years. The cause of this 
 incorrect opinion is twofold. In the first place, 
 p actually recedes from the eye, and this which 
 was considered as a lessening of M, would only 
 take place if r were to withdraw from the organ. 
 Secondly, the pupil grows smaller, and conse-
 
 54 
 
 ANOMALIES OF REFRACTION. 
 
 quently, on account of smaller circles of diffu- 
 sion, the subject can often see better at a dis- 
 tance during advanced age, in spite of a slightly 
 increased M. 
 
 LXXXIII. Pr is not excluded by minor grades 
 
 /O /S 20 2S 30 35 40 45 SO 55 60 65 70 7S SO 
 
 Fig. 12. 
 
 of M. It is said to be in existence the moment 
 that P is > 22 cm. In cases in which M = 1.5 
 diopters with A = 1.5 diopters' strength,^ is 
 situated at thirty-three centimeters so that 
 Pr = 4,5 diopters — 3 diopters = 1.50 diopters. 
 
 LXXXIV, The accompanying diagram (fig-
 
 V AND A AS MODIFIED BY AGE. 
 
 55 
 
 lire 13) exhibits approximately the course that 
 accommodation, as an attribute of age takes in 
 H. The dotted Hne r^ r\ gives the progress of 
 the total H, while r,„ r',„ illustrates that of the 
 manifest. 
 
 It is apparent that H, which is entirely latent 
 at the outset, becomes increasingly manifest 
 
 Meter 
 
 /O /5 20 25 30 35 40 45 50 55 60 65 70 75 80 
 
 /{ 
 
 9 
 7.5 
 6 
 45 
 3 
 1.5 
 
 15 
 3 
 
 4.5 
 6 
 
 7.5 
 [9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 V 
 
 
 
 
 
 
 
 
 Tm. 
 
 
 
 
 
 ^ 
 
 
 \ 
 
 < 
 
 
 
 
 
 
 
 
 
 
 
 
 
 'rm- 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 If 
 
 
 
 
 
 
 
 
 V 
 
 
 ->?, 
 
 '^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 13. 
 
 until by reason of increasing H, it is finally ren- 
 dered wholly manifest. 
 
 LXXXV. Numerous observations have made 
 it probable that eyes which towards the age of 
 full growth have become emmetropic, have had, 
 in earlier life-time, a minor degree of hyper-
 
 56 ANOMALIES OF REFRACTION. 
 
 metropia. This is in conformance with the 
 observation that M constantly augments during 
 the years of development, 
 
 LXXXVI. Difficulties with regard to seeing 
 at close range arise sooner with H than they 
 do with E. This, however, is not Pr, but is 
 asthenopia. Pr is involved therewith, when, 
 through neutralization of H by the use of an 
 artificial convex lens, P has become >^ 22 cm. 
 
 LXXXVII. The lessening of the amplitude 
 of accommodation, with the increase of age, 
 takes place with great regularity. Favorable 
 exceptions do not exist here. Well may ^ 
 lessen too rapidly by reason of illness, but out 
 of many thousands of cases examined, I have 
 never seen any unusual continuance. He who, 
 in his forty-eighth year, under definitely deter- 
 mined conditions, does not need spectacles, 
 is, without suspecting it, more or less myopic 
 (sees distant objects more clearly through 
 slightly concave lenses). An unusual degree 
 of V may permit the possibility of a postpone- 
 ment for one or two years at the most. He 
 who, though possessing V = i, needs spectacles 
 for reading, writing, etc., before his forty-fifth 
 year, is generally more or less hypermetropic 
 (sees clearly at a distance through slightly con- 
 vex lenses).
 
 CONSEQUENCES OF M AND OF H. 57 
 
 6. CONSEQUENCES OF M AND OF H. 
 
 LXXXVIII. The results of a hiorh crrade of 
 M are: 
 
 [a) Diminution of V, which especially becomes 
 more marked with increase of years (compare 
 Paragraphs LXXII, LXXIII, and LXXIV) ; 
 
 [d) Restrained movement of the eyeball with 
 absolute or relative insufficiency (insufficient 
 action) of the internal straight eye-muscles ; 
 
 [c) Divergent strabismus. 
 
 LXXXIX. Easily mobile emmetropic eyes 
 can cause the visual lines to intersect on the 
 centre of the plane of the forehead at less than 
 5.50 centimeters from the eye, within an angle 
 of 80° or 70°. If the point of intersection, c, 
 lies farther away than seven centimeters from 
 the turning point of the eye, corresponding to 
 an angle of convergence of about 51°, then, 
 in a general way it may be assumed that there 
 is an insufficiency of the internal straight eye- 
 muscles. 
 
 XC. In M, even when ocular motion is un- 
 restrained, relative insufficiency is to be sup- 
 posed, the moment that it is found that r^ is 
 situated closer to the eye than c. This occurs 
 the more quickly since the position of the line 
 of vision in relation to the corneal axis, requires 
 - 5
 
 58 ANOMALIES OF REFRACTION. 
 
 a Stronger convergence of the axis of the cornea 
 so as to produce a proper convergence of the 
 visual Hues at a definite distance. Usually, 
 however, in addition, inward movements of eye- 
 balls that are found in high grades of M, are 
 absolutely restrained. 
 
 XCI. M as well as H are connected with 
 strabismus. The condition is present when bin- 
 ocular vision, by reason of deviation of the 
 visual lines, is suspended. Under such cir- 
 cumstances, the visual lines do not intersect at 
 the point on which the attention is fixed ; and, 
 in fact, on but one of the retinae has the image 
 of this point been placed in the fovea centralis 
 of the yellow spot. The other central spot re- 
 ceives an image from another point. 
 
 XCII. M is connected with divergoit strabis- 
 mus. The rule is, that in high grades of M this 
 variety of strabismus is relative, namely, that 
 while the visual lines are correctly directed for 
 seeing at a distance, i. e., they are parallel, the 
 maximum of convero-ence is insufficient for 
 binocular near-vision. 
 
 XCIII. In relative diverge7it strabismus, con- 
 vergence increases, close to its maximum, in 
 proportion as an object approaches the eye. 
 If the object remains at that distance, then the
 
 CONSEQUENCES OF M AND OF H. 59 
 
 one eye soon deviates to the temporal side ; 
 this taking place the moment that it is covered 
 by the hand. Nevertheless, if the hand is taken 
 away, the outward deviation generally remains, 
 showing that the strong convergence was pro- 
 duced simply by an effort to continue binocular 
 vision. 
 
 XCIV. The cause of relative divergent stra- 
 bismus rests alone in the opposed convergence. 
 The effort for cooperation of the retinae, that is 
 suspended in absolute strabismus, can here per- 
 sist uninterruptedly, 
 
 XCV. As one of the results of the highest 
 grades of M, the movement of the eye to the 
 temporal side may also be restrained. For near- 
 vision, there is a resultant relative divergent 
 strabismus ; for distant-vision, there is a relative 
 convergent strabismus ; while for intervening 
 points, binocular vision has a restricted use. 
 
 XCVI. Divergent strabismus is absolute when 
 binocular vision is not retained at any distance 
 whatever. In one hundred cases of absolute 
 divergent strabismus, M was found seventy 
 times in one or both eyes in comparatively high 
 degree. Statistics thus prove a relationship. 
 The relative divergent strabismus, that is char-
 
 6o ANOMALIES OF REFRACTION. 
 
 acteristic of M, teaches that the connection is a 
 causal one. 
 
 XCVII. If, therefore, the muscles are left 
 undisturbed, then, as a rule, strabismus develops. 
 A correct direction of the visual lines is only 
 gotten by an effort to see similar objects directly 
 with both eyes ; that is, to place the images of 
 the same object on both yellow spots. If one 
 eye is blind, it in most instances, deviates to the 
 temporal side. 
 
 XCVIII. Relative divergent strabismus pro- 
 duces dissimilar images on the two yellow spots 
 during near-vision : through this, the need of 
 similarity of images in general is diminished. 
 A commencing deviation, arising from increased 
 convero;ence, reaches at once a hiph deo^ree. 
 An exertion to converge is rather tedious be- 
 cause it brings with it an undue effort of ac- 
 commodation, and therefore causes r to come 
 nearer to the eye. Inaction and decreased 
 energy of the internal rectus muscles are the 
 results of this. Feeble . resistance against 
 double images and weakened power of the 
 internal straight muscles thus coincide. When, 
 during this condition, the action of these mus- 
 cles is inadequate for seeing at a distance, then 
 an absolute divergent strabismus is created. 
 This condition develops itself the sooner : a,
 
 CONSEQUENCES OF M AND OF H. 6i 
 
 because in the absence of proper V at a dis- 
 tance, double images are but slightly disturb- 
 ing ; b, by reason that when a parallelism of 
 the visual lines requires an effort of the inter- 
 nal recti muscles, any exertion of accommoda- 
 tion coincides with it, and reduces V for dis- 
 tance ; c, because the relationship existing be- 
 tween the visual axis and the line of vision in 
 myopes (compare Paragraph LVI) is not favor- 
 able for obtaining a parallelism of the visual 
 lines. 
 
 XCIX. By this means, a reason is offered 
 for the origin of the greater number of cases 
 of divergent strabismus. Cases comino^ into 
 existence separately from the influence of M, 
 are for the greater part the results of palsy or 
 blindness of one eye (compare Paragraph XC VI). 
 In injuries, contractures and complicated con- 
 genital anomalies, the cause is relatively seldom 
 to be found. 
 
 C. With E in one eye and M in the fellow, 
 and still more especially, with a low grade of 
 M in the one and a high one in the other, 
 divergent strabismus is the rule. Various 
 forms can here be differentiated. In a general 
 way, the interpretation of this rests in the facts 
 that, in part, with the dissimilarity in the clear- 
 ness and the size of the images, binocular
 
 62 ANOMALIES OF REFRACTION. 
 
 vision loses the greatest portion of its value; 
 and that conversely, the convergence, which is 
 already physically hindered, associates itself 
 with an exertion for accommodation, and thus 
 diminishes the visual acuity of the slightly 
 myopic eye for distance. 
 
 In this form of strabismus, especially, many 
 subjects are aware of the existent deviation, 
 and are capable of temporarily neutralizing it 
 at will, 
 
 CI. The results of H are asthenopia and 
 convergent strabismus. The former is a quite 
 ordinary symptom, while the latter is compara- 
 tively seldom seen. 
 
 CII. Asthenopia manifests itself as a fatigue- 
 symptom that soon appears after near-vision. 
 The eye is not apparently diseased, and it is not 
 painful, even when it is exerted. Visual acuity 
 and the ocular movements are both normal. 
 Distant V is considered perfect, but reading, 
 writing", etc., cause a sensation of tension over 
 the eyes. Objects become indistinct. The pa- 
 tient rubs the forehead, closes his eyes, and 
 recommences his work, only to sooner discon- 
 tinue than before. Rest relieves the ocular 
 fatigue, allowing a resumption of the work for 
 a period of time that is commensurate with the 
 amount of rest that has been taken.
 
 CONSEQUENCES OF M AND OF H. 63 
 
 CIII. Asthenopia has been confused with all 
 manner of anomalies and has been especially 
 sought for in the retina. By some it has been 
 looked for in the organs of accommodation and 
 by them has been ascribed to external condi- 
 tions and undue efforts of the eyes. 1 have 
 shown that asthenopia is not an accommodative 
 anomaly, but that it is one of refraction ; 
 namely, a definite degree of H. Excessive 
 action is consequently not the cause, but the 
 essential inordinate exertion presents difficul- 
 ties that expose the primarily existing anomaly. 
 
 CIV. The production of asthenopia from H is 
 easy to understand. Visual acuity for distance 
 requires an exertion of the accommodation to 
 neutralize H. Begun thus with a deficiency, 
 the accommodation soon evidences its ineffi- 
 ciency with increasing convergence. It is true, 
 the eye accustoms itself to accommodate rela- 
 tively very strongly with but slight convergence 
 (compare Paragraphs XXXVI and XXXVII), 
 but the positive part of ^ is for moderate con- 
 vergence very small in comparison with the 
 negative portion ; after slight fatigue it becomes 
 equal to O ; that is, p^ withdraws to the posi- 
 tion at which fine work has to be done. Should 
 the object be removed to a greater distance, 
 this chanae eives but a few moments' lono-er 
 relief, for while at this point, | is also almost
 
 64 ANOMALIES OF REFRACTION. 
 
 entirely negative, increasing fatigue makes p^ 
 follow closely to the greater distance. For/^, 
 all eyes are asthenopic, especially emmetropic 
 ones. 
 
 CV. The stronofer ^ is, the hiofher in orrade 
 can H be without producing asthenopia. 
 Whereas ^ decreases with increasing years, 
 asthenopia manifests itself so much the more 
 tardily as H is low in degree. In H0.75, 
 asthenopia is not to be found, or rather it 
 merges into Pr. 
 
 CVI. The symptoms of asthenopia and Pr 
 are unlike: Presbyopia entirely precludes acute 
 vision, for instance, at twenty centimeters, 
 but at a point that is somewhat farther re- 
 moved, for example at forty centimeters, not 
 even fatigue may be present ; asthenopia fre- 
 quently permits vision at a situation inside of 
 twenty centimeters, but vision at a greater dis- 
 tance, for example, forty centimeters, is soon 
 followed by fatigue. 
 
 CVII. To realize the difference between 
 asthenopia and Pr, consideration should be 
 given to the accompanying distinctive charac- 
 teristics : I. The loss of any fixed proportion 
 of ^ by fatigue has a more greatly increased 
 influence on P and P^ in young hypermetropic
 
 CONSEQUENCES OF M AND OF H. 65 
 
 subjects than it has in Pr, for the reason that in 
 the latter, -^ itself is much smaller. 2. At a 
 
 greater distance than p^, the positive part of ^ 
 increases in cases of Pr more quickly than it 
 does in asthenopia. 3. The lines pj, p^ and p, 
 and r, rj and r^, designate the change of the 
 dioptric system, and not the exercise of the 
 muscular apparatus, of which effort it may be 
 taken for granted that, especially in Pr, each 
 addition produces a proportionately lessened 
 change of the crystalline lens in direct relation 
 as the bulk of the lens approaches its maxi- 
 mum. The result of this is that the positive 
 part of ^, particularly in Pr, expressed as a 
 muscular effort, should be much greater than 
 the negative portion. 
 
 CVIII. The real result of our acquaintance- 
 ship with the origin of asthenopia, is that vari- 
 ous wearisome and troublesome kinds of treat- 
 ment, succeeded by an acknowledgment of 
 irremediability, have been abandoned for con- 
 vex lenses of sufficient streno-ths to render neu- 
 tral at least the manifest H, while each effort 
 to methodically accustom the eyes to increas- 
 ingly weaker lenses has been discontinued. 
 
 CIX. Convergent strabismus is, ordinarily, 
 dependent on H. The typical variety is de-
 
 66 ANOMALIES OF REFRACTION. 
 
 cidedly thus connected. It generally appears 
 from the fourth to the seventh years of age, and 
 at times later, without any complaint in regard 
 to double images, as a periodic monocular 
 squint. At first, most frequently noticed only 
 while gazing at near objects, followed later by 
 its appearance while fixing upon more distant 
 ones, it can be restrained in its development as 
 long as it remains inconstant by the use of con- 
 vex lenses. Soon, however, it passes into the 
 permanent variety with a constant deviation 
 that is generally confined to one and the same 
 eye (strabismus simplex). In this stage, there 
 is a shortening of the internal recti muscles, 
 additional motility inwards, and lessened motion 
 outwards in both eyes, this being associated with 
 a decreased acuity of direct vision in the devi- 
 ated eye as well as for indirect vision in the 
 visual field that has remained common to both 
 eyes. This lowering of V is gradually devel- 
 oped to such a degree that the deviated eye, 
 during closure of its fellow, fails to fix on an 
 object, but receives the image on a part of the 
 retina that is situated to the inner side of the 
 yellow spot, and thus actually distinguishes 
 the object better than by direct vision, i. e., by 
 the receipt of the image in the yellow spot. 
 
 ex. The relationship between H and con- 
 vergent strabismus is quite manifest : By
 
 CONSEQUENCES OF M AND OF H. 67 
 
 Stronger convergence, H can be more easily 
 overcome, and thus by an abandonment of 
 binocular vision, the subject is able to see more 
 sharply with one eye and to employ it more 
 constantly for near-vision. Herein lies the rea- 
 son why deviation at first occurs only during 
 fixation, and this at an age when keener obser- 
 vation begins. Further, while at the time of 
 deviation, attention is directed upon a specific 
 object, yet it is not odd that neither its double- 
 image nor the object which forms its image on 
 the yellow spot of the deviating eye, should 
 operate in a disturbing manner. 
 
 CXI, However natural it may be to thus ex- 
 plain convergent strabismus from a causative 
 H, yet the condition is by no means an essen- 
 tial result thereof. The number of hyperme- 
 tropes in whom strabismus is found is in reality 
 relatively small. Manifestly, the origin is, as a 
 rule, opposed by an inherent adherence to 
 binocular vision. 
 
 CXII. The conditions that promote the for- 
 mation of strabismus in H are of a twofold 
 character : a, those which decrease the im- 
 portance of binocular vision ; b, those which 
 make convergence easier. 
 
 CXIII. The usefulness of binocular vision is
 
 68 ANOMALIES OF REFRACTION. 
 
 decreased by diminished V in one eye, fre- 
 quently as a consequence of acquired corneal 
 spots ; often also inborn, and in this case, not 
 seldom dependent upon astigmatism. 
 
 CXIV. Convergence is rendered easier : i . 
 Absolutely, when the eyeballs offer but slight 
 resistance to movements to the nasal sides, and 
 the internal straight muscles possess an innate 
 preponderance or are readily controlled by 
 nerve influence; 2. relatively, when the line of 
 vision forms a particularly broad angle with the 
 axis of the cornea, and thus, for vision at a dis- 
 tance, a pronounced divergence of the axes of 
 the cornea is required. (Actually, I have found 
 the angle a greater in convergent strabismus 
 than in the ordinary examples of H without 
 squint.) 
 
 CXV. In developed convergent strabismus 
 in which there is an effort for near-vision, the 
 deviation is very slight, in spite of the fact that 
 exertion for convercjence is at this time un- 
 doubtedly much greater. Consequently, as 
 soon as strabismus is found to be present, a 
 definite amount of H does not so easily pro- 
 duce asthenopia. When by tenotomy, a proper 
 position has been gotten, convergent strabis- 
 mus often reappears from an exertion of ac- 
 commodation. Under these new conditions,
 
 REGULAR ASTIGMATISM. 69 
 
 the eyeball moves (sometimes arbitrarily) in- 
 wards under an impulse that as long as the de- 
 viation was present, gave but slight movement. 
 A return of the strabismus is, in such cases 
 only to be prevented by the employment of 
 convex lenses that neutralize the H. 
 
 CXVI. Convergent strabismus may, by way 
 of exception, depend upon a shortening of the 
 muscles caused by paralysis of the antagonist, 
 by wounds, and by contractures. It may be 
 congenital, principally as a portion of a com- 
 plicated anomaly. Lastly, it may be caused 
 by a subconjunctival inflammation which has 
 involved the muscle, this also in measure ex- 
 plaining the association between maculae of the 
 cornea and strabismus. 
 
 The essential points in tJie summmy obtained 
 are : Hypennetropia gives rise to an accommo- 
 dative asthenopia, ivhich can be counteracted by 
 an actively produced convergent strabismus. 
 
 Myopia leads to muscular asthenopia which 
 yields to a passively obtained divergent stra- 
 bismus. 
 
 7. REGULAR ASTIGMATISM. 
 
 CXVII. The focal distance of the dioptric 
 media of the eye is, In its various meridians, 
 not precisely alike {regular astigmatism. As).
 
 70 ANOMALIES OF REFRACTION. 
 
 If by disregarding the distance k' k" and h' h", 
 the dioptric system can be imaginarily reduced 
 to one refracting surface, then this practically 
 becomes the summit of an ellipsoid with three 
 axes. The longest one is the visual axis, while 
 the other two, which are perpendicular to one 
 another, are situated in a vertical plane. The 
 directions of the latter two are inconstant. 
 Usually, however, the one deviates but slightly 
 from the horizontal plane, while the other de- 
 viates but little from the vertical. In four-fifths 
 of the cases, the latter is the shorter. 
 
 The meridians extending through the visual 
 axis and one of the short axes, are known as 
 the chief meridians ; that of maximum of curv- 
 ature is expressed by ni, while that of minimum 
 of curvature is designated as m'. 
 
 CXVIII. Irregidar astigmatism may be 
 traced to two causes : a, the curvature of the 
 various meridians mutually differing, without 
 absolutely corresponding to those of an ellip- 
 soid with three axes ; b, monochromatic homo- 
 centric rays, refracted in one and the same 
 meridian, failinof to remain homocentric. 
 
 CXIX. Irregular astigmatism depends almost 
 always upon the crystalline lens, which is irreg- 
 ular in every respect. This may be inferred 
 from personal observations. It is, however.
 
 REGULAR ASTIGMATISM. 71 
 
 directly apparent from i. monocular polyopia; 
 2. the rays showing points of light, and 3. 
 the radiary lines of light seen in the entoptic 
 spectrum (Listing) — all of which disappear in 
 aphakia (want of the crystalline lens). All of 
 these appearances arise from the same causal 
 factor and bear a direct relationship to irregu- 
 lar astigmatism. 
 
 CXX. In aphakia, only a definite amount of 
 regular astigmatism remains, manifesting itself 
 by a pure linear extension of a point of light 
 in two opposite directions (limits of Sturm's 
 focal interval), the light at the centre of the 
 focal interval being seen as a round surface. 
 In nine cases of aphakia with V = i or V> i, 
 m was about seven times vertical in position 
 and but once absolutely horizontal, this being 
 proven by the direction of the boundary lines 
 of the focal space. These findings were proved 
 by measurements of the corneal radius in the 
 horizontal and the vertical meridians. 
 
 CXXI. The amount of regular astigmatism. 
 As, is noted by ^,, /' being the focal distance of a 
 cylindrical lens which, added to m ', should 
 make the focal distance in m ' equal to that of 
 m. I' is expressed in meters. 
 
 CXXII. All eyes are astigmatic. In ordinary
 
 72 ANOMALIES OF REFRACTION. 
 
 deofrees, this can be demonstrated in a well- 
 acknowledged manner. In very slight degrees, 
 and if there be much associated irregular A, 
 its recognition is more difficult. It, however, 
 can even then be made apparent by noting the 
 visual changes produced by rotating weak 
 cylindrical lenses (0.25 diopter cylinder or 0.50 
 diopter cylinder) before the eye, for by this 
 plan, the combined value of the astigmatism of 
 the lens and the eye is obtained in certain posi- 
 tions of the lens, while in the opposite position, 
 the difference between the two is grotten. 
 
 CXXIII. As < 0.75 diopters may be consid- 
 ered as normal; As. 0.75 diopters is abnor- 
 mal, because V in this condition is generally 
 lowered and the use of cylindrical lenses is 
 often of service. As of 6.00 diopters and 5.00 
 diopters is not rare. I have even seen As = 
 7,00 diopters. 
 
 CXXIV. The asymmetry just noted was dis- 
 covered by Thomas Young in his own eyes ; to 
 a very abnormal degree it was first taken cog- 
 nizance of by the astronomer Airy, he finding 
 it in his left eye, A few more instances have 
 been met with in Eng-land. Whewell crave 
 the condition the name '.astigmatism.' From 
 the Continent of Europe but a single instance 
 has been brought to our attention. This was
 
 REGULAR ASTIGMATISM. 73 
 
 described by a clergyman living in Switzerland 
 who determined its presence in his own eye. 
 These cases were improperly considered as 
 curiosities. It has appeared to me that out of 
 every thirty or forty eyes one is affected with 
 an abnormal decree of regular astig^matism. 
 To this type belong most of the cases of con- 
 genitally defective vision. 
 
 CXXV, Just as for normal astigmatism, so 
 likewise for the abnormal variety of the defect, 
 is its seat, almost without exception, to be 
 looked ior pinncipally in the cornea. This has 
 been made apparent by comparing the degree 
 of As with the variation in the radius of corneal 
 curvature in the vertical and the horizontal 
 meridians, or rather, approximatively in ;;/ and 
 m' . Only when the radius of curvature is 
 known in the principal corneal meridians, can 
 the positive and the negative portions of the 
 crystalline lens be exactly computed by com- 
 parison with the degree of As and with m and 
 m' of the entire dioptric system. 
 
 CXXVI. Recently I have found a method to 
 
 determine the principal corneal meridians and 
 
 their radii of curvature. The three lio-hts whose 
 
 reflectingr images, in imitation of Bessel's 
 
 method, were employed by Helmholtz for his 
 
 studies with the ophthalmometer, are made 
 6
 
 74 ANOMALIES OF REFRACTION. 
 
 movable in a vertical plane around a point lying 
 in the axis of the instrument which, during the 
 examination, is arranged so as to coincide with 
 the cornea. Without permitting any movement 
 of the head, the radii of curvature in every 
 meridian may accordingly be measured by rotat- 
 ing the lights, thus allowinof the maximum and 
 the minimum meridians to be determined. 
 
 CXXVII. Abnormal As. also corresponds 
 with the normal variety in this, that, as a rule, 
 ni approaches the vertical meridian, and m' the 
 horizontal one. In consequence, it is to be 
 considered as a hiQ^her decree of the same form 
 of asymmetry which is so characteristic of nor- 
 mal eyes. 
 
 CXXVIII. In order to ascertain the degree 
 of As in diminished V., we should commence 
 by endeavoring to determine the direction of 
 the principal meridians. This may be accom- 
 plished in two ways : i . From the directions of 
 the lines under which a point of light is seen at 
 the anterior and the posterior boundary of the 
 focal interval. (These directions are only inac- 
 curately indicated when there is relatively much 
 associated As.) 2. By rotating a cylindrical 
 lens that is approximately correct in front of 
 the eye, by which the minimum, and especially.
 
 REGULAR ASTIGMATISM. 75 
 
 the maximum degrees of V. can ordinarily be 
 determined with exactness. 
 
 CXXIX. If the direction of the principal 
 meridians is known, the most practical way is 
 to estimate R in each of them. 
 
 This is accomplished by means of a narrow 
 slit (by preference, a transparent strip situated 
 between two blackened small glass plates that 
 are turned toward one another). This is to be 
 rotated before the eye, first in the direction of 
 the one principal meridian, then in that of the 
 other. In these two meridians, the strongest 
 convex lens or the weakest concave one by 
 which the best distant visual acuity can be got- 
 ten, is to be employed. 
 
 CXXX, By this means, it is determined 
 whether E exists in one of the meridians, and 
 to what amount ametropia is present in one or 
 both of the meridians. The degree of As is 
 obtained at the same time by the difference 
 of refraction in the two meridians. 
 
 CXXXI. If E or H be present in one of the 
 meridians, it is well, so as to obtain a very 
 exact result, to previously paralyze the accom- 
 modation by means of atropine. Determina- 
 tions of As for/ by accommodation often pro- 
 duce variable results, because of the difference
 
 76 ANOMALIES OF REFRACTION. 
 
 of accommodative power of both meridians in 
 two successive examinations. As a rule, how- 
 ever, the same eye appears to retain about the 
 same deo-ree of As durincr different accommo- 
 dative conditions. 
 
 CXXXII. The astigmatic lens contrived by 
 Stokes to determine the degree of astigmatism, 
 allows, after correction of the astigmatism, the 
 continuance of ametropia. It therefore can- 
 not ordinarily be used to advantage unless 
 myopia in m and 7)1 ' (which is rarely so) be 
 present, in which case, it may be employed for 
 near reading-tests : It neither teaches (what 
 is also necessary to know) the amount of 
 ametropia in each of the principal meridians. 
 In connection with spherical lenses, Stokes' 
 method is, and ordinarily, cylindrical lenses are 
 also, very valuable as control-tests. 
 
 CXXXIII. The method of Airy, too, is 
 merely of value in myopia with astigmatism, 
 and in such cases in which there is but slight 
 associated irregular astigmatism, gives alone 
 fairly good answers. Modified for eyes that 
 are not myopic, the plan becomes less useful. 
 
 CXXXIV. As. may be separated into sev- 
 eral types : Myopic, iVm ; hypermetropic. Ah
 
 REGULAR ASTIGMATISM. 77 
 
 (which is by far the most frequent) ; and mixed 
 astigmatism, Ahm or Amh. Am is said to be 
 simple, when E exists in m ', and M on the 
 other hand is in ni. It is known as coiupoimd 
 when M exists in in ' as well as in iii, conse- 
 quently giving M + Am. Likewise, Ah is simple, 
 with E in in and H in in' . It is compound when 
 there is H in both m ' and in, this being ex- 
 pressed as H + Ah. In mixed As, H is asso- 
 ciated with m ', and M with in. If M is predomi- 
 natino- the condition is known as Amh ; if H is 
 predominant, the condition is designated by 
 Ahm. 
 
 CXXXV. As. is neutralized (although not 
 with mathematical exactness) by cylindrical 
 lenses. By this correction, V is bettered, and 
 even at times, it is doubled or quadrupled. 
 
 In order to obtain R = <» in in and in' (and 
 consequently, almost so in all meridians), are 
 required : 
 
 I. Simple cylindrical lenses : 
 
 {a) Positive ones, usually biconvex in char- 
 acter, with parallel axes of both cylinders. Such 
 lenses are expressed by =-c, in which, the focal 
 distance L is indicated In meters. They are 
 used for the correction of simple Ah. 
 
 {b) Negative ones, ordinarily biconcave in 
 type with parallel axes. These are designated
 
 78 ANOMALIES OF REFRACTION. 
 
 by — -c and are used for the correction of 
 simple Am. 
 
 2. Bicylindrical lenses, the one surface be- 
 ing concave and the other convex, with their 
 axes situated at riofht angles to one another : 
 :^cr— Y^c. They are employed for the correc- 
 tion of Amh and Ahm. 
 
 3. Sphero-cylindrical lenses, one surface be- 
 ing spherical and the other cylindrical. When 
 both surfaces are convex, then they are ex- 
 pressed as -^sc^C; when both are concave, 
 
 they are designated by — ^ s c — ~ C: compound 
 Ah and Am, — that is, in H + Ah and in M + Am. 
 When they are employed In such cases they 
 cause R to equal co. The M and H of these 
 compound refractive conditions are corrected 
 by the spherical surfaces, while the remaining 
 Ah and Am are neutralized respectively by the 
 convex and by the concave cylindrical surfaces. 
 The adaptation of the lenses for cases in 
 which it is desirable to bring R to a determinate 
 finite distance, is accomplished in accordance 
 with definitely known rules, this being mostly 
 done by alterations in the spherical surface. 
 
 CXXXVI. The symptoms of abnormal As. 
 are: i. Diminution of V (through a peculiar 
 deformity of the images of the retina) ; some- 
 times to as much as one-fifth of normal.
 
 REGULAR ASTIGMATISM. 79 
 
 2. Indifference to markedly dissimilar spheri- 
 cal lenses. 
 
 3. Broadened image of a point of light which 
 is elongated in two opposite directions, this 
 being obtained by holding different spherical 
 lenses before the eye. 
 
 4. P and R quite different for lines in two 
 opposite directions that correspond with in and 
 in'. 
 
 5. Estimation of measurements in the said 
 directions likewise variable, this being in meas- 
 ure due to a difference in the calculated size of 
 the retinal images by reason of accommodation 
 (because of the variability of position oi k" in m 
 and m'\ and partly on account of irradiation 
 from unstable and inexact accommodation. 
 
 6. V improved by gazing through a slit, es- 
 pecially when the positions of the slit are the 
 same as the angles of in or in' . 
 
 7. The appearance of two blue edges and two 
 vertically opposite red edges on an illuminated 
 square, when a violet glass is held in front of 
 the eye (this in consequence of achromatism). 
 
 CXXXVII. All these symptoms can be per- 
 sonally observed by holding a cylindrical lens 
 before the eye, thus producing a fairly regular 
 astigmatism. 
 
 CXXXVIII. By adequate study, As can be
 
 8o ANOMALIES OF REFRACTION. 
 
 determined objectively by a recognition of the 
 difference in the effort of accommodation made, 
 in order to sharply see ophthalmoscopically in 
 the perpendicular image, vessels of the retina 
 that are running off in an opposite direction. 
 In this way, I am even enabled to decide very 
 exactly in reference to the ametropia in two 
 opposite meridians, and in consequence, the 
 degree of As. The surface of the optic nerve 
 head appears elliptically distorted, when, as a 
 rule, it is round (Knapp). During examinations 
 with the upright and the inverted image, it will 
 be found that this distortion appears in oppo- 
 site directions, this difference of shape proving, 
 as confirmed by further examination, the ex- 
 istence of As (Schweigger). 
 
 CXXXIX. As. may also be recognized as 
 the result of corneal diseases, but in such cases, 
 it is usually associated with much irregular As. 
 The same is the case when, through partial 
 luxation, the crystalline lens attains an oblique 
 position. If a portion of the lens disappears 
 from the pupillary area, a high degree of irreg- 
 ular As. becomes one of the results.
 
 BIBLIOGRAPHY. 
 
 F. C. Donders — Nederlandsch Tijdschrift voor Geneeskiinde, 1858, 
 p. 465, and 1S63, V. 
 " Ametropie €71 Iiare gevolgen. Utrecht, i860. 
 
 " Archiv fur Ophthalmologie, iv, vi, vii, und viii. 
 
 " Verslageji en Mededeelinge7i van de Konmklijke 
 
 Akademie vatt Wetenschappe7i, xi, 159 ; xiv, 
 351 ; xvi, etc. 
 " Astigmatisme e7t cilindrische glazen. Utrecht, 1862. 
 
 (German edition, Schweigger, Berlin ; French 
 edition, Dor, Paris.) 
 De Ruijter — De Actioiie At7-op(V Belladon7i(E 171 iridem. Inaugural 
 
 Dissertation, 1854. [Nederhutdsch Lancet, iii.) 
 McGillavry — Over de hoegrootheid va7i het accominodatie-vermoge7i. 
 
 Utrecht, 1858. 
 A. H. Kuijper — O/idei-zoekiiige/t betrekkelijk de kimstiiiatige vet-wij- 
 
 ding van de7t oogappel. Utrecht, 1859. 
 H. de Brieder — De sfoor/iisse7t der accom7Hodaiie van het oog. Utrecht, 
 
 1861. 
 De Haas — Geschiedkimdig o7iderzoek onitre7it de hyper7)ietropie e7i hare 
 
 gevolge7i. Utrecht, 1862. 
 F. C. Donders and D. Doijer — De ligging van het draaipunt va7t 
 het oog (in emmetropische en ametropicische oogen), in Verslage7i 
 en Mededeeli7ige7i va/i de Ko7ii7iklijke Akade/iiie va7i Wetenschap- 
 pe7t, xiv, 1862, 351. 
 Dor — Des differe7ices individtiallcs de la refraction de rail. Journal 
 
 de Phvsiologie (Brown-Sequard). Paris, i860. 
 Not without connection with the subject, there also appeared: 
 H. Snellen — Letterproeve/i ter bepali7ig der gezigtsscheipte. Utrecht, 
 
 1862. 
 J. Vroesom de Hann — O7iderzoeki7ige7i 7iaar den i/ivloed va7i de7i 
 Iceftijd op de gesigtsscherpte. Inaugural Dissertation, Utrecht, 
 1862. 
 
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