Refraction and motility of the eye, with chapters on color blindness and the field of vision

Front matter

Glass.

Book.

COPYRIGHT DEPOSIT

Preface To Second Edition

This little book has been reprinted a number of times without change since its first appearance, but the recent remarkable recrudescence of interest in Ophthalmology has made another edition desirable, with some changes and additions.

Prepared originally as a series of lectures to the writer's post-graduate students it included a number of topics not usually found in books on refraction. Every effort was made to avoid the theoretical without sacrificing the essential; to have each subject prepare for and lead up to the following one; to avoid the laying down of dogmatic rules, but to explain reasons so that the student should eventually rely on himself and be prepared to undertake the entire functional examination of the eye.

The common belief that Eefraction is nearer an exact science than any other department of medicine has been a great misfortune to Ophthalmology. On this postulate men with equal training should arrive at exactly the same results. It leads many ophthalmologists to consider refraction as professional drudgery, as uninteresting as the measurement of the schematic eye, except for the fee involved; and is the chief basis for the lay belief that it is not essentially a department of medicine at all.

Refraction is more than a science. It is an art based on a science, and the pre-eminent scientist may notoriously be a very poor artist.

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j v PREFACE TO SECOND EDITION.

Theoretically there are few eyes that could not be "glassed." But if the physician believes that glasses are a nuisance which, like drugs, should only be prescribed when clearly indicated; if he considers not the eyes alone but the whole patient and finally prescribes what he thinks that patient needs, whether it be simply ocular hygiene, or glasses, or an operation; if he then instead of washing his hands of the result like a mere scientist, watches it sympathetically and hopefully, he converts what might be drudgery into service and earns some of the proverbial joy of the artist.

E. M. A.

INTEODUCTIOE".

The preparation of this work is the result of several years of post-graduate teaching, and while portions of it may be of interest to those who are already competent ophthalmologists, it is especially designed to meet what the writer conceives to be the needs of tAvo individuals, the general practitioner and the embryo ophthalmologist.

Whatever may be our personal estimate of the permanent value of writings such as those of Gould, Stevens, Eanney and others, we must all admit that they have worked a great change in the popular idea, whether lay or professional, of the scope of ophthalmology. The physician has always been ready to admit the value of fundus examinations in occasional cases of nephritis, meningitis and the like, but these occasions were so rare that he has thought best to devote his attention to diagnostic methods of wider application. He has always been ready to admit the necessity of glasses to those who could not see but, as he had neither the time nor the skill to provide them, he neglected the subject entirely. But of recent years a great change has taken place. A few men have long taught, almost unheeded by the profession, that the relation between the eves and other organs is so intimate, that defects in one often result in functional defects in the others. The laity first viewed the idea with incredulity, later with increased favor. Very possibly they will let their enthusiasm carry them too far, and lead them to expect too much, but at present there is a public demand so large and so profitable, that v i INTRODUCTION.

it "has attracted the attention of irregulars of all sorts as the advertising pages of every magazine will show.

The physician is being compelled to investigate that he may meet the inquiries of his own patients, and even if he has no time or desire to enter the special field himself, he must have an intelligent conception of the possible role of the eyes in a given case.

The limits of the field are not yet clearly denned: probably they will expand in some directions and contract in others, but they overlap more or less nearly every department of medicine. The pediatrist is beginning to understand that defective eyes are responsible for much of the mental hebetude of children, for truancy and dislike for the mental tasks which are normally attractive to the young, for headaches, habit spasms, and possibly for some epilepsies as well. The internist is coming to recognize that malfunction of the eyes may at times cause some of those vague conditions which it used to be the fashion to call vertigo, biliousness, and malaria and more recently uricacidemia, autotoxemia, and the like ; for many cases of functional neurosis of the stomach, the heart, the intestines. The neurologist must admit the eyes as a factor of importance in man'y cases of headache, insomnia, and those persistent and discouraging states of mental and physical irritability or depression which he calls neurasthenia. The gynecologist is beginning to recognize that many of the headaches and nervous manifestations usually ascribed to the menopause are due rather to the simultaneous onset of presbyopia and are relievable by glasses.

But we shall never know the exact limits of the field, except by a vast amount of more or less experimental collaboration between general practitioners and specialists, and if we expect to secure this collaboration we must give

INTRODUCTION. vii

in return results based on work that is both honest and skillful. In the first respect I do not doubt we can meet the demand but no one who makes a practice of investigating the previous treatment of his new patients can avoid the conclusion that the general average of work is very far from what it should be.

The reason for this is the almost universal lack of systematic instruction. The embryo specialist has too often with the lapse of years become very rusty in his physics, anatomy, and physiology. When he begins his post-graduate work in one of the large cities he is invariably impatient of the preliminary drudgery which he ought to have mastered at home, and, fascinated by the variety of instruments and the facility with which others use them, he is apt to forget that the making of a good ophthalmologist requires much more than the possession of a complete office.

The man who neglects the fundamentals in his eagerness to work on patients, and to see and do operations, rarely acquires more than a smattering of his subject.

By mastering the principles at home, one subject at a time, with a few simple instruments and a schematic eye, the student when he finally comes to his post-graduate work will be surprised at the ease with which he takes it up. He not only derives many times more benefit from his instructors but actually saves much time.

There are two great classes of patients who consult the physician regarding their eyes : the first need glasses simply to improve their sight, while the second come to be relieved of headaches or reflex troubles of some kind. Though it requires a larger outfit, the task is in the first class often absurdly simple, and since the practitioner will certainly have more skill than the itinerant optician or department store clerk to whom most of these people now resort, he may v iii INTRODUCTION.

without hesitation attempt their correction. The relief of the second class often demands an exactness of correction which is apparently beyond the reach of many professed ophthalmologists, and certainly should not be attempted by the general practitioner if other help is available. Even if he makes no attempt to correct personally the errors he discovers, he can often throw light on a puzzling case and perhaps bring new hope to some miserable sufferer.

In conclusion the writer wishes to acknowledge his obligation to text-books such as those of G-anot, Foster, Fuchs and Ball, and to the special works of many others. It may seem an impossible task to harmonize the views of such dh^erse authorities as Gould, Stevens, Savage, Duane and Valk, but the writer can at least acknowledge his deep obligation to every one of them. From the last-named in particular he has derived through the personal contact of many years not only instruction and advice but the stimulating influence of an inquiring mind and a perennial enthusiasm.

E. M. A.

Chapter I. Page

iii

Light: Emission and wave theories. Reflection: Regular and irregular — Its laws — Mirrors, plane, concave and convex. Refraction: Its laws — Prisms, their action, strength and numbering — Lenses composed of infinite number of prisms — varieties — Convex spherical lens — action — axial ray — focus — nodal points — optic centre— secondary axes and foci — conjugate foci— images and their construction— real and virtual images- Concave spherical lenses — action, foci and images — Cylindrical lenses, convex and concave, action, axis, strength — Numbering of lenses— Metric and inch systems— Recognition — Centreing and measurement of lenses — Combinations.

CHAPTER II. The Emmetropic Eye 37

Anatomy: Supporting, nutritional and sensory structures. Refracting Media: Cornea, aqueous, lens and vitreous — Function of iris — The emmetropic eye — The standard or reduced eye — Formation of images — Optic axis — Visual angle — Distant vision — Near vision — Diffusion circles. Accommodation: Mechanism and effect — Far point and near point — Region and amplitude of accommodation — Effects of age. Examination of the Patient: Personal history— Eye history, general scope — Test cards for distant and near vision— Records — The trial case.

Chapter III

The Ametropic Eye: Varieties— Examination— Lateral illumination— Purkinje-Sanson reflexes. The Ophthalmoscope: Construction and theory — Direct method — Opacities in the refracting media, their localization— The pupil and its reaction — The fundus oculi — The nerve head and its physiological and pathological variations — Retinal and chorioidal vessels— The macula— Estimation of refraction with the ophthalmoscope — Em-

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x CONTENTS.

PAGE

metropia — Hyperopia — Myopia— Astigmatism — Differences cf level in the fundus. Indirect Method: Its technique — Advantages and disadvantages.

Chapter IV

Retinoscopy: Its value as a test and advantages- Requisites: relaxed accommodation in patient and keen vision in surgeon — The mirror — The light — The reflex or shadow — Its real motion — Its apparent motion — High hyperopia — Myopia — Emmetropia — Myopia of one dioptre — Rule for retinoscopy — Estimation of astigmatism of various types — Difficulties — Corneal and lenticular opacities — Spherical aberration — The scissors reflex. Retinoscopy Without a Cycloplegic not an exact but a useful test Rule.

Chapter V

The Pupil — Cycloplegics — Miotics — Static Refraction ... Ill

The Pupil: Its contraction and dilation — Various reactions — Anisocoria — The Argyll-Robertson pupil. Cycloplegics and Mydriatics and their action — Indications for cycloplegia in refraction — Choice of a cycloplegic — Atropin and homatropin Static Refraction — Its meaning and best method of estimating — Use of the trial case — Final prescription as based on static refraction. Miotics: Their action and use — Ciliary tonics.

CHAPTER VI. Hyperopia . . 127

Hyperopia: Definition — Refractive and axial — Vision in hyperopia — Manifest — Latent — Total — Facultative — Absolute hyperopia — Near vision — Symptoms, subjective and objective — Diagnosis—Treatment — Retinoscopy — Ophthalmoscopy — Keratometry — Trial case — Illustrative cases — Hyperopia simulating myopia- Complicating strabismus — Spasm of accommodation — When to use cycloplegics and when to avoid them — Final prescription for glasses — General rules.

CHAPTER VII. Myopia 144

Myopia: Definition — Refractive and axial— Causes of myopia — The myopic a diseased eye— Anatomical changes in chorioid and papilla — The myopic crescent — Symptoms of myopia— Region and amplitude as compared to those of emine-

CONTENTS. xi

PAGE

tropia an<i hyperopia— Advantages and disadvantages of myopia —Postponement of presbyopia— Progressive myopia— Lack of reflex symptoms and pain in pure myopia — Prognosis — Ciliary spasm and myopia — Diagnosis of myopia— Differentiation of benign from progressive myopia by the corneal radius — Treatment of myopia — Danger of over-correction — Advantages of cycloplegia — Retinoscopy— Ophthalmoscope unreliable in myopia — Subjective tests— Full or partial correction — Hygiene — Operative method in high myopia — Probable reduction of myopia by removal of lens.

CHAPTER VIII. Astigmatism 163

Irregular Astigmatism: Corneal and lenticular types —Their limited treatment. Regular Astigmatism: Corneal and lenticular— Refraction — Causes — Vision in various types — Asthenopia and other symptoms— Estimation by retinoscopy, the ophthalmometer and trial case — Cycloplegia or not — The ophthalmometer or keratometer — Its advantages and disadvantages — Astigmatic charts. Htperopic Astigmatism: Simple and compound — Detection and correction both with and without cycloplegia. Myopic Astigmatism: simple and compound and their correction. Mixed Astigmatism.

CHAPTER IX. Presbyopia — Anisometropia — Aphakia 194

Presbyopia: What it means and what it depends on — Symptoms, subjective and objective — Treatment in emmetropia — In ametropia of various types. Anisometropia: Symptoms subjective and objective— When to treat and when to let alone. Aphakia: Congenital and operative — The fitting of glasses after cataract extraction.

CHAPTER X. Binoci lab Vision 208

Binocular Single Vision: Its physiology— The eyeball and its possible movements— Primary position — Convergence — Divergence — Rotation— Torsion— The extrinsic muscles and their action singly and together— Their nerve supply — Basal centres — Fusion centres for co-ordination — Cortical centres for voluntary rotation— Tests of binocular vision — Diplopia, homonymous, crossed and vertical.

xii CONTENTS.

CHAPTER XL FAGE

Position of Rest at far and near points — Prism tests — Maddox rod — Duane's parallax test — Stevens', lens and Hardy's cone tests — Torsion equilibrium— Maddox rods and Maddox double prism — Relation of convergence and accommodation — Metre angle — Cover test — Graefe 'equilibrium test. Fusion Powers: Requisites for fusion — Prism convergence — Divergence — Sursumvergence — Deorsumvergence — Torsion power — Stevens' clinoscope — Maddox rods— Relation of fusion powers. Voluntary Motions: Rotations — Linear measurement— Use of perimeter and Stevens' tropometer.

CHAPTER XII. Heterophoria 242

Orthophoria: Meaning and rarity. Heterophoria: Varieties and nomenclature — Causes, congenital and acquired — Symptoms, subjective and objective — Treatment— Refraction — Increase of fusion power or nerve stimulus — Increase of muscle power — The stereoscope and prism exercises — Prisms for constant use — Operation a last resort — Partial tenotomy — Complete tenotomy — Shortening an ocular muscle — Advancement— Indications for and choice of operation. Esophoria: Its varieties, diagnosis and treatment. Exophoria — Hyperphoria — Cyclophoria and the various conjugate imbalances.

CHAPTER XIII. Heterotropia — Strabismus — Squint 270

Strabismus: Primary and secondary deviations — Diagnosis from paralytic squint — Measurement, — linear, — by perimeter — Amblyopia in squint, congenital and acquired — Apparent squint — Varieties of squint— Etiology, congenital and acquired— Refraction an important factor — Lack of fusion power — Organic changes in muscles — Treatment of patients who are not amblyopic — Refraction— Education of fusion powers — Worth's amblyoscope and the stereoscope — Operation the last resort— Choice of operation — Results, happy and unhappy — Test of cure — Treatment of amblyopic cases — Cosmetic effect only — Refraction of good eye— Operation on bad eye— Choice of operation.

CHAPTER XIV. Ocular Paralysis 296

Motor Paralyses: Primary and secondary deviations — Diplopia— False orientation— Limited motion — Vertigo — Contrac-

CONTENTS. xiij

l'AGE

tures — Varieties of paralysis — Etiolcgic factors — Localization of lesion — Localization by diplopia — Theoretical effect of various single paralyses— Practical method— Means of excluding or identifying paralysis of obliques — Rule for identifying straight muscles involved — The. perimeter and tropometer in paralyses — complicated cases— Causal treatment— Local treatment by pads and prisnis — Operation in old paralyses. Fusion Paralyses: Of convergence and divergence — Symptoms — Diagnosis — Treatment. Conjugate Paralyses to right and left and up and down — Symptoms — Diagnosis — Treatment.

CHAPTER XV. Color-Blixdness 319

Colors: Spectral and pigmentary — Primary and secondary. Color-Sexsatioxs: Young, Helmholz and Hering theories. Color-Blixdxess: Congenital and acquired — Significance of latter varieties — Tests — Spectroscope — Lantern tests — Wool tests k — Rules — Quantitative testing.

CHAPTER XVI. Field of Vision 333

Central and peripheral vision — Projection and orientation- Confrontation test — Application in cataract — Perimeter test — Perimeter charts — Fields for white and the color fields — Scotomata of various types— Diagnostic value of color fields- Characteristic fields in glaucoma — Atrophy — Retinitis pigmentosa — Retrobulbar neuritis — Chorioiditis — Neurasthenia — Hysteria— Binocular defects in brain lesions— Course of optic nerve— Effect of interruption at various points on field and pupil— Hemianopsia and its significance— Homonymous — Nasal —Temporal.

CHAPTER XVII. The Relation of Functional Eye Diseases to General Medicine 354

EYE-STRAIN: Its definition— Objective symptoms— Subjective symptoms— Ocular headaches— Migraine— Epilepsy— Choreiform movements— Neurasthenia— Functional disturbances of metabolism— Complicating the menopause— Spinal resultants- Spasmodic torticollis — Differential diagnosis — Treatment.

x i v CONTENTS.

Chapter XVIII. Page

Purpose of tests — General principles — Objective tests — Subjective tests — Pupillary indications — Fusion tests — Diplopia tests — Exclusion tests — Color tests — Stereoscopic tests — Field of vision.

Index 379

Refeaotion" and Motility or the Eye.

Chapter I. Optics

Light may be defined as that form of energy which, by its stimulation of the retina, excites the sensation of vision. Every luminous body emits light. The older corpuscular or emission theory of light taught that infinitesimal particles were given off by such bodies which traveled with infinite velocity. The more modern . undulatory theory presupposes an agitation of the luminiferous ether which travels in all directions from its source in the form of oscillations or waves.

On the emission theory the particles were supposed to be in actual motion, like bullets discharged from a gun, while on the undulatory theory there is no actual motion of the particles themselves, but only a state of disturbance which manifests itself by a series of waves with transverse vibrations like those caused by striking a stretched wire. In the illustration (Fig. 1) the straight lines show the direction in which the rays of light travel from a luminous body, while the curved lines show the manner of progress. These waves may have different heights and lengths, and produce varying sensations in proportion to these, but always travel in straight lines, so long as the medium is of a constant demit v.

A ray of light may be defined as the smallest conceivable portion of light. Eays of light starting from their source and proceeding in all directions must necessarily be more or less divergent, but it is evident that rays coming in the same general direction from a source infinitely distant will diverge so little that they may be considered as parallel, and for our purposes rays from a source twenty feet distant may be considered practically parallel. A pencil of light consists of a number of rays practically

Fig. L parallel to a central ray, while a learn of light is simply a larger collection of parallel rays. Though rays of light always travel in straight lines while in a homogeneous medium, they cease to do so when the medium changes, and undergo reflection, refraction, absorption and dispersion, the amount of each depending on the nature of the new medium.

When rays of light are absorbed, they cease for the time to exist as light, but are transformed into heat, or may be given off again in the form of fluorescence or of phosphorescence. Absorption of light is generally associated with reflection. Appreciation of color is due to the absorption by the object viewed of all the light except those rays which, when reflected or transmitted, excite in the retina the sensation of some definite color. Thus, a red glass absorbs all the light except the red rays.

The dispersion of light does not concern us especially. It is sufficient to say that it is by the scattered rays of light that non-luminous objects are visible, and it is due to the reflection of rays from very irregular surfaces.

Reflection is inseparable from refraction. If an object were so absolutely transparent that all rays of light passed through it, it would be invisible. Plate glass is perhaps the nearest approach to perfect transparency, and yet many rays are reflected from the most perfect of plates.

When a ray of light impinges on a surface, the angle which it makes with a perpendicular to this surface is the angle of incidence, while the angle it makes in passing away is the angle of reflection.

The angles of incidence and reflection are always equal, and the incident and reflected rays are always in a plane perpendicular to the reflecting surface. The two laws may be demonstrated by the apparatus represented in Fig. 2. It consists of a graduated circle in a vertical plane. Two brass slides move around the circumference, on one of which is a ground glass screen, P, and on the other an opaque screen, N, with a small central opening. Fixed to the latter is a small mirror, which can be adjusted, but is always in a plane perpendicular to the plane of the graduated circle. At the centre of the circle a small plane mirror is placed horizontally, 0.

A pencil of sunlight is reflected by the mirror through the aperture N so as to fall upon the mirror 0, whence it is reflected and caught on the screen P, which is moved to the necessary position. The number of degrees

REFRACTION AND MOTILITY OF THE EYE.

in the arc AN will be found equal to those in AP. Therefore, the angle of incidence, AON, must be equal the angle of reflection, A OP, and since the plane of the circle is perpendicular to the plane of the mirror by construction, the plane of the rays must also be perpendicular to it. This can be proven to be true for any other position of N, which causes a corresponding change in the

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Fig. 2.

position of P. If the source of light, N, is moved to A perpendicular to 0, the screen, P, would have to be moved to the same spot to intercept the reflection. Consequently, when light is reflected back to its source, its path must, be exactly perpendicular to the reflecting surface at the point of reflection.

Fig. 3 shows two rays of light from a common source reflected from points C and D of a plane surface. The angles aCA and a'CA, being the angles of incidence and

OPTICS.

reflection of one ray, must be equal. Similarly aDB and a"DB must be equal. Then the angles aCA and aDB of incidence, must have the same relation to each other as the angles of reflection which are their exact equivalents. Therefore, rays from a common source after reflection from a plane surface are equally divergent after reflection. By

C D supposing that rays from a' and a" are convergent, we can show that they are equally convergent after reflection, and the case is easier still if we suppose parallel rays, since the angles would all be equal.

Let MN represent a plane mirror on which rays of light from the object, AB, are reflected to the eye. Eays

Fig. 4.

from A appear to come from a, while rays from B appear to come from b. Therefore, the object, AB, appears to be situated at ab, behind the mirror, and it can easily be proven to be as far behind MN as the object actually is in front of it. Such an image is called a virtual one.

Since the distance of objects from the eye .is estimated with the aid of experience by the angle which rays coming from them to the eye make with each other, which is unchanged by plane mirrors (see "Visual Angle"), the apparent distance of A B from the eye is equal to the sum of the incident and reflected rays. The case is very different, however, if the reflecting surface is a rough one. If we substitute in Fig. 4 a lamp for the object and a printed page for the mirror the rays, striking the page undergo the irregular reflection or dispersion alluded to before. We get no image of the lamp but the page becomes itself a source of light from which rays emanate and enter the eye as though they came from MN. The page remains visible so long as light falls upon it no. matter what change is made in the position of the lamp. On this principle we illuminate the fundus of the eye by a mirror and its details become visible, and since the illuminated area acts as a source of light we can estimate the refraction by tracing the course of the emergent rays, disregarding entirely the course of the entering ones.

The appearance of images in a mirror of objects which we are accustomed to consider as having a right and left side is changed. For instance, in the reflection of a person in a plane mirror the right side of the body is reflected in the right side of the mirror, but as the image appears to face the observer, a motion of the right hand will appear in the mirror like a corresponding motion of the left hand on the part of the reflection. The same thing occurs in the reflection of letters on a page or test card. This is known as lateral inversion.

Reflections from concave mirrors are based on exactly the same laws of the equality of the angles of incidence and reflection (Fig. 5).

If MN represents such a concave mirror, with parallel rays of light impinging on it, and C the centre of curvature, the ray, CF, passing through the centre of curvature must be perpendicular to MN and will be reflected back from F, the vertex or middle of the mirror. CF is then the principal axis of the mirror, while any other rays passing through C must also be perpendicular to the mirror at the point of intersection and constitute secondary axes. Eays parallel to the principal axis after reflection will intersect the principal axis at , the angles of incidence and reflection being equal. The other parallel rays will intersect the principal axis at the same point which is known as the focus of the mirror, and its distance from F as the focal

Fig. 5.

length. The focal length of weak concave mirrors is approximately half the radius of the curvature.

Eays of light from infinity are parallel and after reflection will all pass through the focus, and, conversely, rays emanating from its focus will after reflection emerge parallel. As the source of rays approaches the mirror, the rays become more divergent and come to a focus nearer and nearer to the* centre of curvature; when the rays emanate from the centre of curvature, being perpendicular, they are all reflected back to their source. When the light is between C and 0, the rays cut the principal axis further and further from the mirror, till it reaches 0, when they become parallel, and as the light is carried still nearer the mirror, the rays become divergent and their focus a virtual one formed behind the mirror by projection of the rays.

Hitherto it has been supposed that the luminous object placed in front of a mirror was simply a point, but if the object is larger we can imagine it as composed of a number of points, each on a secondary axis, and by locating the focus of each we should determine the position of the image of the object.

Fig. 6.

The reflection of AB in a concave mirror is constructed thus. A ray, AD, parallel to the principal axis of the mirror, is reflected so as to pass through the principal focus, and the point where it meets the secondary axis, drawn from A, through the centre of curvature, (7, will be the point where the image of A is formed, namely, a. In a similar way we locate the image of B at b, then all the imaginary points between A and B will be reflected so as to fall between a and b.

This image may be seen in two ways, either by placing the eye at ab, or it may be intercepted on a screen at the same place; therefore the image is real, inverted, smaller and placed between the centre of curvature and the principal focus. If we place the object at ab between the centre of curvature and the focus, the image will be at AB, larger, inverted and real. If the object is placed at the focus, no image is formed, since the rays after reflection will be parallel to the principal axis.

If the object is at AB (Fig. 7) within the focus, the reflection of A will occur at D and that of B at E. Conse-

OPTICS.

quently, the only place where the secondary axes, CA and CB, can intersect these lines is behind the mirror at a and h, which represent the extremities of the image. This image is then virtual in that it cannot be projected on a screen, it is larger than the object and is erect.

Fig. 7.

If the mirror be a convex one, the rays are divergent, no matter how near or how far AB is from the mirror. Consequently, the only points where these rays could intersect the secondary axes, AC and BC, is at the two points behind the mirror, which determine the position of the

Fig. 8.

image. Consequently, the reflection in a convex mirror is always erect, small and virtual.

Refraction. — When rays of light pass from one medium to another of different density, they are refracted or bent.

A very good illustration of refraction is the apparent bending of a cane thrust obliquely into a pool of water.

REFRACTION AND MOTILITY OF THE EYE.

Let A, B and C represent three silver coins, so arranged on the bottom of an empty pail, that the light from the candle reflected from B comes to the eye of the observer and makes it visible. The other coins are invisible, because one (A) receives no light from the candle and the other (C) is hidden behind the edge of the pail. But if the pail be filled with water all three coins at once become visible. If the sides of the pail be considered as perpendicular, we see at once that the rays from the candle passing from the air into a denser medium have been