THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES s^^njT^^ Skiascopy A Treatise on the Shadow Test in Its Practical Application to the Work of Refraction EXPLANATION IN DETAIL OF THE OPTICAL PRINCIPLES ON WHICH THE SCIENCE IS BASED WITH SIXTY-NINE ILLUSTRATIONS AND FOUR PLATES SECOND EDITION PUBLISHED BY THE KEYSTONE THE ORGAN OF THE JEWEI.RY AND OPTICAI^ TRADES 19TH & Brown Sts., Philadelphia, Pa., U. S. A. 1903 All Rights Reserved Copyright, 1899, by B. Thorpe Publisher of The Keystone THIS TREATISE Skiascopy GEO. A. ROGERS Formerly professor in the Northern Illinois College of Ophthalmology and Otology, Chicago ; Principal of the Chicago Post-graduate College of Optometry, Lecturer and Specialist on ' Scientific Eye Refraction, is recognized as the clearest exposition of the shadow test and most reliable guide on the use of the retinoscope available to the ophthalmologist. Skiascopy ^ C O PREFACE TO SECOND EDITION The demand for a second edition of this work so soon after the original publication substantiates every claim that was made for it in the preface to the first edition. Teachers and students of optics, as well as practicing opticians, have found it not merely a guide and reference book, but a thorough education on the subject of the shadow test, a complete mastery of which is now regarded as one of the essential qualifications of every optician. In refraction work especially "a little learning is a dangerous thing," and the treatise which is all method and no explanation is a good work to avoid. The present volume contains both. This second edition in its handsome silk binding will be a graceful as well as a valuable addition to the optician's library. PREFACE TO FIRST EDITION The compilation of this volume was undertaken in response to a general demand on the part of oculists and opticians for a work which would cover the subject more fully than any thus far published. Any treatise on skiascopy is obviously incomplete which merely describes the method of applying the shadow test without satisfactory explanation of the optical principles involved. The works on the subject thus far published are open to this criticism. The present volume aims at supplying the deficiency, covering, as it does, not only the method of applying the test and the phenomena revealed in its application, but also the why and wherefore of such phenomena. One can readily understand that the practical value to the refractionist of skiascopic manifestations will be greatly enhanced by a proper understanding of their cause and the scientific principles con- trolling them. A valuable feature of this work is a description of skiascopic apparatus, including all the latest and most improved instruments for the use of the refractionist in applying the test. Another very serviceable feature is a copious index alphabetically arranged, which will greatly facilitate reference. CONTENTS. PAGE. Introductory 13 Popularity of Skiascopy. A Purely Optical Test. Chapter 1. Subject Defined and Outlined 17 Elementary Principles of the Test and Their Application in Skiascopic Examinations. Chapter 2. General Optical Principles 47 Notation of Light and of Curved Surfaces. Dynamic Prop- erties of a Wave of Light. Chapter 3. General Optical Principles 71 Refraction of the Eye. Coef^cient of Emmetropia. The Dioptric Surfaces. Transition of Image in Skiascopy. Chapter .}. General Optical Principles 92 Focus, Dififusion, Aberration, Inversion and Magnification. Chapter 5. Static Factors of Skiascopy no The Four Areas. The Three Intervals. Subsidiary Areas and Intervals. Analysis of Static Factors. Static Effects. Chapter 6. Dynamic Factors of Skiascopy 130 Tilting Mirror and its Dynamic Effects. Motion at Lumin- ous Area. Changing the Intervals. Other Dynamic Principles. 9 lO CONTENTS. Chapter 7. I'AGE. The Study of the Eye by Skiascopy 148 Emmetropia and Symmetrical Ametropia. The Three Pri- mary Cases. Static and Dynamic Appearances. Chapter 8. The Study of the Eye by Ski.\scopy 164 Unsymmetrical Ametropia. Regular Astigmatism. Irregu- lar Astigmatism. Static and Dynamic Properties. Patho- logical Cases. Chapter 9. Conditions Favorable to Successful Work in Skiascopy. ... 1S3 The Operating Room and its Arrangements. Practical Operating Suggestions to Beginners. Chapter 10. Skiascopic Devices and Inventions 195 Ingenious Appliances Devised to Make the Method Mechani- cally Perfect and Comfortable for the Operator. Appendix 211 Abbreviations, Symbols and Designating Letters. Glossary of Optical Terms 213 Index 21Q INTRODUCTORY. A MONG all the methods of practical optometry none has -^^^ proved of greater interest or incited closer study than that which is known as skiascopy or "the shadow test." That this should be the case is not surprising, for by no other method, subjective or objective, can the full dioptric power of an eye with strict reference to the work it is required, in per- fect vision, to perform be so quickly and accurately measured. It is safe to presume that the method will grow in favor from year to year, and that eventually no one who cannot or will not employ it will attain the highest professional standing. Practically the method is simple, but no method goes deeper into the fundamental principles of optics for its founda- tion. To learn to use it practically is but the work of a few days under a competent instructor, but to understand the varied and peculiar phenomena made manifest in a skiascopic examination requires that the optician or oculist be grounded in the most elementary principles of optics, more thoroughly grounded than he can be by weeks of study of standard and current optical literature. In fact, optical literature, as it is to-day, does not adequately account for some of the appear- ances in skiascopy. It does not seem to have been recognized that in using the method the skilled operator is encountering anything un- usual — anything that normal vision has not encountered be- fore. And yet it is unquestionably provable that the ski- ascopist is looking really at "optical illusions" during the critical period of his examination, and that that which he sees has really no objective existence, inasmuch as it is an effect at his own retina — not at the retina of the eye he is examining — that produces reversal, and causes the reflex to appear to move in a direction opposite to its actual motion. 13 14 INTRODUCTORY. It is our purpose in this work to go more deeply into the fundamental principles of optics upon which the appearances in skiascopy depend than has heretofore been reached; to make not only the phenomenon of reversal, but all the other characteristic phenomena of skiascopy subservient to gen- eral optical laws, and to do that the optical laws must be am- plified somewhat. This special work we have endeavored to bring into three special optical chapters (II., III. and IV.), making them the basis of a closer study, in the subsequent chapters, of skiascopic phenomena. The three chapters referred to have no special reference to skiascopy, and are equally applicable to all optical phe- nomena, but the student who attempts to account for some of the most characteristic phenomena of skiascopy without them will be seriously handicapped. POPULARITY OF SKIASCOPY. The popularity of skiascopy as a method of optometry, and the enthusiasm of those who have taken the pains to mas- ter it practically, is due to three principal causes — all of them very attractive to optical workers. These three chief at- tractions are: 1. It is an objective test. 2. It is wonderfully exact. 3. It is optometrically complete. These attractions are irresistible to the one who is inocu- lated with the real professional zeal. To be able to determine in what direction an eye needs lens help, and the dioptric power of the lens required without asking the patient any questions, appeals to the sense of pro- fessional pride. It is prima facie evidence of more than or- dinary professional skill. It inspires confidence, and confidence creates a demand for such services, and that means increased business and a higher reputation — things that no one clothed in human flesh disdains. But there is a satisfaction in the use of the method aside from its business-winning features. In all subjective testing the oculist or optician depends upon the testimony of one who, probably, has never experi- INTRODUCTORY. 15 enced perfect vision for all his guiding data, while by ob- jective methods the revelation of ametropia is to the skilled observer, direct. By the former method the patient in a sense diagnoses his own case and fits himself. If there is any mis- take the patient is the one to make it. And how could it be otherwise, since he is called upon to bear witness to something that his presence in the optical office is a confession that he is incompetent to testify about? The exactness of skiascopy is due to the fact that it is a dynamic rather than a static test. Motion or action, rather than a mere appearance, is the revealing phenomenon. We may mistake appearances, but we are not easily misled when we judge a quantity or value by motion. This is one of the most general principles of guidance in the ordinary affairs of life. What a thing's action is, that is the thing. In skiascopy we judge the eye's condition by a motion that is developed apparently in the objective pupil — the mo- tion of what is termed the reflex — the direction of motion showing the kind, the rapidity of motion approximating the amount of ametropia. To determine the exact amount it is only necessary to determine what lens power is required to cause motion to culminate and reverse. Motion culminates with the culmination of dif¥usion, and the three phenomena — • culmination of motion, culmination of diffusion and reversal of motion are brought about at one and the same time. It is customary to speak of this interesting point in a skia- scopic examination as neutralizing motion, or as reaching the point of reversal, or as obtaining the maximum of dififusion. The one always implies the others. The maximum of dif- fusion eliminates the moving image as such, leaving only an illuminated area to move. Hence, motion is neutralized. But up to the point of neutralization motion grows more and more rapid, hence it is apparent that the point of reversal is not reached as long as motion is apparent, and a lens of higher power is required to neutralize it. But with the culmination and elimination of motion dif- fusion is at its greatest, causing the reflex to appear as an ex- tended luminous area covering the pupil or occupying zones of the pupil, and beyond this point motion in the opposite l6 INTRODUCTORY. direction develops, so that there can be no mistake about being at the point of reversal; or if not at it on which side of it you are. When you reach such point a simple calculation gives the dioptric assistance required by the eye being examined. But the method is also dioptrically complete — that is, it covers the whole dioptric ground. It is not a partial measure, but the measure of the full dioptric power of the eye, includ- ing every dioptric surface in it. It is of no importance in the result to know what each surface does individually, but it is indispensable to know what all do together, and this is what skiascopy determines. A PURELY OPTICAL TEST. Skiascopy is an optical test in all respects. There is no question of anatomy, physiology or pathology involved in it. To understand it thoroughly requires a knowledge of the prin- ciples upon which the method is based. It is not enough sim- ply to know the rules. Rules are necessary for the blind, but not for those who understand principles. The rules of skia- scopy are exceedingly simple, and the general practical feat- ures of the method may be learned in one lesson. But skill in the use of the method is obtained only by experience, and knowledge of its fundamental principles is acquired only by study. It is our hope and expectation that the following chap- ters will prove useful in extending knowledge of this exceed- ingly interesting method, and lead to a better understanding of its fundamental principles. CHAPTER I. SUBJECT DEFINED AND OUTLINED. ELEMENTARY PRINCIPLES OF THE TEST AND THEIR APPLICATION IN SKIASCOPIC EX- AMINATIONS. OKIASCOPY, in its practical application, is the art of de- ^^ termining- the refractive condition of an eye by the study of the reflex from the retina when the image of a luminous area is cast upon it. In its scientific aspects it is a branch of the general science of optics, being individual only in its method of application of general optical principles. Simple as the test is, primarily, there is hardly an optical principle, or principle of reflection or refraction, that is not made use of in it, for the mirror develops the former while the dioptric media of the observed or observing eye, or both, develop the latter. The subject of skiascopy, like all branches of physical science, presents two phases or aspects to the student. It has its static elements, features, limitations or qualities, and its dynamic properties, attributes or principles. To thoroughly understand its dynamic elements the static foundation must first be thoroughly understood. But before entering at large upon these, it will be well to look at the primary or elementary practical features of the test. We shall do this entirely from an opticist's standpoint, as there is really nothing to the test that is not wholly optical, presuming, for the present, at least, that the reader is grounded in the general optical principles and nomenclature which we shall employ. observer's POSITION. Skiascopy, as defined above, implies an observer, one who surveys from some advantageous position objective optical phenomena displayed upon the retina of an observed eye, and 17 l8 SUBJECT DEFINED AND OUTLINED. of course through its pupil. It also implies that such display is the image of a luminous area of some kind. The definition does not state how the observer is to see such display, for the seeing, rather than the means employed to see, is the essen- tial point. As a matter of fact he does see the display by the use of a small circular mirror having a minute perforation in its centre, called a skiascope. With this mirror he reflects pen- cils of light from the luminous area — back of or at least out of the range of vision of the observed eye — upon and around the eve to be examined. Smaller pencils of these pencils are ad- mitted by the pupil of the observed eye, and its dioptric media focus, as nearly as may be, these pencils upon its retina, forming an image of the luminous area there. The skiascop- ist applies his eye to the perforation in the mirror, and from this point of vantage observes the display upon the retina of the observed eye through its pupillary space. Why does not the skiascopist allow the one under exam- ination to look in a direction that will give the eye to be ex- amined pencils of light from the luminous area direct, or with- out the intervention of a mirror; and why does he not observe the pupillary display from an open position, instead of handi- capping his observations with a small peep-hole? It is because the incident pencils that form the image upon the retina of the observed eye, and the emergent pencils by which the observer sees the pupillary display, traverse the same course in opposite directions. The luminous area, the pupil of the observed eye and the pupil of the observing eye must be in one straight line. If the observing eye is m front of the luminous area it and the head obstruct the incident pencils by which the image is to be formed; if the luminous area is in front of the observing eye it obstructs the emergent pencils or view of the observing eye. The mirror may, however, be in front of the observing eye, and reflect pencils to the observed eye as though they came from a point back of the observer's head. This answers the same purpose as if they came in fact from that point. The peep-hole in the mirror, to which the observer applies his eye, allows the emergent pencils to enter the pupil of the observing eye and thus obtain a view of the display at the pupil of the observed eye. SUBJECT DEFINED AND OUTLINED. IQ PUPILLARY DISPLAY. The observed eye is not directed to the mirror but into space at one side of the mirror, since looking into the mirror directly would stimulate the accommodation of the eye under examination. But the direction is near enough to the mirror to make its pupil accessible to the reflected pencils which fall upon the eye and a small area surrounding it. Smaller pen- cils of these pencils enter the pupil and are refracted by the eye's dioptric media, forming an image of the luminous area, more or less distinct, upon the retina. As the luminous area is usually at a finite distance — i 1-5 to 2 or 3 meters — these incident pencils would not be exactly focused upon the retina of an eye whose accommodation was passive — that is, unless it were myopic to the exact degree required. An emmetropic eye, or a hyperopic eye, or a myopic eye of more or less diop- tric power than would be necessary to balance the incident pencils would display an imperfect image upon the retina — an image produced by diffusion circles rather than foci. Such an image is, we may say, invariable under a skiascopic exam.- ination. Even when the eye is fully corrected by a lens, the image of the luminous area upon the retina, when the accom- modation is passive, is imperfect — th& product of diffusion circles. The skiascopist is not primarily concerned in the char- acter of this image — produced by incident pencils from the luminous area — but in the image at the retina of his own ob- serving eye, produced by pencils emitted from or by this im- perfect image through the dioptric media, the error of which he wishes to determine. These emitted or emergent pencils pro- duce results at his own retina, which are projected into the pupil of the observed eye, forming the pupillary display. The two sets of pencils, incident and emergent, do not join each other point to point, for, although there are diffusion circles upon the retina of the observed eye, the emitted pencils start from points, not areas, of the retinal image, whether it be per- fect or imperfect. The potential foci of the incident pencils may be forward or back of the retina of the observed eye, but the emitted pencils start from points upon the retina, whatever 20 SUBJECT DEFINED AND OUTLINED. the character of the image. If the eye under examination is emmetropic, and its accommodation is passive, these emitted pencils emerge at the cornea as neutral pencils of light — that is, they are neither convergent nor divergent, but consist of plane waves, or, if you choose, of parallel rays. But if the eye under examination is hyperopic, the pencils from the image on the retina are not fully neutralized by the dioptric media, and emerge at the cornea as divergent pencils — that is, they consist of convex waves of light, or, if you choose, of diverg- ent rays. An eye that is myopic emits pencils, that, refracted by its dioptric media, emerge at the cornea as convergent pencils, or pencils consisting of concave waves, or, if you choose, of converging rays. . The pencils do not converge, one to the other, but since the waves of which they are com- posed are concave, their centers of curvature, or potential foci, are somewhere anterior to the cornea of the observed eye. They will form at that point, or area, an image of the retinal image from which they sprung, if allowed to reach their foci without interruption. Such image may be back of the observing eye, at the cornea or in front of it, and between Incident Pencil.— Emmetropia. Emergent Pencil.— Emmetropia. the observed and observing eye. Upon its position with refer- ence to the observing eye depends an important primary skia- scopic manifestation — the direction of motion of the pupillary display when the mirror is tilted. Fig. I A represents an incident pencil of light from a finite SUBJECT DEFINED AND OUTLINED. 21 distance (one meter) being refracted by an emmetropic eye whose accommodation is passive. F, back of the retina, is the f>otential focus, and a diffusion circle is upon the retina. Fig. I B represents a pencil of light emerging from the emmetropic eye, or from the image formed by the diffusion circles, when the accommodation is passive The emergent pencil is neu- tralized by the eye's static retraction, but the incident pencil from a finite distance is not focused upon the retina by the eye's static refraction, although a pencil from infinity would Fig. 2. M) Incident Pencil.— Hyperopia. Emergent Pencil.— Hyperopia. be. Fig. 2 A represents an incident pencil of light from a finite distance being refracted by a hyperopic eye whose accom- modation is passive. The potential focus is of course far back from the retina and a larger diffusion circle than that formed by the incident pencil in Fig. i A results. Fig. 2 B represents a pencil of light emerging from the hyperopic eye, or from the imperfect image produced by the diffusion circles of the incident pencils. It starts at a point in the retina, but as the eye is hyperopic, or of insufficient static power, the pencil emerges as a divergent pencil, composed of convex waves or diverging rays. In other words the eye is as defective in neu- tralizing the emergent pencils as it is in focusing incident pen- cils at F. 22 SUBJECT DEFINED AXD OUTLINED. Fig. 3 A represents an incident pencil of light being re- fracted by a myopic eye. The myopia is slight, for the poten- tial focus is between F (the focal point of emmetropia) and the retina, or at F'. Fig. 3 B represents an emergent pencil, refracted by this myopic eye. As the pencil is a little more than neutralized by the refraction of the dioptric media, it emerges as a slightly converging pencil, composed of waves the least bit concave, and therefore having a potential real focus anterior to the cornea of the observed eve. But this Fig. 3. Incident Pencil.— Slight Myopia. Emergent Pencil.— Slight Myopia. focus, if the eye is less than i D. myopic — which it must be in the case shown with the light at one meter or more — is pos- terior to the observed eye at one meter's distance, or to its cornea, C, in the figure. In other words, with both the light and the observing eye at one meter its degree of myopia is in- dicated by the position of the potential focus of the incident pencil forward of F, and by the position of the potential an- terior focus beyond one meter from the cornea of the observed eye, and therefore posterior to the cornea of the observing eye. SUBJECT DEFINED AND OUTLINED. 23 Fig. 4 A represents a case of myopia in which the focus of the incident pencil is at the retina, although only the static power of the eye is in use. A system of pencils such as this would produce a perfect image of the candle flame upon the retina, if the candle flame were at one meter. This eye would show, by such result, i D. of myopia, for with its static power it would focus a pencil of light from one meter. Fig. 4 B rep- resents its refraction of an emergent pencil. The emergent pencil is refracted to the same extent as the incident pencil, and is therefore focused at the same distance in front of the cornea Fig. 4. rA) Incident Pencil —Myopia 1 D. ( S ) Emergent Pencil.— Myopia 1 D. as the light is, or one meter. If the light were a little further away the focus of the incident pencil would be a little forward of the retina, but the focus of the emergent pencil would be no different— that is, for an eye i D. myopic. The focus of the emergent pencil will be at the cornea of the observing eye, C, if it is one meter in front of the observed eye. As all incident pencils from the candle flame, and all emergent pencils from the retinal image of that flame, are refracted in that way, there will be in such case a true image of the preceding retinal 24 SUBJECT DEFINED AND OUTLINED. image at the cornea of the observing- eye, or would be if it were possible to have the light and the observing eve each at one meter from the observed eye. It is the impossibility of obtain- ing these conditions that classifies the pencils into incident and emergent in skiascopy, for they cannot coincide as in direct vision, where the eye is accommodated for the object. Fig. 5 A represents the pencil of light as being focused forward of the retina, at F'. This eye is more than i D. my- opic. The image at the retina will not be perfect, for it will be formed of diffusion circles, the same as the image in Fig. Incident Pencil.— Myopia, above 1 D. Emergent Pencil— Myopia, above 1 D. 3 A, only, in this case, the foci of the pencils are forward of the retina instead of back of it. To place the foci of the incident pencils upon the retina, the eye must be myopic to that pre- cise degree represented by the distance of light. If the light is 2 meters distant and the eye is ^ D. myopic, the image on the retina will be perfect. If the light is ^ meter distant ;and the eye is 2 D. myopic, the same result will be obtained. But in either of these cases, or in any case of myopia, the emergent pencils will be convergent. Fig. 5 B represents the refraction of a pencil of light emerging from the eye in SUBJECT DEFINED AND OUTLINED. 25 Fig. 5 A. As the eye is more than i D. myopic the anterior focus of this pencil is nearer than one meter, or forward of the observing eye if at one meter, or between the observed and observing eye. As all pencils of light whether incident or emergent, will follow the same rule as these pencils, there will be, between the observed and observing eye, all the conditions essential for the formation of a true image there. A true image v^ll be there in fact, a real and physical image, although no screen or reacting surface displays it. It is an image of the image upon the retina of the observed eye. As the image upon the retina of the observed eye is inverted this "aerial" image will be erect. As the aerial image is erect, and it is from it that the observing eye receives its pencils, the image upon the retina of the observing eye will be inverted — an in- verted image of the candle flame. And thus you have the re- fractive effects of all classes of eyes whose ametropia is symmetrical or equal in all meridians. The case represented in Fig. 4 B is of special skiascopic interest, as it shows the position at which reversal of motion takes place with the observing eye at one meter. STATIC ELEMENTS. It is seen that skiascopy presents seven static factors or elements for study. These factors consist of four areas and three intervals. The four areas are as follows: 1. The luminous area. 2. The mirror. 3. The retina of the observed eye. 4. The retina of the observing eye. And the intervals consist of spaces as follows: 1. The space from area i to area 2. 2. The space from area 2 to area 3. 3. The space from area 3 to area 4. As area i, though in front of the mirror, has the effect, by the reflection, of being behind it, intervals i and 2 together form the space in which the incident pencils are developed be- fore reaching the cornea of the observed eye, and area i is eliminated. But as area 2 and area 4 are practically coinci- 26 SUBJECT DEFINED AND OUTLINED. dent in position, intervals 2 and 3 are practically equal in ex- tent. As pencils of light, in passing across these spaces, are in homogeneous air only prior to entering or subsequent to emerging from a cornea, the corneas of the observed and ob- serving eye are the real limits in which the pencils may be developed naturally, and intervals 2 and 3 are shortened by .1 space equal, in the former case, to the diameter of the observed eye, and in the latter by the diameters of both the observed and the observing eye. These spaces are trifling in themselves: but are noted that accurate conclusions may be drawn. We shall have occasion to deal with these static factors more Fig. 6. - - ^-^'' ' static Factors.— Skiascopy. 4 Areas and 3 Intervals. completely in a subsequent chapter. Fig. 6 illustrates the four areas and three intervals. DYNAMIC FACTORS. By a dynamic principle in optics those phenomena that result from and during the change of a static factor are meant. Dynamic factors result from motion of static factors. The mere shift from one static foundation to another, as the short- ening or lengthening of an interval, is not dynamic except in the phenomena that result from and during the change of posi- tion. If any of the areas above is given motion and the ob- serving eye studies the effects or optical phenomena resulting from such motion during the motion, dynamic phenomena appear. This may be accomplished by motion of the lumin- ous area, by lateral motion of the observed eye, by lateral mo- tion of the observing eye, by shortening or lengthening inter- vals, or by motion of the mirror. The latter is the mode SUBJECT DEFINED AND OUTLINED. 27 ordinarily employed in skiascopy to evolve dynamic phe- nomena. TILTING THE MIRROR. The mirror receives only a small part or portion of each pencil emitted by the luminous area. The rest of each of these pencils is dissipated in the darkened room. The mirror is so held as to reflect the pencils it receives upon the eye and the face of the one whose eye is being examined. But only a small portion of each reflected pencil is admitted into the eye under observation. We may call the pencils reflected by the mirror the major pencils and those admitted into the eye the minor pencils. If the mirror is tilted the major pencils are Fig. 7. reflected in a different direction, and the "light on the face" moves about. Its motion is actual and due to a change in the angle of incidence which causes a change in the direction of the reflected major pencils. But as a result of their motion and change of direction, the observed eye, if still within range of these pencils, will receive an entirely new set of minor pen- cils, also pursuing a slightly different direction than these that have passed ofif. This causes the image upon the retina of the observed eye, which is fixed in its direction, to move when the mirror moves. To the observed eye, the virtual image in the 28 SUBJECT DEFINED AND OUTLINED. mirror, which is nothing more than a projection of its retinal image, appears to move, when the mirror is moved, in a direc- tion contrary to the actual motion of the major pencils and the image upon its own retina. This is due to the principle of inversion in projection, the principle that causes an image on the right area of a retina to be projected to a left position in the world, and vice versa. If the plane mirror is so tilted as to cause the reflected major pencils and "light on the face" to move to the right (the observer's not the observed's right) the image on the retina of the observed eye, no matter whether it be myopic, hyper- opic or emmetropic, will move to the right also. The image moves with the mirror — that is, it moves with the "light on the face," or in the same direction. (See Fig. 8.) By the "same' direction, that direction which is in harmony with the motion of the mirror is meant. Two opposite felloes on the same wheel move in the same direction, although in a sense their motion is contrary to each other. That is because of their opposite positions, not because of their opposite motions. Tf the light on the face moves upward or downward or to the left, the image upon the retina of the observed eye goes in the same direction. From the standpoint of the one under examination the virtual image appears to move contrary to the tilting of the mirror, but we are not writing for the benefit of any one but the observer, and the appearances and motions from his standpoint are the essential phenomena. VIEW OF OBSERVER. But, nowithstanding the harmony of motion explained above, to the observer the motion of the image and of the dark areas that surround it will appear to be — under certain condi- tions — directly contrary to this rule. When the "light on the face" moves to the right, the pupillary display in the observed eye moves, or appears to move, to the left. (See Fig. 9.) This phenomenon (with a plane mirror) only occurs when the ob- served eye is myopic, and its emergent pencils focus, as shown in Fig. 5 B, in front of the observing eye. The motion of the retinal image is all right, but the observer views this image SUBJECT DEFINED AND OUTLINED. 29 and its motion throug-h an imperfectly focused lens or micro- scope — the dioptric media of the observed eye. If the eye is myopic the lens is more powerful than the work it has to do. We may consider that it is too far away from die object, and the pencils it emits from that object — the imperfect retinal image — emerge from the cornea as convergent pencils. They focus and form a true image anterior to both the observed and observing eye — that is, between them. The true image thus formed in front of the observing eye is an inversion of the preceding retinal image. All the pencils of light emitted by the observed eye are transposed at this true image, and "forwarded" in this form to the observing eye. The image directly in front of the observing eye is the im- mediate source of the pencils that reach the observing eye, the same as the retinal image is the immediate source of the pen- FiG. 8. Fig. 9. cils emitted from the observed eye. The observing eye, if not too near this aerial image, focuses these transposed pencils and a re-inverted image appears upon the retina of the observing eye. As a result we trace the inversions as follows : The lum- inous area is erect, but the image upon the retina of the 30 SUBJECT DEFINED AND OUTLINED. observed eye is inverted; the first retinal image is inverted but the aerial image is therefore erect; since the aerial image i? erect the image at the retina of the observing eye is inverted. The two retinal images are therefore the same in position. Now, when the image upon area 3 moves to the right (the ob- server's right) the image upon area 4 (the observer's own retina) moves to the right also. The observer projects this motion upon his retina as motion to the left, for the same rea- son and under the same principle that the person under exam- ination projects motion of the image upon his retina, the vir- tual image, as motion in the opposite direction. This reverse direction of motion may appear clearer with- out tracing the effect at area 4, thus : When the image on area 3 moves to the right the true image in front of the observing eye moves to the left, because it is an inverse image of the retinal image at area 3. As the newly transposed pencils come to the observing eye from a position further to the left, the image or display appears to move in that direction. It is as though an object in front of the observer's eye actually moved to the left. It would of course appear then to move to the left, although the image upon his retina would move to the right as heretofore noted. But if the pencils are not focused in front of his eye they are focused more or less accurately upon his retina, and his retina receives the first inverted image pro- duced by the pencils from area 3. Motion on his retina is then opposite to that at area 3. AREA OF REVERSAL. The area of reversal is the position of the aerial image, wherever it may be. Real reversal of motion appears only when the observing eye is far enough back of the area of reversal to obtain something like an image upon its retina. If the ob- serving eye is at or very near the area of reversal, the image upon its retina is so diffuse in character — composed as it is of large diffusion circles — that nothing but a radiance or glow appears in the pupillary space. But at a point a little forward or back of the area of reversal, the observing eye may get a sufficiently good image of the light within the observed eye SUBJECT DEFINED AND OUTLINED. 3I to discover the direction of motion at the pupil, and if forward of it get corresponding motion; but at a point a little back oi the area of reversal it will be able to get reverse motion only. The first and primary work of the skiascopist is to find the area of reversal. If the eye under observation is emmetropic or hyperopic there will be no anterior image, and if it is but slightly myopic the potential anterior image will be back of the observing eye. But by placing a plus lens in front of the eye under observation, and increasing the power of the lens, the observed eye may be made artificially myopic — suffi- ciently myopic to bring the area of reversal to a position in front of the observing eye. This is the plan of procedure in skiascopy. The first and primary purpose is, with or without a lens as the case may require, to get the area of reversal at the cornea of the observer. If he is one meter from the observed eye and the area of reversal is at his cornea, the observed eye, with or without a lens, as the case may be, is one diopter myopic. If it takes a + 3 D. lens to locate the area of reversal at this point, the eye under examination is -3 D. + I D. . -2D. two diopters hyperopic. The — 3D. used above expresses the eye's deficiency (skiascopically) in giving the skiascopist what he wants — the area of reversal at one meter. The + i D. expresses the over dioptric power of an eye that would give him w^hat he requires. The sum of these two, — 2D. ex- presses the eye's dioptric deficiency. It would take, of course, a + 2 D. lens to overcome a — 2D. deficiency, and + 2 D. would be the lens required. GETTING REVERSAL. In working out a case, then, the skiascopist's first or primary purpose is to bring the area of reversal to his cornea, or to determine what lens would be or is necessary to produce that result. But when the area of reversal is at his cornea 32 SUBJECT DEFINED AND OUTLINED. he sees no image at all in the pupillary space, but only a glow, nor can he tell whether motion is one way or the other, for there is no motion if there is no image, of course. He getj> the primary result by gauging the two opposite positions. If, with a + 2.75 D. lens there is very rapid corresponding mo- tion, a + 3 D. lens will probably eliminate both the image or pupillary display, and motion also. A + 3.25 D, may then give very rapid reverse motion. The area of reversal, with a + 2.75 D., is then back of the cornea, but with a + 3.25 D. it is in front of the cornea. With a + 3 D. and the total disappear- ance, as it were, of pupillary display, there is no doubt but that the area of reversal is at the cornea. Perhaps .12^ D. may bring the results nearer — that is, a + 2.87^ D. lens may still give motion with the mirror and a + 3.12^ D. may reverse the motion. In that case + 3 D. is undoubtedly the lens required to bring the area of reversal to the cornea. The above is but an example. It may take minus lenses to bring the area of reversal to the cornea, as a — 2D. lens, or it may take a stronger plus lens, as a + 5 D. or + 8 D. But in any of these cases the procedure is the same. If the eye under observation shows the opposite motion — or motion against the mirror — to start with, it is certainly myopic, and sufficiently myopic to place the image, or area of reversal, be- tween the observed and the observing eyes. In this case the skiascopist places minus lenses before it to bring the area of reversal back to his cornea. If a — 1.75 D. lens still gives opposite motion, a — 2D. lens will possibly stop it. It may even reverse the motion, or make it with the mirror. If — 2 D. lens gives motion with the mirror and — 1.75 D. gives motion against it, a — 1-87^ D. would undoubtedly neutralize all motion and cause the pupillary display of motion to dis- appear. The area of reversal would be at the cornea of the observing eye, or so near it that a more exact location could not be found. RAPIDITY OF MOTION. The apparent motion as seen at the pupil of the observed eye is slowest when the area of reversal is farthest from the cornea of the observing eye. As lenses are added bringing SUBJECT DEFINED AND OUTLINED. 33 the area of reversal nearer to the observing eye, motion at the pupil of the observed eye grows more rapid. It is most rapid just before the pupillary display or motion at the pupil dis- appears altogether. The nearer the skiascopist gets to his primary result the more distinctly marked is the motion. This is a great point in the test, especially for fine degrees of error. He knows when the case gets "hot" or "cold" by the rapidity of motion. If the motion is very sluggish he wastes no time on weak lenses, but takes a 5 D. or even an 8 or 10 D. lens to start with. If it is too strong it is as easy to weaken it by less powerful lenses as to strengthen a too weak lens. In a little while he gets so well acquainted with the degree of motion for different degrees of error, that he will be able to take a lens within .50 D. of what he wants to start with. It then takes but one change usually to get exactly what he is in search of. The difficulties that will beset beginners in the practice of this test will be chiefly in obtaining this primary result — ^bring- ing the area of reversal to the cornea. The pupillary space which they see will seem "dreadfully" small in which to ob- serve motion. And when they get near to the primary result, if they ever do, the motion will be so "lightning" like that "where it comes from and whither it goetli" will be like ask- ing the source and destination of sheet lightning, as seen in the horizon on a summer's evening. But practice will sharpen the perceptive faculties — practice with the schematic e)'e to begin with and later with human eyes. The confusing reflections at first noticed will soon be eliminated and close work begin to be done. CAUSE OF RAPID MOTION. The cause of rapidity of motion, as the area of reversal is brought near to the cornea of the observing eye, is not, as a well-known writer on the subject asserts, due to magnifica- tion, but simply to the nearness of the immediate source of light to the observing eye — the image which constitutes the area of reversal. It is precisely upon the same principles that a near object, moving with the same speed as a distant object, passes across the field of vision more rapidly. We know the j4 SUBJECT DEFINED AND OUTLINED. object is near us, and so do not consider its motion rapid be- cause its image passes across the retina rapidly. But this aerial image, slight though its actual motion may be, is pro- jected into the pupil of the observed eye. It may be an inch from the cornea, but a very slight motion on its part, projected to a point a meter or so away, seems very rapid. It is rapid in crossing the field of vision. If we could know it was so near, however, it might be just as hard to see it, but we would not refer it to a point so far away and would therefore judge its real motion more accurately. One may pass his hand be- fore the eye at a point so near that it flashes across the field of vision quite as quickly as this image when the area of re- versal is near. There is no difference in the two cases. THE FINAL CORRECTION. But bringing the area of reversal to the cornea does not dispose of the case. The final correction must be added to complete the whole. If an eye with a plus lens before it has an anterior image it is artificially myopic — how myopic de- pends upon the distance of the anterior image. If it is one meter from the observed eye, that eye is artificially myopic I D. It is necessary then to add — i D. to the lens which brings the area of reversal to that point. If such lens is a -r 4 D. the addition is simple, for + 4D. - I D. + 3D- is the complete correction. If the primary lens is a — 5 D., for instance, the correction is -5D. — I D. — 6 D. all told. But the observer may choose a greater or less dis- tance than one meter. If the distance is two meters, then the observed eye has been made by the lens in front of it ^ or .5 D. artificially myopic. In that case — .5 D. should be added SUBJECT DEFINED AND OUTLINED. 35 to the primary lens. If ^ meter is the distance of observation — 2D. should be added to the primary lens. Whatever the distance of the observers, the final correction should be for as many diopters as the reciprocal of the distance in meters. When the final correction has been added the eye will be the same in refractive power as an emmetropic eye. It will be artificially emmetropic, which is the precise result wanted. W'ith its correction all on, viewed skiascopically the pupillary display will be the same as that of an emmetrope. The image or pupillary figure will move with the mirror. An expe- rienced skiascopist can tell very closely what this motion should be, without going- to the trouble of making the primary results appear. It is safer, however, to follow the routine de- scribed, for no two emmetropic eyes, or hardly a pair of emme- tropic eyes, are alike, except in being emmetropic. Their dioptric power differs because their anterio-posterior diam- eters differ. But getting the primary lens with great accu- racy is the special fine point in skiascopy. It is there that the error is really measured. Adding the secondary result to that, for the purpose of completing the correction, is perfunctory — according to set rule. Unless the primary modification is made with delicacy and exactness, the secondary or final mod- ification will not make the whole result exact. THE INCIDENT PENCILS. In neither of the corrections above, primary or second- ary, is any attention paid to the incident pencils. They are of course modified at the same time and to the same degree as the emergent pencils when lenses are placed before the ob- served eye, but the purpose of the skiascopist is not to produce a perfect image on area 3 by the lens, but to secure correct emergent pencils. When the accommodation is passive and the luminous area is nearer the observed eye than infinity, a lens in front of the eye will not focus the incident pencils and neutralize the emergent pencils at the same time. The lens that neutralizes the emergent pencils causes the incident pen- cils to focus posterior to the retina, and therefore gives rise to circles of diffusion and an imperfect image at area 3. The primary lens, which brings the area of reversal to the cornea. 36 SUBJECT DEFINED AND OUTLINED. more nearly focuses the incident pencils upon the retina. But it doesn't exactly focus them, because the sum of intervals i and 2 are always a little more than interval 3, since interval 2 equals interval 3. The nearer the luminous area is to the mirror the more nearly are the foci of the incident pencils placed upon the retina with the primary lens. The more dis- tant the luminous area is from the mirror the more nearly the incident pencils focus upon the retina with complete correc- tion. It is seen, then, that in skiascopy, the two sets of pen- cils, incident and emergent, are never quite together, point to point, upon the retina, except in myopia of the exact degree required to focus the incident pencils. But when the cor- rected eye views ordinary objects, whether luminous or non- luminous, and whether w^th or without the use of the accom- modation, the two sets of pencils are together, point to point, for, whatever engages the vision, the eye is accommodated to that distance and focuses the incident pencils upon the retina. The emergent pencils are in like manner focused at the object. These pencils are disjoined in skiascopy by giving the eye divergent pencils while the accommodation is passive. The direction of the visual axis does not allow these pencils to center at the macula, although diffusion circles may spread over the macula. It is essential in making the test without a mydriatic that the accommodation be not stimulated into action. Hence, the necessity that the eye be directed to one side of the mirror that the incident pencils may not fall where they would (unless the person under examination knows how to avoid it) stimulate the accommodation. Such stimulus may be neutralized by will power, but it is hardly to be expected that a person being examined would know how, or attempt if he did know, to neutralize the stimulus. A means may be found of removing any danger of such action being excited. Of such means we shall speak in the future. REGULAR ASTIGMATISM. Astigmatism is want of symmetry in the refracting power of the eye for dififerent meridians. Either or both principal meridians may be hyperopic, either or both myopic, or one SUBJECT DEFINED AND OUTLINED. 37 meridian may be hyperopia while the other is myopic. As the refraction of the eye is positive in all meridians, astigmatism merely shows that positive refraction is greater in one meridian than the other. If the meridian of greatest power is emme- tropic, the meridian of least power is hyperopia, and all the me- ridians between shade down from the most hyperopia meridian to the emmetropic meridian. But if the meridian of least power is emmetropic, the meridian of greatest power is myopic, and the other meridians shade down from the most myopic merid- ian to the emmetropic meridian. If the astigmatism is com- pound there is simply over- or under-power in both meridians, but a greater over- or under-power in one than in the other. The astigmatic element of the refractive error is really not com- pound but simple, for it is the difference of the two meridians, and that difiference is no greater and no less nor more com- plicated because both are wrong. A correction of one me- ridian by a spherical lens may bring the other meridian nearer to correct refraction, but if the astigmatism is mixed, the cor- rection of one meridian by a spherical lens augments the error of the other. Primarily the correction of astigmatism by skiascopy follows the same order as the correction of symmetrical ame- tropia, but the primary correction is first of one meridian — either the meridian of greatest or least power, or the meridian of greatest or least error. A spherical lens is sought which will bring one of the principal areas of reversal — for there ii an area of reversal for each meridian, both principal and sec- ondary — to the cornea of the observing eye. The remaining primary correction must be made with a cylinder, a cylinder that will bring the other areas of reversal — both that of the other principal meridian at right angles to the first, and those of all intermediate meridians — to a position of coincidence with the area of reversal of the primarily corrected meridian. This eliminates the astigmatism and leaves only the secondary or final correction to make the correction complete. This final correction will be spherical, or symmetrical for all merid- ians. There are in all cases of regular astigmatism two prin- cipal meridians at right angles to each other, but each inter- mediate meridian has power in proportion to its position 38 SUBJECT DEFINED AND OUTLINED. between the two principal meridians. If an eye is 3 D. hyper- opic in the vertical meridian and 2 D. hyperopia in the hori- zontal, the astigmatic element is i D. But meridian 45°, mid- way between 90° and o, is 2^ D. hyperopia and meridian 60°, 75°, etc., are less than 3 D. but more than 2^ D. hyperopia, shading gradually from 2 D. at o or 180° to 90°. A + 2 D. sph. corrects hyperopia in the horizontal but leaves i D. in the vertical. In that case the intermediate meridians have a dif- ferent dioptric power, but shade from o D. in 0° to i D. in 90°. The rule for the intermediate meridians will be given in Chapter VIII., as it is only desired here to show that sphericals change the dioptric power of all meridians, but do not affect the astigmatic element. A + 3 D. sph. would neutralize 90° but produce — i D. in meridian 180°. Corresponding to the two principal meridians of an astig- matic eye, there are, in skiascopy, two principal areas of rever- sal, and corresponding to the intermediate meridians of an astigmatic eye, there are, in skiascopy, intermediate areas of reversal for these intermediate meridians. When the observ- ing eye is between the two principal areas of reversal it is necessarily at an area of reversal of some one of the inter- mediate meridians, and as, in this position, other areas of re- versal are both forward and back of it, the effects are confus- ing. A spherical lens may bring the observing eye, without changing its distance, to one of the principal areas of reversal, or it may obtain such position by advancing toward or reced- ing from the observed eye. It is important to find one of the principal areas of reversal and to bring it to the cornea of the observing eye, for then all the other areas of reversal, being posterior or anterior to it, will be posterior or anterior to the observing eye. To ascertain the position of the two principal meridians is almost the first step, and this may be done by developing what is known as the "banded" appearance. THE BANDED APPEARANCE. This is a display at the pupil of the observed eye as though a band of light, narrower than the pupil usually, ex- tended across it. The direction of the band shows the position SUBJECT DEFINED AND OUTLINED. 39 of one of the principal meridians. The development of this banded appearance in astigmatism occurs quite distinctly when the observing eye is at one of the principal areas of re- versal, but it may be made more striking even then. To pro- duce the most striking banded pupillary display, the observing eye must not only be at one of the principal areas of reversal, but the aerial image at the cornea should be made doubly cor- rect by a correct focus in one meridian of the observed eye, so that the preceding retinal image is diffuse in but one merid- ian. An astigmatic eye refracts both the incident and emerg- ent pencils unsymmetrically. If there is diffusion in both principal meridians at area 3, the aerial image at the cornea of the observing eye will be an exaggerated reproduction of such image; but if the original source of light, the lamp f^ame or luminous area, is the same distance from the mirror, in front of it, as the second principal area of reversal is from the mir- ror, or cornea, back of it, one meridian of the observed eye will focus the luminous area. This is apparent from the fact that the anterior focus of one meridian is at the same distance from the observed eye as the luminous area. If such anterior focus is, for instance, -J meter posterior to the cornea or i^ meters from the observed eye, and the luminous area is -} meter in front of the mirror or i-| meters' by way of the mirror, from the observed eye, that meridian of the eye which focuses an emergent pencil from the retina at a distance of i^ meters would also focus upon the retina an incident pencil from i-| meters. If in the above example we suppose the horizontal merid- ian of the observed eye to be the weaker meridian, it will be the meridian to produce a focus of an emergent pencil at i^ meters. It will also focus upon the retina a pencil from i^ meters. But the vertical or stronger meridian will focus the incident pencils anterior to the retina and produce dififusion in the vertical. As a result the retinal image at area 3 will be elongated vertically but correct horizontally. Pencils from this image will be focused in the vertical meridian at one meter or at the cornea of the observing eye, and be there transposed; but in the horizontal meridian the pencils will not have come to their foci. The aerial image at the cornea is 40 SUBJECT DEFINED AND OUTLINED. thus elongated horizontally. The emmetropic observing eye now refracts both meridians symmetrically, but the pencils upon which it acts are divergent in the vertical and convergent in the horizontal. The observing eye may get a nearly correct focus by its horizontal meridian, but there will be large dif- fusion circles in the vertical. This gives an image elongated in the vertical the same as the preceding retinal image in the observed eye, it does not matter whether inverted or upright, since it would be vertical in either case. The optician need not pause in his work to analyze these effects, but by remov- ing the luminous area to a greater or less distance he will bring out the banded appearance. He may also bring out the banded appearance by approaching or receding from the observed eye, provided he does not allow himself to approach or recede from the luminous area at the same time, for that would affect all three intervals at once when it is only desired to affect the sum of intervals i and 2. In the case given the banded appearance would be verti- cal and indicate that the vertical was one chief meridian. Now, this gives the meridian of greatest power as the vertical meridian. A positive cylinder, axis vertical, would equalize the meridians, complete the primary correction, and bring all areas of reversal to the cornea. The dioptric power of such cylinder — that is, whether it should be -|- .5 D., + .75 D., + 1.5 D., or of some other power, would be revealed by trial. There may be a -f 3 D. spherical lens, however, before the eye that is brought to the conditions given, or a — 2D. or some other spherical lens. If the cylinder proves to be a 4- I D., and there is a -{- 3 D. sph. already before the eye, the primary correction is : + 3 D. sph. C + I D- cyl. ax. 90°. But adding the secondary correction of — i D, to this gives: 4- 2 D. sph. C + I D. cyl. ax. 90°. which is the complete correction. But the spherical correc- tion may have been a — 2D. sph. In that case the completed primary correction is: — 2D. sph. 3 + I D. cyl. ax. 90°. SUBJECT DEFINED AND OUTLINED, 41 But this combination reduces to: — I D. sph. C — I D. cyl. ax. i8o°. Adding the secondary correction of — i D. to this we have: — 2D. sph. C — I D. cyl. ax. i8o°. This is the complete correction in its simplest form. In each of the following figures three common conditions are supposed to exist: (i) The light or source of the pencils is at a finite distance, one meter; (2) the accommodation is passive; (3) a degree of astigrnatism exists in each eye. Incident Pencil.— Simple Hyperopia Astigmatism. o C— Luminous Area. X>— Retinal Figure, enlarged. Emergent Pencil. — Simple Hyperopic Astigmatism. Fig. 10 A represents the refraction of an incident pencil of light by an eye having simple hyperopic astigmatism, the potential focus of the emmetropic meridian being at F, pos- terior to the retina, and that of the hyperopic meridian being at F' posterior to F. As a result of these conditions diffusion will prevail at the retina for all meridians, but diffusion will be greatest along the meridian of hyperopia. An image of the candle flame would thus be elongated in the meridian of hy- peropia, at right angles to the meridian of emmetropia. If 42 SUBJECT DEFINED AND OUTLINED. the pencil were from infinity or the eye were accommodated for one meter, F would be at the retina, but F' would still be posterior to it, and diffusion would be confined to the meridian of greatest hyperopia. Fig-. ID B represents an emergent pencil from the same eye. The emmetropic meridian neutralizes the pencil, but the hyperopic meridian is unable to do so. If a positive spherical lens or emmetropic eye focused the emergent pencils in the emmetropic meridian of the observed eye it would be unable to focus the pencil exactly in the two meridians at the same time. At one meter the difference of the two meridians would be reduced by the evolution of the waves of the hyperopic Fig. 11. Incident Pencil.— Compound Hyperopic Astigmatism. Emergent Pencil.— Compound Hyperopic Astigmatism. meridian, tending to make them neutral in all meridians. If the astigmatism were one diopter and the eye were accommo- dated for one meter, the emergent pencil would be focused by the emmetropic meridian at one meter, but the ametroplc meridian (i D. hyperopic) would simply neutralize the pencil. The emergent pencils, in this case, would form at one meter an image diffuse in hyperopic meridian but focused in the emmetropic, the same as a + i D. cylinder, but the original of this aerial image would be the preceding retinal image. Fig. II A represents a pencil of light being refracted by an eye having compound hyperopic astigmatism, F' being the SUBJECT DEFINED AND OUTLINED. 43 potential focus of the meridian of least hyperopia and F" the focus of the meridian of greatest hyperopia. F represents the position of the focus for emmetropia under the conditions named. It is evident, in this case, that diffusion will be greatest at the retina for that meridian which has the greatest degree of hyperopia, and the image of the candle flame will be corre- spondingly elongated in that meridian. Fig. ii B represents an emergent pencil for the same eye. If the eye is one diopter hyperopic in the horizontal and two diopters hyperopic in the vertical, a + i D. lens would neutralize the emergent pencil in the horizontal and place F' at F for the incident pencil. A + 2 D. lens would place F' at the retina and F" at F, making the eye artificially myopic one diopter in the horizontal and emmetropic in the vertical. With such + 2 D. lens diffusion would be confined to the emmetropic vertical meridian, for the incident pencil would be focused by the myopic horizontal meridian. But the emergent pencils from the retinal image would be focused at one meter by the myopic horizontal meridian, and diffuse in the vertical, forming an aerial image doubly diffuse in the vertical, for it would be diffuse in the ver- tical if it were a direct reproduction of the retinal image, and diffusion would be increased in the vertical by the incapacity of that meridian to focus the emergent'pencils. With a + 3 D. lens the horizontal meridian would become 2 D. myopic, the vertical i D. myopic. The incident pencils would be focused upon the retina by the vertical meridian, but forward of the retina by the horizontal meridian, resulting in diffusion, in the horizontal, at the retina. The aerial display at -J meter would be diffuse in the vertical but focused by the horizontal, but as such aerial image is an image of the preceding retinal image, which is diffuse in the horizontal, there would be diffusion in both meridians. At one meter, however, the vertical meridian would focus and the horizontal become diffuse, producing double diffusion in the horizontal. Fig. 12 A represents an incident pencil being refracted by an eye having simple myopic astigmatism of one diop- ter. The incident pencil is focused by the myopic meridian at the retina, the emmetropic meridian focusing at F posterior to the retina. Tlie one diopter of work given all meridians of 44 SUniECT DEFINED AND OUTLINED. the eye by the nearness of the object is performed by the myopic meridian; but the emmetropic meridian is unable to focus at the retina without the use of one dioptry of accommo- dation. Diffusion in the emmetropic meridian results. Fig. 12 B represents an emergent pencil being refracted by such eye. The emmetropic meridian neutralizes the pencil merely, but the myopic meridian focuses it at one meter. If the observed •eye is one diopter myopic in the vertical and emmetropic in the horizontal, the retinal image produced by the incident pen- cils will be diffuse in the horizontal, forming a figure elongated horizontally because of diffusion in the horizontal. Emergent Fig. 12 Incident Pencil.— Simple Myopic Astigmatism —1 Diopter Emergent Pencil.— Simple Myopic Astigmatism.— 1 Diopter. pencils proceeding from this figure will be focused at one meter by the vertical meridian, forming an aerial image doubly elongated in the horizontal — elongated by the original retinal image, and by diffusion in the horizontal for emergent pencils. But if an observing emmetropic eye be at one meter it will focus the pencils in the horizontal but not in the vertical, pro- ducing, at the retina of the observing eye, diffusion in the verti- cal. The eye has no capacity to refocus pencils already focused at or within its dioptric media by some preceding lens action. But horizontal diffusion at the retina of the observed eye will not be overcome by vertical diffusion at the retina of the observing eye. There will be, therefore, in this case, diffusion in both meridians. SUBJECT DEFINED AND OUTLINED. 45 Fig. 13 A represents the refraction of an incident pencil ■of light by an eye having compound myopic astigmatism, Fig. 13. Incident Pencil.— Compound Myopic Astigmatism. Emergent Pencil.— Compound Myopic Astigmatism. myopia being of one diopter in the least myopic meridian, and more than one diopter in the opposite meridian. The incident pencil is focused upon the retina by the least myopic meridian, but forward of it by the other chief meridian. Fig. 13 B rep- resents a pencil of light emerging from the above eye. The emergent pencil is focused at one meter by the least myopic meridian, but nearer than one meter by the meridian of greatest myopia. If the astigmatic element is one diopter, a — i D. sph. would convert the case into one of simple myopic astigmatism of one diopter. Fig. 14. Incident Pencil.— Mixed Astigmatism. Emergent Pencil.— Mixed Astigmatism. Fig. 14 A represents an incident pencil of light being refracted by an eye having mixed astigmatism. The degree 46 SUBJECT DEFINED AND OUTLINED. of myopia shown is more than one diopter, while the degree of hyperopia is not indicated. Myopia is shown to be in excess of one diopter by the position of the focus forward of the retina in Fig. 14 A. But it is also shown by the position of the focus of the emergent pencil within one meter of the eye. The foregoing constitutes the elementary principles of the practice of skiascopy. But the only way to understand a sys- tem is to know the system all through. The following chapters will be devoted to evolving the principles, describing the methods and means, developing further possibilities of the test and grounding the reader upon the general principles of optics as related to this interesting method of examination. CHAPTER 11. GENERAL OPTICAL PRINCIPLES. NOTATION OF LIGHT AND OF CURVED SURFACES. DYNAMIC PROPERTIES OF A WAVE OF LIGHT. BEFORE proceeding further it seems necessary to make a little excursion into the field of general optics, and to prepare the reader to understand the language it will be neces- sary to employ in the succeeding chapters of this book, for it will be necessary to use terms not at present in general optical text-books and writings. This new optical language grows out of the analysis of the force with which optics deals — the force of light. We will start with the pencil of light. Most opticians would at once consider that they comprehend fully what a pencil of light is, and undoubtedly they do, but an analysis of this primary factor in all optical phenomena will show that there is a chance to get a better idea of something we are in the habit of considering every day. A pencil uf light is com- posite. Of what is it composed? We do not refer now to its chromatic elements but to its simple optical elements. Probably two-thirds of all the opticians would say that a pen- cil of light is composed of rays of light, or that a pencil of light is, as some writers express it, a "bundle of rays." We do not consider this answer to be satisfactory, and will show why. What is a ray of light? A ray of light may be considered as a mere mathematical line, or as a physical part of a pencil of light. Of course in the former light it is not a part of the pencil any more than the equator is a part of the earth, but in the latter aspect it is a minute fractional part of a pencil of light — so minute that, for all practical purposes, it may be regarded as a line. To say then that a pencil of light is composed of rays of light, is to say that it is composed 48 GENERAL OPTICAL PRINCIPLES. of fractional parts. That, surely, is not a good answer, for every unit is, as a matter of course, composed of fractional parts. If you were asked, "Of what is an apple composed?" would it be a good answer to say, "An apple is composed of four quarters of an apple, or of quarters, or hundredths, or thousandths, or millionths?" Certainly not. That would be simply avoiding the question. But if you should say of its skin, its pulp and core with seeds, the answer would be more satisfactory. Within the apple there are seeds. A seed may be of exactly one-hundredth of the bulk of the apple or one- fiftieth of its weight, but the seed is an elementary part of the apple aside from any consideration of this kind. The seed is as much a unit as the apple, but it is a different kind of unit. A pencil of light is composite in the same way. It is com- posed of more elementary units, not rays, but something else. Light is propagated in a homogenous medium in great spherical waves. At starting these spheres are very minute, but they enlarge very rapidly. Light is generated at points, and each luminous point is the center of a whole series of spherical waves. But by the reflection of rough surfaces, although the preceding order of the waves is broken, new spherical waves, composed of the impulses of the dissociated incident waves, are formed. So, whether from a luminous point or an opaque point of reflection, these series of waves of light extend out into space. A pencil of light is a definite conic section of such a sphere. It is conjjDosed of a fractional part of each wave from the point of starting outward. There is a definite distance from crest to crest between these waves, but that is of little optical importance, for the crests and hol- lows, or extreme positions of molecular motion, are no more important than the slopes. The principal element of optical importance in the waves is their degree of curvature. The degree of curvature is great- est at and near the point of starting or center of curvature. The curvature of the waves decreases with their distance from this center of curvature, and it is with respect to curvature that a notation or nomenclature is of optical value. The author has improvised such a notation by designating the curvature GENERAL OPTICAL PRINCIPLES. 49 of a wave one meter from its center of curvature, as one curv- ometer, or i Cm. The curvature of a wave ^ meter from its center is then 2 Cm., and 2 meters from its center of curvature Fig. 15. is ^ Cm. In other words, the curvature of a wave is inversely proportional to its distance in meters from the center of curv- ature. A wave 8 in. from such center has then a curvature of 40/8 = 5 Cm. Fig-. 15 illustrates this notation, showing the regular decrease of curvature as the wave advances into space. Fig. 16. But with the evolution of decreased curvature there is a coordinate and compensating expansion of the wave. It evolves, as it advances, increased extent in direct proportion to its radii. Measured by the arc that subtends a given angle, or by the sine of such angle, the extent of the wave is directly proportional to the radii, and therefore the curvature is in- versely proportional to the sines of a given central angle. In Fig. 16 let M be the center of curvature of a wave, and G E and 50 GENERAL OPTICAL PRINCIPLES. D K represent the positions of a wave, respectively one and two intervals from M, then will sine F E = ^ sine P K. The truth of the above is established by the proposition that "a line parallel to the base line of a triangle divides the other sides proportionally, and is itself in the same ratio to the base line." But F G is also ^ oi P D, for, since: (i) M G:M D::M F:M P, then (2) M G:M F: \MD\MP, and (3) M G — M F:M G::M D — M P:MD, or (4) FGiM G::PD:M D, from which (5) FG:PD: :MG:MD, and F G = ^ P D. The same principle would apply to a wave at any distance from M, if evolved in a homogeneous medium, for a given angle at the center. But the principle would apply for any angle at the center, although for a different angle than m the case would be a different one, and vary the sines pro- portionately. For instance, if a wave of light is generated at any other point on M D, or M D extended, as at H, and the instant the wave from H reaches L, the same distance from K as M, a wave starts from M, both waves will reach K at the same instant. But their curvature at K will not be the same, but inversely proportional to H K and M K. If the wave started from M at the instant the wave from H reached M, both would reach P at the same instant, but their curvature at P would be inversely proportional to H P and M P. With both waves at K, P K will be the common sine of both waves or both angles, m and n, although the sine of each will pertain to the different circles. Now if through K a line is drawn parallel to H D, and, with K as a center and M K as a. radius, an arc is struck across the two parallels, and the sines, M S and L T are drawn, the latter will be the sines of the two angles in the same circle, for angle n = angle n and n' + = m. Now, these two sines are inversely proportional to the radii of the two circles. That is: (i) Sine L T: sine M S::M K:H K. For L T K and H K P are similar triangles because mutually equiangular, and corresponding sides are proportional, hence: (2) LT:P K::LK:H K. GENERAL OPTICAL PRINCIPLES. 51 But, SiS P K = M S and L K = M K, this proportion (2) reduces to (i) by the substitution of these equivalent terms, and L T, the sine of angle n of the large circle, is to P K, the sine of angle ni of the small circle, as the radius M K of the small circle is to radius H K oi the large circle. Hence of two unequal circles, angles at the center of which are subtended by a common sine, the sines of such angles in equal circles are inversely proportional to the radii of the circles. But as the curvature of the waves are also inversely proportional to radii, it follows that such curvature is directly proportional to the sines of the two angles in equal circles. That is, the curvature of the wave from M at K is to the curvature of the wave from H at K, as P K is to L T. For a very minute pencil of light at P — one so minute that a representation of it by a drawing would be practically impossible, would evidently be governed by the same rule. But in such a pencil L would be so near M that both might be considered as one. Sine L T would thus reduce to zero, but P K would also become zero under this hypothesis. For the most minute distance imaginable separating L and M, the ratio of sines would be maintained, however, and would be practically as M P io H P, and the two waves at P, one from H, the other from M, would be to each other, in curvature, in inverse ratio of M P to H P, but at D in inverse ratio of M D to H D. In Fig. 17 we have represented a pencil of light being acted upon by a bi-convex lens. The lens focuses the pencil from C at C. Now, it will be noticed that the pencil is com- posed of three parts or sections: (i) the section anterior to the 4 52 GENERAL OPTICAL PRINCIPLES. lens; (2) the section within the lens, and (3) the section poste- rior to the lens. But at each surface the wave is partly within and partly without the lens, during the time of its entrance into or emergence from the lens. The figure represents the lens as exactly neutralizing or taking all curvature out of the incident wave at the anterior surface, and converting it into a concave wave at the second surface. A lens may or may not have this action. If this pencil had started from a point farther away than C, the first surface alone would have converted the waves into concave waves (Fig. 18), but if C were nearer the Fig. 18. lens, refraction at the first surface would have left the waves convex, though less so than before. But if refraction at the first surface were different than it is the results at the second surface would also be different. Perhaps the focus C would be farther away, or perhaps both surfaces of the lens would barely neutralize the pencil and make the emergent waves plane. The effects of a lens upon a pencil of light depends, then, upon the curvature of the waves of which the pencil is com- posed as well as upon the power of the lens, and the curvature of the waves upon which a lens acts depends upon the nearness of the center of curvature. What is the force by which a lens changes the curvature of these waves of light? It is the force of resistance. The glass of which the lens is composed resists the propagation of the waves in it. As this increased resistance is applied, at the first surface, to that point in the wave which reaches it first, it is delayed while all other points in the wave are gaining upon it. But at the second surface the point in the wave first to enter the glass, may be, by the shape of the lens, the last to be released from its resisting. influence. As a result GENERAL OPTICAL PRINCIPLES. 53 refraction at the second surface gives the other points of a wave still further advantage, and the w^ave is transposed, or changed, by the lens from convex to concave. In this transposition it will be noted that the center of curvature of the waves of the pencil is sent to infinity on one side of the lens by refraction at the first surface, but that it is brought back to a finite position on the other side of the lens by refraction at the second surface. These are important optical effects. The mere deflection of rays by the lens, as shown by the change of direction of the lines, does not give a clear conception of this optical transformation of the pencil or of the waves of the pencil. Rays of light are of dififerent pen- cils and are confused with one another, but when the attention is directed to the waves of which the pencil is composed no such confusion can arise. The bending of the rays is a conse- quence of the modification of the waves. The waves are the physical elements upon which the lens acts. Now the curvature of the waves anterior to the lens (Fig. 17) is convex, the curvature of the. waves within the lens is neutral, and the curvature of the waves posterior to the lens is concave. These are different classes of waves, although these waves are all of one pencil of light. ^The curvature of the waves posterior to the lens is determined by their position with reference to C not C. If a wave is one meter from C and con- cave, its curvature is i Cm. as before, but our nomenclature should distinguish the kind or class of waves as well as their degree of curvature. For this purpose we call all convex waves — the waves as they are generated, or natural waves — positive or plus waves; while waves that are optically trans- posed into concave waves are negative or minus waves. Waves having no curvature are simply neutral waves. A wave then of + 5 Cm. is a convex wave one-fifth of a meter or eight inches from the point from which it started; and a — 8 Cm. wave is a concave wave one-eighth of a meter, or five inches from its new center of curvature. Statically considered a + 5 Cm. wave and a — 5 Cm. are exactly alike. It is true one is convex and the other is concave, but what is the difference between convex and concave except in the point of view? Whatever is convex on one side is concave on the other. 54 GENERAL OPTICAL PRINCIPLES. DYNAMIC PROPERTIES. But dynamically considered there are great differences between these positive and negative waves. Let us note some of their important differences: 1. Positive waves are natural — the only waves that nature spontaneously generates. Negative waves are artificial or optical. 2. Positive waves start from their centers of curvature and proceed outward into space. Negative waves are on their way to their centers of curvature. 3. Positive waves grow weaker in curvature as they advance, and at infinity their curvature is o. Negative waves grow stronger or increase in curvature as they advance and, at their center of curvature, their curvature is infinite. 4. A positive wave remains a positive wave as long as it has its freedom of action. Negative waves are transposed into positive waves at their center of curvature by natural evolution. 5. The center of curvature of positive waves is a luminous point, or a point of reflection from which the series starts. The center of curvature of a series of concave waves is a focus. These points give a comprehension of the real differences between these two opposite classes of waves. Now, it must be borne in mind that transposition of a pencil of light does not bring out a new and different pencil. The pencil of concave waves is the pencil of convex waves transposed. The series of waves is the same series. There is no loss of identity by trans- position, any more than there is the loss of identity of a coat by being turned inside out. The focus of the negative pencil is the center of curvature of the positive pencil, located in a new place. Whatever the molecular activity at the center of curvature of a positive pencil of light that activity is repro- duced or duplicated at the focus, or new center of curvature, to which the waves of the pencil converge. When the foci of numberless pencils are thus brought near to each other, and a screen or receiving surface is so placed as to react upon the pencils at that critical point in their career, an image, the GENERAL OPTICAL PRINCIPLES. 55 exact counterpart of the object or luminous area, except that it is inverted, and may be of different size, is displayed upon the screen. To see this image thus displayed general light must be excluded from the screen, but the image is on the screen whether general light is excluded or not. The screen, even, is unnecessary, except for the display of the image, for the image is wherever the foci of the pencils are thus grouped, no matter whether displayed or not. Such an image is a true image, because it is an image intermediate to and lying between the object and the eye. A virtual image is the pro- jection of a real image upon the retina to some other position than that occupied by the object. The object itself, considered visually, is nothing more than the projection of a retinal image. . This gives us a comprehension of the composite pencil of light that no study of the rays as such gives. Perhaps the most wonderful feature of these ethereal waves is their non- interference. Each series acts across a space where thousands of other series are playing as freely as if it had an exclusive franchise to the space. Millions of pencils and series of waves pass simultaneously through a lens, and in as many directions, without interfering with one another, each pencil being focused, if the lens is capable of transposing it, in or at its own individual point. But pencils from points in the same straight line, axial to the lens, are acted upon by the lens simul- taneously. The foci of the pencils from the near points are far away, and the foci of the pencils from far away points are near the lens. The foci of such a system of pencils form a straight line on the posterior side of the lens, the same as the points of origin form a line on the anterior side. Pencils that fall upon a lens from an oblique direction are deflected or turned to one side, apparently while in the lens. Such a pencil is merely a minor pencil of some larger major pencil. The minor pencils of a pencil whose center is upon the principal axis of the lens are deflected by the lens in the same way. The action of the lens is symmetrical, but by reason of its position an outer minor pencil only of the larger major pen- cil reaches it. The iris of the eye excludes from the crystalline lens all except a minor pencil from one side of the major pencil, and deflection at both surfaces is toward the axial ray — that 56 GENERAL OPTICAL PRINCIPLES. point in the wave which is, or would be if given access to the lens, refracted twice, equally, and in opposite directions, at its two surfaces. OPTICAL MODIFICATIONS. All optical effects or phenomena are due to the modifica- tion of waves of light, and there are two directions in which such modification may be made. Referring to Fig. 17, the modification of the waves by the first surface of the lens is toward or in the direction of neutralization, but modification at the second surface is toward or in a direction away from neutralization. Both of these refractions are, however, of the same class and in the same direction, for each neutralizes posi- tive curvature. The refraction of the first surface takes away all positive curvature, but the refraction of the second surface makes the waves concavfe or negative — still farther removed from positive curvature. This direction of optical modification is the positive direction, or positive refraction. Positive refrac- tion, or positive optical modification of waves of light, is modi- fication tending to neutralize positive or convex curvature of the waves. Negative refraction or modification is the opposite of this, for it tends to neutralize the curvature of negative Waves but augments the curvature of positive waves. A surface of resistance may be neutral in refractive effect, even though highly convex or concave. It is neutral when the waves of light that fall upon it are in curvature complementary to it — that is, when their curvature conforms to the curvature of the surface upon which they fall, one being concave and the other convex, and both of the same curvature. Such neutrality is rare, except for plane surfaces and neutral waves. But neutral refraction or optical modification, as above explained, is confined, when it occurs, to a single surface usu- ally. In any of the forms of lenses neutral refraction could occur at but one of the surfaces, and then absolutely but for one series of waves. A plane surface of glass is not necessarily neutral, except for plane waves that conform with it, but the refractions at the opposite surfaces, when parallel, neutralize each other. A surface, ordinarily positive in its refractive effects, may be negative upon waves of light having a cor- responding curvature, but of a greater, degree of curvature GENERAL OPTICAL PRINCIPLES. 57 than it has, but the efficacy of lenses, or their refractive power, is the sum of effects at the two surfaces, not the different effects at either, which vary constantly. OPTICAL INSTRUMENTS. Optical instruments — that is, primary optical instruments, consist essentially of lenses, mirrors and prisms. Under the term lenses, cylindrical surfaces, and possibly prisms, may be included, leaving but lenses and mirrors. A positive optical instrument is one that produces a positive effect or positive effects upon the waves of light upon which it acts — that is, it modifies the waves in a positive direction as explained above. A negative instrument modifies the waves in a negative direction. To express the power of a lens we have the unit, one diopter. This unit is usually defined as that power in a lens which enables it to focus parallel rays of light at one meter. This is a narrow definition. The diopter is really a unit of work. It expresses the work performed by a lens, or by any optical instrument — lens or mirror. What is the work which it does? It neutralizes or augments the curva- ture of waves of light one curvometer. A + i D. lens, acting upon + 5 Cm. waves, neutralizes one curvometer, or makes them -f 4 Cm. in curvature. If a + 5 D. lens acts upon + 5 Cm. waves it neutralizes all curvature, and makes the waves plane or neutral. If a + 5 D. lens acts upon + i Cm. waves, it trans- poses them into — 4 Cm. waves. If it acts upon neutral waves it makes them — 5 Cm. In any and all cases the lens does five diopters of positive work. Part of this work may be the neutralization of the positive quality in the waves upon which it acts, and the other part be in imparting the negative quality to them; or all of its power may be devoted to neutralization of the positive quality, and it may be insufficient in power for that. A positive lens does positive work to the extent of its power. It exhausts its power upon the pencils upon which it acts. Its work and the power of the lens are equal. We may consider the work performed by the lens as composed of two parts — that part previous to neutralization and that part 58 GENERAL OPTICAL PRINCIPLES. subsequent to neutralization. We may consider these two parts as pertaining- to the two sides (not surfaces) of the lens. For instance, if a + 8 D. lens acts upon + 3 Cm. waves, its anterior work is + 3 D., and its posterior work is + 5 D. The sum of its anterior work and posterior work is + 3 D. + 5 D. = + 8 D. But this is necessarily equal to the algebraic dif- ference of the curvometers anterior and posterior to the lens. That is the algebraic difference of + 3 Cm. — 5 Cm. + 8 Cm. The lens will neutralize a series of + 8 Cm. waves, or if it acts upon neutral waves it will focus them at 40/8 = 5 inches. What the posterior work required of a lens may be depends upon its anterior work and whether that exhausts the power of the lens or not. If it does exhaust it, it does no posterior work. If a + 8 D. lens has + 10 D. of work anterior to it, it will not be able to perform it all. It will, however, exhaust its power upon the work. As it acts upon +10 Cm. waves it will reduce their curvature 8 Cm., and its work will be 8 D., although it leaves 2 Cm. of positive curvature in the waves. Their algebraic difiference (a) + 10 Cm. (c) + 2 Cm. (b) + 8 Cm. is still expressive of the efficacy of the lens, its capacity to neutralize + 8 Cm. waves. We may assume that that is its capacity, and obtain the curvature of the emergent waves by subtracting its effect upon the neutral or plane waves from the given waves, thus : (a) + 10 Cm. (b) + 8 Cm. (c) + 2 Cm, The curvature of the incident waves (a) is the sum of the curva- ture of the emergent waves (c) and the neutralizing power of the lens (b). GENERAL OPTICAL PRINCIPLES. 59 Negative lenses come under the same principles, although they act in an opposite direction. A — 2D. lens does two diopters of negative work. If it acts upon + 3 Cm, waves, it converts them into + 5 Cm. waves. Here the algebraic differ- ence of curvature equals the power of the lens. That is: + 3 Cm. + 5 Cm. 2 Cm. The lens will therefore neutralize — 2 Cm. waves, or reduce the curvature of — 5 Cm. waves to — 3 Cm. The diopter is a unit of work. We see no reason why it may not be applied to the action, or capacity of action, of a mirror, as well as to the capacity of action or power of a lens. There is no difference in the work they do — only a difference in the means of doing it. We have engines of 50 horse-power, because they perform 50 units of work, each of which is one horse-power. Why not mirrors of 3 diopters, if they per- form 3 of the units of work performed by a lens of + i D.? It does not matter so much what the derivation of the word is. Our scientific language is full of departures from the original meanings of words. The unit is more«valuable than its deriva- tion. The diopter as applied to cylinders is of the same signifi- cance as when applied to spherical lenses, but it applies to the meridian of highest power at right angles to the axis of the cylinder. Cylinders are neutral in one meridian only — the axial meridian. In all oblique meridians their power is proportional to their nearness to the meridian of highest power. VALUE OF NOTATION. With this notation for waves of light and the notation of optical instruments now in general use, it is possible to describe optical phenomena or effects with precision. It makes the foundation of optometry complete, and the two notations are always numerically equal, because based upon the meter. We should note here that this system of notation of curvature is quite as applicable to the curvature of lenses and mirrors as to (DO GENERAL OPTICAL PRINCIPLES. waves of light, and provides a simple means of determining the curvature of lenses or mirrors of a given dioptric power, of which later. Another important point is this: the notation is applicable to the waves of a pencil considered individually, not to pencils considered collectively. Diffusion, for instance, is an effect that pertains to individual pencils, while magnifi- cation is an effect that pertains to a group of pencils. Only one pencil of light is necessary to produce diffusion; an indefinite number of pencils are required to produce magnification. An example of the consequences of confusing the two ideas is found in a popular work on skiascopy, in which, in the author's analysis of the effects at the retina of the observed eye, or area 3, these two distinct phenomena are hopelessly entangled, and we find the author speaking gravely of the "magnification" resulting from the action of the dioptric media of the eye upon a single pencil of light, and of the indefinite "magnification" of a point in the retina. At least two points and two pencils are necessary for magnification, for if there are not two points how can they be separated, since magnification is separation of points, or an enlargement of the retinal image. But we will dis- cuss this matter more fully in its appropriate place. Chapter IV. POWER AND CURVATURE. The power of lenses and mirrors is proportional to their curvature. Power and curvature have, in each case, a direct relation to each other. What is the relation? Power, as we have seen, is the capacity of a lens or mirror to modify the curvature of the waves of light, so that the relation of the power of an instrument to the curvature of its surface is the relation of its capacity to modify wave curvature to the curva- ture of the glass. Both curvatures thus pertain to the glass: one being the curvature of the glass, the other the capacity of the instrument to modify wave curvature. For instance, a + 8 D. lens modifies wave curvature 8 Cm. in a positive direc- tion: now the curvature of the glass has a direct relation or ratio to 8 Cm, What the relation or ratio is depends upon the index of refraction of the glass. The index of refraction is not the ratio, but it contains the ratio, as we shall see. GENERAL OPTICAL PRINCIPLES. 6l As a lens (or mirror) is made of solid material its curva- ture is fixed in the making, but the waves of light upon which it acts,- or may act, are various and variable in curvature, depending primarily upon the distance of the object. If we can find the ratio of the curvature in the glass to the capacity of the instrument to modify wave curvature, all that will be required will be a simple multiplication or division to deter- mine either when the other is known. The ratio is the multi- plier or divisor, as the case may be, and it reduces wave curva- ture to glass curvature, or glass curvature to wave curvature, the same as the factor i6 reduces avoirdupois pounds to ounces or ounces back to pounds. But as the index of refraction varies for different media, this ratio also varies. So that it would be a better comparison to say that this ratio is like price — the price of coal. If coal is $4.50 a ton, 4.5 is the index of values between the dollar and the ton of coal. Divide the dollars by the index, and you get the number of tons of coal it will buy. Multiply the tons of coal by 4.5, and you get its value in dollars. If the price of coal changes, the problem is a new one, although worked on the same plan under the new index. It the index of refraction of the body of glass of which a lens is composed is 1.60, what does tfiis mean? It means pri- marily that the resistance of the glass to the propagation of light waves is 1.6 times the resistance of air, the standard medium. Light waves are transmitted in such glass with diminished speed. Speed of the light waves is reduced 60/160 and remains in the glass 100/160 of its speed in the air. 100/160 is therefore the index of speed in glass, compared with speed in air, the standard medium. Since 1.6 = 160/100 is the resistance of the glass compared with air, and 100/160 is the speed of the waves in the glass compared with air, and these two terms are the inverse of each other, we may presume that there is a foundational law that resistance and speed are in- versely proportional to one another in a case of this kind. The propagation of light waves is not subject to the laws of mate- rial bodies moving through other material substances — that is, to the modifying effects of friction — as shown by the fact that resistance lasts only while the wave is in the resisting medium, 62 GENERAL OPTICAL PRINCIPLES. and by the restoration of the original speed when the wave emerg-es into air. The delaying influence within the medium is not resistance in the mechanical sense, but want of sympathy with or responsiveness to molecular motion. It is a want of conductivity. To generalize the law we may represent the coefficient of wave velocity in air by a, the coefficient of wave speed in the other medium by b, and their difference by c. Then if a > h, which it usually is, a = b -\r c,h = a — c, c = fl — b. But b/a = the ratio of wave speed in the other substance (.r) to wave speed in air, for the ratio of one quantity to another is the quo- tient obtained by dividing the quantity considered to be a part of another by the quantity of which it is considered to be a part. Now, if we take air as the standard medium of resistance, its resistance is i, and the resistance of the other substance, whose wave speed is b/a of wave speed in air, is i ^ b/a = a/b. That is, the relative resistance of the two media, with the" resistance of air as the standard, is a/b, or the resistance of the other medium is a/b of the resistance of air. Representing the other medium by x, we may express the law in the following proportions: (i) Wave speed in x : wave speed in air :: b : a = b/a; (2) Resistance in x : resistance in air : : a : 6 = a/&; from which it appears that a/b, the ratio of resistance in x to resist- ance in air, is the inverse of the ratio of wave speed in x to wave speed in air, and the so-called index of refraction, or index of resistance of x, with air as the standard. But c, the difference between the coefficient of speed, is c/a of a and c/b of b, and c/a = the ratio of loss of wave speed in x to wave speed in air; and c/b = the ratio of loss of wave speed in x to actual speed in x. But, since a/b = the ratio of resistance in X to the resistance of air, and a = b -\- c, -^ = i + c/b = the ratio of resistance in x to resistance in air. If from the last quantity, i, the resistance of air, be subtracted, the remainder, c/b is the ratio of loss of speed in x to actual speed in x. When light waves pass from air into a medium of greater resistance they lose c speed, or c/a of preceding speed, a. But when they pass from such medium of greater resistance into air again, they gain c speed, or c/b of preceding speed, b, which restores them to a speed again, for c/a of o = c, and c/b of b GENERAL OPTICAL PRINCIPLES. 63 = c, and therefore c/a oi a = c/b of b. If the resisting sub- stance is glass with an index of refraction of 1.60, we may let 160 represent wave speed in air; 100 will then represent wave speed in the glass, and 60 will represent loss of wave speed in passing from air into the glass. Wave speed in glass is then 100/160 of wave speed in air; loss of wave speed is 60/160 of wave speed in air. But the resistance of the glass is 160/100 of the resistance of air. At the incident surface, the waves lose 60/160 of their previous speed, 160; but at the emergent sur- face they gain 60/100 of their preceding speed of 100, which restores them to their original speed in air, 160. The gain in speed at the surface of emergence exactly compensates for their loss of speed at the surface of incidence. We may now deter- mine the effects upon the curvature of the waves of such resistance, and show the relation of resistance to refraction. Fig. 19 ..W_5 vAA^v\ -B^'^'Vv/V.. A spherical wave of light cannot fall upon the surface of a medium of different resistance at all points simultaneously unless the surface of the resisting substance conforms exactly with the wave, a necessarily rare occurrence. The point in the wave first to reach the surface of resistance is the one pur- suing a course perpendicular to such surface. In Fig. 19 let M represent a point in air, A B the plane surface of a resisting medium whose index of refraction is 1.5, and let M P be per- pendicular to A B, and i^ be a point in ^ 5 i^ times M P from M. Now, a wave of light from M would expand in all direc- tions from M, and along the radial lines M P and M K, at the same rate of speed. We may consider the spaces between the circular lines as wave intervals, and M P as embracing two 64 GENERAL OPTICAL PRINCIPLES. such intervals, while il/ K embraces three. The resistance of the glass would be applied to the wave first at P and then suc- cessively at all points from P to K. When the wave reaches P on M P it will reach E on M K, and while the wave is ad- vancing one interval, or from £ to i^ on il/ K, it will also advance along P D though but f of the distance to D be- cause of the resistance of the glass. All points in the wave between P and E, will, during the next interval of time, travel partly in air and partly in glass, the relative distances each travels depending upon its nearness to E at the beginning of the interval of time, or to K at the end of it. But each wave point is retarded during the interval relative to its nearness to P at the beginning, or at the end of the interval. The result of resistance applied in this way is the reformation of the wave, or its change of curvature for an amount in excess of that which would be produced by natural evolution either in air or glass. If E, and all points on arc E P, traveled in glass," natural evolution would reduce the curvature in the inverse ratio of M P to M 0, and the wave would extend from to F; but if P, and all points on P E, traveled in air, natural evo- lution would reduce the curvature in inverse ratio of M P to M Dot M EtoM K. But, M P : M : : 2 : 2| = |; and M P: M D : : 2 : 3 = f . But the wave really extends from to K, and to determine the curvature at either or K, the modifying effect of the resistance of the glass must be determined. The curvature of the wave at either or K may be considered as consisting of three elements: (i) The natural curvature evolved from M to P or from M to i^ in the air, (2) the modifying effect of the resistance of the glass at P or K, and (3) the evo- lution of curvature within the glass from or K onward. At K the third factor is zero, but just within the glass the other factors have operated. But at the three factors have operated. Assuming that the wave form to i^ is spherical its curvature at i^ is as L T to iv P, the sines of equal circles, one for angle n, the other for angle m. But L T : P K L K : H K, whatever the former ratio may be. But L T P K :: P : P D = f , as heretofore shown. Hence L K H K :: 2 : 3, or // /v is i^ times L K or its equal il/ K, and tlie curvature of the wave at K anterior to the glass, is to its curva- GENERAL OPTICAL PRIN'CIPLES. 65 tiire of the wave at K posterior to the glass as 2 is to 3, or f . The reduction of curvature at K, considered as a small area of A B, is therefore -J. It may be proved that the reduction of curvature at any point on F X' is also -J, and hence at P the reduction is ^-. But a reduction of ^ at F places the center of curvature of the wave at P within the glass at i^ P M from P or at G, which is nearer M than H. At all points between P and K the new center of curvature will be between G and H. The curvature at in the glass is greater than the curvature at K in the glass, because the evolution of curvature, or reduc- tion of curvature, between P and in the glass, has been less than reduction of curvature between E and K in air, both of which are evolutionary elements. Hence, although modifica- tion produced by the resistance of the glass at all points is the same (| reduction of previous curvature) is forward of the spherical arc having H K a.s a radius and centering at H. For a considerable angle such as in the variation of curvature is considerable, but for small pencils of light it is slight and the curvature at K and may be regarded as practically the same. This difiference of centers for the single wave is spherical aber- ration, of which we will have more to say later. The primary optical effect in the above is the reduction in the speed of the wave c/a or ^, due 'to the increasing resist- ance of the glass, and the application of such resistance to different points of the wave successively. As a result of such reduction of speed so applied, curvature is reduced the same amount, c/a = -J, and becomes, at the point of incidence b/d — f of previous curvature, at which the evolutionary fac- tor becomes the same again for all areas. But at the second surface or surface of emergence, the wave is accelerated c/b = ^ of previous speed, and at a plane surface the wave emerges at D first and K' last. Curvature is modified at the second surface in the same ratio, c/b, that speed is modified. As a result curvature at K' and D becomes c/b = ^ greater, and the new center of curvature for K' is at a point on H D ^ oi H K' from K'. This, as it is a restoration of wave speed, is also a restoration of curvature, or would be but for the evolutionary element acting during the interval in which the wave is pass- ing through the glass. The two effects at the two plane 66 GENERAL OPTICAL PRINCIPLES. surfaces neutralize each other for c/a of a — c/b of b, but the •evolutionary element is not of course neutralized. Every index of refraction, so-called, is the index of resistance of the two media, air being the standard or divisor, for the index of resistance being a/b, and a = b -{- c, -^^ = i + c/b. In the index 1.6, .6 = c/b. In an index 1.52, .52 = c/b. The index of resistance is always i + c/b which is always equal to a/b. Now, this ratio, c/b, is also the ratio of the curvature of the glass on both surfaces of a lens to its capacity to modify the curvature of waves of light. If one surface of the lens has a curvature of + 20 Cm. (convex with 2 in. radius) and the other surface has a curvature of + 8 Cm. (convex the other way, with 5 in. radius) both surfaces have a combined positive curvature of + 28 Cm. If the index of refraction is 1.52, c/b = .52. Now this lens will modify the curvature of a wave ot light .52 of 28 Cm. = 14.56 Cm., and as both modifications are in the positive direction, it is a + 14.56 D. lens. The given lens is what is known as a bi-convex lens, although the curva- ture of its two faces are opposite ; but as one is a surface of in- cidence and the other is a surface of emergence, both are posi- tive to positive waves of light. Its entire curvature is + 28 Cm, w^hether its two faces are as given, or each has a curvature cf + 14 Cm., or if one surface is plane and the other has a curva- ture of + 28 Cm. If the lens were periscopic, one surface hav- ing a curvature of — 5 Cm., the other would need to have a curvature of + 33 Cm., so that there would be + 5 Cm. to neu- tralize the — 5 Cm. and + 28 Cm. to spare. But in the above lenses, each of + 28 Cm-, and of + 14.56 D. power, the focal point of a pencil of light would be slightly different on account of the different location of the surfaces \vitli the edge of the lens in one fixed position. The power of each lens is, however, the same. To make a lens of a specific dioptric power, as of + 10 D., the index of refraction being 1.52, the combined curvature of its two surfaces must be 10 Cm./.52 = 19-23 Cm. But the rule of curvatures does not apply to single surfaces, for a single sur- face may be plane and have power, or curved and have no power, for its power depends as much upon the curvature of the wave as upon the curvature of the glass. In the dioptric GENERAL OPTICAL PRIN'CIPLES. 6/ power of spherical mirrors the factor used in reducing curva- ture to power or power to curvature is 2, and its dioptric power is twice its curvature. A mirror whose radius of curva- ture is 10 in. has a curvature of 40/10 = 4 Cm. and a power of 8 D. If the mirror is concave it is positive; if convex it is negative, for the determined power. The use of factor .52 or c/b, whatever the index of resist- ance or refraction, is due to the modification of wave curva- ture produced by lenses. The indices of refraction and diverg- ence are based upon the index of resistance of the two media, W'ith air as the standard or divisor or second term of the ratio. They are an effect due to a more primary cause — the differ- ence of resistance of the two media — the resistance of the so- called refracting substance as compared with the resistance of air. The index of refraction, 1.52, is primarily the index of resistance, the a/h as hereinbefore described; the index of ■deviation, .52, is primarily the sum of effects at the two sur- faces of the refracting body, the c/h as above described. If we represent the speed of the waves in air by 152 = a, in the glass their speed will be 100 = &, a reduction of c/a of a, or 52/152 of 152 = 52, leaving 100. The modification of wave curvature is then c/a or 52/152 of previous curvature found at the surface of incidence, whether of the glass alone, the wave alone, or both. But at the surface of emergence speed is accelerated c/h = 52/100 of previous speed, h, or 100; 52/100 of 100 = 52, and restores speed to o again. The modifi- cation of wave curvature at the second surface is then c/b or 52/100 of all preceding curvature, whether of the wave alone, the glass alone, or both. Now, if the convex surface of a plano-convex lens intercepts a neutral or plane wave of light, the wave will be given a curvature of c/a = 52/152 of the curvature of the glass, because the curvature of the glass em- braces all curvature found at the surface of incidence. But at the second surface, which is plane, the total curvature will be in the wave, and is 52/152 of preceding glass curvature plus a negligible increase of curvature evolved in the glass, greatest at and near the axis of the lens and least near the periphery. At this surface curvature is increased 52/100 of preceding curvature, or 52/100 of 52/152 of the curvature of the glass at 68 GENERAL OPTICAL PRINCIPLES. the incident surface. The total modifying effect at both sur- faces, neglecting the evolutionary element produced in the glass, is then 52/152 + 52/100 of 52/152 of the curvature of the anterior face of the lens, or c/a + c/h of c/a. But c/b of c/a = c^/ah, and the entire modification is c/a + nil Cb 1 o / J Cb + C- C (b + C) Ca /; rr^l , • ^•Vo& = ^ + c-/ah - --^^^ = -^-j^ - ^^ = c/b. That is, the entire modification is c/b of the curvature of the anterior face of the lens. If the lens has an anterior curvature of + 12 Cm. modification of a plane wave of light by it is .52 (c/b) of 12 Cm. = 6.24 Cm. The lens is therefore a + 6.24 D. lens. Hence the use of the factor .52 or c/b in reducing the curva- ture of lens to power. All lenses are modified forms of the plano-convex lens, and the rule is applicable to all. Distinc- tion must be made for positive and negative faces, however, one of which tends to neutralize the other, and the total curva- ture is the excess of one over the other. If the anterior surface has a curvature of + 5 Cm. and the object is 10 in. distant, the incident waves have a curvature of -f 4 Cm. The sum of the tw-o curvatures is 9 Cm., and the wave will be modified at such anterior surface c/a of 9 Cm., for it would be modified by a plane surface c/a of 4 Cm., and a plane wave would be modified c/a of 5 Cm. by this surface. The sum of the two effects is then c/a of 9 Cm. = 3.0789 Cm. But this modification does not complete the total lens action, for a posterior plane surface must still be passed, -f 4 Cm. — 3.0789 Cm. = .9211 Cm., the positive cur\'ature of the wave transmitted through the glass. The posterior plane surface will act negatively upon such positive wave, increasing its curvature c/b of .9211 Cm., making it i H- c/b of .9211 Cm. = a/b of .9211 Cm. = 1.5 of .9211 Cm. = 1.4 Cm. The total modification is -f 4 Cm. — 1.4 Cm. = 2.6 Cm., and the lens is a + 2.6 D. lens. Its power is c/b or .52 of 5 Cm., the curva- ture of the glass = 2.6 Cm. The center of curvature of the wave is 40/1.4 = 28.57 in. anterior to the glass. By the method of surfaces, the thickness of the lens being taken into account, the exact position of the focus, for the most central part of the lens, with reference to either surface may be deter- mined. The above lens will not. however, focus the above pencil, but the position of the anterior center of curvature, GENERAL OPTICAL PRINCIPLES. 69 often called a negative focus, though with little propriety, may be exactly ascertained. In refraction of a central pencil wave curvature is modified but no deviation is produced, except in minute axial pencils oblique to the principal axis, and there are two deviations of these, the one counteracting the other. But for peripheral minor pencils there is modification of wave curvature and deviation also. Modification of wave curvature, the index of refraction being fixed, is always the same for the total curva- ture of glass and wave, but deviation is proportional to the distance of periphery from the axial area. If the wave is plane only the curvature of the glass has to be considered, for a plane wave is static the same as the glass, with respect to curvature. If the wave is convex or concave its curvature is not static, and it will have, unless it conforms in curvature with the glass, different curvature at peripheral than at central areas. Hence the glass surface will have a different wave curvature to modify at different points, or the sum of the two curvatures (of glass and wave) will not be exactly the same at all points. Modification of curvature is, however, always the same, c/a at the first surface + c/h of c/a at a second plane surface, of the curvature of the anterior surface, and c/h of the curvature of the posterior surface, making c/h of the curvature of both. Peripheral areas of the wave are deviated toward the axis of the lens, so that barring aberration, each wave finds its center at the same point upon its axis, or the axis of the lens that passes through the point of origin of the pencil. The factor 2 used in reducing the curvature of mirrors to^ dioptric power is due to the complete reaction of the mirror. Its reaction is not partial nor fractional, as in refraction, but full and complete. If a luminous point is located at the center of curvature of a concave mirror, the wave would be reflected directly back to the point of starting. This would exactly re- verse the curvature of the wave, as from + 5 Cm. to 5 Cm. If the radius of curvature were different, the result would be the same. Transposing a + 5 Cm. wave as above to a — 5 Cm. is performing 10 D. of work, and the mirror does exactly the same work that a + 10 D, lens would do. Hence it is a + 10 D. mirror. It would focus neutral waves at 4 in. There are. 70 GENERAL OPTICAL PRINCIPLES. of course, the same limitations upon a mirror as upon lenses, for only a small area of the mirror near the axis can be used on account of spherical aberration, which causes peripheral areas to produce different results. CHAPTER III. GENERAL OPTICAL PRINCIPLES. REFRACTION OF THE EYE. COEFFICIENT OF EMMETROPIA. THE DIOPTRIC SUR- FACES. TRANSITION OF IMAGE IN SKIASCOPY. npHE first work of the oculist or optician in an optical diag- nosis is to determine the capacity of the dioptric media with reference to the work required of them — the focusing of pencils of light from the distant object upon the retina with the employment of the static power of the eye only. The next step is determining the amount of its incapacity by optometric methods, whether such incapacity pertains to one or both eyes, or to one or all meridians of the same eye. Whether the measurement is made objectively or subjectively, the purpose is the same — to produce normal refractive power. In this connection it is desirable to have a concise formula in which to express the eye's dioptric power in' connection with the work it is required to perform. Such a formula would be compound, except for emmetropic eyes, and consist of two parts; to wit: (i) the dioptric power required to enable it to focus neutral pencils of light — pencils usually, though not necessarily, from the distant object — upon the retina, and (2) its dioptric incapacity to do this work exactly, either through the over or under power of the media, or want of symmetry in diiTerent meridians. eye's DIOPTRIC WORK, An eye, to be emmetropic, must be able to focus neutral pencils in all meridians, by the employment of its static power only, exactly upon the retina, especially at its most sensitive area, the macula lutea. What is the dioptric power required of an eye in doing this work ? It is different for different eyes and different individuals, ranging, perhaps, from as low as 71 "^2 GENERAL OPTICAL PRINCIPLES. -{- 40 D. to + 60 D. A short eye — one whose anterio-posterior diameter is short — requires higher dioptric power than a long eye, other things being equal. But the length of the eye is not the only determining factor, for the nearer a surface of refraction is to the anterior surface of the eye, the more effec- tive it is, for that gives it a longer distance in which to focus each pencil. A myopic eye ma}^ have less real dioptric power than a hyperopic eye, but on account of its longer anterio- posterior diameter less power be required of it to focus the pencils at the more distant retina. Different emmetropic eyes are by no means the same, for the same reason. An eye that, with passive accommodation, focuses neutral pencils upon the retina, is emmetropic whether the eye be long or short. A short emmetropic eye has uecessaril}' greater static power than a long emmetropic eye. But, disregarding the absolute diop- try of an eye to enable it to focus neutral pencils at the retina, we may adopt a literal coefficient to represent that power. The Greek letter "-" will serve the purpose. Bytheterm"i -D." let that power, whether it be 40, 50 or 60 diopters, required to focus neutral pencils at the retina, with passive accommoda- tion, be understood. If an eye possesses a static power of + - D. then it is emmetropic. If not, it is either myopic or hyperopic. If one or more meridians of an eye — there will, of course, be more if there is one — is hyperopic or myopic, the eye is astigmatic to the extent of the difference of the extreme or principal meridians. + - D. may express more than the eye's static power or it may express less. If it is either more or less the eye is ametropic. An eye possessing, under passive accommodation, less than H - D. may gain a power of + - D. by exercising its power of accommodation. It is ametropic none the less, for its static power is not equal to + - D. If an eye requires to use 3 D. of accommodation to focus neutral waves upon the retina or see the distant object clearly, its static power is + (- — 3) D. With 3 D. of accommodation in force it has a power of + - D. It may possess more dynamic power than 3D. If it has 5 D. of dynamic power, only 2 D. of such power is available for focusing pencils of light from the near point at the retina. Its static power is -(- ('^ — 3) D. Add + 5 D. to that and you have -f (- + 2) D. for its full GENERAL OPTICAL PRINCIPLES. 73 power. Its dynamic power is the difference between its static power and its full power, or + (r + 2) D. + ("-3)D- 5D. Such an eye is, without regard being paid to latent elements, 3 D. hyperopic and has 5 D. of accommodation. These formulae are convenient for expressing at once the work required of the dioptric media and their incapacity to per- form the work. What "-" is, in any case, we do not really inquire into, but - — a expresses a dioptric insufficiency, whether - be 40, 50 or 60, and - -[- 3 or r + a expresses over- power, and shows 3 D. or a D. of myopia. We always want to know whether the eye is or has over- power or under -power, and the formula shows which and how much. It can be made to answer all the dioptric questions required in correcting. For instance, if the static and dynamic power are as follows : s. P. : + (- + 4) D. D. P. : + ('^ • + 12) D. ^ D. ■we know that its accommodation is 8 D.; that the eye is 4 D. myopic ; that its punctum remotum is 10 in., and its punctum proximum is 3^ in. A — 4 D. lens would place its punctum remotum at infinity and its punctum proximum at 5 in. A record in this form for each diagnosis would be valuable, for if the person came back complaining of the glasses the former measurement would be on record. It is not often that glasses are given that exactly correct the degree of error found, but the optician would know, by referring to the record, what ex- act condition he found in the previous examination. The glasses brought back or the prescription would not tell him that unless he prescribed exactly for the error found. The glasses cannot change and can easily be measured over again, but the eyes may change and be quite different than before. By a new diagnosis and a comparison with the record, whether they have changed or not and how much is readily determined. 74 GENERAL OPTICAL PRINCIPLES, These formulae, two for each eye if refraction is unsym- metrical, make a complete statement of the case. Each for- mula, or set of formulae, is for an individual eye. The two eyes may show the following : Right eye : S. P. + (- — 2) D. D. P. + (:r + 3) D. Ace. 5 D. Left eye: S. P. + (- — 2>^) D. D. P. + (- + 2%) D. Ace. 5 D. But the eyes may be astigmatic, having different power in different meridians. In that case a formula would be required for each chief meridian, as above. Supposing the principal meridians to be 90° and 180°, the formulae may be as follows for right eye: Right eye : 180° S. P. (- — 2) D. D. P. (- + 3) D. Ace. 5 D. 90° S. P. (-— i) D. D. P. (- + 4) D. Ace. 5 D. Showing two diopters of hyperopia in 180° and one diopter in 90°, and, hence, one diopter of astigmatism. The refrac- tion of the other eye could be formulated in the same manner. Of course, these formulae do not express the eye's real dioptric power, for "-" in the term "+ - D. " is an undeter- mined quantity. But in skiascopy it is of great importance to comprehend this coefficient of power — not absolutely, but rela- tive to the three surfaces of refraction — for this gives a com- prehension of the appearances when the observing eye is at or near the so-called area of reversal. REFRACTING SURFACES. The dioptric power of the eye is primarily the sum of the refractive effects at three surfaces. These surfaces are: (i) The anterior surface of the cornea. (2) The anterior surface of the crystalline lens. (3) The posterior surface of the crystalline lens. It will be convenient to refer to these surfaces by letter^ and we will call them, in the order named above, surfaces r, .f and t — that is: GENERAL OPTICAL PRINCIPLES. 75 r — anterior surface of cornea. ^ = anterior surface of lens. t — posterior surface of lens. Of these three refracting surfaces r is by far the most effective in proportion to its curvature. Unless the pencils have been modified anterior to r by a lens or mirror the waves come to it as natural convex waves, their curvature depending upon the nearness of the object. But, if modified by a pre- ceding lens or mirror, they may be any sort of waves. If the pencils are natural (not optically modified) r, which is positive for all positive waves, reduces such curvature. Of the thou- sands or millions of series of natural waves of light speeding through space toward the eye from every direction, none can conform with it in curvature since it is convex in the other direction and its curvature is opposite to the curvature of all waves that can reach it. But this surface is specially effective because it has the benefit of its full index of refraction, 1.33 because it receives, and is the only surface to receive, pencils of light from air. It resists the waves or transmits them at f of their speed in air from which they come, or takes away ^ of their speed, or reduces wave length ^. The crystalline lens, although it has a higher index of refraction, compared with air (1.43) receives waves transmitted to' it through the aqueous humor or emits them into the vitreous humor, both of which have an index of refraction of about 1.33, the same as the cornea. It therefore does not delay or retard the waves as much or shorten wave length to such a degree as the cornea. The effective index of refraction of the crystalline lens is 1. 43/1. 33 = 1.075, which, compared with the cornea, is slight, about 4/13 as much, for equal curvatures. The cornea reduces wave length |, and that wave length (f of air) is maintained in the aqueous humor to the lens. The lens then reduces wave length about 1/13 more, and hence the two effects are as | tor 1/13 for equal curvatures, or as 13 to 4. We will now endeavor to trace a pencil or wave light through the dioptric media of the eye, considering the effect at each surface of refraction. In doing this we will take official figures as to curvatures and distances, as far as possible, but we must remember that these figures are not to be 76 GENERAL OPTICAL PRINCIPLES. depended upon, except in the most general way; for no two eyes, emmetropic or ametropic, can be exactly alike. They are as different as finger-nails, palm markings or the length of finger-joints. It is our grossness of perception that causes dissimilar things to appear similar, and while education develops the perceptive faculties, life is too short to enable one to perceive many of the most obvious dissimilarities, unless specially educated to do so. For the eye under consideration we will presume the radius of curvature of the cornea to be .3 in. ; the space from r to s, along the principal or optic axis in static refraction to be .11 in, ; the radius of curvature of 5 to be, in static refraction, .4 in.; the thickness of the lens to be .145 in.; and the indices of refraction to be as already specified. The radius of curva- ture of the posterior surface of the lens is given (ofiicial) as 6 mm. = .24 in. and the anterio-posterior diameter of the eye as .92 in. These will provide the data required. We start then with a plane wave at the cornea. As its radius of curvature is .3 in. its curvature is 40/.3 = 133 Cm. The index of refraction being 1.33, the modifying effect of the cornea upon a plane wave is c/a = 33/133 of the corneal curvature = 33/133 of 133 Cm. = 33 Cm. or the exercise of 33 diopters of power. The wave becomes, at r, a — 33 Cm. wave. Its focus is then 40/33 = 1.21 in. posterior to r, or 1.21 — .92 = .29 in. posterior to the retina. But in passing from r to s, through homogeneous media, the wave would evolve increased curvature. Since 5 is, according to hypothesis, .11 in. posterior to r, it is 1.21 — .11 = 1. 10 in. from the potential focus of r when it reaches s, or has a curvature of 40/1. 10 = — 36.36 Cm. At this point it meets the anterior surface of the lens. Now, the curvature of s, by hypothesis, is 40/.4 (.4 in. being its radius of curv^ature) = 100 Cm. But as such curva- ture is convex, while the curvature of the wave is concave, or — 36.36 Cm., these curvatures are not opposite, but conforma- tory. The surface .y will act positively, because its cur\-ature is in excess of the curvature of the wave, 100 — 36.36 = 63.64 Cm. As its available index of refraction is 1.075, ^/^ becomes 75/1075, for this is the decrease of wave speed, or wave length, in the new medium. The curvature of the wave will then be GENERAL OPTICAL PRINCIPLES. TJ increased 75/1075 of previous curvature; 75/1075 of 63.64 Cm. — 4.44 Cm., and tlie wave would become at ^ — 36.36 — 4.44 — — 40.8 Cm. The surface has produced an effect amounting to + 4.44 diopters. The new focus of this wave would be 40/40.8 = .98 in. posterior to s. But in passing from .f to t through a practically homogeneous medium, the lens, it would evolve increased curvature. Since t is, by hypothesis, .145 in. posterior to s, it is .98 in. — .145 in. = .835 in. from the potential focus of s, or the wave has a curvature at t of 40/.835 = 47.9 Cm., the incident curvature at t, the last dioptric surface. Instead of determining the effect of this surface with the official radius of curvature as 6 millimeters or .24 in., we will work the problem in the opposite direction. That is, since / is .92 in — (.11 in. + .145) = .92 — .255 = .665 in. from the retina, the wave that emerges from t will require a curvature of 40/.665 — — 60.15 Cm. to focus at the retina. But its in- cident curvature of the wave at t, as shown in the previous calculation, is — 47.9 Cm. It then must be increased in curv- ature 60.15 Cm. — 47.9 Cm. = 12.25 Cm. That is, the dioptric effect of t must be 12.25 Cm. or + 12.25 diopters. As this is an emergent surface, the waves will increase in speed, or wave length, c/h = 75/1000, and wave curvature will therefore be modified 75/1000 of the total curvattire at t. But 75/1000 of the wave curvature is one element, and 75/1000 of the lens curvature is the other, for since the curvatures are now oppo- site, both will, at this surface, produce positive refraction. 75/1000 of 47.9 Cm. = 3.59 Cm., and 12.25 Cm. — 3.59 Cm. = 8.66 Cm. that must be produced by the curvature of t, for 3.59 Cm. is exactly what a plane surface at t would do. The posterior surface of the lens must perform an effect equal to + 8.66 •diopters. To do that it will require a curvature of 8.66 -^ 75/1000 = 8.66 X 1000/75 ~ 1 1546 Cm., or a radius of curv- ature of 40/115.46 = .346 in., or .1 in. more than the official radius of curvature of /. The discrepancy is either in the work or in the hypotheses. But we have not used accurate — that is, exact — data, and perhaps the discrepancy is the sum of these. But the official data is not to be depended upon in any event, except as a general average, the same as the length of the human forearm. 78 GENERAL OPTICAL PRINCIPLES. But in all the above calculations the static power of the eye was alone being considered. In calculating the dynamic power, more complicated factors are introduced. Without going into full details, we may note the leading effects. For instance, if the object is S in. distant from an emmetropic eye, the incident waves have a curvature of 40/8 = + 5 Cm. Now, r, although static in curvature, will produce a higher dioptric effect upon + 5 Cm. than upon neutral waves, for a plane cornea would modify the waves c/a = 33/133 of 5 Cm. But since the cornea has a curvature of + 133 Cm., the sum of such plane modifying surface and the spherical cornea is 5 Cm. + 133 Cm. = 138 Cm. and 33/133 of 138 Cm. = 34.24 Cm. or an effect of 34.24 diopters, which is 33/133 of 5 Cm. = 1.24 Cm. = 1.24 diopters greater than the effect of the same surface upon a plane wave. But + 5 Cm. — 34.24 Cm. = — 29.24 Cm., the curvature of the wave at r after refraction, while in static refraction its curvature is — 33 Cm. The potential focus of a — 29.24 Cm. wave is at a distance of 40/29.24 = 1.3673 in. posterior to r, or .4473 in. posterior to the retina. As in static refraction the potential focus of the wave at r is but .29 in. posterior to the retina, there is more dynamic work to be done to make the wave focus at the retina. This work is performed in four different ways at once, although by one muscular action. (i) The curvature of ^ is considerably increased by ciliary action. (2) Surface s is advanced toward surface r, and the evolu- tionary space from r to .? is decreased. (3) But surface s, by such advance, is farther from surface t and from the retina, and the evolutionary space from .y to Hs increased. (4) Surface t is undoubtedly increased slightly in curva- ture. These four factors, combined with the factor of increased dioptric power at r, together produce the full result. Waves emerge from t as minus waves of sufficient curvature to focus at the retina. What part has each of these five factors in dynamic refraction? That depends largely upon the part they perform. GENERAL OPTICAL PRINCIPLES. 79 in static refraction. But no two emmetropic eyes have the same satic refraction even. Can any one tell how large a part each of the different factors in dynamic refraction plays in focus- ing- the near object upon the retina? No one can tell, for even with the same static refraction two eyes will act dififerently. Even one solitary human eye will not, very likely, use these factors proportionately in focusing pencils of light from 8 inch and 5 inch respectively. The corneal element is certainly dif- ferent. That makes the emitted wave and the work of s dif- ferent, but not proportionally different. The shortening of space between r and ^ cannot be in the same proportion as the lengthening of space from .y to t, and the dioptric value of aug- menting the curvature of ^ cannot therefore be proportional to such increase of curvature. This is a problem that, with all the mathematical training possible to be obtained, is hopelessly beyond the reach of the most ambitious. Fig. 20. Fig. 21. In Figs. 20 and 21 we have represented the eye in static and dynamic refraction, designating the surfaces r, s and t as So GENERAL OPTICAL PRINCIPLES. above, and their respective centers of curvature as r', s' and t'. In Fig. 20, which represents the position of the surfaces in static refraction, r', the center of curvature of the cornea, is for- ward of the center of curvature of the main portion or globe of the eye, for it is but .3 of an inch from r while the center of curvature of the eye is a little more than ^ of .92 or .46 in. pos- terior to r. The position of r' is stationary since the curvature of r is unchanged, but is posterior to f, for t is but .11 in. + .145 in. posterior to r, and is .3 — .255 — .045 in. posterior to t. The center of curvature of s, its radius of curvature being 10 millimeters or .4 in., is .4 in. posterior to .f, or .4 + .1 [ = .51 in. posterior to r. This is a trifle posterior to the center of curva- ture of the eye ball. This center changes considerably in dynamic refraction, both on account of the advance of .y toward r, and because of the increased curvature and shortened radius of s. The center of curvature of t is anterior to /. With a radius of curvature of 6 mm. or .24 in., it is of course .24 in. forward of t. But the cornea is but .255 in. forward of t, hence the center of curvature of t would be but slightly posterior to r. In the computation of above we determined the radius cf curvature of t to be .346, which would place its center of curva- ture anterior to r, but a more accurate calculation would prob- ably place it very near r and slightly posterior to it. But in the calculation of the efifect of each dioptric surface we have the data for locating each potential focus. The po- tential focus of the wave after refraction by r ( — 33 Cm.) is, as shown, 40/33 = 1.21 posterior to r, or 1.21 — .92 = .29 in. posterior to the retina. In Fig. 20 we have designated this point as F". But since at .y the wave becomes — 40.8 Cm. and its center is .98 in. from s, it is .98 + .11 = 1.09 in. from r, and 1.09 — .92 = .17 in. posterior to the retina, or .29 — .17 = .12 in. anterior to F". We have designated this point, in Fig. 20, as F'. At /, however, the wave must focus at the retina, or at F In the calculation we have shown that to focus at the retina ii must have or acquire at t a. curvature of — 60.15 Cm., for ir is at that point but .665 in. from the retina. Now, in dynamic refraction, these factors undergo import- ant changes. As .y advances forward, s' would, without modi- fication of the curvature of s, advance; but the increased curva- GENERAL OPTICAL PRINCIPLES. 8i ture of ^ advances the center s' still farther. If .? did the whole of the additional + 5 D. of work in the case given (the object being 8 in. from the cornea), and did it by increased curvature alone, it would require an increased curvature of 5 -^ 75/io75 ~ 5 '^ ^P^ ~ 71.66 Cm., which, added to its static curvature of 100 Cm., would make its total dynamic curvature + 171.66 Cm., and its radius of curvature 40 -^ 171.66 = .233 in. But that is not the case, although increased curvature of s is un- doubtedly the largest element in dynamic refraction. Fig. 21 illustrates the variation of dynamic factors in dynamic refrac- tion, rs is shortened; st is lengthened; the center of curvature of s, s', advances toward r', the center of curvature of r, or may pass it; t' probably recedes a trifle toward s, and between them all the dynamic work is done. But r' remains stationary although the cornea does increased dioptric work. The posi- tion of the two potential foci, F" and F' are farther posterior to the retina — at least F" is — but the increased power of s and its increased distance from the retina will place F' very nearly in the position it occupies in static refraction. Fig. 22. ^1— Anterior Work + V^i D. Posterior Work + 10 D. iJ— Anterior Work -r 5 D. Posterior Work + 5 D. Sum + 133^ D. Sum -f 10 D. To understand the dioptric effect of the advance of .s toward r we may study ordinary lens action to advantage. For 82 GENERAL OPTICAL PRINCIPLES. instance, take the effects represented in Fig. 22 A and B. Let us suppose that it is required to focus a pencil of Hght from C upon a screen at .B, 16 in. away. If a lens is placed 12 in. from C and 4 in. from B, its anterior work will be the neutraliz- ing of waves whose curvature is 40/12 ==4-3^ Cm. and its posterior work the focusing of these neutralized waves at B, 4 inches away. The lens will require then 40/4 = + 10 D. additional power, making + 37^ D. -}- 10 D. = + 13^ D. power all told. But, if the lens is placed midway between C and B, it will be required to do 40/8 = + 5 D. of anterior and 40/8 = + 5 D. of posterior work, making but + 10 D. of work all told. The second position, midway between C and B, is the more advantageous position of the two. But if the lens is advanced nearer to C, as to within 5 in., + 8 D. will be required for an- terior work and 40/11 = + 37/11 D. for posterior work, mak- ing + 11 7/11 D. in all. Hence, at the midway point between object and screen, a lens of a given dioptric power is most effec- tive in focusing a pencil at the screen. The advance of .y in dynamic refraction is necessarily an advance toward the mid- way point, for the screen or retina is less than one inch pos- terior to .y always, and the object could not be seen, except by an eye having an unusual degree of myopia, at such distance. Among the official data of the refraction of the eye is the datum that the curvature of the cornea is, in static refraction, 100 Cm. — ^that is, that its radius of curvature is 10 millimeters in an emmetrope. This is of course an assumption that all emme- tropic eyes are the same — an unwarranted assumption — but let that go. The same report affirms that when the emmetrope is accommodated for an object 13.5 Cm. = 13.5 -^- 40 = 5.4 in., distant from the eye, the curvature of .y becomes 6 mm. = 1000/6 = i66| Cm., or that its curvature is increased from 100 Cm. to i66| Cm. At this distance the dioptric media have 40/5.4 = 7.4 D. anterior work to perform, and according to official theories the extra 66| Cm. of .y does it. But such in- creased curvature is not alone sufficient, for the effect of s would be but 75/1075 of 66| Cm. =4.65 Cm. greater on account of such increased curvature alone, which lacks 7.4 — 4.65 = 2.75 Cm. of being enough if .y was unchanged in position and unassisted in the dynamic work by other dynamic factors. But GENERAL OPTICAL PRINCIPLES. 83 with such increased curvature, and the advance of ^ toward r, and the dynamic work performed by r, and alteration of the evolutionary space sf, and a shght increase of the curvature of t, we have the combination of dynamic factors that produce the desired effect. That the increased curvature of s is the great- est of these factors is undoubted, for the tension of the Hga- ment chiefly afifects the curvature of s, and its relaxation allows expansion of s chiefly or its increase of curvature. But it also allows its advance toward r. The latter is not, however, an important factor, since it is so slight in comparison with other evolutionary distances. The increased effect of r in dynamic refraction is, however, important. Each is a little link in the chain of effects by which the dynamic power of the eye is ob- tained. But within the eye, under normal vision, the waves of light are from r onward, whether in static or dynamic refrac- tion, concave in curvature, the reverse of natural waves, which are always convex. In all cases of natural vision, the view of objects, near or far, convex waves of light come to the eye. But the first sur- face of refraction transposes them — makes them concave, and the other two surfaces increase their concave curvature, bring the center of curvature nearer to the wave. Each of the diop- tric surfaces acts positively, for this is positive refraction — re- fraction in the direction of natural evolution. The evolution- ary spaces in the eye — from r to s, from .y to t, and from t to the retina — increase the negative curvature of the waves, and each refracting surface within the eye does the same. But r also acts in the direction of evolution, for it reduces the curvature of convex waves. It over-acts, for it makes the convex waves concave. It w^ould neutralize -f- 33 Cm. waves, or waves from 1. 2 1 in., but s and t together would be unable to center these waves at the retina, for it would require about + 43.48 D. to do that, if the lens were in the position of r, and more on ac- count of its nearness to the retina. In static refraction the curvature of r is opposite to the slightly convex waves of light from infinity, but the curvature of .y is the same or confirmatory, although greater in degree, which makes it a positive surface. Surface t is always, in nat- ural vision, opposite in curvature to the waves that come to it; 84 GENERAL OPTICAL PRINCIPLES. hence, in static refraction, t produces a greater dioptric effect than s, both because it is opposite in curvature to the waves and because it has greater curvature than s. In our calcula- tion above, the dioptric effect of ^ is but + 4.44 D., while that of t, even with a radius of curvature of .346 in., is 12.25 ^^ With a radius of curvature of .24 in. its curvature would be 40/.24 = + 166.66 Cm., which, added to the curvature of the wave of 47.9, would give the total curvature at t 166.66 Cm. + 47.9 Cm. = 214.56 Cm., and the dioptric effect at t would therefore be .075 of 214.56 Cm. — 16.09 diopters. In dynamic refraction all the surfaces are positive, for r has more convex waves; and the waves at s, though concave, are less so, and therefore do not conform with s, both because they are less concave and .s is more convex; and at t the two curvatures are opposite. But, if by the action of a preceding lens or mirror, concave waves come to r and it transmits more concave waves to s, waves so concave that they focus and are transferred in the crystalline lens, and, hence, convex waves of great curvature reach t from a center nearer to t than fs center of curvature, we shall have effects such as are produced in skiascopy, and very peculiar effects they are. Any of the dioptric surfaces of the eye may, under these conditions, become a negative surface, or all of them may be negative at the same time. For instance, if a wave at the cornea were — 133 Cm., the curvature of the cornea being +133 Cm., it would not affect the curvature of the wave. But if the wave were — 153 Cm., refraction at the cornea would carry the focus back toward its center of curva- ture r'. So also, if a wave at .s is — 100 Cm., the curvature of s being + 100 Cm., it would have no effect. But it would refract negatively a wave of — 120 Cm., or carry its center or potential focus, farther back toward s'. A wave also that focused posterior to .y but anterior to / would have necessarily a greater curvature at t than the curvature of t, whose center of curvature is anterior to s. In that case t would be a negative surface and act negatively upon such waves. In the case of the cornea supposed, it would reduce the curvature of the — • 153 Cm. wave, not 153 — 133 = 20 Cm., the difference be- tween the two curvatures, but 33/133 of 20 Cm. = 4.2 Cm., or produce an effect of — 4.2 diopters. GENERAL OPTICAL PRINCIPLES. 85 It is with this class of pencils of light — pencils whose waves have been optically transposed by the dioptric media of the observed eye and that come to the observing eye as con- cave waves — that the skiascopist has to deal. When he brings the foci to his eye it has a class of waves to refract that cannot be focused upon the retina on account of the incapacity of the dioptric media to do so. His eye is not engaged visually in the sense that it is engaged when seeing ordinary objects in the world. The dioptric surfaces, when the area of reversal is at the observer's eye, are of slight effect, for all the dioptric work has been done by the observed eye. The observer or skiascopist does not have a sharply defined image at his retina, but large diffusion circles that, although they give abundance of light, produce no image or real visual effect. The real image — that which should be upon the retina for distinct vision — is far out in the eye. In fact, it may be anywhere in front of the retina, from retina to cornea, or anterior to the cornea. Its advance from the retina forward increases diffusion at the retina until it has advanced so far that the dioptric surfaces begin to act positively again and to re-focns the pencils transmitted by the preceding image. It will be interesting to trace the image, in such advance, from the retina to and beyond the cornea, and consider the retinal effects. The purpose of analyzing the refractive or dioptric value of the different surfaces of refraction has been to give the skiascopist the basis for understanding the effects at his own retina, but which he projects into the pupil of the observed eye, which is also imaged upon his retina when engaged in refracting these peculiar pencils of light, especially when near the point of reversal in the skiascopic examination, or the point at which the reflex appears to change its direction of motion. We say "appears," because the image on the retina of the observed eye does not change its direction of motion actually. Reversal of motion actually takes place on the retina of the observer's, the skiascopist's, own eye. and is projected as reversal of motion at the pupil of the observed eye. In Fig. 23, C D is a luminous arrow and A B a. concave mirror, center of curvature M, and CMC and D M D' are lines axial to the mirror. Bv reflection at A B an inverted 86 GENERAL OPTICAL PRINCIPLES. image would fall upon a screen placed so as to intercept the foci at C D'. Not only is a pencil from C focused at C and one from D at D', but a pencil from each point of C I> is focused somewhere along C D'. All the pencils focus along C D', whether the screen is there or not. If it is not there each pencil is transposed at its focus and proceeds onward. Fig. 23. Before reaching C D' each pencil is composed of concave waves on the way to their focus, but after passing C D' the waves of each pencil become convex again. Beyond C D', not only are what were upper pencils lower ones, but what was the upper part of each pencil before reaching C D' be- comes the lower part of that pencil beyond C D'. The image at C D' is an inverted image, and each pencil is, Ave may say, inverted at C D'. We wish now, without having a screen at C D', to study the effect upon the retina of an observing eye that looks into or at the mirror from points at, anterior to and posterior to C D' — that is, the appearances of the virtual image, apparently back of the mirror, but really nowhere except upon the retina of the observing eye, which projects it into space. We first consider the effects when the eye is at R, forward of C D' or between C D' and the mirror. As the pencils of light that reach the eye at R have been transposed by the mirror from positive to negative w^aves, the eye will receive nothing but GENERAL OPTICAL PRINCIPLES. 87 negative waves — waves on their way to their foci or potential foci at C D'. If the eye at R is emmetropic, with passive ac- commodation, what can it do with these waves? As in such state it focuses neutral waves at the retina it will evidently focus these pencils forward of the retina, forming a true image or focal area forward of the retina. The dynamic power of the eye, if used, will be of no assistance to it, for it will bring the focal area farther forward, and there is no dioptric resource in the eye to enable it to focus these pencils at the retina. With this focal area or the true image forward of the retina there will be, necessarily, diffusion circles at the retina: But will the eye receive pencils or waves from every point in CD? Perhaps it will at R, but a little above R it would be out of range of the pencil from C, which would pass entirely below it; and a little below R it would be out of range of the pencil from D, which would pass above it. The same would be true if the eye were moved to the right or the left, although the pencils have a narrower range in those directions. There will be diffusion circles upon the retina of the eye at R and an enlarged image there, but the image will not be a distinct one. It is a product of diffusion circles, instead of exact foci. But if the eye at R were hyperopic it might receive just the assistance it required to enable it to focus the pencils. It would receive that assistance at some point between the mirror and C D\ Its position for such assistance would depend upon the degree of hyperopia, and it would receive more and more assistance^ up to that degree, the greater its distance from the mirror. At 5 in. from C D' it would receive 8 diopters, at 4 in. 10 D., at 2 in. 20 D., for these negative waves increase in curvature as they approach their foci. The most hyperopic eye would receive waves it could not possibly focus at the retina consid- erably forward of C D'. A myopic eye would have more difficulty at R than an emmetropic eye, and diffusion circles would be larger, because the focal area, which is forward of the retina for neutral pencils, would be still farther forward for these peculiar pencils. It would be the same if A B were a plane mirror and a plus lens, whose focus of the reflected pencils was at C D', were held between the eye and the mirror; or if the glass of the OO GENERAL OPTICAL PRINCIPLES. mirror were plano-convex and the amalgam were spread upon its plane posterior surface. Diffusion is unavoidable, except for a hyperopic eye, of the exact degree of hyperopia re- quired, at R. The effect of diffusion at the retina must not be confounded with magnification, but the distinction between these two different optical results will be explained fully in the next chapter. We will now consider the eft'ects of the recession of the eye from R toward C D' and finally to C D' and thence to R', and will study these effects with special reference to: (i) The capacity and action of the eye's dioptric media, and retinal results, and (2) The limitations upon the number of pencils that may find access into the eye. At R an emmetropic eye certainly cannot focus these negative pencils at the retina. The true image or focal area of these pencils, in an emmetropic eye, is necessarily forward of the retina, and at the retina there are overlapping diffusion circles, producing an image, but not a sharp definition, such as is required for perfect vision. The emmetropic eye is, as it were, myopic for these negative pencils, while the myopic eye as, in the same sense, more myopic. But recession of the eye toward C D' only makes a bad matter worse, for the curvature of the waves of each pencil constantly increases toward C D', and the incapacity or over-capacity of the dioptric media grows constantly greater. But recession also carries the eye or pupil out of range of more and more pencils from the mirror, or from the arrow C D hy way of the mirror. Even that which the eye sees imperfectly on account of diffusion is limited in one way by limitations upon the number of pencils that find the pupil, but each pencil provides the eye with more and more of its light, so that the volume or intensity of light at the retina increases rather than diminishes. As the eye continues to recede toward C D', the focal area or image within it forward of the retina advances, and diffusion circles at the retina grow. Eventually the focal area reaches one of the dioptric surfaces, t (Fig. 24 A), but before reaching / even, it must reach and pass s', the center of curvature of s. GENERAL OPTICAL PRINCIPLES. 89 and then r', the center for r. When it reaches the center of curvature of s, the refraction of r and t as well as the refraction of ^ help to place it there; but when the wave at s becomes — 100 Cm., wherever the image or real focal area, s ceases to be a positive surface; and whenever the incident waves at r become — 133 Cm., r ceases to be a positive surface; and when- ever the waves at t are positive, but of greater curvature than /, t becomes a negative surface, which occurs the moment that the focal area passes t in its advance. When the focal 90 GENERAL OPTICAL PRIN'CIPLES. area is within the lens it is forward of the center of curvature of r and ^ and back of the center of curvature of t, and all three surfaces are negative. But when the focal area passes ^\, s becomes a positive surface again. It is at this position that the work of re-focusing the pencils from the image begins. The action of .s^ is slight on the very convex waves, but it soon re- duces their curvature to such an extent that the waves at t are made less convex than t, and t becomes a positive surface. But r remains negative until the focal area passes out of the eye altogether. When the focal area is at m n, Fig. 24 A, diffu- sion at the retina is slight. But when it reaches m n, Fig. 24 B, diffusion has become wide. But diffusion reaches the max- imum when the focal area is at or just forward of .y — that is, about at the pupil — for then, although .y has become positive, r and / are both negative, and there can be nothing resembling an image at the retina. But few pencils find access to the eye; but the whole intensity of the pencils that do find access is poured into the eye, producing a brilliant illumination of the retina, but no image. It is no doubt between .y and r that positive refraction becomes sufficient to produce an effect in re-focusing the pencils, and re-focusing means, of course, re- inversion of the image upon the retina and reversal of motion. All of these effects, it will be borne in mind, are at the retina of the observing, not the observed, eye. When the eye reaches C D' , all the surfaces become positive, but even with surface r to help, r, .s and t are not sufficient to refocus the pencils, or produce an accurate image. Further recession of the eye, Fig. 23, reduces the curv- ature at r of these very convex waves. The eye soon reaches a position in which, with the use of the accommodation, it gets a tolerably accurate image. Such image is, of course, an in- version of the aerial image at C D', or corresponds to the original C D. It is because this image is erect on the retina of the observing eye that the object or arrow appears inverted and motion is reversed. Somewhere between R and R', Fig. 23, motion is reversed, because the image is re-inverted on the retina. In the observing eye it is luidoubtedly at or very near the plane of the pupil. It may be at the cornea, or at the point where all three surfaces become positive, but these points are GENERAL OPTICAL PRINCIPLES. 9I not widely separated, and the image passes out of the eye almost as soon as it reaches the pupil. The image C D' in the above corresponds to the area of reversal in skiascopy. There is, however, a focal area within the observed eye that may be regarded as the area of reversal also. This area of reversal within the eye comes to the surface only when C D' is at the cornea, but reversal itself may occur before the eye reaches this point. Some writers have placed the area of reversal, or plane of reversal, within the eye, at the nodal point. We cannot consider this to be correct, for the focal area is at the nodal points when all three dioptric sur- faces are acting negatively, and nothing tends to lessen, but everything tends to increase diffusion. The nodal point is a sort of convenient optical peg on which to hang any old optical garment that cannot be satisfactorily placed elsewhere. Undoubtedly reversal occurs just as diffusion at the retina reaches the maximum. We are inclined on that account to place it at the pupil. But when it is at the pupil the cornea is acting negatively, and the potential foci of waves at the cornea are but a few millimeters posterior to it. CHAPTER IV. GENERAL OPTICAL PRIN'CIPLES FOCUS, DIFFL'SION, ABERRA- TION, INXERSION AND MAGNIFICATION. I ^HERE is more or less confusion and uncertainty in optical literature arising from the failure to distinguish between an optical effect upon individual pencils of light, and an effect upon a group or system of pencils considered collectively. The terms focus, diffusion and aberration are terms that relate to individual pencils; inversion pertains to individual pencils and- to the group or system of pencils of which it is a member; while magnification is a phenomenon applying strictly to an effect upon a group of pencils proceeding from the same object and focused at the same area. The effects upon the individual pen- cils are optical, but the effects upon the group thus optically modified are natural, the effects of drawing mental conclusions from physical appearances. This will be seen by analysis. A FOCUS. The word "focus" is strictly applicable to an individual pencil of light, really the center of curvature of a series of con- cave or negative waves. There is no such thing as the focus of a group of pencils, nor is the term properly applicable to a lens. If a system of positive pencils of light are transposed by the action of a lens or mirror each pencil has its focus separate from the foci of all other pencils, and the assemblage of the foci constitute the real image of the object. The lens has dioptric power or potency or capacity to modify the waves of light iti each pencil or a group of pencils transmitted through it. If it transposes and focuses each pencil, such foci are the foci of the pencils, not of the lens. By the reversal of the curvature of the waves their centers of curvature are given a new posi GENERAL OPTICAL PRINCIPLES. 93 tion in advance of the waves, and then, by natural evolution (or involution) the waves, as they advance, assume a curva- ture proportional to their distance from such center. At the ■center their curvature is infinite, and from that point convex waves are evolved. Waves of light are static in curvature only when they are neutral or plane. This is due to their dynamic property of -evolving curvature or change of curvature by propagation through space, for in such propagation they are necessarily advancing toward or receding from their center of curvature, if they have one. But plane waves, having no center of curva- ture do not evolve curvature by propagation. If waves are convex they evolve less and less curvature until they become neutral, or practically so. If they are concave their curvature increases as they advance until they reach the point of infinite curvature, the focus, and convex waves are evolved. Natural evolution of the wave, in a homogeneous medium, is constantly in the direction of neutralization, or toward the static state, al- though, with concave waves, the point of infinite curvature must be first passed. The action of a lens or mirror, if in the -direction of natural evolution, reduces its work; but, if in an opposite direction, it increases its work. It is action in har- mony with natural evolution, or in tlie same direction as nat- ural evolution, that makes a lens, mirror or surface positive; while action in opposition to or in a contrary direction from natural evoluton makes a lens, mirror or surface negative. The optical force affecting waves of light is transitory or im- pulsive, but the force of evolution is perpetual. The lens or mirror or surface acts and instantly surrenders the wave to the force of evolution again. In this respect the action of a lens or mirror upon light waves resem- bles the action of an impulsive force upon a body sub- ject to the constant force of gravity. Throw a body down- ward and gravity adds 32 feet per second to its velocity each second until it reaches support. .Throw it upward and gravity reduces its velocity 32 feet per second until it neutral- izes motion in that direction. The body then begins to fall, gaining an increment of 32 feet per second to its velocity each second of its fall. It passes the point of starting with the same 94 GENERAL OPTICAL PRINCIPLES. velocity it was given when projected upward. Nature trans- poses negative waves of light as gravity transposes motion in opposition to it. A positive lens acts in harmony with evolu- tion up to the point of neutralization, and beyond, for the lens has simply overdone by carrying its action beyond the point of neutralization. Evolution was acting in the same direction before the lens acted, and evolution takes up and follows the same direction of work after the lens acts. The action of a lens or mirror is transitory, but the effect goes on in the wave for- ever. Evolution cannot regain the lost ground or lost time nor eliminate the modification the optical instrument has pro- duced. The action of the lens or mirror is upon the waves of the individual pencils, not upon the group or system of pencils, al- though the waves of each pencil are similarly affected. That is a mere analogy. A focus is the center of curvature of con- cave waves of light, and therefore in advance of the waves or in the direction of propagation of the waves which are neces- sarily proceeding toward it. But only one series of waves, or one pencil of light, has a single focus. Each other series of waves or pencil has its center, and if the waves are concave, that center is also a focus. A positive lens or mirror that trans- poses the waves of one pencil of light will transpose the waves of all pencils from the same distance, or having the same curva- ture, at the same time; but its action is none the less upon the waves of the individual pencils. Where the focus of a pencil may be depends upon the efficacy of the lens for waves of that degree of curvature, as well as upon the direction of propaga- tion of the waves. The position of the focus of each pencil depends upon the same rule. A focus of a pencil is not the focus of a lens, but of the waves of light of which the pencil is composed or of the pencil of light. If an object is one meter distant from a + 5 D. lens, the lens transposes all the pencils of light from the object. One diopter of its power is required to neutralize the + i Cm. waves of each pencil that come to it, leaving + 4 D. to be expended in focusing each pencil. The foci of the individual pencils will be 10 in. from the lens, but they will be at different points, in an area at right angles to the principal axis of the lens. If the GENERAL' OPTICAL PRINCIPLES. 95 object be placed in the position of these foci, lo in. from the lens, it will require + 4 D. of its power to neutralize the + 4 Cm. waves that come to it, leaving + i D. with which to focus the pencils at one meter. The points on the opposite sides of the lens that are respectively the point of origin and focus of a pencil, are called conjugate foci, for each is the potential, if not actual, focus of the other, or of a pencil of light from the other, for this lens. A group or system of pencils thus focused, pro- duces a group of foci at about the same distance from the lens. If a screen be so placed as to react upon each pencil at or near its focus, it will display, under suitable optical conditions, an inverted image of the object. The inversion of the image and its extent compared with the object, are effects of a different character than the mere transposition of each pencil. DIFFUSION. This is also an eftect upon individual pencils of light. It is the effect of the reaction of a screen at some other point or area, either posterior or anterior, than the focus or focal area. That such reaction affects each pencil of a group in the same manner and at the same time renders the action none the less an action upon the individual pencils'. We can, of course, see the result of reaction only upon the group taken collectively, but the reaction is upon the individual pencils. If the screen be held quite near the focal area of the group, there will be developed upon it a small diffusion circle for each pencil. Approach toward the exact focal position reduces the area of each diffusion circle and "sharpens" the definition, while re- cession from the focal position enlarges the diffusion circles and dims the image. If the screen is posterior to the focal position all the waves reaching it are convex; but if it is anterior to the focal position all the waves are concave. In the former case the waves develop upon the screen from the center outward; but in the latter case they develop from the circumference of the diffusion circle inward. The latter devel- opment also reflects the waves inward, which accounts for the beautiful display of geometric figures on the area of diffusion when a bright area of light is imaged. 96 GENERAL OPTICAL PRINCIPLES. Fig. 25 illustrates the development of the waves in a group of diffusion circles, each for an individual pencil of light. It can be readily seen that, whether the waves are developed from the center outward or from the circumference inward, they are proceeding, between centers, in opposite directions. These diffusion circles overlap, for each point on the screen is the center of a diffusion circle, and while the diffusion circle Fig. 25. that centers at A is most intense in molecular activity at A, its activity there is impaired or reduced by its activity at other points in the diffusion circle of the pencil. But other pencils spread their activities over A as well as receive its activities. There is, then, an exchange or mingling of molecular activities by pencils whose diffusion circles overlap, and each center is less individual than it would be if reaction were at but one point. This mingling tends to destroy the identity of the foci, although the foci or diffusion circles of adjacent pencils may be so small in extent as to preserve a fair image of the object. A clear definition of the image and diffusion circles are incom- patible on this account, although it requires wide diffusion to utterly destroy the image. The loss to the clearness of the image by diffusion is not a loss of light necessarily, but a loss of individuality of the centers at the screen, and therefore loss of identification of such centers with points in the object. An image produced by diffusion circles lacks distinctness GENERAL OPTICAL PRINCIPLES. 97 in proportion to the extent of the diffusion circles. While the area lighted by the pencils may be bright, brightness does not make the image. The diffusion circles along the margin of the area of light give an indefinite marginal line to it, and if, instead of circles, the figures are oblong, on account of unsym- metrical refraction (as those produced by a sphero-cylinder), the image will be most extended in the direction of greatest diffusion. But whatever the effects of diffusion circles upon a screen, they are an effect upon individual pencils of light. The diffuse image is simply the sum of these effects, and whatever the dift'usion upon the screen, the pencils that are formed at it from the dissociated impulses of the incident pencil or pencils, by which the eye sees the image, are composed of symmetrical or spherical waves and are capable of being focused by a lens or emmetropic eye. The diffusion upon the screen is the diffusion of incident pencils entirely. The emmetropic eye that views such image will obtain a true pict- ure of the figure or effect at the screen, whether the incident pencils be accurately focused there or not — that is, of course, if the screen is within the range of the observing eye's accom- modation. In skiascopy there may be diffusion in both places, the retina of the observed eye answering to the screen. There is necessarily diffusion at the retina of Ihe observing eye when the area of reversal is at the cornea or pupil, although if the light is at one meter and there is one diopter of myopia, natural or artificial, in the observed eye, the image upon the retina of the latter will be perfect and without diffusion. The secondary correction of — i D. relieves the observing eye of its own diffusion, but imparts diffusion at the retina of the observed eye. But when the observed eye, with passive accommodation, views the distant object, or when, Avith the necessary exercise of its accommodation, it views the near object, there will be no diffusion. Diffusion, after the secondary correction is made, is due to the nearness of the luminous area while the accom- modation is passive. SPHERICAL ABERRATION. This is also an effect upon individual pencils or the waves of individual pencils of light. We may obtain a clear idea of 98 GENERAL OPTICAL PRINCIPLES. the nature of this optical effect by the study of the modifying influence of a lens upon a wave of light that is transmitted throiigh it. It will serve the purpose also of illustrating the operation of the rule governing the relation of the curvature of the glass to its modifying effect upon the curvature of the waves of light, stated in Chapter II. In Fig. 26 let A B he 3i Fig. 26. plano-convex lens, index of refraction, a/b, 1.50, theradius of curvature of its anterior surface being 2 in., or its curvature 40/2 = + 20 Cm. Let H P he a plane or neutral wave of light proceeding in the direction G C, the principal axis of the lens. At the point G the wave will be modified in curvature c/a = 50/150 = -^ of the curvature of the glass. -^ of + 20 Cm. = 6J Cm., and as the refraction is positive and the wave before re- fraction is neutral, after refraction its curvature becomes, at G, — 6J Cm. Its radius of curvature at G is therefore 3 G M, M being the center of curvature of the glass. But at D the wave will become — 6^ Cm. also, and its radius of curvature will be 3 D M. No point on G C can be 3 G M from G and 3 D M from D, nor will the wave at D have the same curvature as the wave F, the point to which it has advanced on G C while H was passing to D. At F the wave will have a greater curva- ture than at D and its center is G F nearer to G than the center of the wave at D is to D. But at L also the wave will acquire curvature of — 6^ Cm. and its center cannot be as near as the center of V, nor as distant as the center of D. At F the wave will be G F nearer its center than at G, and it will also be G F GENERAL OPTICAL PRINCIPLES. 99 nearer its center than at D; and at A' it will be G V nearer its center than at L, and will be L O = ^' F nearer its center than D. Hence the wave is not centered at one point or focus, but along a line equal to G F, the focus of F being near- est M, and its focal length equal to 3 G M. This is spherical aberration at the first surface. But treating such aberration, for the time being, as a negligible quantity, which is equivalent to treating the thickness of the glass as a negligible quantity also, and supposing the wave to be spherical, or of equal curva- ture ( — 6^ Cm.) at D, and F, at the plane surface of emerg- ence it will be again modified in curvature c/b of 6^ Cm. = .50 of 6^ Cm. = 3^ Cm. and become at ^S 6-^ + 3^ = — 9^1 Cm. The modification takes place at ^S before it does at T, for the wave reaches 6" before it reaches T. As the wave is no longer static in curvature, at T it w'ill have evolved greater cvirvature than at 6" without considering its increased curvature due to aberra- tion at the first surface. But with the emergence of the wave at 6^ into air it will not only acquire increased curvature, but it will evolve increased curvature from 5" onward i^ times as rapidly. Hence, while modification at S and T will be equal, <:/b, T will have greater incident curvature and the wave from ^9 onward will gain curvature or approach its center more rapidly than the wave from R until R also emerges in air at T. When all points of the wave have emerged from the glass, evolution of curvature will be equal at all points, but during the brief time that the wave is passing from R to T peripheral areas of the wave will gain upon central areas, and tend to neutralize spherical aberration in the opposite direction at the anterior surface. But spherical aberration at the posterior plane surface will not neutralize aberration at the anterior sur- face, since wave modification is but c/b = -^ of wave modifica- tion at the anterior surface. The new center of curvature of the wave at S is c/b oi S C from S, or at P, and the new center of curvature of the wave at T is c/b of T C' from T, or at P'. Spherical aberration is an effect produced upon individual pencils of light, for it is an effect upon the individual waves of a pencil. Other waves of the same pencil following in succes- sion would, of course, undergo the same efifects as those described above. The waves of other pencils would follow the 7 lOO GENERAL OPTICAL PRINCIPLES. same principle or rule, or be governed by the same law. But aberration is an effect upon different areas of one wave and of all the waves of a pencil, not a comparison or relation of effects upon different waves. The law for each wave is independent of the law or application of the law for any other wave. There is simply an analogy between the effects upon one wave and the effects upon all waves, and it is in the view of the aberra- tion of all waves that w^e observe its effects. INVERSION. Inversion is an effect produced upon the individual pencils in that beyond the focus each minor pencil is inverted in posi- tion. Fig. 27 represents the transposition of a pencil of light Fig. 27 B. by the lens A B. The minor pencils, a and h, of the larger major pencil are transposed at C with the major pencil. All focus at C, but beyond C, a and b have changed positions. All of the minor pencils are inverted in position in the same man- ner; and the minimum pencils, or rays of light, are inverted in the same manner, and inversion is complete. Such inversion is due to the action of the lens. But there is another inversion than this — the inversion of the different pencils wath reference to each other. If, in Fig. Fig. 28 A. # 28, A B represents a circular luminous area 3 in. in. diameter, C D an opaque disc of the same size with. a circular opening GENERAL OPTICAL PRINCIPLES. lOI I in, in diameter, central to the disc, and E F a. circular screen of the same area and form as A B, and the three be placed as represented in the figure, A B and E F being 20 in. apart, and C D midway between them, the pencil of light from A will fall upon H F, but part of it will pass below the disc. The pencil from B will, in like manner, fall upon G E, but part of it will pass above the receiving disc. The light will be displayed upon the disc as shown in Fig. 28 B, or would be if but these two pencils illuminated the disc. In that case M would be illuminated by the light from B and n by the light from A. The pencils of light from A and B are thus inverted at the screen by natural evolution, and not by the action of a lens. li E F were 5 in., instead of 3 in., in diameter, it would intercept all the light from A B hy way of the aperture in C D, for the area of light from A 2I E F has twice the diameter of the aperture in C D, or is 2 in. in diameter, and that of the light from B is also 2 in., half of each falling outside of the screen. U A B were removed to the left to a position of 20 in. from C D, or ii E F were removed to a position 5 in. from C D, all the light from A B would be intercepted by the screen. But in their actual positions, no reduction of the size of the aperture in C D would make either pencil fall entirely upon E F, for to reduce the two half pencils that fall outside oi E F ^ each, would close the aperture in C D. Enlargement of the aperture would increase at one and the same time the light upon the screen and the amount passing above and below it from these points. Fig. 29. But without changing the positions oi A B, C D or E F, or the size of the aperture in C D, all the light from A B passing through the opening may be made to fall upon E F. This could be done by placing a + 8 D. lens at the aperture, which would focus all the pencils Irom A B upon E F, and thus prevent the loss of the light from marginal points of A B. Fig. 29 illustrates the action of such a lens. The focus of the I02 CEXERAL OPTICAL PRINCIPLES. pencil from A will fall at F or a trifle above it, and that from B at E, or a trifle below it, on account of the slight deviation toward the axis of each pencil within the lens. The lens will produce an inverted image of A B upon E F. The inversion of the image is not due to the inversion of each pencil at its focus, but to the inversion of the pencils. The lens has not produced the inversion of the dififerent pencils, for they are inverted without a lens. They have inverted themselves, or are inverted naturally. There is nothing phenomenal in this result, at least more phenomenal than that two persons travel- ing in diagonal directions and passing through the same gate- way should cross each other's paths. Inversion of the image is nothing more than a natural result of position and direction of motion of moving things. It is not due to the action of the lens, but grows out of natural causes. The inversion of each pencil is, however, an optical effect, the result of the trans- position of the waves of light in a pencil of light by the action of a lens. The retransposition of the pencil at the focus does not restore but makes manifest the inversion. It is the action of the lens that focuses the pencil; but, being thus focused, the minor pencils are inverted at the focus by natural evolu- tion the same as different pencils in the image. MAGNIFICATION. The direction, size and distance of an object seen is judged by the mind. Vision, in connection with feeling, and the cogniz- ance of space, from associating time and muscular energy with distance, in a few brief years of experience, enable us to judge distance, size and direction by vision alone. The retinal images provide the data upon which the judgment is founded — that is, the images upon the two retinae in connection with the image upon each retina. An object at a distance gives a smaller retinal image than the same object near at hand. We see a speck upon the brow of a distant ridge to which the road leads. What it is we do not know, but we may observe that its location relative to trees and the general landscape is changing. We rightly conclude that it is in motion, and we know, by similar comparison with surrounding objects, some- thing as to its size. Perhaps, from its general appearance and GENERAL OPTICAL PRINCIPLES. IO3 direction of motion along the road, we conclude that it is a conveyance of some kind, if too large to be a man or dog, although we cannot discover what kind of a conveyance it is. Its nearer approach enlarges the retinal images, and we grad- ually make out a span of horses and other details that show it to be the stage or mail coach. The details become more and more apparent each moment' — one horse is white, the other a bay; the driver is a colored man with a straw hat on, and there is a boy beside him on the driver's seat, and trunk on the roof. These details grow until the coach passes along the road a few rods from where we stand, and then begins to recede in the opposite direction. Perhaps a paper has been thrown out as the coach passes, and a few minutes later we are reading current history from printed characters so minute that they cannot be clearly distinguished farther away than 14 in. from the eyes. The difference in these effects is due to the difference in the extent or area of images upon the retinae. A little punctua- tion mark in the paper now covers a larger area of the retinae than the stage coach, horses, driver and all a half hour before. The enlargement is due to the nearness of the objects. Now, we do not call any of these effects magnification. They are but natural enlargement of the image "on the retinae, due to nearness. With a field glass of eight diameters magnifying power the stage coach at two miles distance would appear but a quarter of a mile aw.ay, and the images upon the retinae would occupy eight times eight, or sixty-four times as large a retinal area. Association and experience in seeing would give the mind, through the sensatory channels, the data for judging distance and size, and the object would seem one-eighth of its actual distance from the eye. But the higher intellectual facul- ties would revise this judgment and determine the true cause of the analogy. The effects produced by the field glass are properly termed magnification. Magnification is not a sensa- tory thing merely, but it is a sensatory effect that natural sensatory capacities do- not account for. Magnification is an artificial enlargement of retinal images by optical means ex- terior to the eye itself. Such artificial enlargement of the retinal image may produce one of two effects: (i) The object I04 GENERAL OPTICAL PRINCIPLES. will seem to be nearer than it actually is, or (2) it will seem to be larger than it actually is. Sensation accepts the former in preference to the latter when it can, for that is a matter of daily and hourly experience. But sensation will not accept nearness within the punctum proximum of ordinary, naked-eye vision, for it has no experience to correspond with that. If a spider's foot is within an inch or half an inch of the eye, which, with an assisting positive lens, is enabled to get a sharply defined image of the object on the retina notwithstanding its nearness, the sensatory verdict is that it Is large and not nearer than the ordinary punctum proximum. But the distant object is brought nearer and given its ordinary size. These are the distinguish- ing effects of microscopy and telescopy. Telescopy brings tlie object nearer and thus accounts for its enlargement; micro- scopy cannot allow the object to be as near as it actually is, but on account of the enlarged image the object appears, at the punctum proximum, proportionally enlarged. Both of these effects are, however, magnification. Magnification is an effect upon the group or system of pencils of light from the object. An enlarged retinal image is merely the separation on the retina of the foci of pencils from points in the object. As the term foci pertains to more than one pencil, two or more pencils are necessarily involved in magnification. The foci are as exactly placed upon the retina in magnification as in ordinary vision, the only difference being in the separation of the foci. The definition is as sharp in one case as in the other, or the principle of magnification is lost. If the pencils do not focus upon the retina — an effect pertain- ing to the individual pencils — diffusion results. Diffusion begins where magnification ends. It is in the confusion of these two distinct phenomena that Dr. Jackson is most unsatisfactory. He speaks of the magnifi- cation of the retina when the point of reversal approaches the observing eye, and of indefinite magnification when it reaches it. In skiascopy it is not the retina but the reflex that is being observed. The apparent enlargement of the reflex is due to increased diffusion at the retina, not of the observed, but of the observing eye, such diffusion reaching the maximum at the moment when the pencils of light from the observed eye focus GENERAL OPTICAL PRINCIPLES. I05 at or just posterior to the cornea of the observing eye. There may be diffusion at the retina of the observed eye also, but it is slight in comparison to the diffusion at area 4. If the observed eye is myopic to the exact degree required for it to focus, with passive accommodation, the luminous area upon the retina, and no lens is in front of it, it will focus emergent pencils at the same distance as the light. If the observing eye is at that point there will be the greatest degree of diffusion upon its retina, although there is none at the retina of the observed eye. Magnification has no standing in these peculiar effects. The diffusion at the retina of the observing eye is projected to the pupil of the observed eye, and it is this effect that the doctor calls indefinite magnification. The doctor also seems to think that a pencil of light from one point on the retina of the observed eye monopolizes the pupillary space in coming out. There is no chance for such monopoly, for the pupil allows ten million pencils, each filling its entire space, to pass through it simultaneously, and there is not the least inter- ference between them. One pencil occupying the pupillary space is no bar to others. In emmetropia and hyperopia there is magnification of the reflex, for the reflex is either at or within the focal length of the dioptric media. But neither a liyperope nor emmetrope will focus the luminous area at the retina without the use of the accommodation, hence there is diffusion at the retina of the observed eye in these cases, and that is all the diffusion seen until a lens makes the eye artificially myopic. Then the retina and reflex are no longer nearer than the focus, and the emerg- ent pencils are convergent, and magnification of the retina or reflex is at an end, the same as when a lens of + 5 D. is held more than 8 in. from the object to be observed through it, and diffusion begins. Fig. 30. Lenses are placed near the eye, or at it, usually to over- come the eye's dioptric defects, but they are placed at fixed I06 GENERAL OPTICAL PRINCIPLES. distances from the object usually to be within their focal distance from it. In the former case magnification is not the thing sought for, but a perfect definition at the retina. In the latter case magnification is the purpose. If a lens is at its focal distance from the object, all its power being exercised in neutralizing the pencils, as shown in Fig. 30, the direction of propagation of each pencil is unchanged, but if the observing eye is far away, only pencils from a small area of the object reach it at all. But the im.age of such small area will be en- larged on the retina because of the action of the lens. If the lens were a little nearer to the object it would not neutralize the pencils, and more pencils from the object or from a larger area than A B would reach the eye, which would have to use a little of its accommodation to focus them. The object would appear smaller, and magnification would be less, because the retinal image would be reduced. A lens used in this way gives its maximum of magnifying power when at its focal distance- from the object, or when it simply neutralizes the pencils. A little farther from the object, only part of its power is required to neutralize the pencils, and it therefore focuses them posteri- orly at a greater or less distance, and the observing eye, within such focal distance, receives concave waves. An em- metropic eye has no capacity to focus these pencils at its retina. A hyperopic eye may do so if it is not too near the focus; but no eye can focus them if at the focus, for they are already focused by the lens. Diffusion necessarily results, and diffusion is at the maxium when the observing eye is at such focus and its dioptric media are utterly incapacitated. Fig. 31. Fig. 31 represents an eye, unassisted, focusing pencils from A B. The crescent on the lens represents the accom- modation. No accommodation is required by the eye in Fig. 30, if emmetropic, as the waves are neutral. It will be noticed in Fig. 30 also that the lower part of the pencil from B and GENERAL OPTICAL PRINCIPLES. IO7 the upper part of the pencil from A alone reach the eye, and the source of the pencil from A seems to be at A' and that from B at B', because the foci are on the axes A' F and B' E of the observing eye. In these two cases (Figs. 30 and 31) the retinal images may be equal in extend, although A B in Fig. 31 is much larger than A B in Fig. 30. In each case the image is inverted at the retina. Why, then, does the object appear erect? This question is equivalent to the question: "Why does a feeling feel the way it feels?" which is not ver}^ intelligible. Projection of the two equal images gives the idea of two equal objects, and A B in Fig. 30 appears to be of the same size as A B in Fig. 31. As they are at equal distances, this is magnifi- cation. If the lens in Fig. 30 were a stronger lens, or if it were farther from the object A B, it would transpose all the pencils from A B, giving the observing ey^, unless it were beyond such foci, negative waves. Within the focal distance the obeserving eye would have negative waves, but if the observ- ing eye were beyond the foci a true image oi A B would lie between it and the lens, and from such true image positive waves would be evolved and pass on to the observing eye. Now, if the observing eye is at the focal area, or at A' B' , as shown in Fig. 32, it will be utterly incapable of focusing the pencils; but if it is beyond A' B' and not too near, it may re- transpose the pencils transposed at A' B' and get an image of A B upon its retina. But only minor pencils of the original pencils, acted upon by the lens, will reach the observing eye. The pencil that focuses at B" will have been previously focused at B' , and will come from B and be transposed by the upper part of the lens. It is in the upper position in the intermediate image at A' B', but in the lower position at A" B". The same double inversion will be noted for A" from A', which is from A. I08 GENERAL OPTICAL PRINCIPLES. That is, A" B" is an inverted image of an inverted image, and the double inversion has caused it to correspond in position with the original A B. But the object will now appear to the observing eye inverted, for projection produces this eflfect, and it is only when the retinal image is inverted that the object appears erect. To the observing eye A B appears enlarged and inverted. li A B is, an arrow pointing upward, the aerial image A' B' will be an arrow pointing downward, but A" B", the retinal image, will be an arrow pointing upward, but it will be pro^ jected as an arrow pointing downward, for that is the rule of projection, a sensatory law established by experience. A B will be magnified, for A' B', which is the immediate source of the pencils that reach the eye, would appear larger because of nearness to the observing eye, \l A B and A' B' were equal in size. But as A' B' is farther from the lens than A B (we will suppose twice as far) it has double the extent of A B. But if we also suppose that A' B' is double the distance from the dioptric media of the observing eye that the retina is from such media, A" B" will be of but ^ the extent of A' B', and therefore equal in extent to A B. The retinal image will be, therefore, of the same size as the object. Sensation can give the data for but one conclusion from this — ^that the object is large, about as large as the lens that transmits the pencils, for it will not allow that the object is nearer than the lens, for the retinal image of the lens covers the image of A B. The lines of projection for the lens and A B are about the same. Since A' B' is of twice the extent oi A B and but half as far from the retina, A B is magnified four diameters, and m n appears to be four times the extent of A B. If L is moved laterally a few millimeters, A B will appear to move in the same direction, but more rapidly than the lens. Magnification is a sensory eflfect giving data for a mental conclusion. The conclusion would be that certain objects are nearer or larger than ordinary vision in connection with the other senses, proves them to be. There is, fortunately, a higher court to decide the question. That higher court decides that sensation is misleading in the case; that its evidence is to be discounted, so far as it effects conclusions as to the nearness GENERAL OPTICAL PRINCIPLES. IDQ or size of the object. It accepts the evidence of ordinary vision and decrees that the object is not nearer nor larger, but that superphysiological causes have given the retina a larger image than it is naturally entitled to. The difference between what it is naturally entitled to and what it really gets by reason of such superphysiological agencies, is the measure of the mag- nification. But the higher court does not disdain to use the data of the misled sensations just the same. It accepts them in everything except the trivial matter of size and distance. It acknowledges the existence of stars, and moons, and comets, and nebulae on no other testimony. It accepts the proofs of superphysiological sensation, or rather the proofs that involve superphysiological agencies, as if they were the results of the ordinary and natural physiological phenomena. In this respect magnification has revealed great facts that could never have been conjectured without it. CHAPTER V. STATIC FACTORS OF SKIASCOPY. THE FOUR AREAS. THE THREE INTERVALS. SUBSIDIARY AREAS AND INTERVALS. ANALYSIS OF STATIC FACTORS. STATIC EFFECTS. w ■E have noted in Chapter I the static factors of skiascopy, classing them into areas and intervals, of which there are, primarily, four areas and three intervals. It will now be in order to consider these factors analytically, and the part each plays in a simple skiascopic examination. Each factor pos- sesses certain features it will be necessary to take into account. The order in which we have named them is probably not the' natural order, although it is the physical order. If vision were a phvsical phenomenon, then the order would naturally be phvsical. But as vision is really mental, the objective world, regarded visually, is a mere projection of a mental impression or phenomenon; and yet we are so material in our aspe:t toward this mentally created world of ours that we have no language in which to state the case from any other than a material standpoint. I. THE LUMINOUS AREA. Adopting, then, the physical basis of treating the subject, we begin with the luminous area. This we must regard as the basic element, the preceding cause, the foundation of all that is to follow. The luminous area in skiascopy should be bright, but not too bright or dazzling. It should be of sufficient ex- tent, neither too large nor too small. It should be a colorless light. It should have a definite form, but might embrace differ- ent forms, as the circle, the square and the triangle. A dark central area surrounded by a ring of light is good form. An argand burner is the most available of skiascopic lights— that is, of lights of the first order. It can be procured almost anywhere in the country and is fed by kerosene, also 110 ^ ?i 3 o '" M o 12 ™ > ft H ?. o 2; 5' o 5K 3 ' n STATIC FACTORS OF SKIASCOPY. Ill procurable in any place that would maintain an optician. Gas or electric light are preferable in the city, because of their -convenience and cleanliness, but they are little, if any, better for their light than a good argand burner. The Welsbach and similar lights are usually regarded as too brilliant, and tend to neutralize the effect of the dark room in dilating the pupil. A skillful operator will be very little handicapped with any sort of luminous area, however, and cases may be worked out accurately by skiascopy with a tallow-candle flame. To give form to the luminous area and eliminate general light, it is customary to use a skiascopic chimney. This is a hollow cylinder of a'^beslos, visually, sufficiently large to go •over a gas or student lamp chimney, but with an opening in it opposite the flame. There are various forms of these chim- neys upon the market, some of which are shown in the figure •or illustration (Fig. 33). The size of the opening in A is con- FiG. 33 A. trolled by revolving discs, which bring differently formed openings in the discs before the opening in the standard chim- ney. The extent and form of the luminous area depends, of course, upon the extent and form of the opening in these opaque revolving discs, which can be set at any figure required. 112 STATIC FACTORS OF SKIASCOPY. In B the opening is practically circular, and its size is regulated by the little lever which causes expansion or contraction of the "iris diaphragm" over the opening. The purposes of the skiascopic chimney are, then, (i) to give the observed eye a small area to focus upon its retina, producing a small image; (2) to confine the illumination so that there will be little general light in the room; (3) to control the form of the luminous area, for, whatever its form, that will be the general form of the image upon the retina of the observed eye, although in unsymmetrical ametropia, astig- matism, tlie form of the image will not correspond exactly to the luminous area, on account of greater diffusion in one meridian than that at right angles to it. But symmetrical ametropia, or even emmetropia, with the area of light at a finite distance during passive accommodation, gives diffusion ; but if the eye is symmetrically ametropic — that is, myopic to the degree required to focus the luminous area at a finite dis- tance, even though accommodation is passive, upon the retina — there will be no diffusion upon the retina of the observed eye, but such ametropia will more than neutralize the emerg- ent pencils and produce diffusion at the retina of the observing emmetropic eye, which will project such diffusion into the observed eye, causing the image to appear to be diffuse there^ although it really is not. If, with a plane mirror, the light from a lamp flame is reflected to a plus lens in such position that it focuses the reflected pencils upon a screen, producing a clear and exact definition of the flame upon the screen, that image, as seen through the lens from the peep-hole of the mirror, would not seem to be clear, for the lens which focuses the reflected pencils from the flame transposes the pencils coming from the image back to the eye, and would focus them at the same distance as the flame. The eye at the peep-hole intercepting these pencils on their way to their foci, receives concave waves or converging rays, which, if it is emmetropic, it cannot focus upon the retina, and diffusion is unavoidable. Tlie extent of the luminous area should be controllable, for it may be necessary to shift the distance of the lamp or light so as to get pencils whose waves have a greater curvature, as in bringing out the banded appearance in astigmatism ; and it STATIC FACTORS OF SKIASCOPY. II3 should be possible to do this without changing the extent of the retinal image, as it would be if the distance were changed without increasing or decreasing the luminous area. The use of translucent discs has an effect upon the interval rather than the area of light, and will be considered under that head. 2. THE MIRROR. The mirror is the skiascope. Originally the concave mirror was thought to be the only serviceable form of mirror to be used for this purpose, but the evolution of skiascopy has brought the plane mirror more and more into favor. The trained skiascopist will, however, use both. Aside from the confusion that might result to beginners by the -opposite action of the plane and concave mirrors, the chief advantage of using both is this, that with the plane mirror the immediate source of light is farther away, necessarily, than the observing eye, but with the concave mirror the immediate source of the in- cident pencils of light is the image anterior to the mirror and nearer the observed eye than the observing eye. In astig- matism the banded appearance may be brought out with the concave mirror by having the more distant area of reversal at the observing eye, while the area of reversal of the opposite meridian is in front of it and near the immediate source of light or image. The plane mirror is better for regular work, and, for beginners particularly, it will prove more acceptable. The circular mirror is the usual form, because of having equal diameters in all directions, and the virtual image there- fore has equal spaces in which tO' move when the mirror is tilted. The two-inch mirror is preferable for work at one meter, although that is a matter of choice, as much a matter of choice as the standard distance at which to work. Some cf the forms of the skiascope, as it appears in the market, are shown in the illustration. The small mirror with a dark marginal area is a favorite mirror with many skiascopists. It narrows the area of the major pencils and produces a smaller area of "light on the face." This is a decided advantage in doing close work within one meter of the observed eye, for the red reflex will be seen if the major pencils cover the eye, even at the margin. In a larger mirror the iris may wholly conceal the 114 STATIC FACTORS OF SKIASCOPE. retinal reflex. However, the question of size is a good deal a matter of individual preference. It is not unlike the preference people have for different kinds of steel pens to do their writing with. One does better work with the instrument that suits him best. y¥ Fig. 34B. The perforation in the mirror seems also to be a matter of preference, both as to size and kind. In the market skia- scopes these vary from i|- to 3 or 4 millimeters. The perfora- tion should be a clean one, leaving no jagged edges to reflect the light that falls upon the surfaces and confuse the observer. The surface should be darkened also. Mirrors are made with no perforation, the substitute being the removal of a small area of the amalgam from the back of the mirror, giving the emitted pencils the thickness of the glass to pass through on their way to the observing eye. This feature is an improve- ment in one respect and a disadvantage in another. The re- flection of the glass answers the purpose of a mirror in com- pleting the retinal image — eliminating the dark area in it where the perforation stands, though not completely. But the reflec- tions at the surfaces of the glass tend to obscure the view of the observing eye by interfering with or reducing the intensity of STATIC FACTORS OF SKIASCOPY II5 the waves of emergent pencils when the area of reversal or any of the waves of emergent pencils cover the perforation. A debatable question is the question whether the observ- ing eye can see the red reflex except when the virtual image covers the perforation. It is interesting to note the points in the question: The virtual image, so-called, in the mirror is but a projection of the real image upon the retina of the observed eye. It has no existence except to the eye that sees it, and to that eye it has no objective existence. Projection is a mental, not a physical act, and, speaking physically, the projection of the retinal image and the image are one and the same thing. But if the virtual image lias no physical existence it can have no physical location, considered apart from the retinal image. It cannot be said to be in the mirror. The image of the flame or luminous area is simply in the retinal image of the mirror. But there is a physical mirror as well as a retinal image of the mirror, neither of which are merely mental. There is also a physical luminous area, although, as we have seen, the virtual image has no physical existence, except as an image at the retina of the observed eye. But although there is no virtual image anterior to the observed eye, either in the mirror or elsewhere, but the virtual image is a mental creation with a real retinal image for a foundation, although such image may be imperfect on account of diffusion, there is a real image of the retinal image anterior to an eye that is, either naturally or artificially, myopic. From the real, though imperfect, image upon the retina of the observed eye pencils of light pass, by way of the pupil, out into space. If the observed eye is myopic all the pencils focus forward of the eye, forming a real image of the retinal image, or of the retina with the image upon it, true to life — clear and sharp if it is sharp, or diffuse and imperfect if it is imperfect — anterior to the eye. This is no mental creation, at least not of the one whose eye is under observation, for he has no cognizance of it. This anterior physical image must be in a position from which it can remit pencils of light transposed at it on to the perforation in the mirror and the observing eye back of it, for otherwise no reflex will be seen. Now, the question is: Does the nosition of this physical image coincide Il6 STATIC FACTORS OF SKIASCOPE. with a mentally created, non-physical, virtual image supposed to be in or back of the mirror or some other impossible place? The question brings us face to face with the problem of visual projection — the attempt to draw a line from a mental point to a point in the world corresponding to the aforesaid mental point of which it is a projection. The philosopher who desires to puzzle his brains over this question may do so. There is as much diversion in it, and prospects of eventual success, as there is for the little poodle who chases his own tail. When we say that the emergent pencils pursue a path cor- responding closely to the path of the incident pencils, though not coincident with it, we are probably coming as close to answering the question as we can. That the emergent pencils do follow such a path is indisputable. But that they do not coincide with them is indisputable also, for incident pencils are always composed of convex waves or diverging rays, while emergent pencils may be composed of convex or concave waves, or of diverging or converging rays. Convex emergent waves cannot coincide with convex incident waves, for they are convex in opposite directions. But neither can concave emergent waves coincide with convex incident waves, unless their curvature is the same, which can only happen when the eye is accommodated for the luminous area or object, which it is not supposed to be during a skiascopic examination. If all the incident pencils were made neutral on their way to the observed eye, so that the eye, if emmetropic, would focus them with passive accommodation, or the lens that enabled the diop- tric media to focus them upon the retina would cause the emergent pencils to become neutral, there would then be coin- cidence, for the lens that focused the incident pencils would neutralize the emergent pencils. The emergent pencils reach the mirror about the same area as that from which minor in- cident pencils that enter the pupil come. They may cover more or less ground. We cannot say, however, that the area from which the incident pencils come is the location of the virtual image, which has no objective location because it is not physical, but it is undoubtedly the area to which we assign the mentally projected virtual image; for if the mirror is titled, to the one under examination the virtual image disappears at the STATIC FACTORS OF SKIASCOP7. 117 margin of the mirror just as the last point in the area of "Hght on the face" passes off the pupil. This, however, is not a solu- tion of the problem of projection, for the mirror, visually con- sidered, is just as much a projection of a retinal image as the virtual image of the luminous area projected to it. We have simply harmonized two projections, or the projection of a smaller area with the projection of a larger area of which it is a part. A skiascope has a handle. To facilitate the tilting of the mirror upon its horizontal axis, it is customary to let the handle rest between the third and fourth fingers, while holding the metal butt of the handle between the tips of the thumb and forefinger. This enables the observer to tilt the mirror in the vertical, or upon its horizontal axis, very slightly and quickly. The accompanying figure represents a back and front view of the Fig. 35. mirror being thus held. To tilt the mirror in the horizontal, or upon its vertical axis, the handle should project downward and be grasped lower down. Some operators prefer to rest the tips of the thumb and fingers upon the edge of the disc in which the mirror is set in tilting it upon its horizontal axis, but either or any way of holding the mirror suitable to the operator is quite proper if he prefers it. The mirror is necessarily inclined at an angle to both the luminous area and the observed eye to Il8 STATIC FACTORS OF SKIASCOPY. give effect to the law of incidence and reflection. This inclina- tion to the observed eye gives a slight obliquity to the perfora- tion. It must be slight or the observed eye would be obscured. All parts of the skiascope, except the mirror and handle, should be dark colored, so as to absorb and neutralize all light falling upon them, especially the inner surface of the small cylindrical perforation. 3. THE OBSERVED EYE. If the interior of the eye were illuminated the observer would be able to see but a small area of the retina, much smaller than an area equal to the pupillary space, although it would be magnified to that space. Tliis fact is due to the magnifying effect of the dioptric media of the observed eye, which, in emmetropia, with passive accommodation, acts as a correctly focused positive lens. In ametropia, or with active accommodation in emmetropia, the dioptric media are not, from the standpoint of the observer, focused to the retina. In myopia and emmetropia with active accommodation, the retina is back of the focal position, while in hypermetropia it is for- ward of it. In the latter position the dioptric media have a magnifying eflfect, the same as a positive lens held nearer the object under examination than the power of the lens permits. Magnification results, but the lens is not at the point or in the position of maximum magnification, for the pencils of light are not fully neutralized. But in the former position all pencils from the retina are transposed, giving the observing eye, within the anterior focal distance, pencils consisting of concave waves, or, beyond it, retransposed and inverted pencils of convex waves. If it were not for the dioptric media of the observed eye, the observer w'ould see an area of the retina a trifle larger than the pupillary space directly back of it. The extent of such space, in comparison with the pupil, would depend upon nearness. A dilated pupil would increase the area within view proportionately to dilation. But the view of the retina and the image upon it through the dioptric media does not follow this simple rule, either as to direction or location or extent, for magnification causes a very small area of the retina to fill the pupillary space — not a point to be sure, but an area in- STATIC FACTORS OF SKIASCOP':^. IIQ versely proportional to the distance of the retina and observing eye from the principal plane of the eye, according to the law of images. But the dioptric media of the observed eye, unless its visual axis is directed straight into the observing eye, deflects the pencils of light emerging from it. The observer may thus see an area of the retina and the image upon it that is actually behind the iris, and an area of the retina in direct line of vision through the pupil, in a homogeneous medium, may be obscured by the iris. This is due to the deflection of oblique pencils by the dioptric media, or to the prismatic effect corresponding to that of a decentered lens. In making skiascopic examinations the observed eye is always directed to a point in space to one side of the observing eye, to avoid stimulus to the accommodation. The pencils that reach the observing eye are therefore deflected. Such deflection brings areas of the retina into view that could not otherwise be seen — areas near or including the macula itself. But the macula would be to one side of the area brought imder observation, which side would depend upon the direction of the observed eye and which eye (right or left) were under observation. But in skiascopy no attempt is made to perceive the macula or optic disc, or to locate tftem in the pupillary dis- play. The observer concerns himself only with the reflex as a whole and the dark areas that border it. He soon learns the appearances of emmetropia and how, with lenses, to bring about the emmetropic appearances. Appearances do not reveal to him the conditions that prevail back of the dioptric media, nor is he anxious to ascertain what they are by this method. They do reveal conditions anterior to the dioptric media which are produced by the dioptric media. If these conditions are not normal, by correcting them he corrects whatever dioptric fault there may be back of them, for the fault is really neither posterior nor anterior to the dioptric media, but in them. When the pupil is "lighted up" as with an internal light, and a "glow" rather than a perceptible image is seen, and motion across the pupillary space is a mere "flash" having no apparent direction of motion, either with or against the mirror, the anterior image of the retinal image in the observed eye is at the pupil of the observing eye, and if the observing eye is one I20 STATIC FACTORS OF SKIASCOPY. meter in front of it, this shows one diopter of myopia in the observed eye. The image or reflex, as seen from the- standpoint of the observer, takes on a bright red color, due to a multipHcity of minute blood-vessels in the vascular layers of the posterior inner surfaces. It is less red than blood, because the capillaries are spaced by intervening distances forming a meshwork of blood-vessels. The retina itself is transparent, and its back- ground is the pigment layer of the choroid coat. It is really upon this layer, rather than upon the retina, the rods and cones of which are imbedded in it, that the image is displayed. A dark absorbing surface gives a brighter display and higher effect because of the contrast it presents to other areas. The areas of the retina not displaying the image of the luminous area are dark, both from the effect of the pigment and the absence of light. The reaction of the pigment layer of the choroid is slight, as most of the energy is, as it were, transmuted from the physical into nervous energy, which is equivalent to absorp- tion by non-sensitive dark surfaces when a real image is cast upon it. But reaction is sufficient, nevertheless, to provide a system of emergent pencils by which the skiascopist determines the dioptric error. The reaction of this surface is analogous to reflection, but as each pencil's energy is confined to a limited area — the area of the diffusion circle produced by it — there is not that dissociation of impulses from many pencils and reasso- ciation such as we have from rough surfaces, and which make the surface or object visible. Each circle of diffusion contains the energy of a limited area of the light and gives back energy of the same identity. At least it is only mixed to the extent of the overlapping of diffusion circles. The case is different if a screen is required through which the image may be seen from the opposite side, as the ground glass field used in the artist's camera. There a surface is required that will transmit the energy, but react sufficiently to display the image. 4. THE OBSERVING EYE. This is the subjective area — objective, however, to the observer's higher intellectual faculties. It is the area at which STATIC FACTORS OF SKIASCOPY. 121 is revealed the condition of the dioptric media of the observed eye — the ".v" or unknown quantity in an algebraic equation all of whose other terms are known. The observer formulates the equation in his examination, and then he has but to reduce, simplify, transpose, eliminate and divide by the coefficient of "x" to determine its value and solve the problem. The observ- ing eye occupies the same relation to the retinal reflex as R and R' in Fig. 23, Chapter III, has to the arrow C D, whose virtual image appears in the concave mirror. The questions that present themselves successively to the skiascopist in an examination with a plane mirror are as follows: 1. What is the character of the pencils of light emitted by the observed eye from the image upon its retina? Are they positive, consisting of convex waves; are they neutral, con- sisting of plane waves, or are they negative, consisting of con- cave waves? 2. If they are positive or negative they can be neutralized, a positive lens neutralizing positive pencils, and a negative lens neutralizing negative pencils; but the first work is not to neutralize them, but make them of a fixed concave curvature — — I Cm. — or to focus them at one meter. It may require a plus lens to do this, or it may require a minus lens. 3. The skiascopist determines at the first glance which sort of lens, plus or minus, is required by noting whether the retinal reflex or image moves zvith or against the mirror or "light on the face." If it moves with the mirror a plus lens is required; if against it, a minus lens is necessary. 4. The power of the lens is determined by trial, but the power is indicated by the rapidity of motion of the reflex. If it moves very rapidly, but a slight increase of power is called for — the more rapidly it moves, short of reversal, the nearer the approach to the point desired. Complete elimination of motion, or motion so rapid or instantaneous that direction of motion cannot be told, completes the primary correction. 5. The above brings the image or area of reversal to the eye of the observer. The waves of the emitted pencils are — i Cm., for they focus at one meter. It is only necessary to add — I D. to the primary correction to neutralize the emergent 122 STATIC FACTORS OF SKIASCOPY. pencils. If, with this full correction, the eye, with passive accommodation, emits neutral pencils of light from an image upon its retina, it w^ill focus neutral pencils or pencils from the distant object at the retina. 6. If different meridians of the eye are different, it is only necessary to find the correction for each of the principal merid- ians and prescribe a compound lens having the requisite power in each meridian. It would seem, from the above, as though area 4 had little to do with the examination, except as it revealed the condition of area 3; but let us see. When a lens is put in front of the observed eye, or the power of such a lens is changed, the waves of the incident pencils from, the luminous area undergo modifi- cation. The lens either assists the eye in doing its work or increases the work it has to do. This afTects the retinal image — increasing or decreasing diffusion, — but it does not reverse the motion of the image on area 3. That is always the same way — with the mirror. The rapidity of motion at area 3 is not materially affected, whatever the lens before the eye. Re- versal of motion and rapidity of motion, or change of rapidity of motion, are phenomena that pertain to area 4 exclusively. The appearance of reversal and change of motion in the pupil of the observed eye is due to the principle of projection. Re- versal of motion is an "optical illusion," so-called, and like all optical illusions, it is explainable on simple optical principles. Reversal of motion on area 4 is due to transposition of the emergent pencils from the observed eye anterior to the observ- ing eye or anterior to a fixed plane in the observing eye, at which the transformation occurs, and which we have assigned as the plane of the pupil. If the real image anterior to the observed eye is anterior to this fixed plane in the observing eye, inversion and reversal of motion at area 4 result. If it is posterior to this fixed plane, neither inversion nor reversal of motion occur. If it is at this fixed plane the image is lost, and motion or the direction of motion is indeterminate. It does not matter so much where that fixed plane in the observing eye may be, but the phenomena of reversal and inversion, which appear at the retina and are sensatory, are the important STATIC FACTORS OF SKIASCOPY I23 elements. Our reason for assigning the location of the fixed plane of reversal in the observing eye at the pupil is this: The pupil is the gateway separating the outer eye and the world from the inner eye. through which all pencils pass. It is similar to the door of a church through which people are passing in or out, and the foci of the pencils are crowded more closely together there than at any other point — not because of the action of the cornea, but because of the lens action of the observed eye in focusing the pencils at the pupil. From this plane the pencils expand on either side, the same as the people within or without the church doorway, and diffusion at the retina is then at the maximum, the lens having little effect in condensing or focusing tli'e pencils from a point so near its anterior surface, especially since the cornea, at this point, gives it no assistance. When the image is at the fixed plane of reversal in the observing eye, no image appears on the retina. All is lost in diffusion at area 4. But on account of aberration, certain areas of the pupil will appear illuminated and others less so, because the area of reversal is not quite the same for different pupillary spaces. But at the slightest motion or quiver of the hand these illuminated spaces vanish, though in what direction can- not be told. They appear to consume themselves, or the darker areas to consume the areas of light. A slight change in the power of the lens or position of the observing eye brings up the illumination and motion again. In bringing the area of reversal to the fixed plane of reversal, the area of reversal in the observing eye, and not the exterior aerial image or area of reversal, is considered. When the aerial or potential image is posterior to the observing eye, the area of reversal or image in the eye is anterior to the retina but posterior to the fixed plane of reversal. As the area of reversal within the observing eye is brought forward toward the fixed plane of reversal by a stronger plus lens or the area of reversal or image anterior to the observing eye is brought back by a stronger minus lens, motion becomes more rapid. As the area of reversal ap- proaches the fixed plane the image grows less and less distinct, ■ although illumination increases, on account of increasing dif- fusion; but such imperfect image, with the slightest motion of 124 STATIC FACTORS OF SKIASCOPY. the mirror, sweeps across the entire retinal field or field of vision on which it is displayed. To reverse motion it is neces- sary that the area of reversal cross the fixed plane of reversal of the observing- eye. Tlie efifect at area 4 depends upon the sort of waves of which the emitted pencils are composed; and what those waves are depends upon the dioptric power of the observed eye com- pared with the distance of its retina from the dioptric media. If the emitted pencils consist of convex waves, they have no anterior foci, nor is there an anterior image. The dioptric media has not sufftcient power and requires a positive lens to supplement it. But the observing- emmetropic eye is able to focus these convex waves by the use of a sufficient degree of its accommodation. If the emitted pencils are neutral or con- sist of plane waves, the eye's accommodation being- passive, its dioptric media is exactly adapted to the distance of the retina from which the pencils come. It will not focus pencils from a finite distance upon the retina, for an emmetropic eye with passive accommodation is not supposed to do that; it would not be emmetropic if it did. Tlie emitted neutral pencils have no anterior focus, but the observing emmetropic eye will focus them without the use of its accommodation. If the emitted pencils are composed of concave waves, then each pencil has a potential or actual focus anterior to the eye — a center of curvature for these negative waves. Together these foci make the anterior image or area of reversal. The aerial image or area of reversal may be posterior to the observing eye, but the area of reversal within the observing eye, in that case, is anterior to the retina, but posterior to the fixed plane of reversal. If the area of reversal is anterior to the fixed plane of reversal, which it would, of course, be if anterior to the cornea, and might be if slightly posterior to it, motion against the mirror results. The observing eye may thus receive either of three kinds of waves: (i) convex waves, (2) neutral waves, or (3) con- cave waves. The first class may be those evolved at area 3, which the dioptric media of the observed eye has been unable to transpose, or it may be the convex waves evolved at an area of reversal anterior to the observing eye, which would STATIC FACTORS OF SKIASCOPY. I25 invert the entire group of pencils and each individual pencil of the group. If the waves are of the former class — convex w^aves evolved at area 3 and unneutralized by the dioptric media of the observed eye — their curvature will be comparatively slight and the dioptric media of the observing eye, with slight use of its dynamic power, will be able to focus them upon the retina. It will also focus neutral waves without the use of its accommodation. This leaves the two important classes of waves in skiascopy yet to be disposed of: (i) convex waves that are evolved at an area of reversal between the observed and observing eye, and (2) concave waves. If the waves are concave their potential foci are posterior to the observing eye, and the area of reversal in the observing eye will be forward of the retina, and there will be diffusion at the retina. The emmetropic observing eye cannot focus these pencils, either with or without its accommodation. Thf farther forward such area of reversal is from the retina, up to the fixed plane of reversal, the greater its incapacity to focus the pencils and the greater the diffusion at the retina. But when the area of reversal has crossed the fixed plane, then the eye has reached and passed the fullness Of its incapacity, and the farther for- ward the area of reversal moves the more potent the observing eye becomes. In passing out of the eye and into space between the two eyes the waves at the cornea become convex, for the centers of curvature of all pencils are anterior to it. But the group of pencils, and each pencil, is inverted, and there is a real image in front of the cornea of the observing eye. Whether the observing eye can focus these transposed and inverted pencils depends upon the convexity of the waves or the near- ness of the aerial image. It cannot focus them if such image is nearer than its punctum proximum, although it will obtain an imperfect or diffuse image — a sufficiently clear image to ■Bee motion — very soon after the area of reversal emerges from the eye. Whatever the class of waves that come to the observing eye, it cannot escape diffusion at the retina, even when it focuses the emitted pencils exactly, for there is, in that case, diffusion at area 3, and the observing eye focuses accurately the pencils emitted from this diffuse image. The picture on 126 STATIC FACTORS OF SKIASCOPY. area 4 is not a good one, not because the emitted pencils are not all right, nor because the observing eye cannot focus them, but because the observed eye, which emits these acceptable pencils, has a diffuse image at its retina, and the image at area 4 cannot be better than its original. But if the image at area 3 is exact for a luminous object at a finite distance, it is trans- posing positive into negative waves — doing anterior and pos- terior work at the same time. The emitted pencils will there- fore consist of concave waves, and these the emmetropic ob- serving eye cannot focus at the retina, hence diffusion at area 4 in spite of the clear image at area 3. Diffusion at area 4 is unavoidable, unless the incident and emergent pencils are reduced to one kind. This could be done only by neutralizing the incident pencils before they should reach the observed eye by a neutralizing lens in the skiascopic chimney or otherwise. If that were done the same lens that neutralized the emergent pencils 'from the retina would focus the neutral incident pencils upon the retina. The distinct skiascopic phenomena at area 4 are inversion and reversal of motion. Inversion is the static and reversal of motion the dynamic phenomenon. Reversal is due to inver- sion, for inversion makes the retinal images the same in both observed and observing eyes, and projection of the image at area 4 is the inverse of the image at area 3, although the two images are the same— the inverse of the object. But the static effect is not easily seen on account of diffusion. Even if the figure of the luminous area were distinctive, as that of a triangle, apex upward, diffusion would tend to obliterate its form. But motion in an opposite direction from the motion of the mirror, or with it, is not easily mistaken. These reverse motions may be obtained by a difference of .25 D. in the lens power, showing that the area of reversal has crossed the fixed plane, giving these opposite effects at area 4. SUBSIDIARY AREAS. We have noted some of the subsidiary areas, as : (i) the area of reversal or focal area, (2) the fixed plane of reversal in the observ'ing eye, (3) the focal area in the observed eye or posterior to it. If a concave mirror is used there is (4) a focal STATIC FACTORS OF SKIASCOPY. 127 area between the mirror and observed eye, which is an area of reversal or inversion, or transposition of the incident pencils. It reverses all of the phenomena pertaining to the skiascopic tests with a plane mirror. If the concave mirror of + 4 D. ■or focal length of 10 in. or 25 centimeters — the usual power of a concave skiascopic mirror — is used and the luminous area is one meter from the mirror, i D. of its power is required to neutralize the pencils, leaving -r 7,1). for focal purposes, which places the image 13 in. or 33 centimeters from the mirror. If the examination distance is one meter, the immediate source of the pencils of light that reach the observed eye will be i meter — 13 in. = 27 in. or 67 centimeters from the observed eye. At i:^ meters the immediate source of light is nearly i meter from the observed eye. THE INTERVALS. The intervals between the areas are important static fac- tors, because they are the evolutionary spaces — the spaces in which the waves evolve a curvature different than that with which they start. I. thj: first ixter\^\l. This extends from the luminous area (area i) to the mirror (area 2). If the luminous ajea is a lamp or gas flame, the flame, and not the chimney that encloses it, is the luminous area. But if a diffusion disc is between the flame and the mirror, tlie interval is the distance of such disc from the mirror, for a diffusion disc reforms the waves of all pencils and be- comes a new center for such pencils. The curvature evolved by the waves in interval i depends upon its length. If it is i meter the waves evolve a curature of + i Cm., if it is 10 in. the waves evolve a curvature of 4- 4 Cm. The plane mirror does not modify such curvature, whatever it may be. It simply changes the direction of the waves which continue to evolve a different curvature as before. If a neutralizing lens is placed so as to intercept and neutralize all pencils from the luminous area, as a + 10 D. lens 4 m. from the flame, the waves of every pencil become static in curvature, or would but for aberration. Distance would increase aberration, but would have no effect upon neutral waves — that is, in modifying their curvature, as 128 STATIC FACTORS OF SKIASCOPY. they would have no curvature to modify. A T-chimney with such a neutralizing lens in it that could be accurately adjusted would undoubtedly offer some new skiascopic data of value. The lens should be less than neutralizing rather than more, for then evolution would tend still further to neutralize the waves, while if the lens transposed the waves, evolution would in- crease their concavity. 2. THE SECOND INTERVAL. The second interval consists of two parts, (i) the distance from the mirror to the cornea of the observed eye, and (2) the distance of the cornea from the retina. The former is the evolutionary space, for there only the waves are in homogene- ous air. As the evolution of the waves in interval 2 is but a continuation of evolution in interval i, intervals i and 2 count as one in the evolution of the waves from the luminous area to the cornea of the observed eye. The two intervals are taken together in determining the distance of the luminous area from the observed eye. 3. THE THIRD INTERVAL. This is again the subjective interval — the interval that ends at the subjective area. It is the space between the observed and observing eye. The evolutionary space is from cornea to cornea, or from the glass in front of the observed eye to the cornea of the observing eye. The entire interval consists, then, of the space from area 3 to the cornea of the observed eye, the space from the cornea of the observed eye to the cornea of the observing eye, and the space from the cornea of the observing eye to area 4. The first and last of these spaces are inconsiderable and unimportant. The dioptric media is supposed to take care of them, and if it does not, there is no way of correcting its defects except upon the outside. But interval 2 and interval 3 are almost identical, since the observing eye is just posterior to the mirror. They might be considered as identical if anything was to be gained by it; but it is really the sum of intervals i and 2, rather than 2 alone, that is the important incident space, and this is always greater with a plane mirror than interval 3. It is greater with any STATIC FACTORS OF SKIASCOPY. I29 kind of a mirror, but with a concave mirror the sum of intervals 1 and 2 divides into two parts — (i) the part from the luminous area, by way of the mirror, to the focal area in front of the mirror, and (2) the part from the focal area in front of the mirror to the cornea of the observed eye. The last is the real evolutionary space, and it is necessarily less than interval 2 or 3. SUBSIDIARY INTERVALS. We have already referred to the subsidiary intervals, though not specifically. They are (i) the space from the lum- inous area to the focal area of a concave mirror, (2) the space from such focal area to the cornea of the observing eye, (3) the space from the cornea of the observed eye to the area of re- versal when anterior to the observing eye, (4) the space from such area of reversal to the cornea of the observing eye. In any and all of the intervals the force of evolution alone modi- fies the curvature of the waves. There are minute intervals — as the intervals between the different dioptric surfaces, but these have already been considered in the chapter on the re- fraction of the eye. CHAPTER VI. DYNAMIC FACTORS OF SKIASCOPY. TILTING MIRROR AND ITS DYNAMIC EFFECTS. MOTION AT LUMINOUS AREA. CHANGING THE INTERVALS. OTHER DYNAMIC PRINCIPLES. SKIASCOPY is essentially a dynamic method of ocular ex- amination. It has its static factors, for dynamics in any department of physical science must have a static founda- tion. All natural phenomena are due to the combination of some static element with a dynamic force. A cannon-ball mov- ing through space has what is termed a "striking force." Its striking force is equal to its weight multiplied by the square of its velocity. Its motion multiplied by its velocity alone is called its momentum. Hence its striking force is its m.omentum mul- tiplied by its velocity again. We have, then, in its striking force the product of tw^o factors: (i) its momentum, and (2) its velocity. Its momentum is the static factor of striking force, and velocity is the dynamic factor. But momentum is itself a compound, for it is the weight of the cannon-ball multiplied by its velocity. Momentum is the product of two factors, (i) weight and (2) velocity. Its weight is the static factor, and its velocity is the dynamic factor. But weight, the static factor of momentum, is a com- pound, the static factor of which is its quantity of matter or mass, and the dynamic factor of which is the force of gravity. Can we go further? Surely. The quantity of matter in the cannon-ball is compound, embodying extension or volume, which is due to molecular motion, heat, which tends to separate the molecules, and cohesion, or the attraction between these molecules, tending to unite them more closely. We have gone some distance in the study of the molecular forces, but there are undiscovered principles as yet far beyond our reach. 130 DYNAMIC FACTORS OF SKIASCOPV. I3I I. TILTING THE MIRROR. A dynamic principle is a principle that manifests itself by force, motion or action. A dynamic effect is the efifect of the operation of force. Visually it manifests itself by motion. We have seen, in Chapter I, how the tilting of the mirror produces dynamic effects. It causes the incident pencils to reach the mirror at a different angle, and as a result the reflected pencils pass from the mirror at a different angle and in a different direction. A change in the inclination of the mirror to the incident pencils of 10° produces a change in the direction of the reflected pencils of 20°. Change of direction of the reflected pencils is, then, a dynamic effect. But this causes the area of light upon which the reflected pencils fall to move, as from right to left or left to right, upward, downward or obliquely. That is, there is motion of the "light on the face." But this gives rise to other dynamic effects. The minor pencils that enter the observed eye are changed, the former ones passing off to be succeeded by others as long as the light area covers the pupil. But as the new minor pencils are pursuing a differ- ent course on account of the change in the inclination of the mirror, the direction from which they come or reach the eye is changed. They become more or less oblique to the visual axis of the observed eye, and the dioptric media focuses them at a new area, either at the retina or anterior or posterior to it. If either of the latter the diffusion circles at the retina and the imperfect image they form is upon a different retinal area. The newly located image is projected in a different direction, and the virtual image appears, to the one under examination, to move. Nor is this all. The image of the luminous area having a different retinal position at area 3, the pencils from this image pursue a different course on their way out of the observed eye. If the retinal image at area 3 has been moved to the left, the emergent pencils must take a direction more to the right, or they will be turned back by the iris. This changes the direction of the emergent pencils that come to the perforation in the mirror and to the observing eye. It gets a new set of pencils pursuing a slightly different general direc- tion. This places the image at area 4, the sensatory subjective area, in a new position on the retina. It projects the new image 132 DYNAMIC FACTORS OF SKIASCOPY. in a different direction. And thus one dynamic effect follows another. The mere tilting of the mirror is the primary cause of all these changes. The different dynamic effects of tilting the mirror, all other static factors remaining stationary, may be summed up as follows: 1. Change of angle of incident pencils. 2. Change of direction of reflected pencils. 3. Motion of "light on the face." 4. Change of minor pencils entering the pupil of the ob- served eye. 5. Change of direction of minor with the major pencils. 6. Change of location of image on area 3. 7. Change of direction of projection of image on area 3. 8. Change of direction of emergent pencils from image on area 3. 9. Change of pencils reaching perforation and observing eye. 10. Change of direction of such pencils. 11. Change of position of image on area 4. 12. Change of direction of projection of such image. This is a list of dynamic effects that seems out of propor- tion to the cause, but the history of the world and of nations, as well as of individuals, is made up of chains of dynamic causes and effects, on the same principle. They do not stop where we have stopped. There were preceding dynamic causes, and there will be succeeding dynamic effects, although these comprise those that are distinctively optical. 2. CHANGE OF DIOPTRIC POWER. If the observed eye, which has the power of accommoda- tion supposed to be passive during a skiascopic examination, should exercise its dynamic power, as by using or putting forth 2 D. of accommodation Vv^hile under examination, the DYNAMIC FACTORS OF SKIASCOPY. I33 dynamic effects would be varied and striking. Suppose an emmetropic eye, being examined from one meter with a plane mirror, the luminous area being one meter from the mirror or two meters from the observed eye, should put forth that power, all other dynamic causes being passive or quiet. To appreciate the dynamic effects we must consider the results of both static conditions — that is, with the accommodation pas- sive and with the accommodation active. 1. With passive accommodation the incident pencils of "+ .5 Cm. would have the potential foci posterior to area 3, and on area 3 there would be an imperfect image produced by diffu- sion circles. But the pencils emitted from this image on the retina would be neutral, and as neutral waves the light would pass from the observed to the observing eye. The observ- ing eye, wdth passive accommodation, would focus these neu- tral pencils upon area 4, but the image would be no better than its original — the image produced by diffusion circles at area 3. This image it would project into the pupil of the observed eye. 2. With 2 D. of its accommodation in force, the dioptric media of the observed eye would transpose the waves of the incident pencils, focusing them forward of the retina, as its dioptric power would be 1.5 D. in excess of that required to focus -1- .5 Cm. waves at the retina. The image at the retina or at area 3 would be imperfect because produced by diffusion circles from a focal area anterior to the retina. But the emerg- ent pencils would be emitted in concave waves — waves that would have a curvature of — 2 Cm., and therefore focus ^ meter anterior to the cornea of the observed eye, where there would be a true image — the so-called area of reversal. But this area of reversal would be anterior to the observing eye also. Hence all the pencils that reached it would have been transposed and inverted at such area of reversal. The observ- ing eye would require 2 D. of its accommodation to focus these pencils, and the image at area 4, though exact as to the image at area 3, would duplicate the effects produced at area 3 by diffusion. But the image at area 4 would be the same in posi- tion as the image at area 3 — that is, since the image at area 3 is inverted, but would be projected as erect, and there is an 134 DYNAMIC FACTORS OF SKIASCOPY. inversion of that image anterior to the observing eye, which image is erect, the re-inversion of such erect image would pro- duce an inverted image at area 4 the same as at area 3, which would be projected as erect. To more clearly show the two static conditions we will suppose the mirror to be tilted in each case. In the first case the motion of the image is with the mirror, because the image on area 4 is the reverse or inverse of the image on area 3, and motion of the image to the right on area 3 is motion to the left on area 4. But the projection of such motion is to the right or with the motion of the image at area 3. In the second case motion to the right of the image on area 3 produces motion to the left of the aerial image between the observed and observing eyes. But motion to the left of the aerial image produces motion to the right of the retinal image at area 4 — the same as at area 3. But projection causes such motion to be to the left or with the aerial image. Hence motion in the pupil of the observed eye appears to be contrary to real motion there. Now we are to consider the effects of the observed eye changing from one of these conditions to the other by putting forth its dynamic power. The exercise of this power requires change or motion. The ciliary muscle contracts, the choroid coat is pulled forward, the tension on the suspensory ligament relaxes, the elasticity of the lens is relieved of restraint, and the lens expands its surfaces, particularly the anterior surface, become more curved, and the lens power is increased. The incident pencils do not feel the influence of the eye's increased power until they reach the anterior surface of the lens. Then the positive refraction of that surface is augmented, while the effect at the posterior surface is slightly increased. Under these influences, if the dynamic power is put forth gradually, the focal area or potential focal area posterior to the retina begins to advance toward the retina, but this effect is not real. The real effect at the retina is that the diffusion circles contract and the image becomes more distinct, until ^ D. of dynamic power is in force, when diffusion is eliminated at the retina. The image becomes clear and sharp. But as more dynamic power is added, the focal area advances and positive diffusion DYNAMIC FACTORS OF SKIASCOPY. 135 begins to become manifest. As the increase of dynamic power goes on the focal area advances and diffusion at the retina grows until the full 2 D. is in force. Now, while these changes in the retinal image at area 3 are taking place, the emitted pencils, which consisted of neutral waves, become concave and form a focal area anterior tO' the observed eye and posterior to the observing eye. But within- the observing eye, at area 4, there was, with passive accom- modation in the observed eye. correctly focused pencils upon area 4. But with the transmission of concave waves to the observing eye its capacity to focus the pencils at the retina ceases. The focal area advances, and when the focal area in the observed eye is at area 3 and the clearest image appears, at area 4 there is diffusion because of the over-power of the dioptric media of the observing eye, for these emitted concave waves. With the advance of the focal area in the observed eye the focal area or area of reversal in the observing eye ad- vances still farther, and diffusion grows at area 4 because of the eye's over-power. It recjuires but the use of i D. of the observed eye's accommodation to bring the area of reversal in the observing eye to the fixed plane of reversal, at which point all the peculiar effects noted when that position is reached appear. Diffusion is at the maximum on area 4, and no image appears, for this is the plane of transition, and the crossing of it by the area of reversal reverses motion and inverts the image at area 4. By the advance of the area of reversal in the ob- serving eye it passes successively (i) the center of curvature of the anterior surface of the lens, (2) the center of curvature of the cornea, (3) the posterior surface of the lens, (4) the anterior surface of the lens, (5) the center of curvature of the posterior surface of the lens, and (6) the cornea. The refracting surfaces, which are in natural vision all positive in their action, become negative when the waves acquire a curvature con- forming with, but greater than, the curvature of the refracting surface. The advance of the area of reversal is not a steady advance, for when a refracting surface begins to act negatively it delays the advance of the focal area. The anterior surface of the lens is first to become negative, but it becomes positive again as soon as the focal area passes in front of it. The 136 DYNAMIC FACTORS OF SKIASCOPY. posterior surface becomes negative when the focal area crosses it, and remains negative until the positive refraction of the anterior surface gives it waves of less curvature than itseff. The cornea is last to become negative in its action and last to become positive again. The focal area thus advances and is delayed or lingers at a fixed position or near it, then going forward rapidly for a space to be delayed again, until it passes out of the eye at the cornea and all the surfaces become positive. When the ob- served eye is exercising i D. of its dynamic power, or the least trifle over i D., the focal area or area of reversal emerges from the observing eye. During all the preceding advances diffu- sion at area 4 has increased, but with the passing of the area of reversal across the fixed plane of reversal diffusion begins to lessen. When the focal area is tangent to the cornea diffu- sion is great, for this position is reached by the focal area almost instantly after passing the fixed plane. Every pencil is composed of convex waves of such high curvature that the dioptric media, though acting in that direction, are quite unable to focus them upon tfie retina, and continue to be unable to do so until the focal area reaches the punctum proximum of the observing eye. Diffusion grows less, however, as the focal area advances, and from the punctum proximum to the posi- tion -J meter in front of the observing eye less and less of its accommodation is used. It does not, however, get a good definition of the luminous area, although it focuses the emitted pencils accurately, because of diffusion at area 3. If during the transition of the focal area from the retina of the observing eye to a position ^ meter in front of it the other dynamic cause, tilting the mirror, were applied, all the skiascopic phenomena would appear. As the area of re- versal passed the fixed plane, motion would he reversed from zvith the mirror to against it. At the fixed plane the image, as such, would disappear. Approach of the area of reversal to the fixed plane would cause motion to grow more and more rapid, but the advance of the area of reversal from the fixed plane would show the most rapid motion when reversal of mo- tion first appeared, and it would grow less rapid in the same degree that diffusion at area 4 lessened. The cause for all these DYNAMIC FACTORS OF SKIASCOPY. I37 peculiar skiascopic phenomena have, we think, been made clear. 3. CHANGING THE INTERVALS. But the use of the accommodation of the observed eye to bring about these effects is a suppositional case merely. It is not a practical skiascopic method. But the same effects, or corresponding effects, are produced in practical skiascopy by two other means: (i) changing the length of the intervals dur- ing an examination, and (2) putting plus lenses before the observed eye. These are the two means the skiascopist con- stantly employs, especially the latter, for that is the purpose of the examination: To determine the lens required to make the eye artificially emmetropic. We will look at these two dynamic factors separately, and determine certain limitations by which they are bounded. The three intervals are peculiarly associated with one another. An interval is shortened or lengthened by changing the position of one or more of the areas. Now, if while areas 2, 3 and 4 are unchanged, area i is brought nearer to or moved farther from area 2, the first interval alone is altered. It is altered the exact amount of the changed position of area i. If, for instance, area i is moved from a position of i m. from area 2 to a position of i meter, interval i is reduced -J meter, as shown in Fig. 36. But as the incident pencils are evolved through the space of intervals i and 2 combined, shortening interval i reduces this evolutionary space ^ meter. If intervals I and 2 are each i meter, the reduction of interval i to ^ meter reduces the entire space from 2 meters to i^ meters, and the waves become -\- f Cm., instead of -1- -J Cm., at the cornea of the observed eye. As area 3 is the retina of the observed eye, it would not be 138 DYNAMIC FACTORS OF SKIASCOPV. proper to require the one under examination to change his position, but the observer or operator may approach or recede from the eye under examination, changing the position of area 4. But as the mirror (area 2) and the observing eye are to- gether, any change of either requires a corresponding change in the other. That is, if the mirror is moved forward or back, the observing eye must also be moved in the same direction and the same distance; and if the observing eye is moved the mirror must be moved correspondingly. If the observing eye is advanced toward the observed eye from a distance of i meter to a distance of -^- meter, this afifects the space in which the emergent pencils are evolved. It may take the observing eye from a position posterior to the focal area to a position at it, or from a position at it to a position anterior to it. But the advance of the observing eye is necessarily accompanied with advance of the mirror, and advance of the mirror shortens both intervals i and 2 the same amount. But as the evolutionary space of the incident waves is the sum of intervals i and 2, the advance of the mirror ^ meter shortens this space i meter by Fig. 37. taking 4 meter from each interval. This is shown in Fig. 37. The change from a position i meter from the observed eye to I meter from it makes interval 3 ^ meter, or -^- what it was be- fore, and the sum of intervals i and 2=1 meter, or ^ what it was before. In the position at i meter the incident waves would have a curvature of + | Cm. at the cornea ot the observ^ed eye, and the emergent pencils, if focused for the observing eye, would have a curvature of — i Cm. At ^ meter the incident pencils at the cornea of the observed eye would be + i Cm., while the emergent pencils, if focused for the observing eye, would be — 2 Cm. The effect of these changes of distance, or length of the evolutionary spaces, must always be taken into account in determining the dioptric condition of the eye under examination. Aside from this consideration of intervals and DYNAMIC FACTORS OF SKIASCOPY. 1 39 their co-relation, changing the intervals and the dynamic effects are precisely the same as if the dioptric power of the observed eye were changed. 4. CORRECTING LENSES. Placing lenses before the observed eye is exactly similar to the employment of the accommodation of the observed eye, except that lens changes are made by more distinct steps; a + 2.75 D. is substituted for a + 2.50 D., or + 2.50 D. for + 2.25 D., or — 1.75 D. for — 1.50 D. The observer cannot see the change take place, but he sees the effect of the entire change resulting from substituting one lens for another. But in making these changes of lenses the operator is working always, in making the primary correction, toward making the area of reversal coincide with the fixed plane of reversal in his own eye. His process is a process of gauging. He gets reverse motion and brings the two areas as close together as possible — within .50 D. or .25 D. of each other, and prescribes the pOAver between + " — i D." In working out a case of astigmatism the process is precisely the same, except that it is for one of the principal meridians at a time. But in working out a case of astigmatism the static principles of skiascopy are relied upon to a large extent; that is, it is sought to obtain a retinal image that is symmetrical in form, and it matters little whether much or little ametropia exists at the time, so long as a tolerably clear outline of the luminous area is displayed at area 3. A correction of the astigmatic element with 3 D. of hypermetropia will correct it for 2 D. of myopia or for em- metropia. Astigmatism is really neither myopic nor hyperopic, nor mixed, nor compound. It is merely a difference of power in two chief meridians and in all intermediate meridians. It is the hyperopia or myopia that is compound, mixed, etc., not the astigmatism. 5. MOTION AT LUMINOUS AREA. Nothing has ever been done, sO' far as we know, to make motion at the luminous area, or motion of the luminous area, provide the dynamic factor for a skiascopic test. Of course, when motion is contrary to the motion of the mirror, an 140 DYNAMIC FACTORS OF SKIASCOPY. upward motion of the luminous area would appear as a down- ward motion, and a downward motion as an upward motion. Right and left would be reversed in the same manner. But to preserve constancy of motion the luminous area would have to be made to vibrate back and forth, and the trouble would be to keep track of the actual motion so as to know when the apparent motion was with or opposite to the actual motion. The author had devised a very pretty plan of securing rotary motion at the luminous area under the impression that reversal would cause the figure to appear to rotate in the opposite di- rection. More careful analysis, however, showed him that such reversal of motion would not occur. If the luminous area were an arrow rotating in the direction of the hands on a dial, inversion of the figure would not reverse the motion, any more than inverting a watch dial would cause tlie hands to move in an apparently opposite direction. To reverse such rotary motion it would be necessary that the observer view the rotation from the opposite side of the rotating figure, and in- version in optics does not produce this effect. But reflection which reverses positions without inversion produces it. The reflection of a clock face in a plane mirror reverses the face without inverting it, and causes the moving hands to appear to be going in the opposite direction. It is difficult to see how this principle could be applied in skiascopy, although it would make a unique exhibit of the effects of reversal if it could be used. Nothing is more startlingly unique, or anomalous, than a reversal of the regular and natural order of events. It is said that the kinnetiscope may be made to reverse motion in this way if the film or plate, or whatever the order of events is recorded upon, is made to pass backward through the ma- chinery. The startling character of such an exhibit may be appreciated if we consider its effect upon the view of a dinner party at which a fine roast turkey and other rich foods have been discussed. All of the guests will at once become en- gaged in taking food from their mouths and putting it back upon their plates, which, in due time, will become loaded and go back to mine host, who will proceed with it to build up on the skeleton of a turkey, the bird as it came from the oven- Half smoked cigars will spring up off the floor to the hands DYNAMIC FACTORS OF SKIASCOPY. I4I and then to the mouths of the smokers, while a cloud of smoke will appear before them and be drawn into their mouths. If conversation could also be made to go backward, the confusion of tongues in the building of the tower of Babel would not be a circumstance in comparison. NEUTRALIZING INCIDENT PENCILS. We have referred elsewhere to the use of a lens in a skiascopic T-chimney to neutralize the pencils of light from the luminous area, or from a diffusion disc close to the flame. The effect of the use of such a neutralizing lens would be to elim- inate inter^'als 1 and 2 as evolutionary spaces, for if the waves upon emergence from such lens were neutral they would be static. Pencils of light composed of neutralized waves would be precisely the same as pencils of light from infinity, except for the element of aberration contained in them. If the ob- serv^ed eye's accommodation were passive and the eye were, either naturally or artificially, emmetropic, the incident pencils W'Ould give a clear image upon the retina, for there would be no diffusion, and emit neutral pencils to the observed eye. This would provide the conditions needed to eliminate diffu- sion at areas 3 and 4 at the same time. If the observed eye were Fig. 38. + .4— Real Luminous ^ ^"""^fcin. i ^^B Fig. 44. Fig. 45. we may regard the light or reflex as entering the pupil from the opposite direction to that in which the light on the face is passing over the eye. The size of the reflex varies in case 3 the same as in case 2, and depends on precisely the same princi- ples. We may readily determine the exact size of the aerial im- age in case 3 by the law of images, but diffusion at area 3 in- creases its size somewhat. But it is not the size alone of this image that determines the size of the reflex, but its nearness to the observing eye. or to its fixed plane of reversal. It is then that diffusion at area 4 reaches the maximum, or becomes in- definite, and the case becomes case 2. CASE 2. This is the condition toward which we begin to work in case I or case 3. The object — the primary object — is to reduce 158 THE STUDY OF THE EYE BY SKIASCOPY. the initial condition, whatever it may be, to case 2 — to develop the maximum of diffusion at area 4, and eliminate motion in the objective pupil. Motion is eliminated because, of all the pencils that enter the pupil of the observing eye, none are indi- vidualized upon the retina. Each spreads over the same area as the others, producing light at area 4 merely, but no image. Motion is really most rapid at the culmination of diffusion, but as the pencils are not individualized we cannot distinguish one from the other. In case 2 we get a kaleidoscopic view of the refiex. It appears as a brilliant glow in the objective pupil, but the glow vanishes at a touch, as though the light had been extinguished by a breath of air, not moved away. We judge the result usually by gauging — that is, by taking a position or using a correction midway between motion with and motion against the mirror. At one meter the whole pupil is usually homogeneous — either filled with light or darkness at reversal. The same is true for distances greater than one meter. But at nearer points than one meter we develop the zonular ap- pearances due to aberration. In that case the central area of the pupil — the "visual'' area as Dr. Jackson terms it — may be the neutral area, or the periphery of the pupil may be neutral- ized while the central area shows motion. But the neutral zone may not be central or peripheral, but sub-central, and ap- pear as a darker ring around an unneutralized central area of light, while the periphery is fringed also by an unneutralized area. When the neutral zone is- central, the zone of motion will be peripheral or marginal and vice versa. In the second case motion is with the mirror in one unneutralized area (central or marginal) and against it in the other; but in the former there is but one area of motion — the unneutralized area. Figs. 46 and 47 represent the double-area display, though diffusion is greater usually than shown in either case. It is an effort of aberration, different areas of the pupil having different anterior focal points. The scissors movement, so-called, is this double-area display, but on account of a slight inclination of the two visual axes — that of the observed and observing eye — a cylindrical value is given to the dioptry of the observed eye, which causes the areas of motion to meet and separate along a central line in a plane at THE STUDY OF THE EYE BY SKIASCOPY. 1 59 right angles to the plane of the angle of inclination of the visual axes. Emmetropia is not indicated by the scissors movement, and the more in line the two visual axes are brought the less the scissors movement becomes manifest unless there is a misplacement of the lens. Aberration is not, nor the skiascopic appearances produced by it, an anomalous phenomenon, but one to be expected and considered at its value. When the scissors movement is shown it does not show that certain areas of the pupil are ametropic and others are emmetropic, but that aberration is unavoidable for so near a point. The human eye is remarkably free from aberra- tion, but really for but two positions — that is at infinity and at its principal focus — anterior and posterior in static refraction. But the use of the accommodation, in dynamic refraction, causes it to be without aberration for that anterior point to which it is accommodated. But the observed eye usually has a lens of some power before it in a skiascopic examination, and if it has no aberration the lens has, and that gives us the effects the same as if the dioptric media of the eye were the cause of it. PRODUCING CASE 2. The primary work, whatever the initial appearance, is to produce the conditions for case 2. There ai^e two ways of doing so: (i) by placing lenses in front of the observed eye, and (2) by changing the distance of the observer. If the observed eye, is either initially or otherwise ^ D. myopic, the area of reversal may be brought to the observing eye by placing + ^ D. before it; or it may be produced by the observer taking a position 2 meters from the observed eye. If the observed eye is 2 D. myopic, the area of reversal may be placed as required in case 2, either by giving it a — i D. lens or by moving the observing eye to a point | meter from the observed eye. Either of these methods would give the primary result. Either would show the location of the area of reversal. In one case the area of reversal is brought to the eye at one meter by a lens ; in the other the observing eye moves to the area of reversal. If the observing eye finds the area of reversal at 27 in. from the observed eye, a — 1.5 D. lens (40/27) is required for its l6o THE STUDY OF THE EYE BY SKIASCOPY. full correction. A — .50 D. lens would place the area of reversal at one meter, making a secondary correction of — i D. lens necessary. The direction of the correction is indicated by the direc- tion of motion of the reflex. If, with the plane mirror, it is with the light on the face, plus lenses will be required to in- crease such motion, and eventually to bring the area of reversal to the point required. If motion is against the mirror or light on the face minus lenses will be necessary to get the primary correction. When the primary correction is obtained, such a secondary correction has to be added as will cause the area of reversal to recede to infinity. For a working distance of one meter a i — D. is the secondary correction. The question is often raised, and raised again, as to what effect the distance of light or luminous area has to do with the problem. So far as its effect upon motion, or the direction of motion, in the objective pupil is concerned, provided the pen- cils are allowed freely to evolve from the luminous area to the observed eye, it has no effect whatever. It may be i meter from the mirror, -J meter, ^ meter, or any distance. It is the distance between the observed and observing eye — the length of interval 3 only — that determines the secondary correction and the lens required to reverse motion. A condensing lens of less than neutralizing power may be placed between the lumin- ous area and mirror, or a concave mirror may be used so near the luminous area that it does not transpose the pencils, but merely reduces the convex curvature of the waves without affecting the result. The use of either of these instrumentali- ties, however, gives a higher retinal illumination at area 3. But if the lens or mirror transposes the incident pencils, focusing them anterior to the observed eye, there is reversal at area 3, which reverses all the rules for the use of the plane mir- ror. But even this simply changes the law of motion — motion with the mirror indicating myopia, motion against it indicating hyperopia, emmetropia or low myopia. It does not change the secondary correction of — i D. for a working distance of i meter, — 2D. for ^ meter, — ^ D. for 2 meters. The emerg- ent pencils of light, which reveal the dioptric condition of the observed eye to the observer, are independent of the incident THE STUDY OF THE EYE BY SKIASCOPY, l6l pencils, although they come from an image produced by inci- dent pencils. The distance of the light from the observed eye is a factor in the image at area 3 — a factor in the amount of diffusion at that area — a factor in the development of the banded appear- ance in astigmatism — a factor in all effects upon incident pen- cils. But it is not a factor in the optical properties of the emergent pencils, except merely that its image at area 3 is the source of these emergent pencils, and the image at area 3 is the original of the image developed at area 4. The image at area 3 is like any image upon a screen — a true image displayed upon a receiving surface. But in skiascopy the definition is im- paired by the eye's ametropia, or because, if emmetropic, the accommodation is passive, although the luminous area is at a finite distance. The other peculiar skiascopic effects are due to the fact that this imperfect image is examined through the same dioptric media that produce it. In hyperopia and emmetropia there is nothing to impair the view of the observ- ing eye, or to prevent its getting a clear definition of the image upon this screen, for the dioptric media of the observed eye simply acts as a magnifying lens. The impairment is in the image it sees displayed upon the retina of the observed eye, and due to its hyperopia in part, and partly to the fact that the object imaged (the luminous area) is nearer than required to be correctly focused at the retina. If the observed eye is hyperopic that simply lessens its magnifying power or effect upon the emergent pencils, for the dioptric media are nearer than required for the maximum of magnification. In emme- tropia magnification is at the maximum, but the image at area 3 is impaired notwithstanding. But when the observed eye is myopic, every degree of my- opia within that required to exactly focus the incident pencil* upon the retina, improves the definition of the luminous area at area 3. If, for instance, the luminous area is, by way of the mirror, i-| meters from the observed eye, which is .75 D. my- opic, the definition at area 3 will be perfect, the image clear and sharp. But the observing eye must see this result through the same ametropic media that produces the image, and since it is .75 D. myopic, the dioptric media, considered as a lens,. l62 THE STUDY OF THE EYE BY SKIASCOPY. is a little beyond the focal position. It therefore emits pencils from such image already transposed and on their way to poten- tial foci i^ meters anterior to the observed eye, and therefore posterior to the observing eye i meter away. The observing eye cannot focus these pencils upon its retina, hence diffusion at area 4 in spite of the perfect definition at area 3. With increased myopia of the observed eye, diffusion develops al area 3 and increases at area 4 until the maximum of diffusion is reached. But the distance of the light from the mirror has nothing to do with diffusion at area 4. ABSOLUTE CONDITION. In skiascopy, as usually practiced, the first view of the eye does not show whether it is myopic, hyperopic or emme- tropic, if motion is with the mirror. It may be hyperopic, em- metropic or slightly myopic. It would be better to ascertain the absolute condition — whether it is emmetropic, myopic or hyperopic — at the first glance. This may be done by the follow- ing simple and direct method : If the Avorking distance is one meter, place a + i D. sph. lens in the rear cell of the trial frame to start with; or if work- ing at 2 meters, place a + ^ D. sph. lens in the cell; or if work- ing at ^ meter, place a + 2 D. sph. lens in the cell. If the eye to be examined is emmetropic this secondary lens wall bring the area of reversal to the observing eye, and the appearances in case 2 will at once be manifest. If the eye is liyperopic, motion will be with the plane mirror still, for its area of re- versal will be more than one meter anterior to the observed, and therefore posterior to the observing eye. If the eye to be examined is myopic, even but .25 D., motion will be against the plane mirror, for the + i D. lens will make it 1.25 D. myopic, and the area of reversal will be but ^ of a meter anterior to the observed eye, and therefore anterior to the observing eye, or between the observed and the observing eyes. But another great advantage of this method is that the lens that brings out the appearances of case 2, or brings the area of reversal to the observing eye, is the full correction with- out subsequent additions or subtractions. This is evident from the fact that the lens in the back cell is not taken into account, THE STUDY OF THE EYE BY SKIASCOPY. 163 but is simply "left out" of the calculation. To leave out a + I D., + ^ D. or + 2 D. lens actually before the eye when motion is neutralized is the same as adding a — i D., — i D. or — 2D. to the primary correction. This plan is simple, opti- cally correct and very convenient. It is probably practiced by many skiascopists, although we have not seen it recommended as a method in any text-book. THE CONCAVE MIRROR. The concave mirror can also be conveniently employed without complicating the rules of motion for plane mirrors. This may be done by using the ordinary concave mirror of 25 centimeters (10 in.) focus at less than 10 inches from the lumin- ous area — that is, by bringing the luminous area to a point, say about 8 inches from the mirror or observing eye. The incident pencils reaching the mirror would be composed of waves of (at 8 in.) a curvature of + 5 Cm. As a concave mirror of 25 centimeters has a power equivalent to a four diopter lens, it would not transpose the pencils but reflect them in convex waves or diverging rays to the observed eye. The major pen- cils producing the "light on the face" would be more intense, on account of the action of the mirror, and the minor pen- cils admitted by the pupil would partake of such increased in- tensity. The reflex would be made brighter without involving any of the skiascopic factors of motion or changing the rule for plane mirrors. In efifect it would remove the luminous area to a greater distance, by placing the center of curvature of each series of waves at a greater distance, and this would sharpen the definition with approach to the full correction by eliminat- ing diffusion. The use of the secondary lens in the back cell would, however, increase diffusion at area 3, for that lens is not a part of the full correction, but is left out and ignored. This method would correspond closely to the use of a neu- tralizing lens in the skiascopic chimney heretofore described, and might prove a more simple solution of securing an ac- ceptable static test, or test by definition rather than by motion. 11 CHAPTER VIII. THE STUDY OF THE EYE BY SKIASCOPY. UNSYMMETRICAL AME- TROPIA. REGULAR ASTIGMATISM. IRREGULAR ASTIG- MATISM. STATIC AND DYNAMIC PROPERTIES. PATHOLOGICAL CASES. AN eye is a positive optical instrument. It is positive in all • meridians. An astigmatic eye is simply one having greater dioptric pov^er in some meridians than in others. In regular astigmatism there is not only a meridian of greatest and a meridian of least dioptric power, but all intermediaze meridians have intermediate power in proportion to their nearness to the meridian of greatest power. The merid- ians of greatest and least power are at right angles to each other, for the astigmatism is due to a cylinder effect of the dioptric media, due usually to a toric curvature of the cornea, or greater curvature in one and less curvature in other of its meridians, the two being at right angles to each other, than any intermediate meridian. The intermediate meridians then have an intermediate degree of curvature proportional to their nearness to the meridian of greatest curvature. It is proved that an intermediate meridian of piano-cyl- inder has a curvature proportional to the square of the sine of its angle to the axis of the cylinder divided by the radius of curvature. That is, if the sine of the angle as measured by the radius be squared, the result is the ratio of the given merid- ian's curvature to the curvature of the meridian of greatest curvature. For instance, if the curvature of a piano-cylinder is lo Cm., or its radius of curvature is 4 in., a meridian 45' from the axis of the cylinder would have a curvature of | of 164 THE STUDY OF THE EYE BY SKIASCOPY. i6= lo Cm. = 5 Cm., or a radius of curvature of 8 in. A meridian at 30° from the axis of the cylinder has a curvature of ^ of 10 Cm. = 2^ Cm., or a radius of curvature of 16 in. A meridian at 15° from the axis has a curvature of .067 of 10 Cm. = .67 Cm., or a radius of curvature of about 60 in. The ^, ^ and .067 Cm. are each the square of the sine of their respective angles as meas- ured by the radius. The sine of 30° is ^ of a chord of 60°, which is equal to the radius; hence the sine of 30° = ^ radius, and Q)' = ■^. The sine of 45° is -J the chord of 90°, which makes the chord and radius each bisect the other at right angles. Hence the sine is 1/ ^ R2 and, since the radius is taken as unity, 1/ ^. The square of ]/ i is of course ^. The ratio of any sine, or the sine of any angle to the radius is found in tables, as the calculation for small angles would be exceedingly tedious. + 77 D "-?$ i»-"~ / / >\ (''*■ '''^) ^ \.^jm^^ S m rs^: \ '^"SK^ \ ^^j f .,Z!b> «^ y Fig. 48. Applying the above principle to the dioptry of an astig- matic eye if, for instance, the dioptry of the veitical meridian is + ?r D., and that of the horizontal is + ( - + i ) D., the horizontal has i D. greater power than the vertical. But the 45th and 135th meridians have each + ( -^ + 2 ) D., and these two meridians are perpendicular to each other the same as 90° and o, and ametropia is symmetrical for these two meridians. However, meridian 60°, 30° from 90°, has a dioptry of + ( TT + I) D., and meridian 150°, at right angles to 60°, has a dioptry of + ( - -f f ) D., for it is 60° from 90°, or 30° from 180°. Its dioptry is therefore i D. less than 180° = + ( 7: + f ) i66 THE STUDY OF THE EYE BY SKIASCOPY. D. Fig. 48 represents the meridians here described, showing the dioptric value or power of each. A case of the kind last described is called, in the vernacu- lar of opticians, simple myopic astigmatism of i diopter, and would be produced artificially in an emmetropic eye by a + I D. cyl. ax. 90°. The eye is emmetropic in but one meridian — the vertical — where its dioptric power is + ~ D. It is my- opic in every other meridian, from the 90th to the i8oth in either direction, being in the latter -f ( - -|- i ) D. The amount of myopia in the oblique meridian increases regularly from o to I D. Now, if this eye, which may be naturally or (u-2)D Fig. 49. artificially astigmatic i D. is supplied with a — i D. spherical lens, the lens will neutralize the horizontal meridian, but pro- duce hyperopia in the vertical meridian — that is, the eye will become + - D. in the horizontal, but + ( ~ — i ) D. in the vertical meridian, as shown in Fig. 49. But this same ef¥eci. may be produced in an emmetropic eye by placing a — i D. cyl. ax. 180° before it. By adding a — i D. sphere to the first case it has been metamorphosed from n case of simple myopic astigmatism into one of simple hyperopic astigmatism. Note also the efifect at the intermediate meridians. Now, if instead of a — i D. sphere a + i D. had been added to the original case, the vertical meridian would have become -f ( r — i ) D., and the horizontal would be H- THE STUDY OF THE EVE BY SKIASCOPY. 107 (:: -f 2) D., as shown in Fig. 50. This is a case of so-called compound myopic astigmatism. So, also, if a — 2D. sph. is added to the original case the vertical meridian becomes r i- (--n) D ( :T + I /z j D - + I %) + (k + 2J D Fk;. 5'. (- — 2) D., and the horizontal + ( ~ — 1 ) D.. a case of compound hyperopic astigmatism, as shown by Fig. 51. But the astigmatic element remains unchanged by the spherical lenses. To produce compound astigmatism in an emmetropic eye a compound lens would Ijc required. That is, to produce Fn:. PI. -[-(-+ I ) D. in the vertical and + ( ~ + 2 ) D. in the hori- zontal of an emmetropic eye, a (i) + I D. sph ~ + I D. cyl. ax. 90° would be necessary. And to produce + (, ~ — 2 ) D. in the vertical and + ( ~ — i ) D. in the horizontal of an emme- tropic eye, a 1 68 THE STUDY OF THE EYE BY SKIASCOPY. (2) — I D. sph. C — I D- cyl. ax. 180° would be necessary. Other compounds would produce the same result, as (3) + 2 D. sph. C — I D. cyl. ax. 180° for (i), or (4) — 2D. sph. 3 + I D. cyl. ax. 90° for (2), it is true, but (i) and (2) embody the least curvature of the lens surfaces. + {n-'/i)D + (rt + /4) + (rT-f ^2^0 Fig. 52. But the original case + - D. in the vertical and + (::■ + i) D. in the horizontal) might as readily be turned into a case of mixed astigmatism by using a spherical of less power than the degree of astigmatism. If, for instance, a — .5 D. sph. were used, the 45th and 135th meridians would be neu- tralized, but the horizontal would become + ( ~ -{- ^ ) D., or -J D. myopic, while the emmetropic vertical meridian would be- come + ( ~ — I) D. or ^ D. hyperopic. Fig. 52 illustrates the last condition. In all of these changes brought about by adding a spheri- cal to an astigmatic eye the intermediate meridians are changed in power according to the principle enunciated at the begin- ning of the chapter and as shown by the different figures. In the last case meridians 45° and 135° become emmetropic, but they have had the same dioptry all through the various changes. But the principal meridians and all the intermediate meridians are unaltered in their relative dioptry. It takes a cylinder to neutralize the different meridians — each in proportion to its need, for a cylinder produces all these THE STUDY OF THE EYE BY SKIASCOPY. 169 conditions in an emmetropic eye. A spherical lens is required to neutralize real myopia or hyperopia, but it cannot take out an astigmatic element. A cylinder neutralizes astigmatism — makes the meridians agree — but it does not neutralize real my- opia or hyperopia. The cylinder harmonizes not only the two principal meridians but all the intermediate meridians. The one emmetropic meridian does not need assistance from the cylinder. It is therefore so placed that the axis of the cylinder and the emmetropic meridian coincide. The power of the cyl- inder is then exercised where it is needed — not only in the one principal but all the intermediate meridians. If neither of the principal meridians are emmetropic, a spherical lens will correct one of them and a cylinder will then correct the others. It is seen from the above analysis that astigmatism is not really hyperopic or myopic, or compound or mixed. Regular astigmatism is a mere proportionate difference in the power of different meridians. It is the hyperopia or myopia that is astigmatic, rather than that the astigmatism is hyperopic or myopic. Simple astigmatic myopia and compound astigmatic myopia would be more significant expressions than simple or compound myopic astigmatism. Mixed astigmatism is really mixed myopia and hyperopia rather than mixed astigmatism. The astigmatism is not the least rfiixed in any case, but my- opia and hyperopia prevail in different meridians, and they may be said to be mixed. Take out the astigmatism and the my- opia or hyperopia may be increased instead of lessened. If an eye is + ( ^^ + 3 ) D. in the vertical and + ( - + 4 ) D. in the horizontal, a + i D. cyl. ax. 180°, or a — i D. cyl. ax. 90° will take out the element of astigmatism. The former will add to the myopia in the vertical and the latter will subtract from the myopia in the horizontal. One will make the eye 4- (:r + 4) D. in all meridians; the other will make it + ( TT -f- 3 ) D. in all meridians. There is then a certain sym- metry to regular astigmatism. We sometimes find cases that follow certain rules of sym- metry, but which yet appear dififerent than regular one-cyl- inder astigmatism. For instance, we find an eye that is + (tt + 5) D. in 120° and + (~ +7 ) D. in 60°. As these two meridians are not at right angles a — 5 D- sphere which 170 THE STUDY OF THE EYE BY SKIASCOPY. neutralizes 120° leaves 60° at + ( ~ + 2) D. But a — 2D. cyl. ax. 150°, which neutralizes 60°, has a power oi ^ oi — 2D. at 120°, 30° from its axis, and therefore — 5 D.^ 3 — 2 D.^ ax. 150° will not correct the case. If we use a — 7 D.^ 3 + 2 D.<^ ax. 30° it will neutralize 120°, but will leave 60° + (" + .5 ) D. in the same manner. We may find cross cylinders that will neutralize both meridians, and therefore all meridians, axes respectively at 30° and 150°. We may determine the dioptry of each cylinder: Let X = diopter of cyl. ax. 150°. Let y = diopter of cyl. ax. 30°. Then, according to rule, we have the equations: (i) X + i y = 7 (2) y + i X = 5 in which the values of .r and y are found to be 6.133+ and 4.466+ respectively. Therefore cross cylinders: — 4.466 D. ax. 30° C — 6.133+ D. ax. 150° will neutralize both and all meridians. But the above cross cylinders can be reduced to a simple sphero-cylinder, the cylinder's greatest dioptric value being neither at 60° nor 120°, and therefore its axis at neither 30° nor 150°. In other words the above meridians (60° and 120'') are not the chief but two intermediate meridians, and two chief or principal meridians of an astigmatic eye cannot be at any other angle to each other than 90 degrees in regular astigma- tism. In the cross cylinders above meridian 75°, for instance, has a dioptric value of -J- of y, and loses but .067 of the diop- tric value of ,r: ^ of 4.466 = 2.233 .933 of 6.133 = 5.722 7-955 Its diopter is therefore 7.955, or more than either 60° or 120'. What lenses do to change the dioptry of the eye in cases cited the accommodation is constantly doing, but no use of the ac- commodation afifects the element of astigmatism. It remains constant in all the changes. THE STUDY OF THE EYE BY SKIASCOPY. I7I SKIASCOPIC APPEARANCES. Under a skiascopic examination astigmatism reveals itself unmistakably, for motion follows the rule of its meridian, and is therefore different in different meridians, the same as in an examination of two eyes having ametropia of different kinds or degrees shows the differences for the two eyes, an astigmatic eye giving you the resultant of the two motions. In a case of astigmatism if the mirror is tilted across one of the principal meridians, at right angles to it, the area of light on the face moves along the other principal meridian, and motion in the pupil shows the dioptric condition of the latter. If there is dis- tinct motion it must be with or against the mirror, and there- fore shows whether the meridian is myopic or hyperopic — that is, with the secondary lens in the rear cell as heretofore described. The speed of motion will be of special value, for by tilting the mirror in opposite meridians and noting the differ- ence of speed of motion an idea of the degree of astigmatism,. if there is any, will be obtained. But the skiascopist does not know, to start with, whether there is astigmatism or not, and if there is astigmatism, he doesn't know what the direction of the principal meridians may be. Hence he is unable to tilt the mirror in either of the principal meridians off hand. He may happen to do so, for in a great majority of cases the 90° and 180° meridians are the principal meridians, but he is quite likely not to do so. If the mirror is tilted so as to cause the light on the face to move along an intermediate meridian, it may show more rapid mo- tion than one and less rapid motion than the other chief me- ridian, or it may be an emmetropic meridian and show no mo- tion. But if it shows motion, the adjacent meridians, some of greater and some of less power, will give a peculiar swirling effect to the image or motion to the reflex, for on one rotary side refraction will tend to make the reflex move faster while in the other it tends to make it move slower. The effect is to make motion in the pupil conform with the principal meridian in which motion is most rapid, whether the mirror is tilted along that meridian or not. The principal meridian may be found by tilting the mirror in the meridian that allows the reflex to move with or against the light on the face instead of 172 THE STUDY OF THE EYE BY SKIASCOPY. at an oblique angle to it. But the principal meridians are more distinctly displayed by developing the banded appearance. Astigmatism is clearly indicated by the dififerent degrees of motion of the reflex in different meridians. This is mani- fest whether motion is with or against the mirror in all merid- ians. It is clearly manifest, of course, when motion in one principal meridian is with the mirror and in the other against the mirror. In that case there is, necessarily, in regular astig- matism one neutral meridian, an intermediate meridian some- where between the two principals, all meridians in one direc- tion (one rotary direction) being of higher and in the other of lower power. But astigmatism is more clearly marked when one of the principal meridians, or motion in one of them, is neutralized, for then diffusion is at the maximum in that me- ridian, for the area of reversal of that principal meridian is at the fixed plane of reversal of the observing eye. There is usu- ally more or less diffusion in the other meridian, but this may be minimized by placing the luminous area at the other principal area of reversal, or at the same distance, by way of the mirror, from the observed eye as the other principal area of reversal. When one principal meridian is thus neutralized the reflex extends, in that meridian, from one pupillary mar- gin to the other. This is the meridian of greatest diffusion. But unless the other meridian is nearly focused at area 4, and therefore without much diffusion, the banded appearance is not distinct. Figs. 53 and 54 illustrate an elongation of the reflex in one meridian, the elongation being in the meridian of great- est diffusion, or the meridian whose area of reversal is nearest the fixed plane in the observing eye. It cannot be said which of these meridians is most myopic, for that depends upon whether the area of reversal of intermediate and area of re- versal of the other principal meridians are anterior or posterior to the observing eye. THE BANDED APPEARANCE. The optical principles upon which the banded appearance depends are not difficult to understand, but unless one under- stands that there is an area of reversal for each principal me- ridian (as well as for all intermediate meridians), one of which Fig. 53. Page 172. Fig. 54. Page 172. Fig. .55 Page 174. Fig. 56. Page 174. :jfriOrx Fig 57. Page 179. Fig. ->H. Page 179. THE study' of the EYE BY SKIASCOPY. I73 is nearer the observed eye than the other, it is hard to explain. To bring up the banded appearance most strikingly it is neces- sary that the observing eye be at one of these principal areas of reversal, and the luminous area (or the virtual image of it) be at the other. In the use of the plane mirror it is necessary that the observing eye be at the area of reversal of the more myopic meridian of the observed eye, for the luminous area is necessarily farther from the observed eye, by v/ay of the mirror, than the observing eye. If the eye under examination is (artificially or naturally) one diopter myopic in the vertical and f D. in the horizontal, the area of reversal for the vertical meridian will be one meter in front of it, but the area of rever- sal for the horizontal will be i^ meters in front of it. Now, if the observing eye is at one meter it will be at the area of reversal for the vertical meridian; and if the luminous area is ^ meter in front of the mirror, the virtual image in the mirror will be i| meters from the observed eye, or at the other area of reversal. The pencils from the luminous area, i^ meters away, by way of the mirror, will be accurately focused by the observed eye in the horizontal; but the vertical meridian will focus them forward of area 3, producing dififusion at the retina in the vertical meridian, the meridian of inaccurate focusing. The figure on the retina will be elongated in the ver- tical because of such dififusion, but it Will amount there to but a trifle for ^ of a diopter's difiference. But before creating an efifect at area 4 it is necessary that emergent pencils start from this image and reach area 4, and to do that they must pass through the dioptric media of the observed eye, as well as through the dioptric media of the observing eye. What then is the result of these emergent pencils passing through the dioptric media of the observed eye? In the verti- cal meridian they are transposed and focused at one meter. In the horizontal meridian they are transposed and focused at ij meters. What would be the result if a screen intercepted them at one meter? In the vertical meridian they would be focused at the screen, but in the horizontal they would not be. There would then be displayed at the screen an image of the figure at area 3, elongated horizontally by dififusion but accurate vertically — a copy of its original at area 3, but enlarged to J 174 THE STUDY OF THE EYE BY SKIASCOPY. the extent of the himinous area plus the dififnsion in the vertical at area 3, for the correct focusing of the vertical does not elim- inate the diffusion of its original at area 3. The f is the ratio- of distances of the luminous area and the screen from the ob- served eye. But instead of having a screen at this point we have the observing eye with its emmetropic media. What can and does it do with these pencils focused at its fixed plane of reversal — practically the cornea — in the vertical; but on their way to their potential foci | meter farther on in the hori- zontal? The observing eye can do practically nothing in the vertical. It has no dioptric capacity or power upon waves of light whose curvature is infinite. It cannot reduce diffusion in the vertical. But in the horizontal it has some power, for the waves are — 2 Cm. in that meridian only. It cannot focus them, even in that meridian, upon area 4, but it will focus them slightly forward of area 4. Result: at area 4 there will be the maximum of diffusion in the vertical and the minimum of dif- fusion in the horizontal. And upon the imaged pupil at area 4 a band of light in the vertical wall extend from margin to mar- gin. The observer projects this result at area 4 out into the world, and the "banded appearance," so-called, is seen in the objective pupil. The band is in the meridian of greatest dif- fusion, in this case the meridian of greatest myopia. See Figs, 55 and 56, To produce, in this eye, the band in the other principal meridian, it would be necessary for the observing eye and the luminous area to change places — for the observing eye to be at the area of reversal most distant from the observed eye while the luminous area is at the other, the nearest area of reversal. But to produce these conditions the luminous area would need to be forward of the mirror — nearer the observed eye than it ;s to the observing eye. As with a plane mirror the distance of the light counts, from the luminous area to the mirror and thence back to the observed eye, it is evident the plane mirror would not do. But with a concave mirror focusing the luminous area between the observed and observing eyes and producing an aerial image there, which is the immediate source of the in- cident pencils reaching the observed eye, the luminous area would be forward (instead of back) of the mirror, and there- THE STUDY OF THE EYE BY SKIASCOPY. I75 fore nearer to the observed eye than the observing eye is. All that would be necessary would be to get the focal area of the mirror and area of reversal anterior to the observing eye together — the same distance from the observed eye. Usually a little adjusting of distances will do this. It is only necessary to bear in mind that the nearer the concave mirror is to the luminous area the farther away its focal area must be. If it is nearer the luminous area than its principal focal length it will have no positive focal area and produce no real image, for it will not, in that position, be able to transpose the pencils. It must therefore be farther from the luminous area than such •distance. If the observer has the area of reversal of the least myopic meridian at his eye he must not alter his position, but the adjusting of distances must be made by moving the light so as to change the position of the focus of the mirror between observed and observing eyes. LIMITATIONS IN BOTH CASES. There are then limitations in bringing out both bands, unless one is provided with both kinds of skiascopic mirrors. For instance, if an eye has 3 diopters of astigmatism and both meridians are hyperopic, one i D. and the other 4 D.. a + 2 D. lens will bring one area of reversal to i meter, but there will be no area of reversal for the other meridian, which is still 2 diop- ters hyperopic. A + 5 D. lens will bring the more hyperopic meridian to reversal at i meter, but the other meridian will re- A^erse at 10 in. from the observed eye. The observing eye may be moved to this point, and the light be placed 30 in. from the mirror, or 30 + 10 = 40 in. from the observed eye, and the banded appearance be developed, but it will be complicated with marginal aberration. It would be better in such a case to use the concave mirror, for if an ordinary 25 centimeter concave mirror were used, the observing eye being at one meter, to place the immediate source of light, the focal area of the mirror, at 10 in. from the observed eye and 30 in. from the observing eye. the light would be placed at the point conjugate to 30 in., or at 15 in. A 25 centimeter mirror is a + 4 D. mir- ror. It has 4 diopters of power. If the reflected pencils are to focus at 30 in., they must be reflected as 40/30 = — i;^ Cm. 1/6 THE STUDY OF THE EYE BY SKIASCOPY. waves. But a 25 centimeter mirror will focus neutral waves at 10 in., or do 4 diopters of work. The mirror must then be given 4 — i^ = 2| diopters of work upon incident pencils, or have pencils of + 2f Cm. waves to reflect. The points of origin of such v^raves must be 40/2! = 15 in. distant. Of course the amount of astigmatism is not known to start with, but if it appears to be considerable — more than one diopter — the con- cave mirror can be used to better advantage in developing the band, especially for a working distance of one meter. But for low degrees of astigmatism the concave mirror is inadequate. If the light is brought nearer than 13 in. to the 25 centimeter mirror, its focal area is beyond the observed eye. If the light is at infinity its focal area is 10 in. in front of the mirror or 30 in. from the observed eye, and cannot be brought nearer the mirror. But neither of these positions would do, for the focal area must be at one of the areas of reversal and cannot be at or beyond the observed eye, but must be between the observed and observing eye; and the light cannot be at infinity, but must be within one meter to give sufBcient illumination. With the light at one meter the focal area of the mirror would be 13 in. in front of the mirror, or 27 in. from the observed eye. So that if the observed eye had ^ D, of astigmatism and area of reversal of its most my- opic meridian were 27 in. from it, and its least myopic meridian focused at one meter, the band would be developed. But a lower degree of astigmatism could not be thus displayed. A low degree of astigmatism is, however, revealed by the plane mirror — the lowest degree imaginable. With the plane mirror the light may be brought very close to the mirror — • within 2 in. of it, if necessary. At a working distance of one meter, two principal areas of reversal that are but 2 in. apart show very slight astigmatism indeed — the difference between 40/40 and 40/38, or the difference between i D. and 1.05 D. = .05 D. As lenses are ground only to .13 D., this is suf- ficient. Since at a distance of 6 in. — that is from 40 to 46 in. — it amounts to but .13 D., this method conies very close indeed to getting all the astigmatism, and does get all that the man- ufactured trial-case lenses will correct. But it is not necessary, in developing the banded appear- THE STUDY OF THE EYE BY SKIASCOPY. 1 77 ance, to secure absolutely the maximum of diffusion in one meridian, and the minimum of diffusion in the other. An advance in that direction is usually all that is required. We may get the maximum of diffusion more easily than we can get the minimum. If we get the greatest diffusion in one principal meridian, and reduce diffusion in the other, we usually develop the bands without any trouble. The develop- ment of the banded appearance is quite a silent protest against the doctrine of "indefinite magnification'' advanced by some writers. If the image at area 3 is indefinitely magnified in one meridian, what is going to be done with the points in a line crossing this band at right angles? The position and direction of a band of light in the pupil shows the position of one of the principal meridians — the meridian in which motion is neutralized and diffusion is at the maximum. In regular astigmatism the other principal merid- ian is at right angles to it. But the band and the direction of the band does not show the amount or degree of astigma- tism. That may be measured by a sphere or cylinder. It is usually measured by a cylinder, for that does not affect the other principal meridian. The cylinder which increases dif- fusion in the second principal meridian — the meridian at right angles to the band of light if developed — and eliminates mo- tion of the band laterally, measures the astigmatism. With the development of diffusion laterally, the band of light — if developed — of course disappears, along with the disappear- ance of the clearly marked reflex. The neutralization of mo- tion in one principal meridian eliminates the warp of the reflex; the neutralization of motion in the other principal meridian eliminates its woof, and there is nothing left. CORRECTING ASTIGMATISM. The kind of a cylinder required to correct astigmatism — whether positive or negative — is shown by motion of the reflex in the meridian to be corrected, whether the banded appearance is developed or not. If motion is with the plane mirror a plus cylinder, axis at right angles to the meridian displaying such motion, or in or along the band of light, if developed, is necessary. If the band of light is vertical, or 178 THE STUDY OF THE EYE BY SKIASCOPY. there is an elongation of the image or reflex in the vertical, the axis of the neutrahzing positive cylinder should be ver- tical, for it is designed to neutralize or equalize motion in the meridian of least diffusion, but slowest motion — the horizon- tal. But if motion is against the plane mirror; or the band, when developed, moves against the plane mirror laterally a minus cylinder is required. With a plane mirror it is evident that, with motion against the mirror in one meridian, there would be no distinct banded appearance, for the least myopic meridian would be neutralized and the observing eye be at its area of reversal. This would give too much diffusion in the second meridian to develop the banded appearance. But a concave mirror, used in this case, would show motion with the mirror. The power of the cylinder required to neutralize motion in all meridians would be determined by trial, the same as the power of spherical lenses. The only difiference is that one meridian is wholly neutralized and all the intermediate meridians are partially neutralized. The cylinder is selected with reference to its neutralizing effect upon the other prin- cipal meridian, but it really neutralizes or completes the neu- tralization of the intermediate meridians, at the same time. In the use of the concave mirror to develop the banded appearance in high degrees of astigmatism, the mirror is used at such a distance from the light or luminous area as to have an area of reversal between it and the observed eye, and not as described in the last chapter — eight inches from the luminous area. The concave mirror is not reliable by that plan in astig- matism, for the necessary inclination of the mirror to reflect the pencils of light to the observed eye develops a cylindrical efYect and gives an astigmatic appearance when no astigma- tism is present. It is useful only in developing the banded ap- pearance in high degrees of astigmatism, and to avoid working at too near a point with the plane mirror in such cases for that purpose. It may also be said of the banded appearance that it serves the purpose only of showing the position of one, and therefore of both, principal meridians in regular astigma- tism. It isn't necessar}- to maintain it through an examination. A spherical lens, which would destroy it, may be used to neu- THE STUDY OF THE EYE BY SKIASCOPY. I79 tralize the other meridian, and the correction of the astigma- tism be made by correcting the elongation of the reflex. The work can be done more accurately, however, by bringing the area of reversal for each principal meridian to the fixed plane of reversal of the observing eye. But even that is not neces- sary to be done for both meridians, for one reveals the other. TEST OF ABERRATION. Aberration, as we have heretofore indicated, is more clearly manifest at a point of observation within one meter — • say at I or :| meter — from the observed eye. In this position of the observing eye an area of reversal for one of the principal meridians is brought to the observing eye, the same as when working at one meter, to get the efifects of maximum of dif- fusion and neutralization of motion in such meridian. The aberration test is a static rather than dynamic test. The zonu- lar appearance shown in symmetrical ametropia is modified somewhat in astigmatism, for there is the maximaim of dif- fusion in but one meridian. The reflex, even in the meridian of maximum diffusion does not extend entirely across the pu- pil, as shown at one meter, but is confined to a central area as shown in Figs. 57 and 58. To neutralize these appear- ances the cylinder is used that gives the central reflex a symmetrical or circular form corresponding to the luminous area. Such cylinder not only produces symmetry in the figure upon area 3 by modifying the incident pencils, but symmetry at area 4 by modifying the emergent pencils. It is a very close test, practically neutralizing the faintest grain of astigmatism. Attention is directed to the central area of light alone, which is very evanescent and disappears at the least provocation. To work to the best advantage a very small luminous area is re- quired — the smallest that may be made with an iris diaphragm. It is not the central area of light, if there is such an area, that focuses at the fixed plane of reversal of the observing eye, but the darker area around it, but by making the central area of light symmetrical the darker subcentral area is made symmetri- cal also. The figure will then show slight lateral motion — slight in extent but not in rapidity. Its motion is quick but its field of motion is small. Neither the central nor marginal area of 12 l8o THE STUDY OF THE EYE BY SKIASCOPY. light can be made to cross the pupil by tilting the mirror. Even if the luminous area is made larger the dark area is not eliminated, nor are the areas of light nicreased in extent, but it requires but slight change in the distance between the ob- served and observing eye to develop the reflex in all areas of the pupil, because no area of reversal is at the fixed plane ; and but slight unsteadiness of the mirror to cause the reflex to dis- appear, because the area of reversal or image anterior to the observed eye has passed from before the perforation in the mir- ror so that the emergent pencils do not reach the observing eye. The purpose of the small luminous area is to make the image at area 3 small, and the image anterior to the observed eye therefore small, so that there will be little unused light, and the real image anterior to the observed eye. may be en- compassed by a small area surrounding the perforation in the mirror. It requires, of course, but the slightest deflection to take such image from before the perforation, because, relative to the motion at area 3, its motion is very quick. Aberration, whether positive or negative, is not to be counted as an abnormal phenomenon, nor is it the least analo- gous to irregular astigmatism. It is, in some respects, anal- ogous to regular astigmatism ; but is quite different from that. Astigmatism is a variation of the refraction of different merid- ians, but aberration is a variation of the refraction of each me- ridian on accoimt of the variation in time of the application of resistance to the waves of light composing a pencil. The zonular appearance is due to the fact that the zones are alike in time of applying resistance to the waves, and waves have, in each zone practically the same degreee of curvature. Of course they vary from point to point, but vision, or visual acuity, is not fine enough to distinguish any but the more gen- eral dififerences. The form of the dioptric surfaces of the eye and the variations in their indices of refraction are such as to minimize aberration for the ordinary visual distances — that is, between the punctum proximum and punctum remotum, for in dynamic as in static refraction aberration is very slight. But near the inner limit of these distances — that is, near the punctum proximum — aberration appears. An en- larged or dilated pupil displays greater aberration, because a THE STUDY OF THE EYE BY SKIASCOPY. l8l larger area of the dioptric surfaces act, and by nearness the action of a larger area of the lens is revealed. But with cor- recting glasses before the observed eye aberration of the glass is the chief element of aberration displayed in skiascopy. IRREGULAR ASTIGMATISM. Unless astigmatism be such that one cylindrical surface in connection with such spherical surface as may be re- quired neutralizes motion in all meridians the astigmatism is irregular. If cross cylinders at right angles to each other cor- rect or neutralize all meridians there is either an intermediate emmetropic meridian or an intermediate meridan that a spher- ical lens will neutralize. But cross cylinders not at right angles to each other are reducible, as we have seen, to one spherical and one cylindrical surface. If cross cylinders such as the above neutralize all meridians there may be found a sphere- cylinder which will have precisely the same dioptry in all me- ridians as the compound. As far as the spherical part of any compound is concerned, that has no effect upon the astigmatic element. It simply increases or decreases the myopia or hy- peropia, as the case may be, leaving the astigmatic element as before. There are cases, however, in which the refraction is so different for different areas of the pupil that neither sphericals, cylindricals or compounds will neutralize motion in all merid- ians or at all areas of the pupil. The conical cornea is an ex- ample of this kind. In a skiascopic examination the conical cornea shows a triangular reflex with its apex at the center of the cornea. A glass could be ground to neutralize such a con- dition, but unless the two apices — that of the cornea and glass — coincided in position on the visual axis, it would derange vision more than ever. The visual axis of the eye would have to pass directly through the center of the glass corresponding to the apex of the conical cornea, since it must pass through that apex of the cornea itself. There are often cases of irregular astigmatism — that is, irregular refraction for different areas of the pupil whether they may be called astigmatism or not — that may be assisted bv glasses. It is usual in such cases to select from the areas l82 THE STUDY OF THE EVE BY SKIASCOPY. showing different power an area most favorably located — near- est the central pupillary area — and give a correction for that area. The area of the pupil directly in front of the macula may thus be made correct, even though other pupillary areas are incorrect and tend to develop diplopia. But cases of astigmatism so irregular as not to come within any rule are found, and there are also pathological cases and cases that have been produced by surgical operations or by accident. Tliese are beyond the scope of a work of this kind, however interesting they may be. Tliey are not cases that the optician would venture to deal with, although as far as refraction work may help them, he is at liberty to do what he can. CHAPTER IX. CONDITIONS FAVORABLE TO SUCCESSFUL WORK IN SKIASCOPY. THE OPERATING ROOM AND ITS ARRANGEMENTS. PRACTICAL OPERATING SUGGESTIONS TO BEGINNERS. T T is surprising what accurate results can be obtained in ski- ■'^ ascopy under the least favorable conditions. It is a method in which the skill of the operator counts for more than by any other method, for it permits the utmost nicety of work. But nevertheless there is no reason why the operator should not be provided with every means to make his work the most successful. While every facility will not make a good opera- tor of one who does his work carelessly, a careful worker is very much aided by desirable arrangements. Some of the most skilled skiascopists work with an open light, using no skiascopic chimney because they fail to derive any advantage from it. Some prefer to work with the concave mirror altogether. Some prefer large mirrors and others pre- fer small ones, as some prefer to work at two meters, others at six meters, others at one or one-half meter. It is a method permitting such choice. But the one meter distance, the plane mirror and the skiascopic chimney to limit the area of light, are more generally acceptable. THE OPERATING ROOM. Tlie best sort of a dark room for the practice of skiascopy is the room in which regular work is done — the regular operat- ing room. There are two ways of making the operating room fill every requirement of the optician, both for subjective test- ing and for the practice of skiascopy or other objective method. One is to have a nice light room with facilities for darkening it for objective testing; the other is to have a nice dark room 183 184 SUCCESSFUL WORK IN SKIASCOPY. with facilities for lighting it. Of the two the latter possesses obvious advantages. A room well lighted naturally — that is by daylight — must have window spaces, and to screen these for dark-room work requires a good deal of curtaining and a good deal of attention. Even then, on bright days, it is difficult to darken the room sufficiently. The variations in light by the hour of the day or position of the sun, and variations due to the weather, make such a room unsatisfactory, even for subjec- tive testing. But a naturally dark room lighted artificially is easily changed from one to the other, and the light, when it is lighted, is uniform. Fig. 59. C^craitn-^ l^aam,- ^CruT. ?l«.f>-. 1. Operator's Chair. 4. Trial Case. 2. Patient's Cliair. 5. Test Cards— 20 ft. 3. Skiasopic Light. 6. Light at Test Cards. 7. General Lights— Ceiling. To control the light in the room the optician should not be compelled to pass around from lamp to lamp to turn off or turn on the light, if that can be avoided. He should be able to turn the light on or off without leaving his chair or his patient. This may be easily managed with incandescent electric light- ing by having the switch that turns the light on or ofif within reach of the hand. There should be three sets of lights: (i) light overhead for the room in general; (2) light near the sub- jective test cards, and (3) light in the- skiascopic chimney. It SUCCESSFUL WORK IN SKIASCOPY, 185 should be so arrang-ed that these Hghts may be turned on or off separately. DIMENSIONS AND ORDER. The room should be about 20 leet long and of sufficient width to contain all furnishings — optical or otherwise — with- out crowding. The skiascopic light should be upon a bracket, allowing the operator to move it nearer or farther, or to elevate or lower it. It will not be found necessary to move the lig"ht to opposite sides of the patient's head or change his line of vision for examining the different eyes, nor for the optician to change his position. The patient might be directed to look to the right and left of the mirror, so as to bring the visual axes to the left of the operator when the left eye is being examined, and to the right when the right eye is being examined, but even that is unnecessary, although by having the patient look in a fixed direction to the operator's right the reflex will be principally to the nasal side of the macula when the right eye is being examined, and to the temporal side of the macula when the left eye is being examined. The trial case of lenses should be upon a stand in front, but to one side of the optician, enabling him to change the lenses with as little inconvenience to himself as possible. The accompanying drawing will indicate the relative positions of the optician and his patient, the position of the ski- ascopic light, trial case, test cards, etc., as well as the general arrangements of the room. PRACTICAL OPERATING. Before taking the first skiascopic view of either eye vision should be tested in the ordinary way upon the test cards for both eyes at the 20 feet. If vision is less than normal actual vision should be noted as B. E. 20/40, or whatever it may be. A H- I D. lens should then be inserted in the rear cell for each eye, of the trial frames, and the frames adjusted comfortably upon the patient. General light in the room may then be turned off, and the patient be directed to look at the test cards 20 feet away. The Hght should then be turned off from the test cards and turned on in the skiascopic chimney. A little time should be allowed for the pupils to dilate and the muscles of convergence and accommodation to relax, even more than l86 SUCCESSFUL WORK IN SKIASCOPY, they would be relaxed for viewing the test cards, under the in- fluence of the darkened room and the dimly-seen objects in it. Tlie patient need not hold the eyes in a fixed position during all this time — really the actual time is very short — but he must be made to "look into distance" when the optician begins to work, slightly to the right (the optician's right) of the mirror. This brings both visual axes near to the mirror and near to the visual axis of the observing eye, and gives a view, in the right eye, of an area of the retina slightly to the nasal side, but upon the area of the macula. As the light from the mirror is cast upon the face around the observed eye and made to cross it in any meridian by the tilting of the mirror, some form of skiascopic phenomenon will appear in the pupil and show at once whether the eye is emme- tropic, myopic or h3'peropic. If the eye is emmetropic the + I D. lens before it will bring the area of reversal to the observ- ing eye — case 2 — or the position in which the motion of the reflex cannot be determined. Hence, if motion is distinctly with the plane mirror, the eye under examination is hyperopic, and the plus lens that neutralizes motion or brings the area of reversal to the fixed plane, practically the cornea, of the ob- serving eye, is the full correction of such hyperopia. If mo- tion is against the plane mirror the eye is myopic, and the minus lens that neutralizes motion at one meter is the full cor- rection of such myopia. We may not be able to distinguish exactly the absolute point at which reversal occurs, but if ^ of a diopter either way produces opposite motions the point mid- way between them is as close as we can come to it. If the lens that neutralizes motion in one meridian does not eliminate motion in all meridians astigmatism is shown. The uncor- rected or unneutralized meridian may be measured either by the sphere that corrects that meridian, although producing motion in the meridian first neutralized; or by the cylinder, axis at right angles to the unneutralized meridian, which neu- tralizes motion in the uncorrected meridian. Each eye is tested separately and its correction found. The operator does not require, if working at one meter, to be an exact meter from the eye under observation. If he is 6 in. nearer, or 34 instead of 40 in., it makes a difference of but SUCCESSFUL WORK IN SKIASCOPY. 187 J of a diopter and for two or three inches the amount would not be worth noticing. A distance of 6 in. more than a meter would make even less difference. The trial case does not con- tain lenses graded fine enough to measure these low degrees. But in working at a distance of less than one meter, every inch counts more and more the nearer the working distance; but at a greater distance, as at two meters, inches cut very little figure. If no astigmatic signs appear, to get the exact correc- tion of an eye by skiascopy requires a wonderfully short space of time. The direction of motion tells what kind of a lens is wanted; the rapidity of motion and the size of the reflex tells about what strength of lens is required. To get that lens from the trial case that most nearly neutralizes motion and produces the maximum of diffusion, if not at an exact meter, at an inch or two in front or back of the meter point, is but the work of a minute or two. The operator may allow himself a range of six inches, three inches to each side of the meter point, to get the exact point of reversal, which none of the trial lenses will give him at exactly one meter; for three inches to either side of the meter point, reduced to diopters, is absolutely insignifi- cant. No trial case lens will measure it, for it is less than 1/12 of a diopter. MOVING THE- LIGHT. The facilities for moving the skiascopic light are of advan- tage in two ways: (i) the light, the observed eye and the ob- serving eye should be in the same horizontal plane, and as patients will have considerable difference of body length or height of the eyes when seated in a chair, the skiascopic light should be adjustable in height; but (2) moving the light is of chief importance in bringing out the banded appearance in as- tigmatism, and this is effected by the adjustment of the dis- tance of the light from the mirror. To make these changes in position, without changing the general direction of the beam of light from the skiascopic chimney, the latter should rest upon a rotary foundation, so that as the light is moved forward or backward upon the bracket or bracket hinges the chimney may be rotated in the opposite direction from the rotation of the bracket. With the plane mirror, when the area of reversal of the loS SUCCESSFUL WORK IN SKIASCOPY. most myopic meridian of the observed eye is at the observing eye, the area of reversal of the least myopic meridian is posterior to the observing eye. If the observed eye has nearly, or quite, or more, than one diopter of astigmatism the light cannot be moved to the distance required for the fullest display of the banded appearance, for with ^ D. of astigmatism it would re- quire to be ^ meter from the mirror, and for ^ D. of astigma- tism it would require to be at i meter from the mirror. That is, if the most myopic meridian is + ( ~ -|- i ) D. and the least myopic meridian is + ( - + f ) D., there is -J D. of astigmatism. To place the light at the same distance as the area of reversal of the least myopic meridian it would require to be i/f = 2)/2 meters from the observed eye, or ^ meter from the mirror. But with ^ D. of myopia the light would require to be 1/^ = 2 meters from the observed eye or i meter from the mirror. It is evident that with one full diopter of astig- matism and the area of reversal of the most myopic meridian at the obsenang eye, the area of reversal of the least myopic me- ridian (which would be emmetropic) would be at infinity, and the light could not be moved to infinity. Hence the necessity of using the concave mirror to develop the most striking ap- pearance of the band if the eye is more than one diopter astigmatic. With the concave mirror the least myopic meridian, or area of reversal of the least myopic meridian, is brought to the observing eye. Then the area of reversal of the most myopic meridian is somewhere between the observed and observing eye. It is only necessary to make the focal area of the concave mirror and the area of reversal of this most myopic meridian of the observed eye to coincide, or be equally distant from the mirror, and therefore equally distant from the observed eye, to develop the banded appearance most strikingly. This is done, with a concave mirror of given power, as a 25 centi- meter mirror, by moving the light. The position iL is neces- sary to place the light indicates the position of the area of re- versal. For instance, if with the anterior area of reversal at the observing eye, and with a 25 cm. (+ 4 D.) mirror the banded appearance is developed most strikingly when the light is 20 in. from the mirror, the focal area of the mirror is 20 in. in SUCCESSFUL WORK IN SKIASCOPY. 189 front of the mirror. Hence the other area of reversal is 20 in. in front of the mirror, or 20 in. from the observed eye, and it ha.s 2 D. of myopia in that meridian. But if the light requires to be within 16 in. of the mirror to develop the banded appear- ance most strikingly, 2^ D. of its 4 D. power is used in neu- tralizing the pencils, leaving but i^ D. to focus them. This places the focal area of the mirror 40/1^ = 27 in. in front of the mirror or 13 in. from the observed eye. Hence that is the position of the area of reversal of the most myopic meridian, and 3 D. of myopia is shown in that meridian. The amount of astigmatism in the former case is i D., in the latter 2 D. Again, if the light has to be 14^ in. from the mirror, 2| D. of its power is used to neutralize the pencils, leaving i^ D. to focus the pencils with at 40/1 5 = 32 in., or 8 in. anterior to the observed eye. This shows 5 D. of myopia in the most myopic meridian, or 4 D. of astigmatism. The nearer the light is brought to the mirror to develop the banded appearance, with a concave mirror, the higher the degree of astigmatism. But the nearer the light, with a plane mirror, the lower the degree of astigmatism. But, as we have said heretofore, it is not necessary that the light be at one area of reversal and the observing eye at the other to develop the banded appearance. If the light is some- what near the other area of reversal, sufficiently near it to make the difference of diffusion in the two meridians striking, the banded appearance is developed. This accounts for the great differences noted in the banded appearance in different eyes. In some the band is distinct but diffusion spreads it entirely across the pupil even in the meridian of least diffusion. We do not ascertain the position of the other area of reversal by calculation, as indicated above, but measure it by the lens needed to neutralize motion in the meridian of least diffusion The calculation is given merely to show the mathematical basis •of the bands. With a concave mirror of 4 D. power (25 centi- meter focus) the light cannot be brought to within 13 in. of the mirror, for at 13 in, 3 D. of its power would be required to neutralize the pencils of light, leaving i D. to focus them, and that would place the focal area of the mirror one meter away, or at the cornea of the observed eye. No eye is so myopic in 190 SUCCESSFUL WORK IN SKIASCOPY. any meridian as to have an area of reversal, or focal area of emergent pencils, at its cornea. Even at 2 in. from the cornea it would show 20 D. of myopia, and if the other area of rever- sal were at one meter, or one diopter myopic, the astigmatic element would be 19 D., a very unusual, if not unheard of, amount. WATCHING THE ACCOMMODATION. Without using a mydriatic the operator must be watchful of the observed eye's accommodation, to see that v: does not come into play and give him erroneous data. It is the eye's static refraction that is sought to be determined, and the use of the accommodation of the observed eye, of course, conceals the real static condition. For this reason, if the use of the accommodation is suspected, the patient should be relieved for a moment by turning the light upon the distant. test cards and requiring him to converge and accommodate for 20 feet or more. The acts of convergence and accommodation are so associated that to do one is usually to do the other, and to relax one is to relax the other. The only near object the patient is likely to fix is the observer or the virtual image, so-called, in the mirror, really to adapt themselves to the pencils from the light that are reflected by the mirror. With children, whose accommodation is so very active, and who cannot be easily made to fix a distant object when near and brighter things may be seen, this matter may be somewhat perplexing. But the photographer has quite as hard a task when they sit for a picture. If the use of mydriatics is ever excusable it is in the case of examining children's eyes, especially by skiascopy. But children under six or eight are seldom examined, and they are not difficult to manage if the operator is ingenious, while little folks of ten or twelve are often quite as tractable as older persons, and can be made to relax the accommodation and convergence with little trouble. HANDLING THE LENSES. It is, of course, necessary as the examination proceeds to change the lenses, reducing or increasing the strength as occa- sion may demand. This should be done without removing the frames, by withdrawing one and inserting the other in its SUCCESSFUL WORK IN SKIASCOPY. I9I place in the cell. It may be necessary to lay aside the mirror and lean forward to make the change. The patient should be discommoded as little as possible, and the optician or oculist should be discommoded as little as possible, for it interrupts his work. An experienced operator shows his skill in the quickness and finesse with which he can do this work, and some operators are very skillful in doing it. But a means of making- these changes quickly, without putting the mirror aside, would undoubtedly be a valuable adjunct in practical skiascopic work, and there are some devices for doing it already in the market to meet the demand, though whether they meet it satisfactorily or not you must judge. If the re- fractive error is compound it may require a number of changes before satisfactory results are obtained. The patient must not be tired out with a long and tedious examination, and the operator will find it convenient to vary the distance and deter- mine about what lens is required in that way, rather than run through the whole category of lenses to get at the glass needed. He can, by varying his distance, measure, with reasonable accuracy, the lens strength needed to bring the area of reversal to the point required. If, for instance, he finds by this method that the area of reversal is -i meter from the observed eye, a — I D. will bring it near the poijit required, and the proper lens may be inserted at once. PROVING RESULTS. Both eyes are tested separately in the same way. Skias- copy is a strictly monocular test, and the error of each eye is measured separately and by itself. It will be necessary, when the suitable correction for each eye is found to prove the result and to determine whether the eyes will bear the full correction or not. The proof of the objective test is the patient's subjec- tive vision and visual comfort. When both glasses are in their place in the trial frame the light should be turned upon the dis- tant card, and the effects of the glasses determined. The operator will know to what extent vision is improved for each eye, and can tell whether normal vision will result or not, but he does not know whether the patient can wear the glasses — the full correction — comfortably or not. The visual test on the 192 SUCCESSFUL WORK IN SKIASCOPY. distant cards will alone clear up this point. When the light is turned on and the patient is asked to report on these mat- ters, the objective test is, of course, completed. If the glasses do not feel comfortable, if they "hurt" the eyes or do not feel ''easy" and "restful," as well as give good vision, there is prob- ably a binocular complication or asthenopic trouble which the glasses do not relieve, or even make more distressing, or pro- duce where it did not exist before. What that trouble is can- not be determined by skiascopy. He must proceed from this point by other methods, but having the full refractive error for each eye will be a great help to him in his further work. It is usually a good plan to obscure one eye while the vision of the other is subjectively tested, so that your patient will understand the accuracy of your work although the binocular effect is unsatisfactory. He will then appreciate the nicety of your work, and be all the more willing to trust to you for the rest. You will gain his confidence at a critical point, whereas, if both eyes were uncovered and he is given to understand that this is the result of your work, no matter how carefully you may have corrected each eye, if there is a binocular complica- tion he will be apt to think that you have failed. Comfortable vision is preferable always to everything else, and everv- cor- rection of the eyes by glasses that improve vision at the sacri- fice of comfort is a failure of the worst kind. We cannot here go into the details of securing the best vision with the greatest comfort, but it will be found necessary in all work to pay the strictest attention to it. SUGGESTIOXS TO BEGINNERS. Skiascopy as a method of ocular examination is one that grows accurate and reliable only with experience. Practice makes perfect. The beginner should become familiar with effects by practice upon a schematic eye before attempting to do work with real eyes. The distinctions between cases i, 2 and 3 should be thoroughly mastered both in theory and prac- tice. The peculiar effects of aberration should also be carefully studied. The appearances under either case i, 2 or 3 are not by any means the same. Under case i we may have motion with the plane mirror, but diffusion and rapidity of motion SUCCESSFUL WORK IN SKIASCOPY. 193 vary with every approach toward or recession from reversal. The same may be said of case 3. But case 2, or the point when diffusion reaches the maximum and motion is indeterminate, is the most important phase of the whole work. It is judged by what you don't see rather than what you do see, but when a low minus lens develops motion in one direction and a low plus lens develops motion in the other direction, there can be no doubt as to the real location. Beginners should work upon cases of symmetrical ame- tropia first. That is the schematic eye should be set at an un- known point, and with the trial case, mirror and light the amount of ametropia should be measured. The correctness of the results can then be ascertained by seeing how near the ex- act result has been determined. This work should be done over and over, working at one meter. If a lens brings the area of reversal to the eye, as shown by the appearances in case 2, the accuracy of the result may be tested without removing the correcting lens, by advancing the mirror and observing eye a few inches toward the observed eye to develop case i, and withdrawing it a few inches from the one meter point to de- velop case 3. In this way the nearness of the area of reversal to the observing eye, if it is not at it exactly, is discovered. It is surprising how quickly under tliis plan the skiascopic in- stinct is developed. The author has seen students in three days' work of an hour, or even less, a day, become very close work- ers for all kinds, or rather degrees, of myopia and hyperopia. The appearances of aberration are confusing at first only. As we have said, these are not abnormalities but natural optical effects. If the dioptric surfaces of the eye were perfectly spher- ical, and the index of refraction for all areas of the cornea and the lens were uniform, spherical aberration in the eye would be more pronounced than it is. Aberration in the diop- tric surfaces is reduced by the want of absolute sphericity, and by variations in the index of refraction in them. It is not pro- duced by such want. Whether aberration is negative or posi- tive is not a matter of any optical importance. No eye is abso- lutely without aberration, and if one were, the placing of a glass lens before it would develop aberration for the compound system. 194 SUCCESSFUL WORK IN SKIASCOPY. For experimental work, and especially for the use of stu- dents, the author has taken an ordinary Thorington eye, taken the lens out and had special lenses ground, one of + 20 D. sph 3 — 2D. cyl., and another of + 20 D. sph. 3 — i D. cyl., which have, with the lens removed, been mounted in paste- board which may be inserted in the eye so that the lens is ex- posed at the pupil. By placing one of the compound lenses in place any form of astigmatism of the schematic eye may be produced by moving- the tube containing retinal area. To measure and neutralize the myopia and hyperopia and neutral- ize the astigmatism gives the beginner real work to do; for he must measure the amount and determine the axis of the neu • tralizing cylinder as well as find the spherical correction. As the compounds contain the full spherical power at one surface, the optical center of the lens is nearer the pupil or farther from the retina than with a bi-convex lens, such as is used in the regular eye. This makes the dioptric marking a little out of plumb, but that need not bother seriously. The object in putting the astigmatic factor m the one lens is merely to conceal it so that a student does not know, except by skia- scopic test, whether the spherical lens or one of the com- pounds is in the eye; and if he finds it is compound, he doesn't know the amount nor direction of the axis without he deter- mines it by test. CHAPTER X. SKIASCOPIC DEVICES AND INVENTIONS. INGENIOUS APPLI- ANCES DEVISED TO MAKE THE METHOD MECHANI- CALLY PERFECT AND COMFORTABLE FOR THE OPERATOR. A METHOD of ocular examination so simple in its essen- tial details, and so exact in its results when skillfully employed, is naturally very attractive to optical workers. It is •chiefly valued because it is an objective method, and successful work by it is prima facie evidence of unusual skill. But it is a method that must be worked finely, if at all, and does not per- mit of any "bull in the china shop" disregard of its fine points. Those who attempt to operate it coarsely usually fail, and then they are apt to condemn the method when their failure is their own fault. To do fine work, however, the different skiascopic phenomena or appearances under cases i, 2 and 3 must be made thoroughly familiar, so that the operator will know at a glance about how near the are^ of reversal is to his eye. To make the method more certain and for the ease or comfort of the operator in using it some ingenious devices have been made. There are no doubt others being devised every year, some practical and valuable, but others of very little use. We will consider a few of the chief instruments of this kind. It will not be necessary to speak here of the forms of the ■skiascopic mirrors or of the chimneys, as they have already received all necessary attention. The direction of the other devices have been: (i) To make the changes of lenses before the observed eye quickly and comfortably without having to lay aside the mirror. (2) To definitely locate the axis of rotation of the mirror in testing an oblique meridian, and therefore locating accu- rately the meridian tested. 13 195 196 SKIASCOPIC DEVICES AND INVENTIONS. (3) To reduce the intervals of evolutionary spaces to cer- tainty as to distance. (4) To make the position of the skiascopic light readily changeable, as required in the development of the banded ap- pearance in astigmatism. (5) To neutralize in whole or in part the incident pencils of light before they reach the observed eye, so as to sharpen the definition and intensify the light or reflex at area 3. Some quite satisfactory results have been obtained in these directions, as will appear from the following descriptions and illustrations: I. LENS HOLDERS. Commercially these are known as skiascopes lather than the skiascopic mirror, which is more frequently called a "retin- oscope" in the West, although the East seems to favor "skia- scope" for the mirror, the same as it favors "skiascopy" rather than "retinoscopy" for the method. I. THE WURDEMANN SKIASCOPE. Fig. 60 illustrates an instrument devised by Dr. Wurde- mann, of Alilwaukee. It consists of batteries of plus and minus lenses arranged in separate rows in an oblong frame, with a handle for the patient to grasp and hold in an upright posi- tion so as to place the lens desired before the observed eye. The patient is given the task of holding the instrument as di- rected by the operator, and changing the position so as to bring different lenses before the eye, while the operator gives his attention to the skiascopic appearances and to manipulating the light and the mirror. This enables the operator to devote his entire attention to his real work, and imposes but a slight burden upon the patient. With this and other instruments of the kind care must be taken to avoid producing a cylindrical SKIASCOPIC DEVICES AND INVENTIONS. 197 effect by inclitiing- the lens to the visual axes, or a prismatic effect by not having- the lens centered over the observed eye. 2. THE GENEVA SKIASCOPE. This instrument is different from the Wurdemann instru- ment chiefly in having the plus lenses on one standard and the minus lenses on another, as shown by the figure (Fig. 61). It gives the patient a lighter weight to hold, and the absence of all interfering material around the lenses makes it easier to get the close position required. Lightness is, of course, quite an advantage, as it makes the assistance of the patient as little burdensome as possible. 3. THE HARDY SKIASCOPE. The Hardy instrument is a further departure from the Wurdemann instrument, as shown by^the figure (Fig. 62). In Fiu. G2. it the lenses are arranged in circular order in a circular disc, which is rotated to bring different lenses before the observed eye. The patient holds the instrument in a fixed position be- 198 SKIASCOPIC DEVICES AND INVENTIONS. fore the observed eye, and brings the different lenses into posi- tion by rotating the wheel as directed by the operator. The same care is required not to tilt the lenses in this as in the other two instruments. 4. DR. grain's device. Dr. C. H. Grain, of Chicago, has devised a more complete instrument than any of the above, as may be seen by the illus- tration (Fig. 63). Foundationally it resembles the Hardy Ski- FlG. 63. ascope, but has additional features. It rests upon a standard and is not held in the hand. It is elevated or lowered to suit the position of the eye to be examined by means of an attach- ment in the standard. It also has a chin-rest and an opaque cover for the eye not under examination, and a bend in the horizontal frame-work to fit the nose when the eye is in place. There is also in front of the disc containing the lenses, at the point where the observed eye is placed, a cell in which to put SKIASCOPIC DEVICES AND INVENTIONS. 199 a trial-case lens or cylinder. When the right eye is examined the patient is seated upon the right of the instrument, and vice versa for the left eye. Two indices are so placed that they indicate the lens that is before the observed eye to an office-assistant, who may rotate the disc or wheel containing Pig. 64. the lenses as desired. Cutting off the vision of the eye not under examination by the opaque disc would interfere with the easiest means of controlling the accommodation — that is, by the principle of convergence — if the eye were not under atropine or other mydriatic, but as the inventor uses a mydri- atic in all cases this principle is of little importance to him. 200 SKIASCOPIC DEVICES AND INVENTIONS. 5. THE JENNINGS' SKIASCOPE. The general appearance of this instrument is shown in the accompanying figure (Fig. 64). It is constructed on the principle of the Morton ophthalmoscope, and different lenses are brought before the observed eye by means of a long axle reaching the operator, by which a wheel in the lower part of the instrument rotates the battery of lenses in the upper part. The operator can in this manner bring any lens desired before the observed eye without changing his own position or neg- lecting his work with the mirror, or requiring the assistance of anyone. It seems to meet the requirements of such an instru- ment better in many respects than any other "skiascope" or lens holder. The author has not seen the instrument, but its operation is simple to anyone acquainted with the Morton opthalmoscope, from a study of the illustration. There are probably other instruments in this line, the pur- pose of all being the same — that of changing the lenses before the observed eye quickly and at as little inconvenience to the operator and his patient as possible. They are a convenience rather than a necessity. 2. MIRROR'S AXIS OF ROTATION. * When the mirror is tilted so as to cause the area of light on the face to pass across the observed eye, it is of course rotated slightly upon an axis corresponding to the position of the handle. It is comparatively easy to fix the vertical (90°) and horizontal (180°) axes of rotation, but when the rota- tion or tilting of the mirror is in an oblique axis a means of determining exactly the axis is important, for the axis of rotation of the mirror is at right angles to the meridian of the eye being tested, or to motion of the light on the face A device to fix the axis of rotation of the mirror has been invented by Dr. Charles Gordon Fuller, of Chicago, which is shown in the accompanying figure (Fig. 65). An opaque disc containing a small skiascopic mirror is set axially in a rim or ring on which are marked the degrees of circular or angular measure. Rota- tion of the disc in the outer rim of course changes the axis of the mirror or disc on which the mirror is set, without changing SKIASCOPIC DEVICES AND INVENTIONS. 201 the plane of the mirror, and the degree marks on the rim show the position of the axis for tilting the mirror. The outer rim is attached to a fixed standard which is vertical in position, but Fig. 65. it may be held in the hand. If the mirror is laid aside, as for the purpose of changing the lens before the observed eye, it may be picked up again, and will, of course, have the same angle or axis of rotation as before. The mirror is used in con- 202 SKIASCOPIC DEVICES AND INVENTIONS. nection with a specially devised skiascopic chimney containing a long arm that confines the pencils of light, and fixes the dis- tance. This is of less value, we think, than the principle above described. 3. FIXING THE INTERVALS. There have been invented quite a number of devices to fix absolutely the distance or spaces of the three intervals. Effort in this matter seems to have been misdirected in most cases, for it fails to take into account the value of being able to change the intervals at will. By this means we may produce nicer shades of skiascopic effects than by any other means. Every change in the position of the observing eye has a value equivalent to a lens before the observed eye. Moving from a distance of one meter to a distance of one-half meter from the observed eye has a value of but one diopter. Motion from one meter to a point an inch nearer the observed eye has a value of less than .03 of a diopter. A half-inch or quarter-incli has still less value. As the observing eye may, under free action, be at any desired distance from the observed eye, the varieties of lens-action such changes are equivalent to are very numer- ous. Fixing the distance eliminates all this. There are also accompanying dynamic effects during the change of any of the intervals, and as skiascopy is essentially a dynamic test, fixing the distances of all the evolutionary spaces would eliminate such special dynamic features. It would be equal to the invention of a ship-builder who devised a rudder by which the ship would be compelled always to sail in one direction as regards the wind. It is a good deal better to have ships that are able to sail in many directions, whatever the wind, and a rudder capable of changing the course as de- sired. Fixing the intervals absolutely would therefore inter- fere with the operator in using the method completely, for im- portant results are obtained by varying the intervals, slightly or considerably, as in developing the banded appearance in astigmatism, or finding an area of reversal that no regular trial lens will bring exactly to the right point. Of course, any de- vice that fixes the length of the intervals absolutely makes the result more accurate for that fixed distance, but it also confines the work of the operator within the same limits. He must SKIASCOPIC DEVICES AND INVENTIONS. 203 get all he wants within these limitations or do without it. It will be found better, w^e think, not to handicap skiascopy in this way. Better a little uncertainty as to amount or quan- tity of error than being fenced into a limited field of operation. The intervals in skiascopy are evolutionary spaces. They are factors in the general results, and it is desirable to be able to use them as factors, which cannot be done if they are fixed absolutely. That is, the dynamic efifects of changing the in- tervals is eliminated the moment the distances are made fixed. 4. POSITION OF LIGHT. The facilities for changing the position of the skiascopic light seem to be met as fully as possible by the adjustable Fig. 67. bracket (Figs. 66 and 6'j'). It gives a variation in the distance of the light from the mirror of nearly two meters, or from as near a point as you wish it to two meters, without changing 204 SKIASCOPIC DEVICES AND INVENTIONS. the position of operator or patient. For degrees of astigma- tism of more than one diopter it is usually better to employ the concave mirror, and control then the position of the imme- diate source of light, which requires but slight variation in the position of the real skiascopic light. The banded appearance may, however, be made sufficiently distinct with a plane mirror to show the meridians, even with a higher degree of astigma- tism than one diopter. The adjustable bracket is made for all kinds of lights, and is a great convenience, as it can be raised or lowered as well as removed farther from or brought nearer the mirror. 5. NEUTRALIZING INCIDENT PENCILS. This may be accomplished in either of two ways: (i) by having a neutralizing or under-neutralizing lens between the light and the mirror, or (2) by using a concave mirror with the skiascopic light at or within its principal focal distance. This introduces optical factors which modify the waves on their way to the observed eye. An exactly neutralizing lens — that is a + 16 D. lens 2^ in. from the light, and so placed in interval I as to intercept the pencils on their way to the mirror, has the effect, so far as the curvature of the waves is concerned, of causing the luminous area to recede to infinity. But the dif- ferent pencils, or rays of the different pencils, have practically the same divergence as before. Such a lens, in its focal posi- tion, has its maximum of magnifying effect upon the luminous area, and hence the luminous area may be small, and should be some characteristic figure, such as a cross or triangle, in order to be confined within the central area of the lens and produce as little aberration as possible. This would sharpen the defini- tion at area 3, if the observed eye is fully corrected, and pro- duce also a clear definition, without diffusion, at area 4, A lens of less than full neutralizing power would tend in the same direction, and the evolution of the waves through the remaining space of interval i and all of interval 2 would tend still further to neutralize them. But if the lens or mirror transposed the pencils, the remaining portion of interval i and all of interval 2 would tend to augment the curv^ature of the waves. SKIASCOPIC DEVICES AND INVENTIONS. 205 In the use of tubes in which to confine the pencils — or shut out extraneous light — we introduce mechanical interfer- ence with the peripheral areas of all the waves, both of the in- cident and emergent pencils, and set up cross waves and reflec- tions unless the walls of the tube are thoroughly deadened by light-absorbing materials or diaphragms inserted to intercept them and reflect them in directions that will not permit their reaching either objective or subjective pupil. Such dia- phragms will have no optical effect — will not modify the curva- ture of the waves passing through — but they make a nice ad- justment of the spaces necessary. The use of diaphragms in optical tubings of this kind has been thought to have a modifying effect upon the pencils of light, but this cannot be the case. It is true that one may produce a very fair image of the flame of a candle through a pin-hole disc, but such image is the product of untransposed pencils of light passing through the pm-hole. The inversion of the image is due to the natural inversion of the different pencils which pass through the same opening but in different directions, as explained under the principle of inversion. Chap- ter R'. The screen that receives or reacts upon these pencils contains little classified areas, each of which receives all the light from one minute pencil, and part of the light from ad- joining pencils. These little areas correspond to diffusion cir- cles when the screen is held slightly beyond its focal position for a lens, except that, in the latter case, the diffusion circles widen rapidly with the removal of the screen from its focal position. In the image produced by a pin-hole disc the screen may be varied in position several inches without producing but little effect on the clearness of the image, since it is but slightly farther from the center of curvature of the waves than before; while with the focused pencils the removal of the screen ^ in. places it just that distance farther from the center of curvature. THE PRENTICE RETINOSCOPE. This is an instrument being manufactured by the Geneva Optical Co., of Chicago, that seems to embody all the valuable principles of a mechanical character embraced in other devices. It has the same principle of tilting the mirror in any axis re- 206 SKIASCOnC DEVICES AND INVENTIONS. quired as Dr. Fuller's invention; it has a lens holder essenti- ally the same as the Hardy skiascope; the intervals are fixed by a system of tubing that confines both the incident and emergent pencils of light; a plane or concave mirror is equally available; a means of inserting a disc giving any desired form to the luminous area, or a lens to neutralize or partly neutral- ize the incident pencils, is provided in the space of the first in- terval; and the tubing is lined with light-absorbing surfaces. Fig. G9. and contains intercepting diaphragms to reduce the pencils of light to the dimensions needed for the purpose of preventing cross waves and reflections. Light may be provided by an in- candescent gas film, electric light or by an acetylene gas lamp. SKIASCOPIC DEVICES AND INVENTIONS. 207 Tig. 68 illustrates a cross-sectional view of the instrument, and Fig. 69 its general appearance. It may be modified in some particulars, but the details as shown will probably not be changed essentially. The observed and observing eyes are, when at the respec- .tive eye cups of the instrument, 20 inches apart, and therefore a + 2 D. lens is necessary to neutralize the distance of the ob- server, or to focus the emergent pencils in emmetropia at his eye. With the instrument the pupillary display is wonderfully distinct, and a dark room is not, of course, required in its oper- ation. Its delicacy is shown by the fact that the insertion of a .13 D. lens will produce distinct reversal. The present instrument does not provide the means for bringing out the most distinct banded appearance in astigma- 208 SKTASCOPIC DEVICES AND INVENTIONS. tism, although with a small opening before the light and one meridian neutralized, the band is plainly seen. An improve- ment in the incident tube by which a movable lens of about + 8 D. could be placed in any desired position from 8 in. to 4 in. of the light would give the means of controlling the position of the light or the source of the incident pencils so as to make the bands the most distinct. Such improvement would, however, increase the cost of the instrument as an achromatic lens would be necessary for the purpose. The in- strument in its present form is, however, a very delicate test for every form of ametropia. The provision in the instrument for controlling the ac- commodation of the eye under examination is an eye clip con- taining a cell for the insertion of a strong positive lens to be placed in front of the second eye of the patient. This would be used only in cases of probable hyperopia with ciliary spasm. Its purpose is to relax the muscle of accommodation in the second eye and, by fixing of that eye upon some exterior ob- ject at a distance, upon the principle of association known to exist between accommodation and convergence, to control the accommodation of the eye under examination. Fig. 70 shows a skiascope invented by Dr. F. G. Murphy, of Kansas City. The model consists mainl)' of a revolving disc, 22 inches in diameter, containing 34 lenses. This disc is placed at the end of a horizontal rod, which rests on a fulcrum and enables the operator to move the lens in front of the patient's eye in any direction. There are 17 plus and 17 minus lenses. An improved chin-rest is another feature. THE RETINO-SKIAMETER. Fig. 71 shows an instrument invented by A. Jay Cross, of New York, for use in connection with the skiascopic mirror. It has been named a retino-skiameter, which expresses its func- tion as a retinal shadow measure. As the illustration shows, it resembles in shape a long-handled opera glass and is some- what similarly operated. The purposes which it is intended to serve are (i) to increase the size of the pupil so that it can be distinctly seen at a distance of one or more meters away; (2) to overcome extraneous light-reflections without interfering SKIASCOPIC DEVICES AND INVENTIONS. 209 with the refractive value of the lens used, and (3) to control the strength of the spherical and cylindrical lenses desired. The magnification or apparent enlargement of the pupil is a condition much to be desired by the skiascopist in certain cases, and Mr. Cross claims that his invention will effect such Fig. 71. enlargement. The use of the retino-skiameter will also permit the skiascopist to remain at a fixed distance from the patient, and he is thus enabled to note any slight rotation in lens power without having to alter his position in order to change the lenses. With one hand the skiascopist controls the mirror, and with the other he governs the lens power of the retino- skiameter. THE DE ZENG LUMINOUS RETINOSCOPE. An improved retinoscope, invented and manufactured by Henry De Zeng, is shown in the illustration on the next page. Among the imperfections of retinoscopes have been insufficient illumination and consequent difficulty in getting a good reflex, and trouble in connecting the mirror and the light for the purpose of illumination. The new retinoscope has everything combined, mirror, light and electric battery. The instrument, as shown in the cut, has a mirror and small electric light of 2-candle power; the two being so nicely and ingeniously fixed together that the operator, looking from 2IO SKIASCOPIC DEVICES AND INVENTIONS. behind the screen, can easily see and examine the eye, which is nicely illuminated. The condensing lens, located between the electric lamp and the reflector, being adjustable, as shown in the illustration, the effect of either a plane or concave mirror can be readily obtained, with any size light beam de- sired. As the electric light in the retinoscope can be given more or less current through the adjustment of its regulator, a bright, medium or faint illumination can be had at will. APPENDIX. Abbreviations, Symbols and Designating Letters. Area i The luminous area. Area 2 The skiascopic mirror. Area 3 The retina of the observed eye. Area 4 The retina of the observing eye. Ace The accommodation. B. E Both eyes. Cm Curvometer. cm Centimeter. D Diopter. D. P Dynamic Power. Interval i . . Space from area i to area 2. Interval 2. .Space from area 2 to area 3. Interval 3.. Space from area 3 to area 4. m Meter. mm Millimeter. S. P Static povirer. a Coefificient of wave speed or of wave length in air. 6 Coefficient of wave speed or wave length in refracting medium (a?). c Difference (o-^) between a and &• c/6 Ratio of resistance in x to resistance in air =: index of refraction. c/a Ratio of curvature to dioptry at anterior surface of lens. o/h Ratio of curvature to dioptry at both surfaces of lens. I -\- cfb Equivalent of a/6, index of refraction. 14 211 212 APPENDIX. ni Designating angle of incidence. n Designating angle of refraction. Designating angle of deviation. r Designating surface of cornea. r' Center of curvature of >'• s Anterior surface of crystalline lens. s' Center of curvature of s. t Posterior surface of crystalline lens. t' Center of curvature of t- X Refracting medium. - Static dioptry of emmetropia. + Positive or plus. — Negative or minus. = Sign of equality. 3 Combined with. : Ratio, or sign of division. :: Proportion, or sign of equality. ■J./ Radical sign, indicating square root of number under. Glossary of Optical Terms. Aberration (i) Spherical aberration is the difference in refrac- tive effect, and therefore of the position of the focus for different points in one meridian of a spherical lens. (2) Chromatic aberration is an effect analagous to chem- ical action at each point in a refracting surface, by which each point in a wave, or its energy, is dissolved or separated into chromatic or color elements. (3) Astigmatic "s^i^xxdlxov^. See " astigmatism." Accommodation — The capacity of the eye to increase and decrease its dioptric power within a certain range. The dynamic power or refraction of the eye. Actinic or Aplanatic Lens. — A lens so composed that spherical and chromatic aberration are neutralized or reduced to the minimum. Aerial Image. — An image in air. Ametropia — That condition of an eye, or of its dioptric media in which its static refraction is pot adapted to focus neutral waves, or pencils of light at the retina, particularly at its most sensitive area, the macula lutea. Aqueous Humor. — The transparent fluid that fills the anterior cavity of the eye-ball — that part between the cornea in front, and the crystalline lens and suspensory ligament posteriorally. Asthenopia. — Painful vision due to excessive use of the accom- modation or convergence. Astigmatism. — Difference in the refractive effect, and therefore of the focus of different meridians of an eye or lens, due to differences of curvature in the different meridians. It is analagous to spherical aberration, but applies to different meridians. See " aberration." Axis. — (i) Principal z.yA'5, of lens is a straight line passing through the poles of its two surfaces, and through the optical center and nodal points. (2) SecoJidary axis of a lens is directed anteriorally to anterior nodal point and posteriorally to posterior nodal point, but within the lens passes through the optical center between the nodes. 213 214 GLOSSARY, (3) Optic axis of the eye, a straight line, extension of that diameter of the eye which passes through the anterior pole of the eye or center of the cornea. (4) Visual axis — that line which joins object with nodal point and yellow spot of the eye. Binocular Vision The vision of the two eyes of one person by which two retinal images are fused and projected as one object. Choroid. — The middle tunic or coat of the eye. Chromatic. — Pertaining to color. See "aberration." Ciliary. — (i) Ciliary muscle — the muscle of accommodation. (2) Ciliary processes — the convolutions of the anterior margin of the choroid. Conjugate Foci Points having such a position, with reference to a lens or mirror, that each is the potential focus of a pencil of light from the other. Convergence. — The act of turning both eyes in towards a point in the median plane. Cornea. — The transparent anterior coat or surface of the eye. Crystalline Lens. — The bi-convex lens of the eye, suspended between the aqueous and vitreous humors directly back of the pupil. Curvometer. — Unit of curvature. The inverse of the radius in meters, representing the degree of curvature of a curved line or surface or the amount of curvature in a given arc or area. Cylinder. — A solid generated by the revolution of a rectangle upon one side as an axis of rotation. Diffusion. — The development upon a screen of the waves of a system of pencils of light when the screen is not at the focal area of the pencils. Diopter. — The unit of refractive power, as measured by a lens of one meter focus. Divergence. — The separation of the rays of a pencil of light. Emmetropia. — That condition of an eye and its dioptric media in which its static refraction focuses neutral waves of light, or pencils from the distant object, at the retina, particularly at its most sensitive area, the macula lutea. Focus — The center of curvature of a series of concave waves of light, the point at which the waves are naturally transposed into convex waves by passing their center of curvature. It is the assemblage of the foci of a system of pencils of light from the same object upon a contiguous area or surface that consti- GLOSSARY. 215 tutes a real image. At the focus the molecular activity at the point of origin of the waves is reproduced in character, though not in intensity or degree. (i) Conjugate foci. See " conjugate foci." (2) Potential foci. The points at which concave waves are centered, though modified or recentered before reaching them — virtual, temporary or transitory, but not actual foci. (3) Negative foci. A term applied, but with little pro- priety, to new centers of curvature of recentered convex waves. Also called virtual, though with little virtue. (4) Principal focus. The term is convenient, though inappropriate, to express the focal distance of neutral pencils modified by a plus lens. Hypermetropia or Hyperopia. — That condition of an eye and of its dioptric media in which, without the use of the accom- modation, the potential foci of the neutral pencils are posterior to the retina. Index. — (i~) Index of Refraction. The ratio of the sine of the angle of incidence to the sine of the angle of refraction {alb). (2) Index of Resistance. The ratio of the resistance of a medium to the resistance of air as a standard, measured by relative wave speed or wave length (^cijb). (3) Index of Deviation. — Ratio of the sine of the angle of refraction to the sine of the angle of deviation {cjb'). (4) Index of Dioptry. — R3tio of dioptric power of lens to curvature of glass or other refracting medium {clb). Iris. — The curtain of the eye, suspended in the aqueous humor between the cornea and crystalline lens, but always in contact at its pupillary margin, with anterior surface of the latter. It contains a central opening or perforation, and two systems of muscles, by which the opening (pupil) may be enlarged or contracted. The iris gives the eye its color. Lens. — An optical instrument, usually of glass, with one or both surfaces ground in spherical or cylindrical form, so as to give it a dioptric power or capacity to modify the curvature of the waves of light transmitted through it. A compound lens is a lens having a spherical and a cylindrical face on opposite sides. See " toric, periscopic." Macula. — The small area of the retina, directly posterior to the optical center of the eye, known also as the yellow spot (the macula lutea). It is the most sensitive area of the retina. Major. — Larger, and including minor parts, as major pencils of light. 2l6 GLOSSARY. Meridian. — The arc (usually semi-circumference) of a great circle passing through or to the poles. It has the same curvature as the surface in which it lies. Meter. — The French unit of measure, equal to 39.37 English inches, or about 40 inches. Minor. — Smaller, and included in the major, as minor pencils of light. Monocular. — Pertaining to one eye alone. Mydriatic. — A drug used to dilate the pupil and paralyze the muscle of accommodation. Myopia. — That condition of an eye and of its dioptric media in which its static refraction focuses neutral pencils of light forward of the retina. Nodal Point. — A point on the principal axis of a lens toward which an incident or emergent ray is directed to either side of the optical center of the lens through which the ray passes. Optical Illusion. — A sensation having a nervous foundation, or due to a bona fide retinal image, or the motion of an image upon the retina, but by some anomalous means not usually encountered in nature. The science and art of measuring errors of refraction. Optometry. — The science and art of measuring errors of refraction. Pathology. — Pertaining to diseases and diseased conditions. Periscopic. — A lens having a convex and a concave surface, but of unequal curvatures. Punctum Proximum. — The nearest point of distinct vision with full accommodation. Punctum Remotum. — The farthest point from which rays of light must come, or appear to come, in order to focus at the retina of the resting eye. Pupil. — The round opening in the iris through which pencils of light are admitted to the crystalline lens and posterior part of the eye. Refraction. — Modification of the curvature of a wave of light produced by the passage of the wave from one medium into another of different resistance or conductivity through a surface not conforming at all points with the wave. Retina. — The nervous coat of the eye ; the net-work of nerves ; an expansion of the optic nerve, upon which, in emmetropia, neutral pencils of light are focused, producing the image, and where the stimulus of the focused pencils is transmitted into nerve energy, by which vision is awakened. GLOSSARY. 217 Skiascope. — The mirror with a perforation used in skiascopy ; also applied to a device for conveniently and quickly changing the lenses before the eye under examination. Skiascopic Chimney. — Chimney of asbestos used in skiascopy to limit the area of light and give form to the luminous area. Skiascopy. — The science and art of determining the refractive condition of an eye by observing objective phenomena in the pupil of the eye examined when light is reflected into it from a mirror. Static Refraction. — The refraction that form and resistance gives without action being put forth, as the refraction of the eye without the use of the accommodation. Suspensory Ligament. — The ligament by which the crystalline lens, enclosed in its capsule, is suspended back of the pupil. Subjective. — A test in which the vision of the subject reveals the dioptry of the eye, and therefore a test in which the optician depends upon the statements of his patient as to what he sees. Toric. — A surface having a maximum of curvature in one meridian and a minimum of curvature in the meridian at right angles to it. A toric lens is a lens so ground that one surface is toric. In dioptric value it is equal to a compound lens having a spherical surface on one face and a cylindrical surface on the other. Vitreous Humor. — The transparent fluid that fills the posterior cavity of the eye, the space back' of the crystalline lens. W^aves. — Undulations of molecules. A wave consists of the unison of movement in a superficial extent of molecules equi- distant from a common center of disturbance or activity. Zone. — A symmetrical area of a spherical surface bounded by great or small circles parallel to each other. INDEX Aberration . . 65, it", 99, 143, 146, 159, 180 Test of 179 Absolute Condition 162 Accommodation 72, 144, 170 Active 133 Passive 133 Stimulus of 147 Watching the 190 Acetylene 206 Actinic 144 Ametropia 25, 72, 149 Aqueous Humor 75 Area of Reversal 30, 38, 91, 123 Asthenopia 192 Astigmatism 72, 139, 164, 171 Compound Hyperopic ... 42, 74, 167 Compound Myopic 45 Correcting 178 Irregular 181, 182 Mixed 45, 169 Regular 36, 164 Simple Hyperopic 41, 74, 166 Simple Myopic 44 Axial Ray 55 Axis of Rotation 200 Cvlinder 169 Visual 30 Banded Appearance 38, 172 Binocular 192 c Choroid 120, 134 Ciliary 134, 147 Concave 20, 53 Conjugate Foci 95 Convergence 20, 29 Convex 20, 53 Cornea 75, 79 Conical 181 Correcting Lenses 139 Crain, Dr 198 Cross, A. Jay 208 Crystalline Lens 19, 75, 134 Curvometer 49, 57 Cylinders 37, 40, 59, 169 Cross 170, 181 Law for 164 D Data, Official 75, 76, 77, 78 Difl'usion 19, 60, 95 Diopter 57, 59 Dioptric Media 18, "1, "4, 75 Dioptry 72 D've'gence 20 Dvnamic , 15, 72, 130, 131 Ktlects 131 Factors, Chapter VI 26 Emergent 20, 126, 17a Emmetropia .... 20, 71, 124, 125, 149 Evolution 49, 83, 93 R Finite 19, 5S Focal Area 88, 135, 136 Focus 23, 92, 94 Conjugate Foci 95 Potential Foci 19, 21, 95 Fuller, Dr 200 H Handling the Lenses 190 Hardv Skiascope 197 Hyperopia . 21, 73, 149 I Image, Real 23, 25, 29, 55, 115 Aerial 25, 29, 155 Potential 123, 152, 156 Retinal 23, 29, 55 Virtual 27, 55, 115 Incident Pencil 20, 35 Index of Resistance 61 Infinity 53, 141 Initial Appearances 150 Intervals 127 Changing the 137 Fixing the 202 Inversion 28, 100 » Iris 55, ISO ' Jackson, Dr 104, 151 Jennings' Skiascope 200 Law of Wave Curvature 49 Of Cylinders 164 Of Images 142 Of Wave Speed 61 Lens 57 Bi-convex 51, 60 Compound 122 Holders 196 Negative or — .... 31, 59, 121, 160 Periscopic 66 Plano-convex 67, 68 INDEX 219 Lens Positive or + 31, 57, 121, 160 Primary 35 Spherical 37, 40 Light on the Face '2.1 Limitations 175 Luminous Area 15, 18, 110 M Macula 71, 119, 146 Magniticatiou 60, 102 Major 27 Meridan 36, 122, 164, 171 Meter (see Glossary) 59 Minor 27, 55 Mirror 27, 113 Centimeter 175 Circular 18 Concave .... 69, 113, 163, 176, 178 Plane . 113, 177 Tilting the 27, 131 Momentum 130 Monocular 191 Morton Ophthalmqscope 200 Motion of Keflex, With .... 15, 121, 160 Against 15, 121, 160 At Luminous Area 339 Cause of Rapidity 33, 156 Rapidity of 32, 121, 171 Mydriatic 190 Myopia 20, 22, 23, 24, 34, 153 IV Negative ... 53, 56, 57, 93 Neutral 20, 53, 56 Neutralization 15, 57, 141 Of Incident Pencils 204 Nodal Point 91 Nomenclature 48, 53 Notation 48, 59 o Objective 148, 151 Observer 17 Observed Eye 17, 18, 118 Observing Eye 17, IS, 120 Operating Room 183 Optical Illusion 13, 122 Opticist 17 Optometry 14 Pathology 182 Pencil of Light 20, 47, 48, 116 Convergent 20, 29 Divergent 20 Emergent .... 20, 23, 35, 41, 116, 173 Incident 20, 23, 35, 41, 116 Major 27 Minor 27 Natural 75 Negative 121 Neutral 20 Positive 121 Periscopic 66 Phenomenon . . . " 15, 56, 126 Position of Liglil 23, 137, 146, 203 Positive . ,53, 57, 93, 121 Potential Foci 20 Power and Curvature 60 Practical Operating I85 Prentice Retinoscope 205 Proving Results , , 191 Punctum Proximum 73, 104 Remotum . 73, 104 I'upil isl 123,' 148 Pupillary Display 19, 148, 171, 182 Pupillary Plane 123 R Ratio 50, 51 Real Focus or Image 23, 25, 29, 55, 92, 115 Reflex 15, 150 Refracting Surfaces 63-70, 74 Refraction, Static 76 Dynamic 78, 80 Index of 61, 75 Negative 56 Of the Eye Chapter III Positive ; 56 Retina 148 Retinoscope 196 The Prentice 205 Retinoscopy 196 Retino-Skiameter 208 Reversal 15, 31, 86, 90, 126 Schematic Eye 33, 193 Scissors Movement 158 Sine 49, 64 Skiascope 18, 117 Skiascopic Chimney Ill Skiascopy ....." 16, 17 Static '. 15 Factors 26, 130 Subsidiary Areas 126 Intervals 129 Suggestions to Beginners 192 Suspensory Ligament . , . 134 T The Initial Condition 150 Thorington Eve 194 Toric . . . . ■ 164 Transposition , 53, 54 V Virtual 27, 75 Visual Area 158 Vitreous Humor 75 w Waves of Light, Convex 20, 53, 54, 83, 125 Concave 20, 53, 54, 125 Natural 75 NegatiM' 54, 94 Neutral 20, 53, 125 Plane 93 Positive 54 Spherical 48, 63 Zone 158, 180 Zonular 146, 158 THE OPTICIAN'S MANUAL VOL. I. By C. H. Brown, M. D. Graduate University of Pennsylvania ; Professor of Optics and Refraction ; formerly Physician "in Philadelphia Hospital; Member of Philadelphia County, Pennsvlvauia State and American Medical Societies. Chapter I. Chapter II. Chapter III. Chapter IV. Chapter V. Chapter VI. Chapter VII. Chapter VIII. Chapter IX. Chapter X. The Optician's Manual, Vol. I., has proved to be the most popular work on practical refraction ever published. The knowledge it contains has been more effective in building up the optical profes- sion than any other educational factor. A study of it is essential to an intelligent appreciation of \'ol. II., for it lays the foundation structure of all optical knowl- edge, as the titles of its ten chapters show : -Introductory Remarks. -The Eye Anatomically. -The Eye Optically ; or, The Physiology of Vision. -Optics. -Lenses. -Numbering of Lenses. -The Use and Value of Glasses. -Outfit Required. -Method of Examination. -Presbyopia. The Optician's Manual, Vol. I., is complete in itself, and has been the entire optical education of many successful opti- cians. For student and teacher it is the best treatise of its kind, being simple in style, accurate in statement and comprehensive in its treatment of refractive procedure and problems. It merits the place of honor beside Vol. II. in every optical library. Bound in Cloth— 422 pages— colored plates and illustrations. Sent postpaid on receipt of S&. OO ( 8s . 4 th^ Published by The Keystone, THE ORGAN OF THE JEWELRY AND OPTIC.A.1^ TRADES, 19TH & Brown Sts., Philadelphia, U. S. A. THE OPTICIAN'S MANUAL VOL. II. By C. H. Brown, M. D.