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 REFRACTION OF THE EYE.
 
 / 
 
 / 
 
 / 
 
 / 
 
 REFRACTION OF THE EYE 
 
 ITS DIAGNOSIS 
 
 AND THE 
 
 ^ N 
 
 CORRECTION OF ITS ERRORS 
 
 ? 
 
 WITH CHAPTER ON 
 
 \f /^KERATOSCOPY 
 
 ± 
 
 o v 
 
 7 
 
 / ^A BY 
 
 \ A. STANFORD! MORTON, M.B., F.R.C.S. Ed. 
 
 SENIOR ASSISTANT SURGEON, ROYAL SOUTH LONDON OPHTHALMIC HOSPITAL | CLINICAL 
 ASSISTANT, MOORF1ELDS OPHTHALMIC HOSPITAL. 
 
 LONDON 
 H. K. LEWIS, 136 GOWER STJREET. 
 
 1 88 1
 
 LONDON 
 
 Printed by H. K. Lewis, 
 
 »36 GOWER-ST,, W.C.
 
 
 PREFACE. 
 
 These notes are published with a view of enabling Prac- 
 titioners to diagnose, and correctly estimate the value of, 
 the phenomena indicating the state of a patient's refraction. 
 They are intended to furnish a basis for observation : and 
 it is hoped that they will make evident the necessity which 
 exists for personally working out a large number of refrac- 
 tion cases in order to acquire anything like proficiency 
 in prescribing correct glasses. 
 
 To those friends who have aided me by their suggestions 
 I would take this opportunity of expressing my best thanks. 
 
 Welbeck Street, W. 
 March, 1881.
 
 TABLE OF CONTENTS. 
 
 PAGE 
 
 Introduction i 
 
 CHAPTER I. 
 
 Old and New Systems of Lenses — Table of Comparison . 3 
 
 CHAPTER II. 
 
 Action of Rays and Lenses .6 
 
 CHAPTER III. 
 
 Definitions . 8 
 
 CHAPTER IV. 
 
 Accommodation . .12 
 
 CHAPTER V. 
 
 Conditions necessary for clear perception of a line . . . -14 
 
 CHAPTER VI. 
 
 Description of Test-types — Mode of use ... iG 
 
 CHAPTER VII. 
 
 Indications afforded by use of Test-types 18 
 
 CHAPTER VIII. 
 
 Indications afforded by Mirror alone — Movements of Image of 
 disc in Emmetropia, Myopia, Hypermetropia and Astigmatism 
 —Explanation of same 20
 
 Vlll CONTENTS. 
 
 PAGE 
 
 CHAPTER IX. 
 
 Indications afforded by Mirror alone — Movements of Image of 
 
 Light and shadow on Retina— Keratoscopy (Retinoscopy) . 27 
 
 CHAPTER X. 
 
 Indications afforded by Mirror and Lens— Change in size of Image 
 of disc in Emmetropia, Myopia, Hypermetropia and Astigma- 
 tism — Explanation • • • 35 
 
 CHAPTER XI. 
 
 Estimation of Refraction by Ophthalmoscope— Condition of Ob- 
 server's own Refraction— Tabular view of different States of 
 Refraction 4° 
 
 CHAPTER XII. 
 
 Test-types and glasses— Prescribing Spectacles in Hypermetropia 
 —Myopia— Astigmatism — Presbyopia — Table of glasses for 
 Presbyopia — Aphakia 45 
 
 CHAPTER XIII. 
 
 Action of Atropine— Calculation for same— Conclusion . . 54
 
 REFRACTION OF THE EYE. 
 
 INTRODUCTION. 
 
 These pages are intended for beginners, and for those, 
 such as Physicians or general Practitioners, who, systemati- 
 cally using the Ophthalmoscope in their investigation of 
 disease, wish to avail themselves of the information thereby 
 afforded regarding the patient's refraction, the errors of 
 which they must be able to detect in order to make due 
 allowance for them. If the patient can assist by his 
 answers, many valuable indications are afforded by the use 
 of test-types and glasses, a description of which, with the 
 information derived therefrom, is therefore introduced. 
 
 Some hints are given as to glasses required in the more 
 ordinary cases, but for the various diseases which accom- 
 pany and complicate many of the errors of refraction and 
 modify the ordering of spectacles, the reader is referred to 
 the works already published on this subject, to the study 
 of which these notes are intended to prepare the way. 
 
 So essential is the remembrance of some of the facts 
 hereafter mentioned, that, at the risk of tautology, they 
 have been kept constantly before the reader. The plan 
 which has been found so useful in other branches of medi- 
 cal study has been adopted here, viz. to work out from the 
 
 B
 
 2 REFRACTION OF THE EYE. 
 
 symptoms the nature of the defect rather than to name the 
 defect and then describe the symptoms accompanying it. 
 
 In examining- refraction it is especially necessary to pro- 
 ceed systematically. On a patient complaining - of bad sight 
 we should examine him somewhat in the following man- 
 ner : — 
 
 i. Listen carefully to the nature of his complaint. 
 
 2. Test and note the near and distant vision without 
 glasses. 
 
 3. Examine the refraction with the ophthalmoscope, 
 and then, having by these means arrived at a conclusion, 
 proceed to confirm the opinion by means of test-glasses. 
 
 Two methods of measuring refraction are at present in 
 vogue (vide Chap. i.). The new system of numeration is 
 the one which has been adopted in the text. The approxi- 
 mately corresponding measurements in English inches have, 
 however, in all cases been given in brackets for the con- 
 venience of those who prefer the old method. 
 
 Only so much ophthalmoscopy has been introduced as 
 was necessary to explain the phenomena of refraction.
 
 SYSTEMS OF MEASUREMENT. 3 
 
 CHAPTER I. 
 
 Old and New Systems of Measurements.* 
 
 In the old system the lenses were numbered according - to 
 their focal lengths in inches. Their refracting power, being 
 the reverse of their focal lengths, was represented by a 
 fraction, of which the numerator was I and the denomina- 
 tor was the focal length in inches. Thus, a lens of 6 ins. 
 
 focus had a refracting power of \, i.e. \ the refracting 
 
 f i S 
 power of a lens whose focal length was i in. — r— : this 
 v s 1 1 in. J 
 
 latter was therefore the unit of measuremet. 
 
 The intervals between the lenses were irregular and the 
 difference between the refracting powers of any two lenses 
 had to be calculated by means of fractions. 
 
 In the new or Dioptric system the unit of measurement is 
 a lens whose focal length = i metre or Dioptre ' 
 
 with a refracting power consequently = Two such 
 
 2 
 
 lenses have double the refracting power or = 2 D. 
 
 with a focal length or — - = 50 cm. Ten 
 
 such lenses have ten times the refracting power = 
 
 I m. 
 
 10 D. and a focal length - 
 
 1 m. 100 cm. 
 
 10 
 
 = 10 cm. 
 
 + Vide Roy. L. Ophth. Hosp. Reports, vol. viii., p. 632, translation of 
 an article by Dr. Landolt from which much in this chapter has been 
 borrowed. 
 
 B2
 
 4 REFRACTION OF THE EYE. 
 
 If we express the number of dioptres'by d. and the focal 
 length by F. then (i) To find the number of dioptres which 
 correspond to the focal length of a lens we have the for- 
 mula d = ——-, and (ii) For the focal length correspond- 
 
 ing to any dioptre the formula F. = — . 
 
 d 
 
 In order to ascertain the corresponding numbers in the 
 two systems for any lens, we must remember that I dioptre 
 (or metre) =37 Paris inches and (39.4 or nearly) 40 English 
 inches and that, therefore, the lens with 1 D. focal length 
 corresponds to the lens in the old series whose focal length 
 is 40 in. Qg-) : 2 D. to a lens with double this refracting 
 power or -^ = JL of the old. 
 
 Where d. then represents the number of dioptres and a. 
 the number of inches, if we wish (i) to ascertain what lens 
 in the old series corresponds to one of the new, we have 
 
 the formula — = -. (ii) For the number of a lens in the 
 
 40 a v ' 
 
 new system corresponding to one in the old we have, 
 
 a 
 The old system of lenses in the trial cases, generally 
 
 in use, have their focal lengths in inches, and do not cor- 
 respond exactly with the measurements in dioptres. The 
 following table gives the lens which, in an ordinary French 
 or English case, will correspond most nearly with any 
 dioptre. 
 
 For greater accuracy in any special case, the reader 
 must calculate according to the formulae given above.
 
 SYSTEMS OF MEASUREMENT. 
 
 Table. 
 
 D. 
 
 Focus in 
 English 
 inches. 
 
 Focus in 
 Paris inches. 
 
 D. 
 
 Focus in 
 English 
 inches. 
 
 Focus in 
 Paris inches. 
 
 0-25 
 
 l60 
 
 144 
 
 5-o 
 
 8 
 
 7 
 
 0-50 
 
 80 
 
 72 
 
 5-50 
 
 l\ 
 
 61 
 
 0'7S 
 
 50 
 
 So 
 
 6-o 
 
 7 
 
 6 
 
 I'O 
 
 40 
 
 36 
 
 7-0 
 
 6 
 
 5 
 
 1-25 
 
 30 
 
 30 
 
 8-o 
 
 5 
 
 4 
 
 1-50 
 
 24 
 
 24 
 
 9-0 
 
 4l 
 
 4 
 
 17s 
 
 22 
 
 20 
 
 io-o 
 
 4 
 
 6-t 
 
 20 
 
 20 
 
 18 
 
 I I'O 
 
 ?l 
 
 6-2 
 
 2'25 
 
 18 
 
 16 
 
 12-0 
 
 ^1 
 
 3 
 
 2-SO 
 
 16 
 
 H 
 
 I3-0 
 
 3 
 
 2^ 
 ^4 
 
 275 
 
 H 
 
 13 
 
 I4-0 
 
 2^- 
 
 ^4 
 
 2l 
 
 3'0 
 
 12 
 
 12 
 
 IS-O 
 
 2^ 
 
 ^4 
 
 2l 
 
 ^2 
 
 350 
 
 I I 
 
 10 
 
 l6o 
 
 a* 
 
 2l 
 z 4 
 
 4-0 
 
 IO 
 
 9 
 
 i8-o 
 
 2| 
 
 2 
 
 4-SO 
 
 9 
 
 8 
 
 20'0 
 
 2 
 
 l 4
 
 REFRACTION OF THE EVE. 
 
 CHAPTER IT. 
 
 Action of Rays and Lenses. 
 
 a. Rays of light issuing - from every point of any object 
 diverge in all directions. The nearer an eye is to such an 
 object the more of its diverging rays does it intercept, and 
 vice versa, the further the eye is removed, the fewer are the 
 divergent rays which reach it : i.e., the more parallel are 
 the rays which enter it. Only from objects at an infinite 
 distance dow e thoretically get absolute parallelism of the 
 rays. 
 
 For practical purposes, however, we may consider those 
 parallel which reach the eye from an object situated at a 
 distance of 6 metres (20 ft.) or more. 
 
 Fig. 1. 
 
 b. Parallel rays (Fig. I., Aa, Bb), falling on a convex 
 spherical lens come to a focus at a point, F, on the other 
 side of the lens called the "principal focus." Conversely, 
 rays from a point at the principal focus of the lens emerge 
 parallel.
 
 ACTION OF RAYS AND LENSES. 7 
 
 c. Diverging rays (Fig-. I., Ma, Mb) meeting- such a lens 
 unite at a point, K, which is behind the principal focus. 
 Conversely, rays from a point further from the lens than 
 its principal focus emerge as convergent rays. 
 
 d. Converging rays (Fig. I., Ca, Cb) falling on a convex 
 lens meet at a point, H, nearer the lens than its principal 
 focus. Conversely, rays from a point within the principal 
 focus are, on emerging from the lens, still divergent, 
 though less so than before meeting it. 
 
 e. Parallel rays (Fig. 2., Aa, JBb) falling on a concave 
 spherical lens acquire a divergence (aC, bC) as if pro- 
 ceeding from a point, F, on the same side of the lens as that 
 from which the parallel rays proceed. The distance of 
 this point from the lens gives the negative focal length of 
 the lens. Conversely, rays with a convergence as if pro- 
 ceeding to this point are rendered parallel. 
 
 /. A cylindrical lens acts according to the same rules 
 as a spherical, but only in a direction at right angles to its 
 axis.
 
 8 REFRACTION OF THE EYE. 
 
 CHAPTER III. 
 
 Definitions. 
 
 Def. i . The refracting surfaces of the eye are, according 
 to Donders — a, the anterior surface of the cornea ; b, the 
 anterior surface of the lens; c, the anterior surface of the 
 vitreous. The transparent media together form the "diop- 
 tric system" of the eye, which has an action similar to that 
 of a biconvex lens. 
 
 Def. 2. "Refraction of the eye" means the effect which, by 
 reason of its form and structure, this organ exerts upon 
 rays of light entering it when completely at rest. 
 
 Fig. 3. 
 
 •A 
 B 
 
 Def. 3. In emmetropia (Fig. 3) parallel rays, Aa, Bb, come 
 to a focus upon the retina, F, when the eye is at rest. Con- 
 versely, rays from the retina emerge parallel from the eye. 
 
 Fig. 4.
 
 DEFINITIONS. 9 
 
 Def. 4. A myopic eye (Fig - . 4) is that in which, when at 
 rest, parallel rays come to a focus in fro?it of the retina, as 
 at F. Conversely, rays issuing- from the retina, R, which 
 is behind the focus of the dioptric system, emerge as con- 
 vergent rays (Chap, ii., c) which meet at a point, M in 
 front of the eye. Further, it is evident that rays from this 
 point (called the "far point") would meet upon the retina. 
 
 Fig. 5. 
 
 -A 
 
 -B 
 
 Def. 5. A hypermetropic eye (Fig. 5) is that in which, 
 when at rest, parallel rays, (Aa, Bb,) come to a focus at F, 
 behind the retina. Consequently, rays issuing from the 
 retina, R, which is within the focus of the dioptric system, 
 emerge from the eye as divergently, (aC, bC), as if pro- 
 ceeding from F. Further, rays with a convergence as if 
 proceeding to F, would unite upon the retina. 
 
 Note. — The distance of this point, F, behind the cornea will, 
 in any case, be equal to the focal length of the convex lens, 
 which, when held close to the eye with its acco??imodation sus- 
 pended, brings pat all el rays to a focus on the retina. It is evident 
 that the same lens will, conversely, render parallel those 
 rays which proceed from the retina. And since a convex 
 lens renders parallel the rays which issue from its principal 
 focus (Chap, ii., b) it follows that the rays which emerge
 
 IO REFRACTION OF THE EYE. 
 
 from the eye must have a divergence as if proceeding- from 
 this point. 
 
 Def. 6. A regularly astigmatic eye is that in which there 
 is a difference of refraction in different meridians : the two 
 principal meridians being always at right angles to each 
 other. 
 
 Astigmatism may exist in five different forms. 
 
 a. Simple myopic = one meridian emmetropic the 
 other myopic. 
 
 b. Simple hypermetropic = one meridian emmetro- 
 pic the other hypermetropic. 
 
 c. Compound myopic = both meridians myopic, one 
 more than the other. 
 
 d. Compound hypermetropic = both meridians hy- 
 permetropic one more than the other. 
 
 e. Mixed = one meridian myopic, the other hyper- 
 metropic. 
 
 Def. 7. An Irregularly Astigmatic eye is one in which 
 there are different degrees of refraction in different parts 
 of the various meridians. 
 
 Def. 8. A Presbyopic eye is that in which, owing to 
 physiological changes, produced by advancing age, there 
 is an inability to define small objects nearer to the eye 
 than 22 cm. or about 9 English inches, {vide Presbyopia 
 chap. xii.). It may exist with any of the above named 
 conditions. 
 
 From what has been stated in this and the preceding 
 chapter we may get the following,
 
 DEFINITIONS. II 
 
 Deductions. 
 
 Deduction I. That for parallel rays to be brought to a 
 focus on the retina of a myope, they must have given to 
 them a divergence as if proceeding from the " far point" 
 {vide def. 4). This is effected by the concave lens whose 
 negative focal length equals the distance of this point, 
 (chap. ii. e.) 
 
 Deduction 2. That to bring parallel rays to a focus on the 
 retina of a hypermetropic eye at rest, we require a convex 
 lens such that it gives to parallel rays a convergence as if 
 proceeding to the point behind the eye from which rays 
 appear to issue, (p. 9, fig. 5, F.) 
 
 Deduction 3. That in a regularly astigmatic eye the two 
 principal meridians must be corrected by means of cylindri- 
 cal lenses or a combination of these with sphericals.
 
 12 REFRACTION OF THE EYE. 
 
 CHAPTER IV. 
 Accommodation. 
 
 Def. 9. By accom?nodation of the eye is meant the power which, 
 by muscular aid, that organ possesses in itself of bringing to 
 a focus on its retina rays proceeding from objects situated at 
 various distances. These distances range between the "far 
 point," for rays from which the eye is adjusted when not 
 using any of its accommodation, and the " near point for rays 
 from which the whole of the accommodative power is called 
 into activity. The amount of accommodation thus exer- 
 cised by an eye in passing - from the former to the latter of 
 these conditions is called the Range or Amplitude (Donders) 
 of accommodation. This amplitude may be represented 
 by the convex lens which, with completely suspended accom- 
 modation, would bring rays from the near point to a focus 
 on the retina. 
 
 A lens whose focal length equals the distance of the near point, 
 will, when placed close to an eye, render parallel the rays 
 entering that organ from its near point. 
 
 Since in an emmetropic eye at rest, parallel rays come to a 
 focus on the retina, (definition 3), such a lens represents in 
 emmetropia the amplitude of accommodation. 
 
 But in a hypermetropic eye at rest parallel rays do not come 
 to a focus on the retina without the aid of a convex lens, 
 (deduction 2, chap. iii). To get the amplitude of accom-
 
 ACCOMMODATION. 13 
 
 modation the strength of the lens thus necessary for parallel 
 rays must therefore be added to that whose focal length 
 equals the distance of the near point. 
 
 And in Myopia, since a concave lens is necessary for 
 parallel rays (chap, iii deduction i.) it is evident that for 
 the amplitude of accommodation, the strength of the lens 
 requisite to bring parallel rays to a focus on the retina 
 must be deducted from that whose focal length equals the 
 distance of the near point. 
 
 e.g. Let us suppose three eyes, a. emmetropic, b. hyper- 
 metropic 2 D (Jq), c. myopic 2 D {£$), each having a near 
 point of 10 cm. (4 inches). The amplitude of accommo- 
 dation will be represented for a. by the lens whose focal 
 length = 10 cm. (4 inches) viz. 10 D (1) ; for b. by the 
 same lens added to that which corrects the hypermetropia, 
 viz. 10 D + 2 D = 12 D (1 + J"o = 3) > an d for c. by the 
 same lens from which is deducted the one that neutralises 
 the myopia, viz. 10 D — 2 D = 8 D (l — J& = i)- 
 
 From these examples we see that with the same near point, 
 the amplitude is greater in hypermetropia and less in myopia 
 than in emmetropia, and it will be evident that with the 
 same amplitude the near point is further from the eye in hy- 
 permetropia and closer to it in myopia, than in emmetro- 
 pia. As age advances the near point recedes further from 
 the eye so that in presbyopia there is absolutely less amplitude 
 for any given eye. If the near point recedes until it 
 reaches the far point, the accommodation becomes nil.
 
 14 REFRACTION OF THE EYE. 
 
 CHAPTER V. 
 
 Perception of a Line. 
 
 The distinctness with which a line is visible depends upon 
 the sharp and well-defined perception of its mat gins ; if 
 these are indistinct the line app>ears hazy. A line may be 
 taken as made up of an infinite number of elements or 
 points, from each of which rays issue in all directions. To 
 gain a distinct image of any line, it is necessary that the 
 rays from these points, which emerge in planes at right 
 angles to its long axis, should be brought to a focus at 
 points on corresponding planes of the retina, otherwise 
 circles of diffusion are formed in this transverse direction 
 of the line, which overlap each other, and finally, by pro- 
 jecting beyond its margins, give to it an ill-defined and 
 blurrred outline, so that no distinct perception of- it is 
 obtained. If, from these same points the rays, emerging 
 in planes parallel to the long axis overlap each other, it is 
 only at the two extremities of the line that, by projecting, 
 they cause any blurring. The margins of the line, thus not 
 being in any way affected, there is no interference with the 
 outline, and a clear image is formed on the retina. 
 
 If then, a patient with his accommodation suspended, 
 and who is emmetropic in one meridian, and myopic or 
 hypermetropic in the other, be placed at 6 m. (20 ft.) from 
 radiating lines of equal definition, he will see most dis-
 
 PERCEPTION OF A LINE. 15 
 
 tinctly that line which runs at right angles to his emmetropic 
 meridian. Rays from points in the transverse planes of this 
 line will, by passing - through the emmetropic meridian, 
 come to a focus on his retina giving a distinct, well-defined 
 image of the margins, and hence a clear perception of the 
 line. The line parallel to the emmetropic meridian will, at 
 the same time, be the most z>zdistinct. Rays from its trans- 
 verse planes pass through the myopic or hypermetropic 
 meridian. They thus come to a focus, in the former case, 
 in front of, and in the latter behind, the retina producing 
 circles of diffusion in these planes, and a consequent blur- 
 ing of the margins of the line, so that no distinct image is 
 obtained. 
 
 Rule I. — We have then the rule that in simple astigma- 
 tism, the patient, at 6 m. (20 ft.) sees, most distinctly, the 
 line parallel to the plane of his error of refraction. 
 
 It follows also, that a patient with either compound or 
 mixed astigmatism, will not see any line distinctly at 6 m. 
 with his accommodation suspended.
 
 l6 REFRACTION OF THE EYE. 
 
 CHAPTER VI. 
 Description of Test-Types : Method of Employing Them. 
 
 Test-types are divided into — a. Those for neat vision, and 
 b, those for distant vision. In using them we are obviously 
 dependent on the answers given by the patient. For 
 children, illiterate adults, and impostors, they are there- 
 fore inferior to the ophthalmoscope as a means of dia- 
 gnosing- and estimating refraction. 
 
 a. Test-Types for Near Vision. 
 
 Those generally in use for this purpose are Jaeger's or 
 Snellen's. The latter are so graduated that each should 
 be read as far off as the distance for which it is marked. 
 The smallest should be seen as far off as 50 cm. (i-| ft.) 
 and the largest at 4 m. (12 ft.). These types are given 
 into the patient's hand, and we then note the smallest he can 
 read and the nearest and farthest points at which it is dis- 
 tinctly visible. The small types are chiefly useful in test- 
 ing the accommodation, but they also afford an indication 
 of the presence and amount of myopia [vide Chap, xii., 
 Myopia). 
 
 b. Test-Types for Distant Vision. 
 
 Snellen's types for this purpose are so graduated that 
 each should be distinctly legible as far off as the distance
 
 TEST-TYPES. 17 
 
 for which it is marked. The largest should be seen at 
 60 metres, and each succeeding line at 36, 24, 18, 12, 9 and 
 6 metres respectively (200 ft., 100, 70, 50, 40, 30, and 20). 
 
 In testing with these types, we so place the patient that 
 rays issuing from them reach the eye as parallel rays. 
 F or practical purposes this is obtained at a distance of 6 m. 
 (20 ft.) {vide Chap, ii., a.) from which point the lowest line 
 should be read by the normal eye without accommodation. 
 For testing astigmatism, we have a fan of radiating lines, 
 all of the same magnitude and definition. These should 
 appear all equally distinct to the normal eye at 6 m. In 
 noting the vision (= V.) we employ a fraction whose 
 numerator denotes the distance at which the patient stands, 
 and whose denominator indicates the lowest line which he can 
 read. The number of the line is designated by the dis- 
 tance in metres or feet, at which it should be legible. Thus 
 normal V. = % (fg) or 1 ; but if at 6 m. (20 ft.) the patient 
 read only the line which should be read as far off as 12 m. 
 (40 ft.) we say V. = T % (fg) or i Seeing that our object 
 in testing refraction is always to have the accommodation 
 suspended, we never place the patient nearer the types 
 than 6 m. Should it be necessary, however, in defective V. 
 from other causes, we may allow him to approach the types 
 till he can read the largest; if this be at a distance of say 
 2 m. (6 ft.) then V. = ¥ 2 o (^o)-
 
 l8 REFRACTION OF THE EYE. 
 
 CHAPTER VII. 
 Indications afforded by use of Test-types. 
 
 Note. — In the following section the patient, is tested 
 without glasses, then : — 
 
 Indication i. If a patient read Jaeger i (= J. i) or Snellen 
 I = (Sn. i) with a good range, and read also f (-§{}) per- 
 fectly he is probably emmetropic. He cannot be myopic 
 though he may be hypermetropic : for a hypermetropic 
 patient with active accommodation could do this. 
 
 Indication 2. If a patient over 40 years of age read only 
 the larger J. or Sn. types {ox perhaps even the smaller) but 
 only on condition that he holds them at a considerable distance : 
 while at the same time he can read f (§£) perfectly, he is 
 simply presbyopic. 
 
 Indication 3. If a patient must hold the types close to his 
 eye but can then read even the Jznest though he cannot see 
 
 <n? (A°o) he is myopic. 
 
 Note. — A patient may read Sn. 1 as far as 50 cm. (No. 
 1 Sn. to \\ ft.) or even Sn. 2 as far as 60 cm. (No. 2. Sn. 
 to 2 ft.) together with some of the larger distance types 
 such as ¥ 6 g- ( T 2 o%)' I n this case he is very slightly ??iyopic. 
 N.B. Since such a patient can read Sn. I ttp to within a short 
 distance f?Vfn his eye he is thus easily distinguished from the 
 following. 
 
 Indication 4. If a patient read only the larger series of
 
 USE OF TEST-TYPES. 19 
 
 the small types, and the smaller series not at all, or only 
 very imperfectly : while at the same time the distant vision 
 is very defective, we suspect either some form of astigma- 
 tism or hypermeti opia without accommodation. 
 
 In a patient under 40 years of age it is probably the former, 
 but in one over that age it may be either, though it is fre- 
 quently only the latter condition which exists. 
 
 Indication 5. If a patient under 40 or 45 can read only 
 such large types as Sn. for 4 m. (J. 16) while he can read 
 f (to) ne has paralysis of accommodation. This may be proved 
 by giving him a strong convex lens such as + 3 D. (+ 12 
 in.) when he will read Sn. 1, or J. 1, at the focal distance 
 of the lens. ( Vide Accommodation, chap, iv.) 
 
 Indication 6. If a patient, whose accommodation is sus- 
 pended, see, quite distinctly, one only of the radiating lines at 
 6 m. he is emmetropic only in the meridian at right angles to 
 this line, and either hypermetropic or myopic in the other. 
 ( Vide chap, v.) 
 
 C2
 
 20 REFRACTION OF THE EYE. 
 
 CHAPTER VIII. 
 
 Indications afforded by means of Mirror alone. "Direct 
 
 Method." 
 
 In order that the following- indications of the refraction 
 afforded by this method may be realised, the observer, if 
 he be not emmetropic, must correct any error of his own 
 refraction by means of spectacles or a lens behind the sight 
 hole of the mirror. He should then seat himself opposite, 
 and 3 or 4 feet away from, the patient who is to gaze 
 steadily at the darkened wall in front of him, looking 
 towards the left side ot observer's head when the left eye 
 is under examination and vice versa. By this means the 
 position of the optic disc is brought into the axis of vision 
 of the observer. The latter must now throw the light from 
 his mirror into the patient's eye, and, keeping the fundus 
 illuminated, should move his head in various directions. 
 
 Indication I. If he then get nothing more than the red 
 reflex of the fundus or at most a blurred image of the disc, 
 the eye is emmetiopic or very slightly myopic. ( Vide ex- 
 planation, page 22.) 
 
 Indication 2. If he see the image of the disc and its 
 vessels moving in the same direction as his own head, the 
 patient is hypermetropic. ( Vide p. 23.) 
 
 Indication 3. If the vessels in one meridian only are visible, 
 and these move in the same direction as the observer's head
 
 INDICATIONS BY MIRROR EXPLANATIONS. 21 
 
 there is hypermetropia in one meridian only, viz., in that which 
 is at right angles to the one in which the vessels are visible. 
 (Vide explanation, p. 25, and compare with Chap. v.). 
 = Simple hypermetropic astigmatism. 
 
 Indication 4. If the disc and vessels move in the opposite 
 direction to that of the observer's head, the eye is myopic. 
 ( Vide p. 24). 
 
 Indication 5. If the vessels are seen in one meridian only 
 and moving in the opposite direction to the observer, there 
 is myopia in the meridian at right angles to that in which the 
 vessels are visible. ( Vide p. 25, and chap. v.). = Simple 
 myopic astigmatisrn. 
 
 Indication 6. If the vessels are seen moving- in one di- 
 rection in one meridian, and in the opposite direction in 
 the other meridian according to the accommodation of the 
 observer, and his distance from the patient, there is mixed 
 astigmatism. This condition is, however, not easy of detec- 
 tion by the mirror alone. 
 
 Indication 7. If instead of the vessels of the disc moving 
 evenly and regularly, they move slowly across the centre 
 of the pupil, but rapidly and irregularly towards the peri- 
 phery, giving the appearance of rotating bent spokes of a 
 wheel, the patient has irregular astigmatism. 
 
 Explanations. 
 
 The above mentioned indications may be explained in 
 the following manner. 
 
 Of all the rays, {vide figs. 6 and 7,) which diverge 
 from any single point, a or b, of the fundus one only,
 
 22 
 
 REFRACTION OF THE EYE. 
 
 o' or o, passes without deflectio7i 
 through the centre of the crysta- 
 lline lens. As many of the re- 
 mainder as the size of the pupil 
 will allow pass out in a cone of 
 rays having- a certain relation, 
 according- to the refraction, to the 
 ray just mentioned. In order to 
 get a view of any part of the 
 fundus it is necessary that rays 
 from both extremities of such por- 
 tion should come to a focus on 
 the observer's retina. 
 
 In e??unelropia, Fig. 6, the rays 
 which issue from the extremities 
 a and b of the disc, emerge as 
 two cylinders (i and 2) of parallel 
 rays taking the same direction re- 
 spectively as those o' and o which 
 from the two extremities a and b 
 pass through the centre of the lens. 
 There are thus parallel rays in two 
 
 |p 
 
 Fig. 6. 
 
 cylinders, one from either extremity of the disc, emerging 
 from the pupil and soon diverging from each other. They 
 thus leave between them an area x in which there are no rays 
 from these two points. If the observer's eye be situated in this 
 space it is evident that he cannot get an image of the whole 
 disc. He will however receive parallel rays from some lumin- 
 ous point of the disc: or even cylinders from two very conligu-
 
 INDICATIONS BY MIRROR EXPLANATIONS. 23 
 
 ous points may run so closely together that on entering the 
 observer's eye they might theoretically form an image of the 
 space between them. Practically however such an image is 
 rarely, if ever, obtained because the absolute suspension of 
 accommodation necessary for its production is scarcely to 
 be met with. We may therefore assume that for practical 
 purposes no details of the fundus are visible with the mirror 
 alone at some distance, and that therefore in eni7netropia the 
 image of the disc is blurred. 
 
 In hypermetropia, Fig. 6, the rays issuing from the ex- 
 tremities a. b. Jf the disc emerge from the pupil as two 
 cones (3 and 4) of rays which appear as if diverging from 
 points b. x b ± situated behind the eye on prolongations 
 backwards of the rays o' and o respectively which from 
 a and b pass through the centre of the lens. By the union 
 of the rays thus prolonged back we get an erect image 
 a 1 b x of the disc a b. (For the distance of this image be- 
 hind the eye, vide chap. iii. note to definition 5). 
 
 The cones 3 and 4 being formed of diverging rays, 
 separate from each other only at a considerable distance 
 from the eye. Some of the rays from each extremity of 
 the disc, or at any rate those from two fairly distant 
 portions of the same, will enter the observer's pupil, and, 
 with the exercise of sufficient accommodation to overcome 
 their divergence, will meet on his retina. 
 
 An object may be supposed as situated at the points 
 whence appear to issue the rays entering the eye. The 
 object therefore which the observer here appears to see is 
 the erect image of the disc. Since the object thus apparently
 
 24 
 
 REFRACTION OF THE EYE. 
 
 seen is further from the observer than the pupil, with which 
 it is, though perhaps unconsciously, compared, it seems to 
 move in the same direction as the observer's head, {vide 
 explanation, p. 25). 
 
 In mjopia, fig. 7, the rays issuing from the extremities, 
 
 a. b. of the disc, emerge as two 
 cones of rays which converge to 
 points, a b' on their secondary 
 axis, o' O, respectively, thus form- 
 ing in front of the eye an inverted 
 aerial image of the disc. If the 
 observer be nearer the eye than 
 where these rays unite, he will 
 not get any image of the disc, 
 since he receives only convergent 
 rays which cannot come to a 
 focus on his retina. If he, how- 
 ever, be far enough removed he 
 will see the inverted image, a b' 
 of the disc. The rays, having 
 converged to form this image, now 
 cross and reach his eye with a 
 divergence 3 and 4, a^ ?/ proceed- 
 ing from an object (the aerial 
 image) situated in front of the pa- 
 tient's eye. 
 
 The object thus apparently 
 seen, being nearer the observer than the patient's pupil, 
 moves in a direction opposite to that of the observer's head. 
 ( Vide explanation, p. 25). 
 
 Fig. 7.
 
 INDICATIONS BY MIRROR EXPLANATIONS. 25 
 
 The apparent movement of the image of the disc may be 
 illustrated by comparing- the patient's eye to an illuminated 
 chamber, outside and opposite to the window of, which 
 the observer stands. The pupil would then be represented 
 by the window, the image of the disc in hypermetropic, by a 
 picture on the opposite wall, and the aerial image of the 
 same in myopia by some small object situated between 
 himself and the window. If he then moves his head to the 
 right while fixing" his eye on the picture the latter will seem 
 to disappear behind that side of the window which is to 
 his right, i.e. it will appear to move in the same direction as 
 his head. 
 
 But, if while moving to the right, he regard now the 
 object which is in front of the window, it will finally inter- 
 vene between him and that side of the window which is to 
 his left, and will therefore appear to have travelled in a 
 direction opposite to that of his own head. 
 
 The same explanation as that just given for the whole 
 disc will apply also to vessels seen in different meridians. 
 
 In simple astigmatism, we do not see vessels at right angles 
 to the emmetropic meridian because rays from their transverse 
 planes {vide chap, v.) passing through the emmetropic 
 meridian will (as was seen for simple emmetropia) not be 
 visible. Whereas rays from the transverse planes of ves- 
 sels at right angles to the myopic or hypermetropic meri- 
 dian will, by passing through these meridians, produce in 
 the former case an inverted, and in the latter an erect, image 
 of the vessels. These follow the same rules of movement 
 as in simple myopia and hypermetropia respectively.
 
 26 REFRACTION OF THE EYE. 
 
 In compound Myopic astigmatism, if the observer use his 
 accommodation, vessels at right angles to the most myopic 
 meridian will be distinctly seen much closet to the patient's 
 eye than will those in the opposite meridian. Rays from 
 the transverse planes of the former converge and form an 
 inverted image much sooner than do those from the latter, 
 just as in high degrees of simple myopia. 
 
 In compound Hypermetropic astigmatism we find that for the 
 vessels at right angles to the most hypermetropic meridian 
 more accommodation is required at a given distance from 
 the eye, than for those in the opposite meridian. A greater 
 extent of the former than of the latter vessels is, however, 
 at the same time visible. Rays from the former are more 
 divergent and the cones take longer to separate, vide 
 Fig. 6. 
 
 In mixed astigmatism images of the vessels may be seen 
 sometimes inverted and at other times erect according to 
 the meridian through which the rays emerge and varying 
 with the observer's accommodation. The details are more 
 visible than- in emmetropia, but, are nevertheless very 
 indefinite.
 
 KERATOSCOPY (RETINOSCOPY) . 27 
 
 CHAPTER IX. 
 
 Keratoscopy (Retinoscopy). 
 
 By means of what has been, unfortunately, called " Kera- 
 toscopy," we have a useful method of diagnosing- errors of 
 refraction with the ophthalmoscope mirror alone; and, 
 what is, perhaps, equally important, we can correct them 
 with ordinary trial lenses quite independently of aid from 
 the patient. As long ago as 1864 (vide "Anomalies of Re- 
 fraction and Accommodation of the Eye," Bonders, p. 490) 
 Mr. Bowman drew attention to " the discovery of regular 
 astigmatism of the cornea, and the direction of the chief 
 meridians, by using the mirror of the ophthalmoscope. 
 .... The area of the pupil then exhibits a somewhat linear 
 shadow in some meridians rather than others." 
 
 Dr. Cuignet, of Lille, seems to have first systematised this 
 method of examination, and, in 1874, published his conclu- 
 sions in an article entitled "Keratoscopy." 
 
 Dr. Forbes in the Ophthal. Hosp. Rept., Vol. x., p. 62, has 
 lately drawn attention to the subject in this country. It 
 would, I think, be preferable, as suggested by Dr. Parent, 
 {Recueil d' Ophthal., Feb., 1880) to adopt the term "Retino- 
 scopy." The appearances, to be presently described, are 
 due to the play of light and shade on the retina. The 
 shadows which we recognise are not formed in the cornea, 
 though this structure, by its different curvatures, as in
 
 28 REFRACTION OF THE EYE. 
 
 astigmatism, undoubtedly exercises an influence on their 
 production, and the manner in which we see them. 
 
 Rays of light from a distant lamp, falling on a concave 
 mirror, issue from the latter convergingly, and, crossing 
 where they form an image of the lamp in front of the 
 mirror, again diverge. 
 
 If, in front of a screen, we place a convex lens at such a 
 distance that diverging rays from a concave mirror are 
 brought to a focus exactly on the screen, there is formed 
 the smallest and brightest possible image of the lamp, and 
 the most sharply defined and densest surrounding shadow. 
 If, then, we shift the lens, it is found that the further it is 
 removed from the point just mentioned, either towards or 
 away from the screen, the larger becomes the area of light 
 and the feebler is the illumination. 
 
 The increasing circles of diffusion render indistinct the 
 line of demarcation between light and shade, and cause 
 the latter to appear fainter. If, with the lens at different 
 distances from the screen, the mirror be variously ro- 
 tated, the area of light and shade will be seen, in every 
 position of the lens, to move, on the screen, in a direc- 
 tion opposite to that in which the mirror is rotated. If we 
 replace the screen and lens by the retina and dioptric sys- 
 tem of the eye (p. 8, Def. i) we have precisely similar 
 results. The area of illumination on the retina, in all states 
 of refraction, really moves in a direction opposite to that in 
 which the mirror is rotated. But since this illuminated 
 portion is seen through the transparent media of the eye, 
 the apparent direction of its movement will be influenced by 
 the refraction of the eye under examination.
 
 KERATOSCOPY (RETINOSCOPY). 2Q 
 
 For making - use of these facts in practice, atropine 
 though not essential, certainly renders material assist- 
 ance. The observer should be seated opposite, and I m. 
 20(48 in.) away from, the patient: the room should be 
 darkened, and the patient's eye shaded by a screen. The 
 mirror used must be concave, and should have a focal length 
 of about 22 cm. (9 ins.). If the observer be not emmetro- 
 pic, he must correct his own error. The patient should 
 regard the opposite wall, while the light from the mirror is 
 thrown into his eye at an angle of io° or 15 ° with his axis 
 of vision. 
 
 The mirror is to be rotated in different directions, and we 
 then see, in the pupillary area, an image of the illuminated 
 and shaded portion of the retina. 
 
 If the rays issuing from the observed eye do not cross 
 before reaching the observer, an erect image of this light 
 and shade is obtained. This image is seen to move in the 
 direction actually taken by the illuminated area on the retina, 
 viz., opposite to that in which the mirror is rotated. This is 
 the case in hypermetropia, emmetropia, and weak myopia. 
 
 If, however, the issuing rays cross before reaching the 
 observer, and form, between him and the patient, an in- 
 verted aerial image of the illuminated and shaded portion of 
 the fundus, then, since the illuminated area on the retina 
 really moves in the opposite direction to the mirror, the aerial 
 image of the same will appear to move in a contrary sense, 
 i e., in the same direction as the mirror. This appearance 
 is met with in cases of myopia of 1 D. (^) and upwards : 
 for if the observer, with good power of accommodation, be
 
 30 REFRACTION OF THE EYE. 
 
 seated as stated, at I m. 20, from the patient, then, 
 where the myopia = I D. ( T \ t ) the aerial image being- 
 formed at I m. (40 ins.) from the patient, and 20 cm. 
 (9 in.) from the observer, will be easily perceived by the 
 latter. Still more is this the case where, with increasing- 
 myopia, the image is formed nearer the patient. If the 
 eye under examination be, to such an extent, myopic that 
 its "far point" is situated at the position of the image of 
 the lamp, say 25 cm. in front of the mirror, or 95 cm. from 
 the eye, then the diverging rays from this image will come 
 to a focus exactly on the patient's retina (Def. 4, p. 9) and 
 there form the smallest and brightest possible image of 
 the lamp. 
 
 The further the departure from this degree, which we 
 may call 1 D. (J^) of myopia, the larger and feebler, as 
 was seen on the screen, will be the illuminated portion of 
 the retina. The shadow will, at the same time, become 
 correspondingly fainter, with its line of demarcation less 
 defined. 
 
 The difference in degree of luminosity of this reflex can 
 be easily appreciated, so that it furnishes a means whereby 
 the amount of error may be approximately estimated. An 
 attempt has been made to use, for the same purpose, the 
 difference in intensity of the shadow, but there are so 
 many antagonistic factors affecting our perception of its 
 definition and density, that this latter does not afford an 
 altogether reliable source of information. 
 
 If, from some distance, say 1 m. 20, we examine an eye 
 with the mirror alone, we find that, the higher the hyper-
 
 KERATOSCOPY (RETINOSCOPY) . 3 1 
 
 metropia or myopia, the smaller is the image which we 
 obtain of the disc : so that, in very high degrees, we see 
 not only the whole disc, but also some of the surrounding 
 fundus in the pupillary area. In emmetropia, on the other 
 hand, so large is this image that only a small portion of it 
 is visible at one time. With equally rapid rotations of the 
 mirror then, the light would have to travel much faster 
 over the large image of the latter, than the small image 
 of the former, condition. This difference in the rate of 
 movement in the various states of refraction, was pointed 
 out by my friend Dr. Charnley : it constitutes probably the 
 best marked and most reliable of the means at our dis- 
 posal for estimating, by this method, different degrees of 
 error. 
 
 In emmetropia and the lower degrees of hypermetropia 
 and myopia, so little is seen of the large image of the illu- 
 minated area and the surrounding shadow, that the small 
 portion of the latter, visible at any one time in the pupil- 
 lary area, appears approximately linear ; while, although 
 with the increasing degrees of H. or M., the nearly circu- 
 lar area of illumination on the retina also enlarges, yet, so 
 much diminished is the image of the same, that more of 
 the circumference of the surrounding shadow is visible at 
 one time in the area of the pupil ; it appears, therefore, 
 more crescentic, while it becomes at the same time nar- 
 rower. 
 
 Taking then the direction of the movement as denoting 
 the kind of error; and the rate of movement, degree of 
 luminosity, and curvature of shadow as indicating approxi-
 
 32 REFRACTION OF THE EYE. 
 
 mately the amount of the same, we may summarise as 
 follows : — 
 
 i. If the image of lig"ht and shade moves in the same 
 direction as that in which the mirror is rotated : and, if 
 the rapidity of movement and curvature of shadow are the 
 same in all meridians, we have a case of simple myopia. 
 
 2. The same conditions, but with the image moving - in a 
 direction opposite to that in which the mirror is rotated, 
 indicate either hypermetropia, emmetropia, or weak my- 'd 
 opia. ' 
 
 3. The slower the movements of the image, the feebler the v 
 illumination, and the more crescentic, and narrower, the V 
 shadow, the higher is the hypermetropia or myopia. 
 
 Note. — Between 1 D. \£q) of myopia and emmetropia, I 
 the convergent rays issuing from the eye, unite either be- - 
 hind the observer, or so close in front of him, that no . . 
 distinct image is received on his retina. In these cases, 
 the direction of the movement, as will be presently ex- 
 plained, taken with the indistinctness, give the best in- 
 dication of this condition. 
 
 4. A difference, in two opposite meridians, of rapidity, or 
 direction of, movement, or curvature of the shadow indi- 
 cates astigmatism. These two dissimilar shadows, moving 
 at right angles to each other, either one vertically and the 
 other horizontally, or both obliquely, denote the meridians 
 of greatest and least refraction. 
 
 Since, however, as we have seen, with the shadow moving 
 in the opposite direction to the mirror there may be one of 
 three conditions, it becomes necessary to distinguish between
 
 KERATOSCOPY (rETINOSCOPY) . 33 
 
 them in the following- manner, a. If, with a convex I D 
 (tu) placed by means of a spectacle frame, in front of the 
 observed eye, the shadow co?ilinues to move in the opposite 
 direction, it shows that the patient is hypermetropic . But if 
 it now move in the same direction, then : — b. Place in front 
 of the eye a convex 0-50 D (-J^) when, if it were previously 
 myopic O'joD (-£q), it will now be made myopic 1 D (-^d), 
 so that, at the distance of 1 m. 20, we shall get an inverted 
 aerial image of the fundus, as before explained, moving - in 
 the same direction, c. If, with -f- 1 D (-£§) the shade moves 
 in the same direction, while with -f- 0-50 D (^) it continues 
 to move in the opposite direction, the observed eye is em- 
 metropic. 
 
 The amount of error may be diagnosed, and corrected, 
 by ordinary trial lenses. Suppose we see the shadow 
 moving in the same direction, it proves the presence of 
 myopia. If, on placing in front of the patient's eye, a 
 concave 3 D (xV)} the shadow still moves in the same 
 direction, we try with concave 4 D ( T V)- If now it moves 
 in the opposite direction, we know that the myopia is not 
 more than 5 D (i) ; for if it were, the concave 4 D (-^) 
 would have left 1 D (±\) uncorrected, so that, at 1 m. 20, 
 the shadow would still have moved in the same direction. 
 The myopia is therefore between 4 D and 5 D (^l 
 and |-). 
 
 We proceed in the same manner, with convex glasses, 
 for hypermetropia, until we find the shadow moving- in the 
 same direction, we then know that there is produced arti- 
 ficial myopia of, at least, 1 D. (^). The amount of H. 
 
 D
 
 34 REFRACTION OF THE EYE. 
 
 in any case will therefore be about I D. (J„) less than the 
 lens producing the result just mentioned. 
 
 In astigmatism, if, by the means just noted, we find one 
 meridian emmetropic, the other may be corrected by a 
 cylinder with its axis at right angles to the direction taken 
 by the shadow, since this latter traverses the pupillary area 
 in a meridian parallel to the error which it indicates. 
 
 In compound or mixed astigmatism, one meridian is cor- 
 rected by a spherical lens, and the other by an additional 
 cylinder with its axis at right angles to the direction taken 
 by the shadow, which indicates the still uncorrected meri- 
 dian. 
 
 Care must be taken not to throw the light too obliquely 
 on the eye, for, owing to the obliquity with which the rays 
 traverse the media, the refraction of the horizontal meri- 
 dian would be increased. It must also be carefully noted 
 that the direction of movement of the shadow, as compared 
 with the mirror, is the reverse of that of the disc or vessels, 
 as compared with the observer's head, {vide Chap. VIII.).
 
 MIRROR AND OBJECT LENS. 35 
 
 CHAPTER X. 
 
 Indications afforded by Mirror and Object Lens. 
 "Indirect Method." 
 
 This method of diagnosing- hypermetropia and myopia 
 was first pointed out by Mr. Hutchinson (Ophlh. Hosp. 
 Rep. vol. iv, p. 189) and Mr. Couper (Med. Times and 
 Gaz. Jan. 30, 1869), has shewn how, by it, astigmatism 
 may also be recognized. It is desirable that the patient 
 should be under atropine, for otherwise an alteration in the 
 pupil may easily lead to the supposition that the disc has 
 changed in size. Upon seeing a change in the shape of 
 the disc great care is requisite to say whether this is due 
 to an elongation in one meridian or a diminution in the 
 other. 
 
 In this mode of examination the observer must place 
 the object lens as close as possible to the patient's eye; then, 
 keeping the optic disc steadily in view, he must gradually 
 withdraw the lens to the distance of a few inches : when — 
 
 Indication 1 . If the disc remain the same size throughout, 
 the patient is emmetropic [vide expl. p 36.) 
 
 Indication 2. If the disc diminish in size on withdrawing 
 the lens the patient is hypermetropic, and the more so in pro- 
 portion to the rapidity of diminution {vide expl. p. 37). 
 
 Indication 3. If the disc decrease in size in one meridian only, 
 the patient is hypermetropic in that meridian only = Simple 
 hypermetropic astigmatism. 
 
 D2
 
 36 REFRACTION OF THE EYE. 
 
 Indication 4. If the disc diminish in every direction, but 
 more in one meridian than the others, there is hypermtltopia 
 all round, but most in that meridian which decreases most = 
 Compound hypermetropic astigmatism. 
 
 Indication 5. Increase in size on withdrawing the lens 
 denotes myopia, and more in proportion to rapidity of 
 increase. ( Vide expl. p. 38). 
 
 Indication 6. Increase in one meridian only shows myopia 
 in that meridian alone = Simple myopic astigmatism. 
 
 Indication 7. Increase in every direction, but more in one 
 meridian, indicates myopia in all directions, but more in that 
 meridian which increases mosl= Compound myopic astigma- 
 tism. 
 
 Indication 8. Increase in one meridian, and a diminution 
 in the opposite meridian denotes myopia in the former 
 direction, and hypermetropia in the latter = Mixed astig- 
 matism. 
 
 Explanation of change in size of the disc. — These changes 
 in size of the image of the disc will be evident on remem- 
 bering that the relative sizes of image and object are as their 
 distances from the lens. To find the distance of the image 
 
 from the lens, we have the formula - = where b, 
 
 f a 
 
 = the distance of the image from the lens, f = the focal 
 length of the lens, and a, == the distance of the object. In 
 each of the following examples the focal length of the lens 
 is 4 cm. 
 
 In emmelropia the rays issuing from the disc emerge from 
 the eye parallel as if proceeding from an object situated at 
 an infinite distance (Def. 3). It is of this supposed object
 
 MIRROR AND OBJECT LENS. 
 
 37 
 
 that we get an image by means of a convex lens held in 
 front of the patient's eye. It matters not, therefore, where 
 this lens is held, the parallel rays from the object will 
 always unite to form an image on the opposite side of the 
 lens at its principal focus (Chap, ii., b). The relative dis- 
 tances of image and object from the lens remaining con- 
 stant, the size of the image of the disc in em- r 
 metropia does not vary with movements of 
 the lens. 
 
 In hypermetropia, fig. 8,° rays issuing from 
 the disc emerge from the eye as if proceed- 
 ing from an object, b, a, at a certain dis- 
 tance behind it (Chap, iii., Def. 5). 
 
 It is of this supposed object b, a, that we 
 gain an image I or I' by means of a lens held 
 in front of the patient's eye. 
 
 Suppose this lens, L, to be at 6 cm. 
 from the object, we ' find by the formula 
 that the distance of the image / is 12 cm. 
 (r b =l— <J = T2 orb= 12). 
 
 If we now withdraw the lens from the 
 object (and also from the eye) till it is 12 cm. 
 from the former as at Z' fig. 8, the dis- 
 tance of the image, T will then be 6 cm. 
 
 ! 1 
 
 .4- 
 
 
 (i 
 
 1 
 4 
 
 iV = i°r3 = 6), 
 
 The ratio of the distance of the image 1 
 
 from the lens as compared with that of the Fig. 8. 
 
 * In Figs. 8 and 9, the distances of the lenses from the objects and 
 images are drawn to scale \ cm. = 1 cm.
 
 38 
 
 REFRACTION OF THE EYE. 
 
 object from the lens being greater in the first case than in 
 the second, so is the size of the image. In 
 hypermetropia on ivithdrawing the lens from the 
 eye, the image of the disc diminishes in size. 
 
 In myopia, fig. 9, rays from the disc emerge 
 from the eye convergently and form, at a 
 certain distance in front of it, an inverted 
 aerial image, a, b, of the disc. This latter 
 we have now to regard as the object, o, 
 whose image, I or I', we obtain by means of 
 a convex lens, Z, or Z', interposed between it 
 and the patient's eye, E. A lens, thus placed, 
 intercepts the rays, Bb, Aa, (which, to avoid 
 confusion, are the only ones shown of all 
 those) which converge towards the points 
 b and a respectively of this object, o. The 
 rays being thus rendered more convergent, 
 produce an image I or F whose extremi- 
 ties will be bounded by the lines, passing 
 from either end respectively of the object, o, through the 
 centre of the lens, Z or II. 
 
 In this case, object and image are on the same side of the 
 lens. The object here, being on the opposite side of the 
 lens from the direction in which the rays proceed, it is 
 customary, in order that the same formula may hold good 
 
 in all cases, to regard— as a negative quantity. For the 
 
 distance of the image from the lens then, we have the 
 
 t 1 * f O l l 
 
 formula -. = -z. — I == .? + -■ 
 
 b f I a) f a 
 
 Fig. 9.
 
 MIRROR AND OBJECT LENS. 3g 
 
 If we first place a lens, Z, 12 cm. nearer the eye than 
 where the object o would be formed, we have the image /at 
 3 cm. from the lens (^ = \ -f y 1 ^ = ^ or b = 3). If we 
 now withdraw the lens from the eye, i.e., towards the object till 
 it is within 6 cm. of the latter, as at Z', the distance of the 
 image T will be nearly 2 cm. (j = 1 -f 1 = ■£% or b = 
 nearly 2). But as the ratio of the distance of the image from 
 the lens, as compared with that of the object from the lens, 
 is greater in the second than the first of these examples, so is 
 the size of the image. In myopia, therefore, on approach- 
 ing the lens to the eye the image diminishes in size, and on 
 withdrawing it from the eye the image increases. 
 
 The above explanation holds good for myopia only so long 
 as the lens is not withdrawn beyond the "far point" of the 
 eye plus its own focal distance : for hypermetropic only so long 
 as the focal power of the lens is greater than the degree 
 of hypermetropia. The exception to this latter condition 
 does not occur in practice if a lens of 3 inch focus be used 
 and need not therefore be considered. In the case of very 
 high degrees of myopia, however, if the lens be further 
 from the eye than the aerial inverted image of the disc 
 plus its own focal distance, an erect image of the disc is 
 formed between the lens and the observer, the variations 
 in size of which are subject to the same rules as those 
 described for the inverted image in hypermetropia.
 
 4-0 REFRACTION OF THE EYE. 
 
 CHAPTER XI. 
 
 Estimation of the Refraction by means of Lenses in 
 the Ophthalmoscope. 
 
 In estimating- refractior. by this method the patient and 
 observer must be seated side by side facing- in opposite 
 directions. Their heads and the lamp should be on the 
 same level ; the latter being placed on the same side of 
 the patient as that under examination, a little out from, and 
 slightly behind the position of, the patient's ear. If now 
 the heads be inclined laterally towards each other, the eyes 
 of the corresponding sides will come opposite one another 
 while the noses and mouths will be left free for breathing. 
 By this means the sight hole of the mirror may generally 
 be placed in the position which, when ordered, the glasses 
 will occupy; the distance of these from the eye need there- 
 fore not be taken into consideration when prescribing from 
 measurements thus obtained. Should it however be unde- 
 sirable to approach thus close, the distance from the 
 patient must be taken into account and the glasses or- 
 dered will have to be somewhat weaker in myopia and 
 stronger in hypermetropic than the lens necessary to see the 
 fundus would indicate. In estimating refraction by the 
 ophthalmoscope it is absolutely essential that the accom- 
 modation of both patient and observer be completely sus- 
 pended. In order to secure the former we must place the 
 patient opposite a dark wall or curtain, or employ atropine.
 
 ESTIMATION BY OPHTHALMOSCOPE. 41 
 
 For the observer voluntarily to relax his own accommo- 
 dation while looking- at an object so near to him as the 
 patient's eye, requires much practice. The best way of 
 overcoming the difficulty is to regard the fundus as situ- 
 ated some hundreds of yards distant. This habit may be 
 acquired by looking alternately at a spot on the window 
 pane and then at some remote object : or by gazing 
 vacantly at the page of a book until the type disappears ; 
 then, having noticed the sensation produced on thus re- 
 laxing the accommodation, endeavour to induce the same 
 condition while observing a fundus. 
 
 In the following indications it is of course necessary that 
 the observer be fully cognisant of the state of his own re- 
 fraction, and in the following cases he is supposed to be 
 emmetropic, (if not vide note, p. 43). With accommoda- 
 tion then entirely suspended, the eye of the emmetropic 
 observer is adjusted for parallel rays. 
 
 Indication I. If therefore he can see distinctly the details 
 of any fundus, the rays issuing thence must he parallel and 
 the eye eminetropic. 
 
 Note. Though this appears to contradict what has been 
 said concerning seeing the disc in emmetropia, (chap, viii, 
 p. 22), yet we must remember that when close up to the 
 patient's pupil, the observer does receive rays from the two 
 extremities of the disc. Moreover if the observer endea- 
 vour to accommodate for the patient's eye, he will find it 
 impossible to do so, since, if he is as close as he should be, 
 the latter, as explained by Mr. Power, is nearer to him 
 than his "near point". The effort is therefore not main- 
 tained and as when the accommodation is partially sus-
 
 42 REFRACTION OF THE EYE. 
 
 pended the disc begins to appear, it is unconsciously 
 altogether relaxed and a distinct view is obtained. 
 
 Indication 2. If however the details of the fundus cannot 
 be seen except by the intervention of a concave lens, this 
 proves the patient to be myopic. The converging rays 
 from such an eye, (definition 4), require a concave lens to 
 render them parallel for perception by the emmetrope. 
 The strength of the lens which effects this change of 
 direction indicates the degree of myopia, for it is evident 
 that the same lens which renders parallel, the converging 
 rays issuing from the retina, will bring parallel rays to a 
 focus on the retina of the same eye. 
 
 Indication 3. If again, with suspended accommodation, 
 the details of the fundus are not visible without the aid of 
 a convex lens, this indicates the patient to have hyperme- 
 tropia. The diverging rays from a hypermetropic eye 
 require a convex lens to render them parallel. The 
 strength of the lens necessary for this purpose denotes 
 the amount of hypermetropia : for the lens which renders 
 parallel, rays proceeding from a retina, will also bring 
 parallel rays to a focus on the same retina. 
 
 Indication 5. If the vessels in one meridian are seen 
 without any lens while a convex or concave lens is required 
 for those in the other meridian, it is a case of simple astig- 
 matism. The emmetropic meridian is the one at right angles 
 to the vessels seen without any lens, {vide chap, v, p. 14). 
 
 Indication 6. If for the two opposite meridians we re- 
 quire either two convex or two concave lenses of unequal 
 power we have to deal with a case of compound astigma- 
 tism : hypermetropic or myopic respectively. The greatest
 
 ESTIMATION BY OPHTHALMOSCOPE. 43 
 
 error of refraction in each case is at right angles to the 
 vessels for which the strongest lens is necessary. 
 
 Indication J. If for vessels in one meridian we require a 
 convex lens, while for those in the other a concave is necessary, 
 it indicates mixed astigmatism. The hypermetropic meridian 
 is at right angles to the vessels seen best with a convex lens : 
 and the myopic to that for which a concave lens is neces- 
 sary. 
 
 In all these forms of astigmatism then, we see that the 
 lens which, with absolutely suspended accommodation, gives 
 the best view of vessels in one meridian, measures the amount 
 of error which exists in the opposite meridian. 
 
 Note. Should the observer not be emmetropic, yet, if he 
 correct his own error with spectacles, he is in the same 
 position as an emmetropic observer. If he however prefer 
 to estimate refraction without his glasses he must make an 
 allowance for his defect by means of the lenses behind the 
 sight hole of the mirror. To see the details of an emme- 
 tropic fundus therefore a hypermetropic or myopic observer 
 starts with a lens corresponding to the amount of his own 
 error. For any particular fundus then the glass required 
 by him must be to that extent more convex or concave re- 
 spectively than would be necessary for an emmetrope to 
 see the same fundus. Consequently the patient will always 
 have that amount less hypermetropia or myopia respectively 
 than the same lens would indicate if the observer were 
 emmetropic ; we have then the 
 
 Rule II. That the observer must deduct the amount of 
 his own hypermetropia or myopia from the lens which 
 enables him to see distinctly any particular fundus.
 
 44 
 
 REFRACTION OF THE EYE. 
 
 
 
 
 
 
 
 
 
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 TEST GLASSES AND TYFES. 45 
 
 CHAPTER XII. 
 
 Test Glasses and Types as applied to the Estimation of 
 
 Refraction. 
 
 When ascertaining - with the distance types the state of the 
 patient's refraction, we must be absolutely certain that his 
 accommodation is completely relaxed. In myopes, it gene- 
 rally is so, but in hypermetropic and astigmatic patients it 
 is frequently a troublesome and misleading factor. If from 
 the varying and inconsistent statements of the patient, it is 
 suspected that he does not relax his accommodation, he 
 may do so more easily if he close his eyes between each 
 change of glasses, not opening them until the fresh ones 
 are in situ. Another method of assisting the patient is to 
 put him on a pair of -f 4 D (10 in.) for ten or fifteen 
 minutes, and then, without removing, gradually neutra- 
 lise them by stronger and stronger concave lenses placed 
 in front, until those are found with which the patient can 
 see in the distance as well as without any glass. The 
 difference then between the concave lens thus required and 
 -f- 4 D (x^), gives the manifest hypermetropia. 
 
 One caution must be especially borne in mind, viz. : never, 
 in any doubtful case, to commence testing vision with con- 
 cave glasses, for to see with such lenses it is necessary for
 
 46 REFRACTION OF THE EYE. 
 
 all, except those whose myopia is equal to or less than the 
 glasses being used, to employ their accommodation, and 
 when once called into activity, this is not easily suspended. 
 Let the patient be placed at 6 cm. (20 ft.) from the 
 types. We have already seen what, with test types, are 
 the indications of emmetropia and simple presbyopia, 
 (P. 18). 
 
 Hypermetropia. 
 
 If the patient read f (fg) perfectly without glasses, still 
 this fact does not exclude hypermetropia, the presence of which 
 \s>p?oved'\{ he can read the distance types as well with, as 
 without, convex lenses. The strongest which are thus toler- 
 ated indicate the degree of manifest hypermetropia, and 
 they at least must be ordered for close work. In young 
 adults, and in the higher degrees of hypermetropia, we 
 must for this purpose even give glasses 1 D or 1-50 D 
 (40 or rt) stronger. In order to rest the ciliary muscle, 
 it is advisable for distant V. to prescribe at any rate the 
 glasses which correct the mariifest hypermetropia. If the 
 H. be measured under atropine, the glasses ordered must 
 be 1 D. (or perhaps even 2 D.) weaker than the total amount 
 thus found. These should be suitable for all purposes, 
 though, for distant V., weaker ones are sometimes neces- 
 sary. 
 
 Myopia. 
 
 As we have already stated, (Chap. VII. Ind. 3) if the 
 patient can read the finest type to within 4 in. or 5 in. of 
 his eye, while at the same time his distant V. does not
 
 TEST GLASSES AND TYPES. 47 
 
 exceed ^ (fg) and is probably not -£$ (-2 2 o%)> ne is myopic. 
 An indication of the degree may be obtained by observing 
 the fuithest point at which either of the smallest types can 
 be read. Provided it be nearer than that for which it is 
 marked, the distance of this point gives the focal length of 
 the lens required to neutralise the myopia. 
 
 e.g. — If Sn. I be legible only as far off as 12 cm. (5 in.) 
 the myopia is measured by the concave lens having this 
 focal length, viz., 8 D (^) or (£ in.). Or again, if No. 4 
 Sn. marked for 1 D, (3 ft.), can be read only at 50 cm., 
 (20 in.) the myopia = 2 D (^) (^). 
 
 In testing the distant V. we commence with the weaker 
 concave glasses, and work up to the stronger. In doing 
 this, we cannot be too careful in ascertaining which is the 
 weakest glass that neutralises the myopia and gives the best 
 V., whether this be f (§§) or less. The glass thus found 
 gives the measure of the myopia, and may in all cases be 
 ordered for distant V. Such glasses may also be given for 
 close work when, with good accommodation, the myopia does ^ 
 not exceed about 6 D or 8 D (^ or i). In most cases where 
 the myopia is higher, and in all where the accommodation 
 is feeble, we must order weaker glasses for close work. 
 These, according to Donders may be found in the fol- 
 lowing manner, viz. : From the neutralising lens deduct 
 the strength of the glass whose focal length equals the 
 distance at which we wish the patient to work. 
 
 e.g. — With myopia = 10 D (1) we wish the patient to 
 do work at 40 cm. (16 in.) From 10 D (£) we deduct 
 therefore the lens whose focal length is 40 cm. (16 in.),
 
 48 RETRACTION OF THE EYE. 
 
 viz. : 2-50 D (jL.), and the glasses ordered will be (10 D — 
 2- 5 oD=)- 7- 5 oD(i- T V=^j 
 
 For the various exceptions to these, only very general 
 indications of glasses to be ordered, as well as for the 
 numerous complications of myopia, the reader must be 
 referred to the larger works on this subject. 
 
 Astigmatism. 
 
 If the V. cannot be brought up to f (§£) with any spherical 
 glasses, we probably have to do with a case of astigmatism. 
 In dealing with this error each eye is to be tested separately. 
 
 If, from the previous examination with the ophthalmo- 
 scope, we have diagnosed, — 
 
 (1.) Simple astigmatism, we can proceed to test with 
 the fan of rays. If our surmise has been correct, the 
 patient should now see quite distinctly, only the line at 
 right angles to his emmetropic meridian, (Chap. V.) If 
 this line were vertical, it would therefore denote that 
 the meridian parallel to it was either hypermetropic or 
 myopic; we should then ascertain what cylinder, with 
 its axis at right angles to this latter meridian is required 
 to correct it : i.e., to render clear the horizontal line. 
 If the correction thus found gives V. = § (fg), it may 
 be ordered for constant use; but if it do not, then, 
 as where none of the rays are distinct, and more particu- 
 larly if first one then another is most clearly seen, we must 
 not hesitate to employ atropine.
 
 TEST GLASSES AND TYPES. 49 
 
 It matters not now, whether we have to deal with — 
 
 (2.) Compound or mixed astigmatism. We have merely 
 to ascertain what spherical lens clears one of the rays, and 
 then, leaving- this glass in situ, try what cylinder, with its 
 axis at right angles to the line thus cleared, renders equally 
 distinct the ray in the opposite meridian. This spherico- 
 cylindrical correction, after due allowance for atropine (Chap. 
 XIII.), is ordered for constant use. 
 
 (3.) Another less scientific, though practically useful 
 plan, is to substitute the test types for the lines, and 
 having found the spherical lens which gives the best V., 
 try what additional cylinder is required. 
 
 (4.) If each meridian has been measured separately with 
 spherical glasses, either for the fan, or in the ophthalmo- 
 scope for the fundus, we shall have to calculate what 
 spherico-cylinder is required, (a.) For compound astigma- 
 tism we generally give the spherical lens, which corrects 
 the meridian of least error, and then add the cylinder 
 (concave for myopic, and convex for hypermetropic as- 
 tigmatism), whose strength equals the difference between 
 the two meridians, (b.) In mixed astigmatism, the difference 
 between the sphericals also gives the degree of astigmatism 
 and the strength of the cylinder required. If, therefore, we 
 correct the myopic meridian with a concave spherical lens, 
 we shall require in addition a convex cylinder and vice versa. 
 
 e.g. — With vertical meridian myopic 2 D (^) and the 
 horizontal meridian hypermetropic to the same extent, the 
 difference between them = 4 D (J^). If, therefore, we give 
 minus 2 D sph. (-£>), we must add + 4 D cyl. (y 1 ^) with its
 
 50 REFRACTION OF THE EYE. 
 
 axis vertical, (i.e., at rt. angles to the hypermetropic meri- 
 dian, Chap. II., p. 7.) But if we give plus 2 D sph. (-^0), 
 we shall require in addition — 4 D cyl. ( T V) axis horizon- 
 tal. The action of atropine (Chap. XIII.), must of course 
 be taken into account. 
 
 5. Another method of testing- astigmatism is by means 
 of Tweedy' s optometer, of which, with the exception that 
 the later instruments, are marked in dioptres and inches 
 instead of only in inches, he has published a description 
 in the Lancet, for Oct. 28, 1876. The patient, under atro- 
 pine, lis made artificially myopic by a convex lens, a card 
 with fine radiating- lines is gradually approached to his 
 eye, until one line becomes quite distinct. The meridian 
 at right angles to this line is then known to be the least 
 refractive. The concave cylinder is found, which, with its 
 axis at right angles to the line first seen, makes the line in 
 the opposite meridian equally distinct. This shews that 
 the latter meridian is now made as little refracting as the 
 former. The distance at which the first line is seen in- 
 dicates the kind and degree of the error for the least 
 refracting meridian. A spherical lens correcting this is 
 then ordered, and, in combination with it, the concave 
 cylinder of the strength, and in the axis, which were found 
 necessary to equalise the two meridians.
 
 TEST GLASSES AND TYPES. 51 
 
 Presbyopia. 
 
 Though the patient does not require glasses for distant 
 V., he may, as age advances, find it more and more diffi- 
 cult to read without them. This defect is called presbyopia, 
 and is caused chiefly by failure in the power of accom- 
 modation, but is also accompanied by a flattening of the 
 crystalline lens. It is indicated by a recession of the near 
 point, and is said by Donders to have commenced when 
 this is further from the eye than 22 cm. (9 in.), i.e., than 
 the focal length of a lens whose refracting power is 4-50 D 
 (i). As we have already seen, (Chap. IV.) such a lens 
 would, in emmetropia, bring rays from the "near" point to 
 a focus on the retina in the absence of all accommodation. 
 
 The difference then between this lens and one whose focal 
 length equals the distance of any given receded near point, 
 denotes for emmetropia the amount of accommodation which 
 is deficient, and the lens necessary to enable the patient 
 again to read at 22 cm. 
 
 e.g. — With near point receded to 40 cm. (16 in.) we 
 must deduct from 4-50 D. (|) the lens, whose focal length 
 is 40 cm. (16 in.) viz., 2*50 D. ( T 2 g-) and have, as the neces- 
 sary lens, + 2 D. (^). 
 
 When all accommodation is lost, even an eye which was 
 originally emmetropic may require a convex lens for parallel 
 rays (Donders). The strength of this lens must, of course, 
 then be added to 4-50 D. (a) in order that such a patient 
 may read at 22 cm. (9 in.) 
 
 E2
 
 52 
 
 REFRACTION OF THE EYE. 
 
 The following table gives, according to Donders, the 
 glasses necessary for presbyopia in emmetropics at different 
 ages. 
 
 Age. 
 
 Glass. 
 
 D. 
 
 English 
 Inches. 
 
 45 
 50 
 
 55 
 60 
 
 65 
 70 
 
 75 
 80 
 
 I 
 
 2 
 
 3 
 
 4 
 
 4'50 
 
 5'5o 
 6 
 
 7 
 
 l 
 40 
 
 1 
 20 
 
 1 
 12 
 
 1 
 
 lO 
 1 
 9 
 
 1 
 
 7 J 
 
 1 
 
 7 
 1 
 6 
 
 Since these are the glasses which enable the emmetropic 
 eye to see at 22 cm. (9 in.), it is evident that, if either 
 myopia or hypermetropia be present, the amount of the 
 former must be deducted from, and that of the latter added 
 to, the lens here specified for any particular age. Though 
 these are theoretically the glasses required, we must test 
 practically each individual case, for the various patients 
 prefer different distances at which to read or work. 
 
 Aphakia. 
 
 or " absence of lens," as after cataract operations, involves 
 loss of accommodation. If we replace the crystalline lens 
 by a glass in front of the eye which focusses parallel rays
 
 TEST GLASSES AND TYPES. 53 
 
 on the retina, we render the eye practically emmetropic. To 
 enable such a patient to read at any specified distance, it is 
 necessary merely to add to that glass, the lens whose focal 
 length equals the distance in question. 
 
 e.g. — If a patient requires -f 13 D. (\) for parallel rays 
 and we wish him to read at a distance of 33 cm. (12 in.), 
 we add together 13 D. (^) and the lens whose focal length 
 is 33 cm. (12 in.), viz.: 3 D. ( t l), thus getting -f- 16 D. (~) 
 as the necessary glass. 
 
 For cataract patients we order two pairs of spectacles. 
 One for distant V., generally + 10 D. to + 13 D. (^ to ^), 
 and the other for reading, from -f- 15 D. to + 20 D. 
 Qr to ^) according to the previous state of the refraction. 
 
 To ascertain whether the glasses given, accord with 
 our prescription, it must be remembered that if, while 
 moving a convex lens to and fro in front of our eye, we 
 regard some distant object, this latter appears to move in 
 the opposite direction. A contrary effect is produced with 
 a concave lens. A concave and a convex lens of equal 
 strength neutralise each other, and there is no movement 
 of the object. 
 
 If this latter result is obtained with a lens of the same 
 strength as that ordered (though of an opposite sign), the 
 glasses are correct. If the lens, thus necessary, is not of 
 the same strength, we ascertain the amount of error by 
 noting the number of the glass required for neutralisation.
 
 54 REFRACTION OF THE EYE. 
 
 CHAPTER XIII. 
 
 Atropine : — Alterations Necessary in Measurements 
 made under its influence. 
 
 According to Def. 3, parallel rays should come to a focus 
 on the retina of an emmetropic eye when the accommoda- 
 tion is completely paralysed by atropine. Emmetropia, 
 however, as thus defined, is rarely met with. An eye may 
 have V. = f (f %) and its distant V. made indistinct by 
 even the weakest convex lens, yet, when fully under atro- 
 pine, it will generally be found that a certain amount of 
 accommodation was being exercised, for a convex lens is 
 now necessary to see f (f§)> *"•*•> to bring practically 
 parallel rays to a focus. That portion of the accommoda- 
 tion which can be overcome only by atropine is due to the 
 "tone" of the ciliary muscle, and must always be taken 
 into the calculation when ordering glasses from the mea- 
 surement of the refraction as determined under atropine. 
 For practical purposes, we may consider that eye emme- 
 tropic, which, when fully under atropine, does not require a 
 convex lens stronger than 1 D (^) for parallel rays. 
 
 In Hypermeiropia the convex lens which brings parallel 
 rays to a focus, when the eye is fully under atropine, should 
 theoretically convert it into an emmetropic eye. It is found, 
 however, practically that, owing to hypertrophy of the ciliary 
 muscle, patients with this error of refraction find great diffi-
 
 ATROPINE. 55 
 
 culty in relaxing - their accommodation to anything like its ful- 
 lest extent. The result of this is, that the lens which brings 
 parallel rays to a focus under atropine, cannot be ordered 
 for the same eye with its accommodation active. The 
 increased convexity of the crystalline lens (produced by 
 accommodation) added to the correcting lens just men- 
 tioned, renders parallel rays too convergent, and brings 
 them to a focus in front of the retina. In hypermetropia 
 then, it becomes necessary to deduct from the measurement 
 made under atropine at least I D. (J^) and in children and 
 young adults, frequently as much as 2 D. {^) for the tone 
 of the ciliary muscle. 
 
 In myopia the concave lens which brings parallel rays to 
 a focus on the retina of an eye under atropine will be 
 found too weak for the same eye when not under atropine. 
 The effect of the accommodation is to bring to a focus in 
 front of the retina, the rays which, under atropine, were 
 focussed upon it : in other words, the myopia is still un- 
 corrected, and requires a concave lens 0*50 D. {^) or o"75 
 D. (Jq) stronger. We have, therefore, the 
 
 Rule III. — That glasses ordered for permanent use 
 must, when convex, be [-50 D. (^) to 2 D. (-J^) weaker, and 
 when concave, 0*50 D. (-J^) to 075 (-g 1 ^) stronger than is indi- 
 cated by the measurements made under atropine. 
 
 The application of this rule need be exemplified only in 
 a case of mixed astigmatism. If, under atropine, one 
 meridian be hypermetropic, 2 D. (^l) and the other my- 
 opic, 2 D. (2V), the fully correcting glass would be either 
 + 2 D. sph. C° — 4 D - cyl. (+ 2V s P h - C — to cy 1 -) or — 
 
 * The sign CI means " combined with."
 
 56 REFRACTION OF THE EYE. 
 
 2 D. sph. C + 4 D. cyl. (— ^ sph. C + tV cy 1 -)- The 
 glasses ordered for permanent use would be, in the first 
 case, 4- i D. sph. C — 4 D. cyl. (+ ^ sph. C — iV c y'-) 
 and in the second — 3D. sph. 3 -f- 4 D. cyl. ( — T \ sph. 
 
 + to c yl- ^ n tne former example, by deducting I D. (^ ) 
 from the convex spherical we at the same time practically add 
 
 1 D. (^q) to the strength of the concave cylinder (for it has 
 thus less neutralisation to perform). While in the second 
 example, by adding 1 D. (-jL) to the concave spherical we 
 lessen the strength of the convex cylinder, since it now has 
 more to neutralise. 
 
 In mixed astigmatism, then, by deducting from the strength 
 of the spherical, we increase that of the cylinder : and, by 
 adding to the strength of the spherical, we diminish that 
 of the cylinder. 
 
 In compound astigmatism, if we add to, or deduct from 
 the strength of the spherical, we at the same time increase 
 or diminish respectively the correction for each meridian. 
 
 The calculations necessary for the action of atropine 
 may thus be made for both meridians simultaneously, by 
 means of the spherical lens alone. 
 
 In simple astigmatism, as we have seen (p. 48) atropine 
 is not necessary. 
 
 Conclusion. 
 
 It need scarcely be mentioned in conclusion that there are 
 many cases in which, though the error of refraction has 
 been duly diagnosed, estimated and corrected, yet, there 
 is no consequent improvement in vision. Such results
 
 conclusion. 57 
 
 may be found in old standing- cases of strabismus or in 
 diseased eyes. Others again, without any error of retrac- 
 tion, may have defective vision owing- to disease; with 
 such, however, we have not here to deal. These pages 
 have been intended merely to indicate the various modes of 
 estimating and correcting errors of refraction ; the reason 
 why, after such correction, the vision is not improved must 
 be ascertained by other means. Some patients, in whom 
 we cannot find either disease or error of refraction may 
 simulate total or partial blindness. The latter may often 
 be detected by holding in front of their eyes different pairs 
 of convex, neutralised by their corresponding concave 
 lenses. With these, thinking they are being aided, such 
 patients may frequently be persuaded to read perfectly. 
 Another method of detecting simulation, especially of one 
 eye, is to hold in front of the blind (?) eye, a prism with 
 its base out or in, when, if there be an attempt (seen by 
 movement of the eye) to fuse the double images, it proves 
 sight present in the eye in question. 
 
 If some such order of procedure, as indicated in these 
 pages, were adopted, one would not, as is now frequently 
 the case, see a beginner fall into the error of supposing a 
 patient myopic because he can read -f (-§£) as well with, as 
 without, a concave lens ; or that hypermetropia is present 
 because the patient can read Sn. i with convex glasses. 
 
 Some of the statements may have appeared somewhat 
 sweeping but it has been thought advisable not to confuse 
 the beginner by enumerating all the possible and minor 
 exceptions to the general rules.
 
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