.\ME -UNIVERS^ O Q; v^lOSANGflfj> o ^ "^ I l^ni A\\EUNIVER% vjclOS ANGELA cc X, ^-^ * -S /, ^ ^ ^ ^OJIIVDJO^ ^KWITVJJO^ H^cAUfoefe ? x-^X. X ^OFCAIIFO^ ^40S-ANKl&> cp ^ -^"^ "^* ** o ^clOS ANGELA ^clOS ANGEL ,-\\\E-UNIVERS/A. ^clOS-AMCEl% <. c^ <>> ^ - *. "^ Sl^5 1 1 5 S 3-|! irl or-l liinr THEORETICAL AND PRACTICAL TREATISE ON ASTIGMATISM BY SWAN M. BURNETT, M. D., Professor of Ophthalmology and Otology in the University of Georgetown , Ophthalmic and Aural Surgeon to the Garfield Hospital, and Director of the Ophthalmic and Aural Clinic at the Central Dispensary and Emergency Hospital, Washington, D. C. WITH FIFTY-NINE DIAGRAMS AND ILLUSTRATIONS. 1887. J. H. CHAMBERS & CO., PUBLISHERS AND DEALERS IN MEDICAL BOOKS, 3fr. Louis, Mo. COPYRIGHTED 1887 BY J. H. CHAMBERS. ALL RIGHTS RESERVED. 1.981 TO THE READER. The addition of one more medica) book even though it be a small one to the scores that are annually issued from the press, carries with it a demand, on the part of the reading pub- lic, for its raison d'etre. The cause of the existence of this little work has its founda- tion in my own needs as developed in my studies of refractive anomalies, and in my conception of the needs of others as manifested to me during the last eight years as a teacher of general and special students and general practitioners. An examination into the statistics of eye-affections shows that the various anomalies of refraction form about one-third of the whole number of eye cases presenting themselves for treatment in private practice, and of these two-thirds, or about 2O C / C of the whole, suffer from astigmatism in an appreciable degree. No one, then, I think, will deny to astigmatism the worth of a treatise special to itself, particularly when there is taken into consideration the great difficulty encountered in clearing away the perplexities, uncertainties and paradoxical manifestations which enshroud many cases of the anomaly, and which are the despair of the beginner in refraction studies. - And, while fully aware that Time and Patience are two most important and indispensible factors in unraveling the tangled threads of evidence, it cannot be doubted that nowhere in the whole range of medical practice, is accurate knowledge, based on positive science, of such avail as in the diagnosis of astigma- tism. To lead to such accurate knowledge through the paths of positive science has been the chief incentive to my labor. The preliminary chapter, embracing the fundamental prin- ciples of optics which are needed for a clear comprehension of what follows, was introduced because experience shows that IV TO THE READER. most students of medicine in this country are lacking in such knowledge. No one can more fully realize than I the almost impossible task of giving a concise yet perfectly clear exposi- tion of optics in a single chapter. Those, therefore, to whom my work appears not sufficiently elementary, I would refer to the appendix to Dr. Loring's "Text-book of Ophthalmoscopy," and to a most excellent and remarkably simple and lucid "Treatise on Simple and Compound Ophthalmic Lenses," by Chas. F. Prentice, of New York, where they will find the sub- ject treated of in the simplest form possible, while those desir- ing a fuller application of these laws will do well to consult the first part of the translation of Dr. Landolt's treatise on the " Refraction and Accommodation of the Eye ;" three works published since this treatise has been in type. One word in regard to the bibliography. Without asking any undue indulgence for its imperfections and shortcomings* we would call to the mind of the captious critic the apothegm of an old and experienced bibliographer: "If a man have a pride of accuracy, and desires to be cured of it, let him make a bibliography." I trust that our labors in this regard may not be without value, particularly to the future writer on the subject, for we believe that, in that far away time, should the New Zealander, prowl- ing among the ruins of the great medical library on the banks of the Potomac, stumble on a copy of this work, he will find recorded there the title of every important paper on the subject that has appeared up to the year of Grace 1886. I desire to return publicly my acknowledgment of valuable assistance in the construction of the work the bibliography in particular received from my former assistant, Dr. Louis Kolipinski. SWAN M. BURNETT. 1734 K ST., WASHINGTON, January, 1887. TABLE OF CONTENTS. CHAPTER I. Definition of astigmatism Fundamental laws of optics Re- fraction by spherical surfaces Formation of images by convex refracting surfaces Test glasses and their number- ing. - 1-13 CHAPTER II. Refraction by ellipses, spheroids and ellipsoids Focal Interval of Sturm Character of the focal lines Cylindrical glasses. H-37 CHAPTER III. Astigmatism in the human eye History of corneal astigma- tism The different forms of ametropia Varieties of as- tigmatism. 38-54 CHAPTER IV. Diagnosis of astigmatism Determination of its form and de- gree and the direction of its principal meridians. 5 5-62 CHAPTER V. Difficulties and obstacles in the way of an accurate diagnosis of astigmatism Influence of accommodation The use of mydriatics. - 6373 CHAPTER VI. Other subjective methods of examination Change in the form of a point of light Adaptation of Scheiner's experiment The Stenopaic slit Modifications of Snellen's fan Op- tometers. 74-88 VI CONTENTS. CHAPTER VII. Objective methods of examination The ophthalmoscope as a means of diagnosis in astigmatism. - 89-114 CHAPTER VIII. Skiascopy (the shadow-test.) 1 15-123 CHAPTER IX. Keratometry and keratoscopy. - 124-138 CHAPTER X. Symptoms of astigmatism. 139-146 CHAPTER XI. Causes of astigmatism Lenticular astigmatism. - 147-154 CHAPTER XII. Correction of astigmatism. 155-176 CHAPTER XIII. Irregular astigmatism Conical cornea. - 177-204 Note to Section 196; pp. 170-171. 203-205 Appendix A statistical record of 806 astigmatic eyes. 206-231 LIST OF ILLUSTRATIONS AND DIAGRAMS. Fig. 1. -Different forms of spherical lenses - 2 Fig. 2. The formation of a spherical plano-convex lens 3 Fig. 3. Refraction of rays by a simple convex surface - 5 Fig. 4. Cardinal points of a bi-conxex lens 6 Fig. 5. An image formed by a convex refracting surface - 8 Fig. 6. An ellipse 15 Fig. 7. Refraction by the sharper end of an ellipse 17 Fig- 8. Refraction by the blunter end of an ellipse - 18 Fig. 9. Refraction by a spheroid - - 19 Fig- 10. Lines formed by the normals to a triaxial ellipsoid 21 Fig. 11. Character of the focal lines in a triaxial ellipsoid 24 Fig. 12. Sections of Sturm's interval at its various parts 27 Fig. 13. Formation of the focal interval of Sturm - - 28 Fig. 14. Formation of a cylindrical lens 3o Fig. 15. Refraction by a cylindrical lens - - 31 Fig. 16. A concave cylinder - 31 Fig. 17. The elliptical form of the cornea - - 40 Fig. 18.- Form of the focal curve of the normal cornea 41 Fig. 19. Emmetropic and ametropic eyes compared - 49 Fig. 20. Diagrammatic representation of the direction of the axis of an astigmatic meridian - 58 Fig. 21. Method of recording a case of compound astig- matism - 59 Fig. 22. Distant point of light as seen by an astigmatic eye 75 Fiir. 2M. Schemer's experiment 78 Fig. 24. Test-types of Pray 82 Fig. 25. The clock-face of Green. 84 Fig. 20. Direct method of examination with the ophthal- moscope 91 Fig. 27. Jager's inaccurate drawing of the fundus of an astigmatic eye - 95 Fig. 28. Appearance of the fundus ot an astigmatic eye as seen in the direct method of examination - - 97 Fig. 29. Refraction ophthalmoscope with a clip for the in- sertion of cylindrical lenses - 100 Fig. 30. Formation of the actual inverted image in the in- direct method of ophthalmoscopic examination - 101 Fig. 31. Change in the size and position of the real image of the hypermetropic eye in the indirect method of ophthalmoscopic examination 103 Viii LIST OF ILLUSTRATIONS AND DIAGRAMS. Fig. 32. How the real image of the myopic eye varie- in size on removal of the auxiliary lens, in the indi- rect method of examination - 1" Fig. 33. Fondue of an eye with mixed astigmatism, when the auxiliary Ions is held close to the cornea 1 (I 7 Fig. 34. Same, where the auxiliary lens is at a great di- t a nee from the cornea 1"^ Fig. 35. Optical principles on which skiascopy is base- 1 1 It; Fig. 36. How the shadow in skiascopy moves across the pupil when the meridians in astigmatism are oblique 1 ~2 1 Via. 37. The ophthalmometer (keratometer) of Javal and Schiotz (after Java 1, 126 Fig. 38. Appearance of the corneal image of the bands in tin- keratometer (after Javal) - 130 Fig. 3!). The keratoscope of Placido Fiir. 40. Wecker' square (after Wecker) - -135 Fig. 41 . Figures for determining the amount of change in the corneal reflection of Wecker's square (after Wecker) 135 Fig. 4 1'. Mryrmvit/'s trial frame (Meyrowitz) 1 "'> Fiir. -I-"-.- Diagram for recording astigmatism - 159 Fig. 44. Effect of a cylindrical lens on the refraction of the sharper end of an ellipsoid where the periph- eral rays of the two meridians are brought together 166 Fig. 45. Another effect of the same 1'>7 Fig 4">. Refraction by the blunter and sharper end of an ellipsoid corrected by a cylinder 1 1^ Fig. 47 Sectorial construction of the human crystalline lens 1 7 s Fir. 4s. Spectrum of the authors crystalline lens 17'.* Fig. 4!>. Appearance of a distant point of light to the au- thor's right eye - 1 s " Fig. 50. Polyopia monocularis (after Helmholtz) 1 s 1 Fig. 51. Keratoseopic appearances in central corned opacity - 1^4 Fig. 52. Same, in small corneal infiltration - 1^:. Fig. 53. Same, in cystoid cicatrix - -185 Fig. 54. Same, after cataract extraction 1^7 Fig. 55. Same, in ophthalmo-malacia 1^ Fig. 56. Lateral view of conical cornea (after Wardrop) I'.rj Fig. 57. Disk and large vessels in kcratoconus in the di- rect ophthalmoscopic examination - lie! Fig. 58. Keratoscopic images at various parts of a con- ical cornea - 1!4 Fig. 50. Keratoscopic images in conical cornea 1J5 CHAPTER I. DEFINITION OF ASTIGMATISM FUNDAMENTAL LAWS OF OPTICS REFRACTION, BY SPHERICAL SURFACES FORMATION OF IM- AGES BY CONVEX REFRACTING SURFACES TEST GLASSES AND THEIR NUMBERING. I. ASTIGMATISM is a condition resulting from any irregu- larity in the refraction of an optical apparatus which renders impossible the formation of clear and distinct images of ob- jects in all their parts. 2. In order to satisfactorily study this irregularity in re- fraction, it will be necessary to first understand those laws which have been found to govern refraction by surfaces having a regular, spherical form. To this end it will be well to call to mind here, at the begin- ning, some of the elementary principles of optics, since they form the foundation of all that follows, and will be indispensa- ble to beginners for their further study of the subject before us. We should bear in mind that: a. From every point of an illuminated object there go out luminous rays in every direction free to the passage of light. b. These rays of light move always in straight lines, even when thrown out of their original course by reflection or re- fraction. c. Rays of light, while always mathematically divergent, when they have arrived at a distance of eighteen or twenty feet from their source, can be, for all practical purposes, con- sidered parallel, and they remain so for an infinite distance. For the lenses in common use in ophthalmology, and for the eye itself, therefore, all distances greater than twenty feet are practically infinite. The laws governing reflection and refraction are few and (52) 2 LAWS OF REFLECTION AND REFRACTION. simple. The law of reflection is that the angle of reflection is equal to the angle which the incident ray makes with per- pendicular to the reflecting surface at the point of inci- dence. The angle (or amount) of refraction is governed by two con- ditions, i) the angle which the incident ray makes with the perpendicnlar to the refracting surface at the point of inci- dence, and 2) by the index of refraction (or density) of the re- fracting medium. All questions in optics, however complicated, must finally be brought into harmony with these few general iaws for their perfect solution. As in astigmatism we have to do mostly with refraction, we shall pass by any consideration of the laws of reflection as ap- plied to optical apparatus. Fig. i. DIFFERENT FORMS OF SPHERICAL LENSES. A, Plano-convex. B, Plano-con- cave. C, Double-convex. D, Double concave. E, Convex meniscus, f, Concave meniscus. 3. The function of every optical appliance is to change the course of the rays of light falling upon it from a source of illumination, and, usually, in such a manner, that there shall be formed an image of some object. The optical apparatus with which we have to do in refrac- tion are called lenses, because they are usually of a shape somewhat resembling the seed of a lentil. Those in common use are divided into two general classes, called convex and concave, according to the character of their curved surfaces. A,\in Fig. i is a convex lens, R is a concave lens. DIFFERENT FORMS OF SPHERICAL LENSES. 3 In these it will be noticed that one surface is curved while the other is straight or plane they are therefore called plano- convex and plano-concave, to distinguish them from those which have both surfaces curved as in C and D, and which are called from this circumstance double (or bf) convex and double (or bi] concave respectively. The forms E and F are called meniscuses because of their fancied resemblance to the moon at its quarter. In meniscuses both surfaces are curved in the same direction. When the concavity is predominant it is called a concave meniscus, F; when the convex curve is in excess it is called a convex meniscus t E. All convex lenses are also desig- nated as plus (+), positive or collecting, and all concave lenses as minus ( ), negative or dispersing. Fig. 2. f The formation of a Spherical plano-convex lens. It will be observed that the curved surface in all these lenses is regular, like that of a globe or sphere, and for this reason they are called spherical. It is to be remembered that these drawings represent only meridional sections of the lenses. It is characteristic of the spherical lens that the sections made in all its diameters or meridians are similar, and therefore the curvature of its various meridians must be the same. 4. All lenses of this character, therefore, are sections of a sphere as shown for the plano-convex form in A Fig. 2; and 4 CARDINAL POINTS OF AN OPTICAL SYSTEM. the radii of curvature of the lens are the radii O e , f, etc.. of the circle of which its surface forms a part. 5. The optical properties of a refracting system depend upon what are called its cardinal points, which are six in num- ber, namely: two principal foci, two nodal points and two prin- cipal points, all of which are situated on the principal axis of the system. The first princ ipal focus is the point where the incident should cross 'in order that the corresponding emergent shall be parallel to the principal axis. The second principal focus is the point of crossing of the emergent rays when the incident rays are parallel to the principal axis. These points are real or virtual according as the refracting surface is positive or negative. The principal points possess the following properties : When an incident ray, prolonged if necessary, passes through the first principal point, the corresponding emergent ray, or its prolongation, passes through the second principal point, but the incident and emergent rays are not parallel. The nodal points have this characteristic: that if an incident ray or its prolongation passes through \\\c first nodal point, the corresponding emergent ray coincides with a straight line par- allel to the incident ray and directed to the second nodal point. The planes passing through the principal foci are called the focal planes, and the planes passing through the principal points are called the principal planes. The principal planes enjoy this property: The incident and emergent rays cut the first and second principal planes in the points situated on the same side and at the same distance from the principal axis of the system. 1\\z first focal distance is the interval between the first prin- cipal point and the first principal focus; the second focal dis- ignce is the distance from the second principal point to the sec- ond principal focus. The simplest form of dioptric system is a curved surface separating two transparent media having different indices of refraction. In Fig. 3 MN represents such a surface with its center of curvatuiip at C, through which the principal axis X X' CARDINAL POINTS OF A SIMPLE CONVEX SURFACE. 5 passes. On account of its limited amplitude the curve M N can be considered as coinciding with a plane tangent to its surface at A. It is evident that any incident ray, D 7, and its correspond- ing refracted ray / G must cut this plane at the same point 7, therefore the two principal planes are one and the same, and the two principal points through which they pass are one and the 3- D S' Show ing the Refraction of Rays by a simple Convex Surface. same and must coincide with the apex A of the curved surface M N. If we draw from vS a line which passes through the center of curvature at C it will be a normal to the surface J-/ JVat 7, since it coincides with one of the radii of curvature. Any incident ray, therefore, following this direction would, after it entered the second medium, continue without deviation through C to- wards S'. C therefore performs the office of the tzvo nodal points, which are reduced to one, and, this coincides with the cen- ter of curvature. The second principal focus will be at F f , be- cause it is the point of crossing of the emergent ray 7 G when its corresponding incident ray D I is parallel to the principal axis XX 1 . Fis the first principal focus, because it is the point where the incident rays should cross in order that the correspond- ing emergent refracted ray 7 E shall be parallel to the principal 6 CARDINAL POINTS OF A BI-CONVEX LENS. axis. The focal distance that is, the intervals between these focal points and the principal points will depend on the radius of curvature and the index of refraction of the second medium. The planes passing through the focal points Fand F are called the focal planes. When the refracting system is a bi-convex lens the re- Fig. 4. CARDINAL POINTS OF A BI-CONVEX LENS. A" A" 7 , the two nodal points. D 2?, the two principal planes. O, the optical center. C C, Focal points. lative positions of the cardinal points are somewhat different. The two nodal points are found within the lens at A' K' as shown in Fig. 4. Let 5 be an incident ray which, after refraction, passes through 0, which is the optical center of the system. After it emerges as a refracted ray, /' R, it will assume a direc- tion parallel to the incident ray SI. A prolongation of the emergent ray R in the lens would strike the principal axis at REDUCTION IN THE NUMBER OF CARDINAL POINTS. / K', and a prolongation of the incident ray 5 in its original direc- tion would strike the principal axis at K. Thus K and K! fulfill all the requirements of nodal points. It has been demonstrated that any incident ray striking the plane D at a certain distance from the axis will have a cor- responding emergent ray cutting the plane D' at an equal dis- tance from the principal axis. D and D' therefore fulfill all the requirements of principal planes, and as they pass through K and K' respectively these points must coincide with the principal points. Therefore the nodal and principal points are the same. Fortunately for the study of lenses placed in air, the six car- dinal points can be reduced to two. The two principal and two nodal points being the same, and the two nodal points falling very close together they can, for glasses in ordinary use, be con- sidered as coinciding with the second nodal point; and where the medium is the same on both sides of the lens the focal distance is the same for the two sides, so that we have to do really with only the one nodal point and one focal distance. The focal distance of a lens, which is but the expression of its refracting power, is governed, as stated in the previous para- graph, by its radius of curvature and the index of refraction of the material of which it is composed. It has been found that when the glass, of which a lens is made, has a certain index of refraction 1 (1.5) the focal distance is just double the radius of curvature. When, therefore*, the lens is a double convex or concave, its focal distance is equal to its radius of curvature. 6. The action of convex and concave lenses on light is of an opposite character. Rays after passing through a convex lens tend to come together at a point in front of the lens, while rays after passing through a concave lens diverge, as though they came from a point behind the lens. It is the office of all collecting systems (of which all 1 It is commonly believed, and many very good authorities have fallen into the error, that flint glass is harder than crown glass. The index of refraction of flint glass is higher than that of crown glass, but the lead entering into its composition makes it softer. 8 FORMATION OF AN IMAGE BY A CONVEX REFRACTING SURFACE. convex lenses and the eye are representatives) to form at their foci small and inverted images of extraneous objects. By the aid of the few laws, which we have laid down in the pre- ceding sections, it is possible to show by construction, and with- out the help of any mathematical formulas, how an image of an object is formed by a convex refracting surface. We have endeavored to do this in the construction of Fig. 5. Let M N represent a curved surface separating two transpar- ent media of different densities (such as air and water), and for the sake of simplicity of construction and demonstration we will assume that the refracting power of the water is twice fig- 5- Showing how an Image is formed by a Convex Refracting Surface. that of air that is the index of refraction (*,) = 2. The center of the curved surface is 0, and Of, O e, O d, and every line drawn from the surface through O are its radii* A /> is an object from all points of which rays proceed in every direction towards M X. Now, in order to have an image of an object, the rays coming from every point of the object must be again brought to another point, and it is the function of the curved surface to do this. Let us take a bundle of rays proceeding from the point . /. Of these one will fall on the surface M N At e, one at /and one at d. We will now follow these rays after their passage into the FORMTIOX OF AN IMAGE BY A CONVEX REFRACTING SURFACE. 9 second medium. The ray A /"being perpendicular to the sur- face and passing through the center (which is the nodal point of the refracting surface) being, in fact, but a prolongation of the radius Of, suffers no refraction, but passes straight on in the direction of iv. The ray A e, however, falls upon the curve M ' N obliquely, and makes an angle with the perpendicular g O to the surface at the point of incidence e. This perpendicular is nothing more than a prolongation of the radius O e. As stated in 2, the amount of refraction which a ray undergoes depends upon the angle it makes with the perpendicular to the surface, and the difference in the refracting power of the media (index of refraction). Observation and experiment have shown that when a ray passes from a rarer to a denser medium, it is dm-ivn towards the perpendicular, and in exact ratio to the difference in their refractive powers as indicated by the index of refraction. This difference is expressed naturally by the difference in the size of the angles made by the incident and refracted rays with the perpendicular. The size of an angle is usually expressed mathematically by its sine, and the index of refraction is said to be equal to the difference of the sines. In constructing such a diagram as Fig. 5 it is easy to meas- ure the size of these angles. The angle of incidence A e g, for example, may be measured directly by means of a gon- iometer, or with e as a center we can describe the arc tv, and with the same radius the arc x' on the perpendicular g 0. The line t h let fall on the perpendicular from the incident ray is the sine of the angle x, and the sine of the angle x' must be just one-half as large that is the length of the line at x f must be half the length of / h, A line e m drawn through e and the extremity of the line at x' must then be the course of the ray A e after refraction, and it will cross the line a b at a. The course after refraction of another ray, A d, can be deter- mined by measuring the sines of the angles y and y' in the same manner, and it will be found that, if M N is a regular curve it will pursue after refraction the course d n and cross the other two rays e m andfzv at a also ; a will therefore be the focus of all the three rays. IO TRIAL I.KNSES. By a similar method of construction it can be shown that all the rays going out from A and falling on the curve M N be- tween d and e, and in fact anywhere on its surface will likcu isc be brought together at a. The point a must therefore be the image of the point A in the object A B. By the same method of construction it can be shown that all rays coming from the point C will be brought to a focus at f, which will be the image of C. By the same law all rays emanating from /> will be united at b forming there an image of that point ; and so for every point between A and B there will be a corresponding focus and image between a and b. a b will therefore be the image of A B. It will be observed that it is ///rr/'Av/and smaller than the object. M N represents only one meridian of a curved surface and A B only the section of a plane surface, but it is evident that if MN were a spherical surface curved equally in all its meridians a small and inverted image of an object on the plane A B will be formed at a b. It will be observed that with the exception of the curve MX all the lines in Fig. 5 are straight, and this in surfaces of very limited amplitude can also be practically considered as a straight line. These lines in this figure go to the construction of a large number of triangles, and since we can always know the size of the object and its distance from the refracting surface, and the index of refraction of the second medium, we can, by the ap- plication of the few simple rules of plane trigonometry, easily find the position and size of the image and its distance from the refracting surface. 1 7. In ophthalmic practice a number of lenses of different refracting powers are used for the purpose of determining the refraction of the eye and for correcting optical anomalies. This series of lenses used for examining the refraction are called trial lenses. These sets are constructed with a view to having all the glasses that are necessary with none that are 1 The simplest exposition of the elements of optics with which I am acquainted is the little volume by Prof. Gavarret of Paris on " Images par reflexion et refraction:" No translation has been published in English. THE TWO SYSTEMS OF NUMBERING GLASSES. II superfluous. In practice we seldom have use for a lens with a focus shorter than two inches, for even an aphakial eye does not often need a lens stronger than two or two and one-half inch- es focus, or longer than 160 inches, since rays become practi- cally parallel at the distance of 240 inches. The majority of trial cases in use are composed of lenses with various foci embrac- ing these two extremes. Most of them have thirty pairs of convex and the same number of concave lenses. It is advantageous to have this series with as nearly as possi- ble regular intervals between adjoining numbers. 8. There are two methods of numbering these lenses, one the inch, or old ; the other the metric, or new. The advant- age of the inch system is that it gives directly the focal dis- tance of the lens ; one of its disadvantages is that the power of the lens must be expressed in vulgar fractions. As the standard of refracting power is a lens with a focal distance of one inch ( 1 / l ) ), and as the refracting power of a lens is in inverse ratio to its focal distance, all lenses with foci longer than one inch must be expressed in fractions ; thus a lens of twelve inches focus has a refracting power of only one-twelfth ; one of eight- teen inches, one eighteenth, etc., etc. ; whereas one of one-half inch focal distance would have a refracting power of two. There are few people who can add and subtract vulgar fractions without resorting to pencil and paper, and this is a great incon- venience in the combinations of lenses which we sometimes find it advantageous to make rapidly in practice. Another dis- advantage is, that the inch has not the same length in all countries ; so that a one twentieth in Prussia or Switzerland would not be the same as one-twentieth in England and Amer- ica. It is very desirable, therefore, to have a universal uniform numbering of lenses, whose power shall be expressed in whole numbers, or decimals, so that they can be easily added and subtracted. 9. This we have in the metric system. Here the standard refracting power is a lens with a focal distance of one meter, and as it is the measure of refraction it has been called a Dioptry ( D ). A lens having twice the refracting power, with 12 HOW TO CONVERT ONE SYSTEM INTO THE OTHER. a focal distance of one-half a meter ( 50 cm.) is numbered 2 D ; one with three times the refracting power but one-third the focal distance (33 cm.) is No. 3 ; while one with one- half the refracting power but double the focal distance (two meters) is called 0.50 D; one with one-quarter the refracting power, but four times the focal distance (four meters), is 0.25 D. It is easy, however, to convert one system into the other. The meter is about forty English inches (39.37), so it is only nec- essary to divide forty by the number of dioptrics in order to have a close approximation to the corresponding focal distance in inches, thus : 2 D = *% = 20 inches ; 4 D = 4 % = 10 inches; 5 D = 4f / 5 = 8 inches, etc., etc. On the other hand, if you have the focal distance in inches, it is easy to find the number of the corresponding D, by dividing forty by the number; thus 10 inches = 40 / )0 = 4 D, 12 inches = */ 12 = 3.33 D, 5 inch = /. = g D, 10 inch = 40 />o = 4 D. The following table comprises the number of glasses usually found in trial cases expressed in dioptrics, with their focal dis- tances given both in millimeters and inches. TABLE I. Number of Dioptries. Focal Distance in Millimeters. Focal Distance in English Inches. Number "f Dioptries. Focal Distance in Millimeters. Focal Distance in F.nglish Inches. 0.25 4OOO '58 5-5 182 7-18 0.50 200O 79 6 1 66 6.6 0.75 '333 1000 52-3 39-5 5- 7 8 '43 125 5-64 4-9 1.25 800 31.6 9 in 4-4 1.50 666 26.3 10 100 3-9 '75 571 22.5 it 9' 3-6 2 500 19.7 12 83 3-3 2.25 444 '7-5 '3 77 3 2.50 400 '5-8 '4 7' ij -75 363 '4-33 '5 67 2.6 1 "'$9" 333 13.1- 16 62 2-5 ,' / 3-5 286 I 1.2 '7 59 2-3 4 250 9.9 18 55 2.2 4-5 222 8.8 20 50 1-9 5 2OO 7-9 BIBLIOGRAPHY. 13 In the following pages, whenever we shall have occasion to designate the power of lenses we shall, in order to give practice to the beginner in the use of the two systems, employ them indiscriminately; the inch system being always expressed in vulgar fractions, and the metric system in whole numbers and decimals. BIBLIOGRAPHY. Airy, Osmund Geometrical Optics, London, MacMillan & Co., 1870. Bonders, F. C. Anomalies of Accom. and Refract, of the Eye, with a preliminary Essay on Physiolog. Optics. N. Syd. Soc. London. 1864. Gavarret, J. Images par Reflec. et par Refract. Paris. 1866. Giraud-Teulon Nouvelle Etude de la Marche des Rayons lumineux dans 1'oeil. Role de chacun des mileux diopt. Ann. d'Ocul. T. 51, p. 145. 1864. Guebhard, A. Expos, elemt. des Decouvertes d. Gauss et d. Listing surles points cardinaux d. Syst. diopt. centres. Annal d'Oculist. T. LXXXI. P. 195. 1879. Haltenhoff, G. Apparat z. optisch. Demonstrat. Zehend. Monatsbl. f. Augen- hlk. XII. P. 198. Helmholtz, H. Optique Physiologique. Trad, par E. Javal et Th. Klein. Paris. 1867. Landolt, E. The Introduct. of the Met. System into Ophth. R. London Oph. Hosp. Rep. Vol. VIII, p. 632. Also in Zehend. Monatsbl. f. Augenhlk. XIV. S. 223. 1876. Mauthner, L. Vorlesungen u d. optisch. Fehler. d. Auges. Wien. W. Braumiiller. 1876. Sous, G. Trait. d'Optiq. consid. dans ses rapports avec 1'exam de Poeil. Paris. 1881. CHAPTER II. REFRACTION BY ELLIPSES, SPHEROIDS AND ELLIPSOIDS FOCAL INTERVAL OF STURM CHARACTER OF THE FOCAL LINES CYLINDRICAL GLASSES. 10. When we come to deal with a surface departing, even to a limited extent, from a spherical form, the few simple rules of refraction laid down in the preceding chapter no longer apply, and there is no one point in the image where all the rays coming from any single point of the object meet. From this circumstance such a surface is called Astigmatic (from , nega- tive prefix, and v-tf.ua, a point.) II. But there are some surfaces deviating from the strictly spherical form for whose refraction some rules can be formu- lated. These are the ellipsoids (including the paraboloids and hyperboloids). This is possible only because the outlines of ellipses follow a regular course in their conformation. All other deviations from the strictly spherical form are irregular in out- line, and refraction by such figures is governed by no rules that can be applied to a class of cases. 12. For this reason ASTIGMATISM is divided into two distinct forms: regular and irregular. * 13. There is one form of regular astigmatic surface where the curve, instead of representing the section of a sphere, is the section of a spheroid, a figure formed by the rotation of an el- lipse around one of its axes. In such a figure, every section parallel to the axis of rotation is an ellipse. All sections of such a figure parallel to the other axis and at right angles to the axis of revolution are circles. 14. Since the total refraction of a spheroid is represented by the sum of the ellipses into which it may be divided, it is of (M) GEOMETRICAL CONSTRUCTION OF THE ELLIPSE. 15 fundamental importance that we study in some detail the op- tical properties of ellipses. Geometrically, an ellipse is " a plane curve traced by a point which moves in such a manner that the sum of the distances from the fixed points is always the same. The two fixed points are called the foci of the ellipse. ' \Loomis' Analyt. Geom., sd ed., p. foj.) Fig. 6. AN ELLIPSE. A B, its Major Axis. C D, its Minor Axis. F' F, its Foci. Fig. 6 represents such a figure. A B is the diameter or major axis, and it is characteristic of it that it passes through the foci F and F and through the center of the figure 0, which is the middle point in the straight line, A B, uniting the two foci. The conjugate or minor axis, C D, is the diameter per- pendicular to the major axis A B at the center 0. The curve A C P B P' D is elliptical because the sum of the distances of its every point from F and F is the same. No matter at what place on its curve PorP r are found, the sums of PF and P F, and P .Fand P'F are always the same. It is evident at a glance that refraction by such a surface must differ from that by a sphere, since in a sphere the radius of curvature, one of the factors on which the focus of the refac- 7 ting surface depends, is the same for all parts of the curve/' while in an ellipse it changes at each successive point. In considering refraction by an elliptical surface we shall l6 REFRACTION BY ELLIPSES. have two separate forms to deal with: one in which the light falls on the sharper end of the ellipse and in the direction of the major axis A B; and the other where it falls on the blunter end, and in the direction of the minor axis CD. We have given in 6, the method for finding the direction of a ray after refraction by a spherical surface and by apply- ing the same laws here we can find the direction of any single ray after its refraction by the surface of an ellipse. We have for that purpose to know only two things, viz: the index of refraction of the refracting medium, and the angle the inci- dent ray makes with the perpendicular to the surface at the point of incidence. The second of these data we could easily get in the sphere, for we have only to prolong the radius of curvature to get the normal to the curved surface at any given point. The angle is then measured as explained in 6. But in an ellipse it is not so easy to get the normal at any given point, because there is no one center of curvature from which radii can be drawn. But there is a well-known theorem which enables us to do it quite readily. 1 According to this theorem, all circles and ellipses whose dia- meters and major axes correspond hare the same subtangcnts. We have constructed Fig. 7, which represents the sharper end of the ellipse in accordance with this theorem. Let a b repre- sent the major axis of the ellipse of which b p is a portion ; from a as a center and a b as a radius, draw the segment r s of a circle. Let i< and y be the rays parallel to the axis and inci- dent at k and /. Through the points k and / draw / c and ;/ d perpendicular to a b. These will cut the circle at q and c-, and the normals at these points coincide with lines drawn through them and the center a; and the lines x K andy / drawn at right angles to these normals will be tangents at the points q, c-. Now, if the circle and ellipse have the same subtangents b u and b t, 'To be found in any treatise on analytical geometry. Compare Loomis' "Ele- ments of Analytical Geometry," 1873, page 113. "Since the subtangent is inde- pendent of the minor axis, it is the same for all ellipses which have the same major axis; and, since the circle on the major axis may be considered as one of these ellip- ses, the subtangent is the same for an ellipse and its circumscribing circle." REFRACTION BY THE SHARPER END OF AN ELLIPSE. I/ then the lines z u and w t, drawn through u and k and t and i must be the tangents to the ellipse at the points k and z, and the lines mfand o e, drawn perpendicular to them, must be normals to the surface at the points of incidence, k and i. We have now all the requisite data, and have only to apply the law of sines, as given in 6, in order to find the course of the rays Fig. 7 . Refraction by the sharper End of an Ellipse. ig and kh. In this case, in order to have the diagram fall within reasonable limits, we have assumed a refracting index = 3. It will be seen at a glance that in the case where the rays fall parallel to the long axis of the ellipse, the ray iy, nearer the axis, crosses the principal axis, an, after refraction, in front of the more peripheral ray kv, that is to say, we have an aberration the opposite in kind to that of an ordinary spherical surface. If, however, the light falls on the ellipse in the direction of the short axis, or on the blunter end, as we have it represented in Fig. 8 (which has been constructed according to the same plan as Fig. 7), we find that the more peripherally refracted ray kp crosses the principal axis in front of the more centrally re- IS ABERRATION IN REFRACTION BY ELLIPSES. fracted ray ih ; in other words, we have an excess of the ordi- nary spherical aberration. It therefore becomes evident,//***/ if we take a series of curves passing over from the flatter to the sharper end of an ellipse, we will have in the refraction, first, an exaggeration of the spherical Fig. 8. Refraction by the blunter End of an Ellipse. aberration which id II be greater in proportion to the difference in the length of the major and minor axes diminishing until the curve becomes a circle, when there will be only the ordinary amount of spherical aberration ; then, as the minor axis becomes shorter, this aberration will still further diminish until it becomes, for any chosen rays, practically zero. As the minor axis still further shortens, the aberration passes over to an opposite kind, and the more central rays cross the principal axis in front of the more peripheral, and this will increase PARI PASSU with tlic short- ening of the minor axis. It follows from this demonstration that deviation from a spherical form does not necessarily involve a lack of focus for some of the rays, and that there is one form of ellipse in which monochromatic aberration is practically abolished. FOCAL ILTERVAL OF THE SPHEROID. 19 In every other form, however, there is a failure to focus all the rays in one point, and this monochromatic aberration in- creases with the difference between the major and minor axes of the ellipse. The foci of corresponding rays falling at equal distances from -the principle axis do not all come together forming a point, but form a line on the principal axis whose length will be in direct ratio to the difference between the major and minor axes. It is apparent, therefore, that in all figures formed by the re- volution of an ellipse about one of the axes, whether in the form of oblate or prolate spheroids, there will be, with the excep- tion of one particular case, a monochromatic aberration such Fig. 9. Refraction by a Spheroid. as to prevent the formation of clear and distinct images on any single focal plane. All rays, however, as we have seen, pro- ceeding from a point on the axis will be united after refraction at some place on that axis, and those which fall on the refrac- ting surface at equal distances on either side of the axis at the same point, since the radii of curvature are the same for all points equidistant from the axis of revolution. The rays A d and A d' in Fig. 9 will be united, in accordance with the law of refraction by ellipses, when the light falls on the blunter end as demonstrated above, at h\ the rays A c and A c' at^-, and A e and A e' at/, and so on for the whole bundle of rays coming from A and falling on the spheroidal surface d d'. The position of the foci will be in an inverse order when d d' is the sharper end of the ellipsoid. If there were an object at A, 2O TRI-AXIAL ELLIPSOIDS therefore, there could not be a distinct image of all the points of its surface on any one plane perpendicular to A B since the rays coming from each individual point would have their foci on the different planes between/and //, according to the position of their points of incidence ondd'. In the place, therefore, of a focal point there is a focal interval f h, which is measured by the distance between the focus of 'the points of least and greatest refraction on the spheroid. It is characteristic of refraction by a spheroid that while refraction in all the meridians is the same, it is not the same at all points of the same meridian. Such a form of refracting surface has its nearest representa- tive in the eye in certain forms of conical cornea, but as this condition is raiely met with in a typical form, being nearly al- ways associated with other irregularities in refraction, we will defer its consideration in detail until we treat of irregular astig- matism. 15. Those spheroids formed by the revolution of an ellipse about one of its axes are sometimes called bi-axial ellipsoids in order to distinguish them from another form of ellipsoid called tri-axial. The latter is also sometimes called a compressed spheroid, because if a spheroid be compressed in the direction of its minor axis so as to shorten it in that meridian, we would have a figure with a major axis and two minor axes, all of dif- ferent lengths. If we make a section of the base of such a figure, we have, instead of a circle as in the spheroid, an ellipse, as shown in Fig. 6, in which A B would be the long minor axis, and CD the short minor axis, the major axis passing through and the apex of the figure. Moreover, it would follow that there would be a meridian of greatest curvature which would correspond to the shorter minor axis, and a meridian of least curvature which would correspond to the longer minor axis. It is further apparent that these f;c<> meridians must be at right angles to each other. Refraction by an ellipsoid with such an irregular sur- face is much more complicated than that by a sphere or spher- oid, and it is impossible to formulate any laws in regard to it that will apply to the surface as a whole. MERIDIANS OF A TRI-AXIAL ELLIPSOID. 21 In the spheroid, the minor axis being the same for all the meridians of the surface, all rays falling at equal distances from the principal axis are brought together at the same point on the optical axis, as shown in 14 (Fig. 9). When, however, the minor axis is different for the two principal meridians, as in Fig. 6, this can no longer be the case, and only those rays falling in the principal meridians are united on the optical axis, and even these will not all be at the same point. The rays falling in the other meridians are scattered, and when meeting at all, cross at some point off the optical axis. Fig. 10. LINES FORMED BY THE NORMALS TO A TRI-AXIAL ELLIPSOID. A A f and B B' are the principal meridians. The curved lines C C f and D D' represent the position of the normals in two intermediate meridians. 1 This scattering of the rays is due to the peculiar " skew " form of the refracting surface, which changes its curvature at each successive point, so that normals to the surface, (which, as we have seen in 4, control the direction of the refracted rays ) fall in the same plane only in the two principal meridians 1 This condition can be very effectively shown on a model of a triaxial ellipsoid made in wax. Pins are stuck in rows corresponding to the various meridians, each pin being perpendicular to the surface and representing a normal at that point. It will be seen on an inspection of these rows, that none except those corresponding to the principal meridians form straight lines. All the others are curved, no two points lying in the same plane passing through the apex of the figure. Fig. 10 represents in C C f and D D' the curve of two intermediate meridians, projected on a plane sur- face. Dr. Knapp was the first, I believe, to construct such a model. 22 FOCAL INTERVAL OF STURM. as shown at A A', and B B' t Fig. 10. Normals to all the other meridians do not fall in the same plane forming right lines like E E' and FF, but each one falling in a different plane make a line curved as in CO and D D' . Rays falling in these meridians, therefore, can not be brought to a focus at the same place, since the refracted rays will no longer lie in the same plane as before their incidence. Some will cross above and some below the optical axis, but they can never meet. Only those rays falling in the principal meridians and in the planes parallel to them can be united after refraction, because it is only those rays which lie in the same plane before and after refraction. 1 6. It is evident, then, that while the rays refracted by such a surface can never meet, at a single point there is, nevertheless, a certain amount of focussing and this will be found on lines at right angles to the corresponding principal meridians, and the planes parallel to them, by which the rays are refracted. As there are two principal meridians, the focus of a triaxial ellipsoid will therefore not be a point, but two lines perpendicular to each other; one being the focal line of the more strongly curved meridian, lying nearest the refracting surface and perpendic- ular to its corresponding meridian ; the other, the focal line of the meridian of least curvature, being farthest from the refract- ing surface and perpendicular to its corresponding meridian. The distance between these two lines is called the focal inten>al of Sturm, in honor of his having first described it. In Fig. 13, 1 8, vv' is the focal line of the meridian of greatest curvature V V, and // //' is the focal line of the meridian of least curvature H ff ; the distance m n between them is \hzfocal inter- val. Preliminary to a further consideration of the nature of this focal interval we will study briefly the character of the focal lints which form its boundaries. It is common with writers on astigmatism to speak of the an- terior and posterior focal planes, meaning by these the planes passing through the foci of the principal meridians. To the use of these terms no exceptions can be taken when they are lim EXPERIMENTAL DEMONSTRATION OF ASTIGMATIC REFRACTION. 23 ited in their application to the planes passing through the points mentioned. When, however, the focal planes are considered, as they undoubtedly are by many, in the sense of planes pass- ing through the focal lines, the terms are misapplied. I think the error has arisen from experimental attempts to demonstrate the character of refraction by an asymmetrical system. One of the simplest as well as the commonest of these methods is the combination of a cylindrical and a spherical lens to be described in 17. This, indeed, makes an astigmatic sys- tem, inasmuch as there is no place where all the rays emanat- ing from any point are united after refraction, and in such ex- periments the anterior and posterior focal lines do correspond approximately with the planes passing through the foci of the meridians of the greatest and least refraction. This is so be- cause the two principal meridians are regularly curved surfaces sections of a sphere subject to only the ordinary amount of monochromatic aberration. If the cylindrical lens acted alone we should have a series of foci on a right line parallel to the axis of the cylinder, as shown in Fig. 1 5 , 2 1 . Every set of parallel rays a a', c c' ', etc., are united after refraction, each in its own plane, which is perpendicular to the axis of the cylinder/, at the points a", c" , etc., on the line F F parallel to the axis/ The rays passing through the cyl- inder parallel to /would, of course, suffer no refraction. When, however, a positive spherical lens is added to this cylinder, it has the effect of uniting those rays passing through the cylinder in planes parallel to its axis / and of advancing the focal line F F, forming the focal interval of Sturm, bounded by the ante- rior and posterior focal lines. In this instance these lines are approximately straight, because the surfaces of both the cylin- drical and spherical lenses are regularly curved, and the difference between the refraction of the central and peripheral portions is expressed by the usual amount of spherical aberration. That is to say, there would be a slight curving of the focal lines, their concavity being toward the refracting surfaces. The conditions are not, however, the same when we come to deal with an ellipsoid of three unequal axes. Here each of the FOCAL LINES OF A TRI-AXIAL ELLIPSOID. meridians is not the section of a sphere, but an ellipse which changes its curve at each successive point. No lenses with such surfaces, so far as my knowledge extends, have been used in making these experiments. It is very easy, however, to picture in the mind's eye the conditions we should have in refraction by such a surface. We Fig. Showing the character of the Focal Lines in refraction by a Tri-axial Ellipsoid. can imagine the ellipsoid cut into a series of adjacent planes parallel to one of the principal meridians. Each of these planes will then represent, as does the principal meridian to which it is parallel, an ellipse. This is shown in V, Fig. 1 1 , where the ellipsoid is divided into a series I, 2, 3, 4, 5, 6, etc. of ellipses parallel to the principal vertical meridian : a It must be evident, when we consider the form and the rela- tion of these ellipses to each other, that there will have to be a FOCAL LINES OF A TRI-AXIAL ELLIPSOID. 2$ wonderful combination of happy circumstances in order to have the foci of rays refracted by all to lie in the same vertical plane. The foci will all lie in the same horizontal plane because the apices of the ellipses, c, e, o, (which are the principal points of the refracting ellipses,) are all found in the same plane a h' , with the apex a of the ellipse I, which is the principal meridian to which they are parallel ; and since all the cardinal points must lie in the same plane, the foci will be found somewhere on the prolongation of the horizontal plane passing through a h'. But it is also very evident from this construction that the principal points can not lie in the same vertical plane, for the apices, a, c, e, o, of the several ellipses, I, 2, 3, etc., form part of a curved line which constitutes the ellipse representing the hor- izontal principal meridian, h h' , at right angles to the principal vertical meridian to which they are parallel, as shown in H, Fig. n. Now, the position of the focus of any one of these ellipses in relation to the focus of the principal meridian depends upon two things ; first, upon the radius of its curvature as compared to that of the principal meridian ; and, secondly, upon the position of its principal point (from which its focal distance is measured) as compared with that of the principal meridian. These rela- tions, again, depend upon the relations which exist between the three axes of the ellipsoid. Thus, the curve of the horizontal meridian h h' in H, Fig. n, formed by the principal points, a, c, e, o, etc., of the vertical ellipses, will depend upon the relative lengths of the antero-posterior and horizontal axes, whereas the curvature of the ellipses themselves, on which their foci depend, will be governed by the relation between the antero-posterior and the vertical axes. Let us take, as an example to illustrate our meaning, the case where rays fall on the sharper end of the ellipsoid, or in the direction of the major axis, and let us assume that the ver- tical meridian is the more strongly curved, and that the ellipsoid is divided into a series of ellipses parallel to the vertical meridi- an. It is apparent that these ellipses become constantly smaller, with shorter radii of curvature, as they pass toward the 26 FOCAL LINES OF A TRI-AXIAL ELLIPSOID. periphery from the principal meridian, for they finally disappear as a point at the apex //' of the ellipse on the blunter end of the ellipsoid. The effect of this would, of course, be a constant shortening of the focal distance. But at the same time there is a constant recession of the principal points, c, e, o, from the principal plane of the principal vertical meridian passing through a, with, of course, a concomitant recession of the foci. Now, if we can have such a nice adjustment of the three axes that these two conditions shall neutralize each other, the line formed by the focal points of the series of ellipses will be a right line, falling in a vertical plane passing through the princi- pal focus of the principal vertical meridian. There is, therefore, one possible form of ellipsoid, and only one, in which the focal line of one of its meridians will be a straight line and lie in the plane passing through the focus of the vertical meridian. When- ever there is any deviation from this form of ellipsoid, the focal line will no longer be straight, but curved, and the direction of its curvature will depend on the predominating influence of the one or the other of the above-named factors. If the relation between the major and the horizontal axis is such as to cause the setting back of the principal points to be the more power- ful, then the curve would be backward, as shown at x' , Fig. 1 1; should the relation of the axes be such that the shortening of the foci would be in excess, then the curve would be in the op- posite direction, or forward, as shown at x. It follows, also, from what has been demonstrated, that in no triaxial ellipsoid can such a relation between the axes exist as to cause both the focal lines to be straight ; for, as we have seen, there is only one relation of the ellipses that can bring about such a result, and as from the very nature of the figure the ellipses in the two meridians must be different, if one has this form the other can- not have it. It is not possible to obtain any general formula which would apply to all forms of ellipsoids. It will be necessary to treat every form (of which there is an almost infinite number) separately, and as the task is a tedious and by no means an envi- able one, it would hardly be worth while to undertake it unless for some special case. DEMONSTRATION OF THE FORM OF STURM S FOCAL INTERVAL. 2/ 17. The focal interval of Sturm, as stated in 16, is the space bounded by the anterior and posterior focal lines which we have just considered as formed by the foci of the meridians of greatest and least refraction. The direction taken by the refracted rays in their passage through this interval is, owing to the conformation of the refract- ing surface peculiar and erratic, but it has been analyzed sufficiently to enable us to unravel some of its complications and 'to understand the general character of figure. Its general features are made manifest by means of the ex- periment with a combination of spherical and cylindrical lenses, alluded to in 16. Place in front of the milk-glass shade of Fig. 12. Showing the sections of Sturm's Interval at its various parts. a lamp a diaphragm with a perforation I mm. in diameter. This will serve as a point of light, an image of which is formed on a movable screen, by means of a -f~4 or +5 spherical lens. This image will be another round point of light as at A, Fig. 12. Now place in front of the spherical a +i cylindrical lens, axis horizontal. The round point of light will be immediately changed into a sharp vertical line (B] with ill-defined ends. This line is formed by the rays which pass through the spheric- al lens in the horizontal meridian unaffected by the cylinder. Those that pass through the cylinder in the vertical meridian cross and are scattered before they reach the screen. Advanc- ing the screen towards the combination of lenses, we have first a vertical oval (C), then a shorter but broader oval (D], and then a circle (E), all of which have ill defined edges, for at none of these points are any of the rays properly focussed. Advanc- 28 FOCAL INTERVAL OF STURM. ing the screen still further we have a horizontal oval (F), which lengthens out at G, and, finally, when the screen is in the focus of the vertical meridian of the system we have again a line (//) horizontal, because it is formed by the rays passing through the vertical meridian. Astigmatic refraction can also be shown by models made of thread, the first of which was constructed by Knapp, and by the direct observation of the refracted rays through water hold- ing crystals of eocine or other fluorescent bodies in suspension. 1 8. All of these experiments and models show the form of focal interval given in Fig. 13. Here V V represents the ver- tical and H H' the horizontal meridian. The rays refracted by fig- 13- Showing the manner of formation of the Focal Interval of Sturm. V V are brought to a focus at m, and those rays falling in the planes parallel to it are focussed on the horizontal line forming the anterior focal line of the interval. These rays, after meeting, diverge in the direction of h h' . The rays re- fracted by the horizontal meridian ////'pass the line ri-' before meeting, forming its limits, and finally are brought together at n on the vertical line // //'. All the rays falling in planes paral- lel to H H' likewise find their foci on this line, which is the posterior focal tine of the interval, and its limits are the continu- ation of the rays that have been refracted by V V and have crossed at v If this interval be divided by sections perpendicular to the FOCAL INTERVAL OF STURM. 2g axis X X' we shall have the forms represented at the lower part of Fig. 13. The figures, it will be seen, are the same as those obtained in the experiment with the combination of spherical and cylindrical lenses shown in Fig. 12. We first have at the focus of the most strongly refracting meridian v v', the anterior focal line, which is horizontal and at right angles to its refracting surface. This gradually merges into an ellipse g r t s, whose long axis, g t, is horizontal; this then gradually passes into a circular figure o e; then passes into an ellipse pi df with its long axis vertical; and, finally, by a gradual decrease in its short and increase in its long axis, it merges into the posterior focal line h h' , which is vertical, be- ing at right angles to its corresponding refracting meridian, H H'. 19. It will be discovered on a study of these figures: first, that the anterior is shorter than the posterior focal line. This is due to the fact that in the two similar triangles v v' n and h h' m with a common altitude n m, the angle // opposite to v v' is smaller than the angle m opposite to h h' . This must always be the case, since the angle h m h' , being the opposite internal angle of y m y' is larger than v n v'. It follows, more- over, for the same reason, that the difference in the size of these angles, with a consequent difference in the length of their op- posing sides, must increase with the lengthening of the focal interval. Second, the circular section of the figure will not be found as is represented in all the figures of the interval I have seen, except those given by Mauthner, and as it is actually de- scribed as being by several, in the middle of the focal interval, but always nearer the anterior focal plane, for the reason that v v' is under all circumstances shorter than h h'. Third, any ellipse anterior to the circle, on the same account, is shorter than any posterior ellipse taken at the same distance from the pos- terior focal line as the anterior is from the anterior focal line. It follows also, from the same reasoning, that the circles of diffusion are greater on the posterior than on the anterior focal plane. 20. It is abundantly apparent from these demonstrations that CYLINDRICAL LENSES. it is impossible to have, by any such refracting surface, a clearly defined image of all parts of an object on any one focal plane. It is also evident that the degree of astigmatism, or the amount of deviation from a spherical refraction, is measured by the length of the focal interval, that is, by the difference in the focus of the meridians of greatest and least refraction. Fig- 14- \ FORMATION OF A CYLINDRICAL LENS. 21. From the foregoing it is seen that ordinary spherical lenses would have no effect in correcting the astigmatic condi- tion. To remedy the defect in form we need lenses which are curved only in one direction. Such lenses are found in sections of cylinders made in the direction of their principal axes. In the cylinder A, Fig. 14, e/is the axis, ano* b c d a sec- tion made parallel to it. In this section one surface is plane, and the other curved, but tlic curvature is only in one direction and that at right angles to the axis. The action of such a lens on an incident bundle of rays is shown in Fig. 15. The axis of the cylinder is/, and the paral- lel rays a a' ,* c', e e', etc., falling in planes perpendicular to the axis will be united, after refraction, in the same planes at REFRACTION BY CYLINDERS. the points a", c" , e", etc., on the line F F ', parallel to the axis of the cylinder/". Those parallel rays falling in planes parallel to /"will remain parallel after their passage through the lens. REFRACTION BY A CYLINDRICAL LENS. Fig. 16. 6 A CONCAVE CYLINDER c /its axis. 22. The curved surface of the cylinder may be either con- vex, as in Fig. 14, or concave, as in Fig. 16; and as the radius of curvature may be of any length, cylindrical lenses may be 32 DIFFERENT FORMS OF CYLINDERS. made of any refracting power. They are numbered according to the same system as spherical lenses, ( 9). 23. As in the case of lenses with spherical surfaces there may be several forms of cylinders. When one surface is plane it is called a plano-convex or plano-concave cylinder; when both surfaces are curved after the same manner it is called double convex or double concave. These latter forms, however, are seldom used. When one surface is cylindrical and the other spherical the combination is called sphero-cylindrical, and when both sur- faces are cylindrical, with their axes at right angles to each other, they are called crossed cylinders. When two plano-convex or concave cylinders having the same radius of curvature are placed with their axes at right angles to each other the refracting effect will be that of a piano convex or piano concave spherical lens, its focal distance being that of the cylinders separately. Thus two -\-2 cys. with their axes at right angles would make a -f 2 spherical. When the opposite side of the cylinder is curved it is not necessarily after the manner of its own curvature. Thus the opposing surface of a plus cylinder may have a concave spher- ical curvature or a concave cylindrical curvature with its axis at right angles to the axis of the positive lens. 24. There is frequently a practical advantage to be derived from certain " over correcting " combinations, and it is possible by this means to do away entirely with " crossed cylinders," which are more difficult of manufacture than sphero-cylinders. Let us suppose, for example, that we wish to use a -f-2 D cy. with a 4 D cy., with their axes at right angles. Instead of hav- ing one surface ground cylindrically convex, of the required strength, and the other concavely so, with their axes at right angles, we can have the following combination : 4 spherical on one side and +6 cylindrical on the other side. This union would leave the 4 undisturbed in the meridian parallel to the axis of the cylinder, while in the meridian at right angles to it the -f 6 would neutralize the minus refraction of the 4 D spher- ical lens and still leave a positive cylindrical refraction of 2 D. 25. When two plane cylinders of opposite refraction are DENNETT S MODIFICATION OF STOKES LENS. 33 placed with their plane surfaces together, and revolved about their common center the result of the combination is a constant variation in refracting power, and in the direction of the axis of the astigmatic system. On this principal Stokes constructed in 1849, the lens which is still known by his name, though there have been modifications made in its mechanism by Javal, Snel- len, Dennett and others. If a plane 3 cy. and a plane +3 cy. are so placed that their axes correspond, the one lens will neutralize the other. When, however, they are turned about their centers so that their axes are at angles, the astigmatic action will increase and the axis of the combined system will change until the axes of the two lenses are perpendicular to each other, when the total astigma- tion will be equal to the sum of the power of the two lenses, that is, 6 D. It was hoped at one time that this apparatus, on account of its compactness and the amount of astigmatic action it was capable of representing, might come into general use in practical ophthalmology. But the combination gives not only a cylindrical action, but also what amounts to a spherical re- fraction, which constantly varies with the rotation, and must always be taken into account when examinations are made, as they usually are, with parallel rays. Dennett, of New York, has recently made a very in- genious modification of the Stokes lens by which it is possible not only to vary the strength of the cylinders, the axes remaining the same, but by turning the same milled head on another set of cogs to vary the direction of the axes. Both the strength of the cylinders and the direc- tion of their axes are read off on the apparatus. The whole in- strument is conveniently mounted so that it can be manipulated by the patient, and for intelligent persons is most useful for self experimentation. It is, of course, open to the objection inher- ent in all crossed cylinders of the description mentioned above. For examination at short range, however, it may prove valuable in speedily obtaining the direction of the principal meridians, and the character and, approximately, the degree of astigma- tism. 34 CYLINDRICAL ACTION OF SPHERICAL LKNSKS. But a cylindric or astigmatic action is also obtained when a spherical lens is placed obliquely to the path of the rays of light. In fact, the astigmatism of the eye was first referred wholly to the oblique position of the crystalline lens by Young, who was the discoverer of ocular astigmatism. This cylindri- cal refraction increases with the degree of inclination of the lens. The amount of this cylindrical action has been computed by Pickering and Williams, and we give in Table II two of their ta- bles. One of these represents the shortening of the focus of a lens of ico inches focal distance for every five degrees of inclination on the horizontal axis. The other shows the same when the lens is rotated on its vertical axis. These authors explain the discrep- ancy in the two tables by the fact that in the vertical inclination the rays are no longer in the same plane. TABLE II. Horizontal Inclination. Vertical Inclination. ' ' 100 100 5 o 99-9 5 98.9 10 99.2 10 96.1 15 97-7 15 91.2 20 96.1 20 84.8 25 93-7 25 77-0 30 OI.I 30 684 35 88.3 35 59-2 40 84-7 40 49.8 45 o 81.1 45 40.6 5 o 77.2 5 32.0 > 55 73-2 55 24.0 60 69.0 60 17.1 65 64.7 65 "3 7 o 604 70 7-0 8$ 56.3 52.1 g 85 48.3 85 04 90 .44-3 90 O.O 26. The rotation of a cylinder on its axis influences its refracting power. Dr. G. Hay has called attention to this 1 and demonstrated mathematically that the focus of a cylindrical lens is shortened Trans. Amer. Oph. Soc., 1875. CHANGE IN REFRACTION OF A CYLINDER BY ROTATING IT. 35 by such a rotation about its axis. Dr. Sous 1 dissents from this view and gives a mathematical demonstration to the opposite effect, and contends that the lens in rotating about its optical axis is not increased, but, on the contrary, diminished in its re- fraction. It is not necessary to enter into a mathematical com- TABLE III. Obliquity Observed Neutralizes in Degrees. Glass. Obliquity Observed in Degrees. Neutralizer Glass. 21 1 l; 32V.I /6 52 ) 53+ ^ - - -Yl8 54 J 27 1 30 \ - -v 54 ) 45 J 55 \ - -Vie 371/2 } -v,' 39 J 57 J 56 1 - } - - -/. 58 / 56 ) 47 ) 58 \ - - - -Yu 48 [ -Yso 59 J 49 J 48 \ i; 59 J 58 | 59 \ - - 61 j - -v, So+1 50^ - - - 1/20 60 \ j , S2V2J 61 / putation to demonstrate the fact that a cylinder does increase in power by being turned about its axis. The following simple experiment is sufficient to establish it. If a +4 cylinder is placed before the eye, with its axis horizontal, and a series of radiating lines (Snellen's fan) is looked at, only the vertical line will be seen distinctly, the horizontal lines being scarcely visible. If a 3 cylinder is now placed before this lens with its axis coin^ ciding with that of the plus cylinder, the horizontal lines will become more distinct, but remain much less distinct than the iTraite d' optique, Paris, 1881, p. 464, et seq. 36 BIBLIOGRAPHY. vertical. There still remains a cylindrical action of -f I D un- corrected. If the 3 is now rotated on its axis, the horizontal lines will increase in clearness, and when it has an inclination of nearly 45 they will be as clear and distinct as the vertical, and the whole fan will be even, showing that the one lens has wholly neutralized the other; in other words, a 3 rotated 45 on its axis has the refracting power of a 4. We copy Table III from Dr. Hays' paper showing the negative glass which a Y TO neutralizes when placed at various inclinations. BIBLIOGRAPHY. Aubert, Prof. H. Phys. Optik. Handb. d. gesammet. Augenheilk. von Grafe tu Sftmisch. B. II. 1876. Ayres, W. C Notes on the Focal Lines in Astig. N. Y. Med. Jr. XXXIV. Pp. 476-483. 1881, Burnett, S. M. Refract in the princpl. meridians of a tri-axial ellipsoid, with re- marks on the Correct of Astig. by cylind. glasses, and an hist note on corneal astig. Arch, of Ophth. XII. No. I. 1883. Burnett, S. M. The action of cyl. glasses in the correction of reg. astig. Amer. Jour. Oph. Dec. 1885. P. 275. Dennett, W. S A Stokes' lens for measuring astigmatism. Trans. Amer. Oph. Soc. 1885. P. 106. Haltenhoff, G. Apparat z. optisch. Demonstrat. Klin. Monatsbl. f. Augenhlk. B.XII.,p. 198. Harlan, G. C. Description of I. L. Borsch's sph. cyl. combination lens, ground on one surface only. Trans. Amer. Oph. Soc. 1885. P. 96. Hay, G. On the increase of refract power of a plano-cylind. lens when rotated about its axis. Trans. Amer. Ophth. Soc., p. 319. 1875. Hay, G. On the analyt condit of that form of Astig. pencil in which the two focal lines are perpendicl. each to the axis of the pencil and to each other, and on the correct of such pencil by a plano-cylind. lens. Arch, of Ophth. and OtoL N. Y Pp. 497-504. 1876. Hay, G. Special applicat to the case of the eye of Knapp's genl. formulae for astig. rays. Arch. Ophth. and OtoL N. Y. II. No. I, pp 79-86. 1871. Helmholtz, H. Optique physiologique. Trad, par E. Javal et Th. Klein. Paris. 1867. Hoorweg, J. L. Versuch einer elemt Theorie der cylind/Linsen. Arch. f. Ophth. XIX: 2. P. 231. Kaiser, H. Die Theorie d. Astig. Graefe's Arch. B. XI. Abt 3, p. 186. 1865. Knapp, H. Demonst of the refract of light by asymmet surfaces and the deter- minat of astig. with glasses and the Ophthalmoscope. Trans. Amer. Med. Ass. 1880. Kugel, C. Ueber die Wirkung schief vors Auge gestellter sphar. Brillengliiser beim regelmassig. Astig. Graefe's Arch. B. X. Abt I, p. 89. 1864. BIBLIOGRAPHY. 37 Leroy, C. J. A Optiq. physiolog. Arch. d'Ophth. T. I. Leroy Les lignes focales d. la refract oblique par une sphere et la theorie de Leroy, C. J. A. Sur la theorie de 1'astig. Rev. gen. d'ophth. I. Pp. 429-477. 1882. Loomis, Elias The Elements of Analyt. Geometry. Harper Bros. N. Y. 1873. Matthiessen, Ludwig Die Brennlinien eines unendlich diinnen astigmatischen Strahlenbiindels nach schiefer Incidenz eines homocentrischen Strahlenbundels in eine krumme Oberflache und das Strahlenconoid von Sturm und Rummer. Eine Replik. Grafe's Archiv. XXX. 2. 141-154. Matthiessen, L. Ueber die Form der Astig, Bilder sehr kleiner gerader Linien bei schiefer Incidienz der Strahlen in ein unendlich kleiner segment einer brechend. sphar. Flache. Graefe's Arch. B. XXIX. Abt. I, p. 147. 1883. Matthiessen, L. Grundriss d. Dioptrik. 1877. Matthiessen, L. Ueber die Form eines unendlich diinnen astig. Strahlenbundels und iiber die Kummerschen Modelle. Klin. Monatsbl. f. Augenhlk. XXI, p. 1013. 1883. Mauthner, L. Vorlesung. iiber die opt. Fehler des Auges. 1876. Meyer, H. Ueber die Strahlen die ein leuchtender Punkt im Auge erzeugt. Poggd. Annal. B. XCVII, p. 233. B. XCVIII, p. 214. 1856. Pickering, E. C., and Williams, C. H. Foci of lenses placed obliquely. Proc. Amer. Acad. of Arts. & Scs. N. S. Vol. II. 1874-5. Reuss, v. A. Untersuch. ueber die optisch. ametrop. Augen. Graefe's Arch. XXIII, 4. XXIV, 3. Shoen, Wm. Beitrage zur Dioptrik des Auges. Folio. Leipsig. 1884. Sturm Memoire sur la theorie de la vision. Poggd. Annal. B. 65. 1845- Sturm Rev. Gen. d'oph. No. II. 1883. Wadsworth, O. F. On the effect of a cylind. lens with vertic. axis placed before one eye. Trans. Amer. O^hth. Soc. 1875. Woinow Ophthalmometrie. Wien. W. Braumiiller. 1871. CHAPTER III. ASTIGMATISM IN THE HUMAN EYE HISTORY OF CORNKAL ASTIGMATISM. THE DIFFERENT FORMS OF AME- TROPIA VARIETIES OF ASTIGMATISM. 27. The human eye, with rare exceptions, suffers, among other imperfections, from astigmatism. Even eyes that have an acuteness of vision which is normal according to a convention- al standard, will be found, on careful examination, to be astig- matic in a greater or less degree. When this astigmatism is not sufficient to lower perceptibly the visual acuteness, it is considered normal. When, however, it is of such a degree that vision no longer reaches the generally accepted standard of normality, it is regarded as abnormal. 28. The refracting media of the eye are the cornea and crys- talline lens, and astigmatism may be found"in either or both. In addition, therefore, to the division into regular and irregular, astigmatism ( 12) may be divided into corneal and lenticu- lar. Corneal astigmatism is, for the most part, regular; while lenticular astigmatism is, most generally, irregular. To this general rule, however, there are exceptions, which will be con- sidered when each form is treated of in detail. 29. The cornea in normal eyes suffers, in addition to the regular form of astigmatism, in which the opposing meridians have different foci, from a monochromatic aberration in these meridians themselves, which undoubtedly exercises an influ- ence on the distinctness of the retinal image. The outline of the corneal surface in the optically normal eye has never been determined with exactness, nor the peculi- arities of its refraction treated of in a thorough manner. I therefore asked my friend Prof Wm. Harkness, of the United- (38) ASTIGMATISM OF THE HORIZONTAL CORNEAL MERIDIAN. 39 States Naval observatory, to take the data derived from the measurements of a number of emmetropic eyes, and determine what the actual refraction of the normal cornea is in one me- ridian of its curvature. This he kindly did, and the results are published in the Ar- chives of Ophthalmology, vol. xii. pp. 919. A resume of his investigations is herewith given : " The cornea of the emmetropic eye seems to have an ellip- soidal form, but the existing data for determining its curvature in the vertical meridian are too meagre to give a satisfactory result. I have therefore confined my attention to the hori- zontal meridian, and have taken the data for it from table VII, upon pages 598599 of Mauthner 1 . That table exhibits the form and dimensions of the cornea in seventeen pairs of em- metropic eyes, and from the mean of these thirty-four eyes, it appears that in the visual axis the radius of curvature is 7.708 millimetres, while 20 to the inner side of that axis it is 8.378 millimetres, and 20 to the outer side 7.884 millimetres. Mauth- ner does not explain the phrase " 20 to the inner (or outer) side of the visual axis," and I have had some trouble in ascer- taining its true meaning. " It is customary to regard the outline of the cornea, along a horizontal section through the visual axis, as part of an ellipse. Let it be part of the ellipse NAME, Fig. 17, of which the major and minor semi-axes are respectively AH and BH; and let C, D, E, be the points at which the radii of curvature are measured. DF, CF and EF are normals to the ellipse at these points, and CFis the visual axis. By the phrase "20 to the inner side of the axis" Mauthner means that the angle CFD, between the visual axis and the normal at D, is 20; and, similarly, by "20 to the outer side of the visual axis" he means that the angle CFE is 20. It may be well to remark that Fig. 17 is accurately drawn to scale, and the arc NAM represents that portion of the ellipse which is included within the limits of the cornea. ******* -pi ie mo nochromatic aberration of the 'Vorlesungen ii. d. optis., Fehler des Auges, 1876. 4O ASTIGMATISM QF THE HORIZONTAL COKM-AL MMKIDIAN. cornea is most conveniently investigated by tracing the paths which a considerable number of parallel rays impinging upon it will pursue within the eye. Eleven such Wys have been con- sidered, all situated in the same horizonta^plane, at intervals Fig. 77. r SHOWING THE ELLIPTICAL FORM OF THE COR' A H the Optical Axis. C F is the Visual Axis; of half a millimetre from each other, and the central one coin- ciding with the visual axis. For their passage a pupil of five millimetres in diameter is necessary. The eleven rays in question furnish eleven values of d, varying by intervals of half a millimetre from -f 2.5 mm (towards the nose), to 2.5""" to- wards the temple), from which the corresponding values of F have been computed." The results of these computations are represented graphic- ally in Fig. 1 8. The center line o is the visual axis, while 3, 2, I, represent the distance toward the temple in millimetres, and -f-3 2, i, the distance towards the nose in millimetres. The ordinates represent the paths of the eleven rays whose foci have been computed. The values of Fare taken as abscissas, FOCAL CURVE OF THE NORMAL CORNEA. and the curved line shows the position of these foci at intervals of one-tenth of a millimetre. From this it is evident that the focal curve is a parabola. Fig. 18. Z z 31.0 30.5 30.0 29.5 012+3 Nose > SHOWING THE FORM OF THE FOCAL CURVE OF THE NORMAL CORNEA. "Table IV shows how the monochromatic aberration actually existing in the normal cornea compares with what would have existed if the cornea had been spherical. Upon each line of the table, the first column, d, contains the assumed diameter of the pupil ; the second, third and fourth columns relate to the normal cornea, and contain respectively the greatest and least focal distance occurring within the area of the pupil, and the amount of astigmatism corresponding to them ; the fifth, sixth, and seventh columns relate to a spherical cornea, and contain similar data for it. In computing the focal distance at various points of a spherical cornea it has been assumed that the radius of curvature r = 7.708""", and the index of refraction >j =1.3366. As the monochromatic aberration we are considering occurs 42 COMPARISON OF THE NORMAL AND A SPHERICAL CORNEA. TABLE IV. Normal Cornea. Spkerical Cornea. a. * " At. F. f A*. mm. I mm. 30.684 mm. 30.502 Par. in. 1:139 mm. 30.608 mm. 30.556 Par. in. 1:476 2 3 4 5 a .728 30.728 359 30.182 29.971 29.724 i: 46 : 33 i: 25 .608 .608 .608 30.608 30.171 29.826 29.376 I 130 I 5 8 I 32 I 21 in a single meridian, its correction by cylindrical lenses is im- practicable, but nevertheless its amount may be expressed in the notation usually employed for astigmatism. The requisite formula is Astigmatism = 0.0396 (FF 1 ) In which F and F' are the lengths in millimetres of the greatest and least focal distances found within the area of the pupil, and the result is expressed in terms of the Paris inch. In conclusion, the results at which we have arrived may be summed up as follows : a. The monochromatic aberration originated by the normal cornea occurs principally on the outer side of the visual axis that is, on the side farthest from the nose. b. The diameter of the pupil is usually about four millime- tres. For diameters less than this, the monochromatic aberra- tion of a spherical cornea would be less than that of the nor- mal cornea. For greater diameters the reverse is true. This is contrary to the generally received opinion. (See Bonders, foot-note on page 310.) f. Bonders says (pp. 456, 457, Anomalies of Ref. and Ac- corn, of the Eye), the astigmatism in sharp eyes is not gener- r ally more than from 1:140 to 1:60, and whenever it exceeds the i latter amount the power of vision suffers under some circum- \ stances. An astigmatism of i :4O he regards as decidedly ab- normal. Nevertheless, with a pupil four millimetres in Miame- ter the normal cornea produces monochromatic aberration to the extent of 1:." NORMAL ASTIGMATISM OF THE CORNEA. 43 Aubert (Archiv. f. d. gesammt Phys. B. xxxv) has recently made some measurements in order to determine more ac- curately the form of the corneal surface, and has found that at about 12 towards either side of the visual axis it becomes very rapidly flattened, thus dividing the stirface into two true zones, the polar and peripheral. The central or polar zone, which is used exclusively for optical purposes, he calls the op- tical zone ; the peripheral, bordering on the sclera, he calls the scleral zone. The regular curve of the optical zone reaches about 17 to either side of the apex of the cornea, but even in a very wide pupil the rays refracted through the scleral zone cannot enter the eye. In these measurements he has not de- termined the question of whether the optical zone is spherical or elliptical. 30. But aside from this monochromatic aberration of the cornea in a single meridian (which must be considered as forming a part of its irregular astigmatism) there exists, in most eyes, a difference in the curvature of the principal merid- ians taken as a whole, constituting regular astigmatism. A number of eyes with normal vision have been measured as to the curvature of their various corneal meridians, and in almost all there has been found a meridian of least curvature (longest radius), and at right angles to this another of greatest curvature (shortest radius). In other words, the human cornea does not represent, by its surface, the section of a sphere with equal radii, but approaches in form more nearly to an ellipsoid with three unequal axes, such as we have studied in Chapter II. In the table V are given the results of measurements of twenty-one normal eyes, showing the amount of astigmatism from which they suffer. It will be seen from an examination of this table that in only two eyes were the two principal corneal meridians the same. In the other nineteen there was a difference, esti- mated' by the focal distance of the lens necessary to correct it, and expressing the amount of the astigmatism, of from 1:280 to 1:38- 44 NORMAL ASTIGMATISM OF THE CORNEA. TABLE V. No. Observer. AW/Vr in Horizontal Meridian. Radius in I 'ertical Meridian. Focnt in Horizontal Meridian. Focus in Vertical Meridian. Astigtnation = i: I 2 d Mm. 7 .80 8.07 Mm. 7.91 8.26 Paris Inches. I.I445 Paris Inches. .1605 .2120 Paris Inches 62 40 3 0. 7-23 7.385 1. 0688 .0835 -38 4 c 7.22 7.08 1-0593 .0 3 88 40 5 774 7.71 1.1356 -'3'3 220 6 7 7-74 8.20 7-74 8.12 '1356 I.203I 1356 .1914 88 B 8-34 8.19 1.2237 .2107 85 9 10 ii i 7-23 8.27 7-73 7-23 8.30 769 1. 0608 I.2I34 I.I342 .0608 .2178 .1283 "tg 12 '3 c c 8.15 7-94 78i 1.1958 1.1855 .1650 *457 34 29 14 e (A 8.02 7-92 1.1767 .1626 76 15 7-42 7-30 10887 .0711 5 1 6 o 749 1.0987 .1019 280 17 o 749 745 1.0987 -093' 1 60 a C 7-84 746 1.1503 .0946 16.9 19 7-75 7-33 1.1371 0755 14.9 20 7.60 I.II5J .1048 89 21 7-55 7.60 I.I078 .1151 127 It should be stated in this connection, however, that the cor- neal astigmatism does not in all cases represent the exact as- tigmatism from which the eye suffers. There may be a concomi- ^ tant lenticular astigmatism which will increase or diminish that of the cornea according to the direction of its faulty meridian and the degree of its astigmatic deviation. The total astigma- tism of the eye is the algebraic sum of its corneal and lenticu- lar astigmatism. This we shall deal with further on under the head of lenticular astigmatism. It will be furthermore observed that in thirteen cases the vertical was the more strongly curved meridian, the horizontal being the stronger in only six cases (those marked in the table). Clinical observation being in accord with this, it is cus- tomary to speak of this relation of the principal meridians in which the vertical is the more strongly curved as being accord- ing to the rule. 31. The existence of a slight degree of astigmatism in a normal REGULAR LENTICULAR ASTIGMATISM. 45 eye can be experimentally demonstrated by turning before it a weak cylindrical glass say, with a focal distance, positive or negative, of 144 inches (0.25 D). In this experiment it will be found that when the axis of the cylinder corresponds to one certain meridian vision will be best, and when it corresponds to the one at right angles to it it is worst. In the first instance the cylinder corrects the existing astigmatism, and, perhaps slightly over corrects it, while in the latter it increases it by the power of the lens. If two very fine threads are crossed at right angles and brought gradually towards the nearest point of distinct vision, it will be found, usually, that one becomes blurred before the other. The point where the first thread becomes indistinct marks the near point of the weakest-refracting meridian, the point where the line at right angles to it becomes blurred is the near-point of the most strongly refracting meridian. The difference between the two points measures the amount of as- tigmatism. This is the method used by Young in demonstrat- ing his astigmatism. 32. Regular astigmatism may also have its seat in the lens. Thomas Young, who was the first to demonstrate the existence of astigmatism in the human eye, found his own astigmatism to reside there. He immersed his eye in a chamber of water bounded by a plane glass surface, thus eliminating the refrac- tion of the cornea, and, as the difference in the refraction of the two meridians did not disappear, he rightly concluded that it must be due to an abnormality of the lens. The causes of lenticular astigmatism are either displacement of the lens in such a manner that its refracting surfaces shall lie obliquely to the visual axis ( 25), or a difference in curvature of its principal meridians, as in corneal astigmatism. Young conceived his astigmatism to be due to an obliquity of the lens. A simple displacement of the lens at right angles to the visual axis would not of itself produce astigmatism. There have been some cases reported of progressive change in the degree of astigmatism and in the direction of the prin- 46 HISTORY OF CORNEAL ASTIGMATISM. cipal meridians. In none has there been any measurement of the corneal radius, and under these circumstances we cannot positively exclude a change in corneal curvature, but it is most probable that the change is due to alteration in the shape of the lens, either from changes in its substance or from a modi- fied action of the ciliary muscle. 33. It is probable that Gerson (1810) was the first to point out the existence of corneal astigmatism, but I do not find that the opinion was based on ophthalmometric measurements, and his statement only became generally known after the fact had been established by the measurements of others. Wilde and Jones refer to ''cylindrical eyes" and "cylindrical cornea," but there are no evidences that these opinions were based on opthalmometric measurements. Wilde says 1 : " It is well known that the cornea is not a cor- rect surface of revolution, but that the curvature of its hori- zontal plane is less than that of its vertical. When this ex- ceeds the normal extent it gives rise to irregular refraction, causing a circle to appear oval." Jones simply quotes from the history of Airy's case. No practical application of these facts seems to have been made by either of these writers. Senf was the first (in 1846) to make measurements of the cornea, which showed it to be ellipsoidal rather than spherical in shape. Helmholtz arrived at the same conclusion from his ophthalmometrical measurements which were published in Grafts Archives B. i, Abt. 2 (1855). In this article (p. 18) he says : " The form of the cornea corresponds approximately to an ellipsoid formed by the revolution of an ellipse about its major axis." He gives these measurements as well as those of Senf in the first part of his " Physiologische Optik " (pages 8 and 1 1 of the French edition), published in 1856; but it is evident that he still considered the cornea to be an ellipsoid of revolution, as his measurements were confined to one meridian (the hori- 1 Dub. Jn'l Med. Sci. 1846-47. P. 105. HISTORY OF CORNEAL ASTIGMATISM. 4/ zontal). He speaks at this time (p. 142) of the astigmatism of Young as being caused by the lens, and of the correction of his own astigmatism (of low degree) by means of an obliquely placed concave lens, but no hint is given that the cause of the astigmation was in the cornea. It was Knapp who first determined by ophthalmometric means that the cornea was not an ellipsoid of revolution but an ellipsoid with three unequal axes. In the "Verhandlungen der vom 3-6 Sept., 1859, * m Heidelberg versammelten Augen JErtze," Berlin, Peters, 1860, we find (p. 19) that "Dr. Knapp gave an account of his measurements on the curved surface of the human eye, made by means of Helm- holtz's ophthalmometer. i. The cornea. Helmholtz's meas- urements were confined to the horizontal meridian. Knapp, on the other hand, had measured four eyes in many different meridians with the following result : I. The centre and apex of the cornea do not coincide. * * * The anterior focal distance of the horizontal ellipse =23.095 mm.\ of the vertical ellipse =23.34 mm. The posterior focal distance of the hor- izontal ellipse =30. 1 8 mm.\ of the vertical ellipse =31.1 mm. * * * In the discussion on this division of the subject, Knapp remarked that in all probability it was the difference between the vertical and horizontal ellipses which rendered cylindrical glasses necessary, and was the cause of the differ- ence in the ' accommodation line ' in the vertical and horizon- tal directions. After cataract-extraction, in sclerectasia and hyperpresbyopia, such glasses were of benefit, as had been shown by Prof. Bonders. " In regard to the accommodation-line, Prof. Bonders re- marked that, in his opinion, it was due to the lens, from the fact that it was in intimate connection with polyopia, which was undoubtedly caused by the lens, as proven by entopic ex- periments." These investigations were published in detail by Knapp in his inaugural thesis, " Bie Krummung der Hornhaut des menschlichen Auges " in 1860. Bonders, in his first papers on the refraction and accommo- 48 HISTORY OF CORNEAL ASTIGMATISM. dation of the eye, published in Graffs Archives, makes in B. vii, Abt. I, p. 176 (1860), an application of this asymmetry to the explanation of abnormal astigmatism, in contradis- tinction to the lenticular theory of Young, and gives reference to Knapp's paper. So far as I know this is the first mention made by Bonders of corneal astigmatism. In Grafe's Archives B. viii, Abt. 2 (1862), appeared Knapp's classical paper, "Ueber die Assymmetrie des Auges in seinen verscheidenen Meridi- anebenen." While this paper was in press Donders published his " Astigmatisme en cylindrische Glazen," which, for the first time, brought the subject of astigmatism and its cor- rection prominently before the profession. Soon afterward (1864), his treatise on the "Anomalies of the. Refraction and Accommodation of the Eye " appeared, which made astigma- tism a part of the general knowledge of the profession. The opinion that regular astigmatism resides almost wholly in the cornea has been most thoroughly substantiated by all observations made since that time. Javal in the Annales d' oculistique, t. 87, pp. 33-43 (1882), says that in the testing and measurement of more than 100 eyes, the total astigmatism corresponded exactly with the corneal astigmatism, with the exception of four cases, and in one of these the difference was only O.2 D ; and additional examinations by him, and by Dr. Nordenson, amounting to more than 250 cases, have confirmed his first observations. My own experience with Javal's ophthalmometer tends to substantiate this opinion in the main, though my percentage of difference between the total and corneal astigmatism is greater than that given by Javal and Nordenson. 34. As stated in 27, when the astigmatism reaches such a degree as to reduce the visual acuteness below the normal standard of */ 4 ( M / M ) it is called abnormal. Exactly what degree of astigmatism should be considered abnormal has not been agreed upon by observers. Some look upon '/i (0.25 D) as abnormal, while others think 1 / 1 , (0.50) normal. It is impossible to formulate any law of universal ap- plication for such a varying and imperfect optical instrument THE EMMETROPIC EYE. 49 as the eye. Prof. Harkness has shown us ( 29) that the nor- mal irregular astigmatism of a single meridian does not proba- bly fall below l / S3 , and since a large majority of persons cannot distinguish any sensible difference in the distinctness of the image of test objects as fine as the finest test-types when a correcting 0.25 is placed before their eye with its curvature corresponding to the faulty meridian, we fee/ justified in con- sidering only those degrees of astigmatism abnormal which ex- ceed 0.25 (Vino)- We would, however, not deny the possi- bility of certain rare cases deriving benefit from the employment of glasses of this low power. 35. When we come to study astigmatism as it affects the human eye in detail, we find that we have several different con- ditions to deal with, and in order to clearly understand the manner and degree of departure of the astigmatic from the optically normal eye we must know in what the latter consists. 36. A normal, standard or emmetropic eye (that is, an eye of proper measure) is one whose retina lies at the focus of its refracting media. Fig. 19. THE EMMETROPIC AND AMETROPIC EYES COMPARED ff, the hypermetropic ; E, the emmetropic ; M, the myopic eye. Parallel rays falling on all meridians of such an eye are brought to a focus at the same point on the retina, E, Fig. 19. 37. An eye which deviates from these standard refractive conditions is called ametropic (not of proper measure). 50 MYOPIA AND HYPERMETROPIA. When the parallel rays are focussed before the retina, M t Fig. 19, the eye is called myopic. When they cross behind the reti- na situated at //, the eye is said to be hypermetropic. 38. In the ordinary myopic and hypermetropic forms of ametropia it has been found from ophthalmometric measure- ments, that, as a rule, the radius of curvature of the cornea is the same for them as for the emmetropic eye. These ame- tropic conditions are due, except in rare cases, to a displace- ment of the retina ; in other words, to a variation in the length of the eyeball. A myopic eye is one that is too long ; a Jiyper-^ me tropic eye is one that is too short. Ordinary myopia and hy- permetropia are, therefore, not strictly speaking anomalies of refraction, since the refracting power of these eyes is normal as compared with that of the .emmetropic eye. The refraction is abnormal only when considered in reference to the position of the retina. In those exceptional instances where the refraction is at fault its seat may be in the cornea or the lens. ' 39. Astigmatism is the only anomaly which is due en- tirely to a defect in the refracting apparatus, for, as we have seen, it is the faulty curvature of the refracting media which is the cause of the optical error. 40. We can now understand how astigmatism, in addition to its own error in ^refraction, may be complicated with the other forms of ametropia. The foci of both meridians may lie in front of the retina, as in myopia, or they may lie behind it, as in hypermetropia, <>r one may be in front and the other behind it, constituting my- opia and hypermetropia at once. It is, therefore, important not only to facilitate study, but, as we shall see, for the practical purpose of correcting the anomaly, that we make subdivisions of astigmatism. The gen- eral forms into which it has been divided are : I. The simple. 2. The compound. 3. The mixed. 41. SIMPLE ASTIGMATISM. When the focus of one merid- ian falls on the retina the astigmatism is called simple. There can, of course, be but two varieties of this form, one in which THE DIFFERENT FORMS OF ASTIGMATISM. 51 the focus of the faulty meridian falls in front of the retina, and the other in which it falls behind it. Borrowing the nomencla- ture of spherical ametropia, the first condition is called simple myopic astigmatism, and the second, simple hypermetropic as- tigmatism. One meridian is emmetropic, the other myopic or hypermetropic. 42. COMPOUND ASTIGMATISM. In the compound form l> both foci fall either in front of or behind the retina. When A. the foci lie before the retina it is called compound myopic astig- matism ; when they both lie behind it there is compound hyper- metropic astigmatism. In this form, therefore, we have an as- tigmatism associated with spherical ametropia. Both meridi- ans are ametropic, and in the same manner, but one of greater degree than the other. 43. MIXED ASTIGMATISM. This is the condition where V, the focus of one meridian lies in front of and the other behind! \ the retina. In other words, one meridian is myopic and the other hypermetropic. Of this form there can of course be but one variety. Every case of regular astigmatism must be of one of these three forms. BIBLIOGRAPHY. Airy, George Biddell On a peculiar defect in the eye, and a mode of correcting it. Trans. Camb. Philos. Soc. V. 2. 1827. P. 267-271. (Read Feb. 21, 1825). Airy, G. B. On a change in the state of an eye with a malformation. Trans. Camb. Philos. Soc. V. 8. 1849. P. 361-362. (Read May 25, 1846). Arago Oeuv. Complt. T. XI. P. 218. 1844. Aubert, H. Phys. Optik., Handb. d. gesammt. Augenheilk von Grafe u. Samisch. B. II. 1876. Aubert, H. Naehert sich die Hornhautkriimmung am meisten der Ellipse. Arch. f. d. gesam. Physiol. Bonn. B. XXXV. P. 587. 1885. Bergeron, G. Astig. N. diet, de med. et de chir. prat. Pp. 740-9. 1865. Briicke, E. Ueber asymmet Strahlenbrech. im mensch. Auge. Sitzbr. d. K Akd.d. Wisschft. 1868. Buckner, J. H. Astig. Cincin. Lancet and Obs. XVIII. Pp. 466-80. 1875. Bumstead, F. J. A few Rem. on Astig. Am. Med. Times. New York. VII Pp. 203-5. 1863. Burnett, S. M. Character of the foe. lines in astig. Arch, of Ophth. New York XII. P. 310. 1883. 52 BIBLIOGRAPHY. Burnett, S. M. Refract in the prihcip. merid. of a triax. ellipsoid, etc. Arch, of Ophth. XII. No. i. 1883. Carter, R. B. On defects of vision. London. 1877. Cohn, Hermann Untersuch. der Aug. v. 10060 Schulkindern. Leipzig. 1867. Donders, F. C. Astigmatism in cylindrische glazen. Utrecht. 1862. Donders, F. C. Der Sitz des Astig. (nach Middleburg) u. d. Excursion der Beweg. des emmetrop. u. ametrop. Auges (nach Schurmann). Graefes Arch. X. Heft. 2. Pp. 83-108. 1864. Donders, F. C. BeitrSg z. Kenntniss der Refract, u. Accommodat. Anomal. Graefes Arch. Bd. 7. Abt I. 1860. Donders, F. C. Ueber Astigmalismus. Zehend. Monatsbl. f. Augenheilk. I 1 ., i. Pp. 496-499. 1863. Fechner Ueber einige Verschiedenheiten des Sehens im verticalen unv horizon- talen Sinne nach verschied. Beobachtern. Fechner's Centralbl. Pp. 73-85, 96-9 374-9.S58-6'- '853- Fischer In G. H. Gerson Dissert. Inaug. De forma corneal. oculi human, deque singulari visis phenom. Gottingae. 1810. Gavarret, J. Astig. Diet. Encycl. d. Sc. Med. Paris. VI. Pp. 772-94. 1867. Gerson, G. H. De form. corn. ocul. hum. deque singl. vis. phenom. Dissert. In- aug. Getting. 1810. Abst in Kl. Monatsbl. f. Augenhlk. IV. P. 57. Giraud-Teulon La Vision et ses Anomalies. Paris. Balliere et Fils. 1881. Goode, Henry On a peculiar defect of vision. Trans. Camb. Philos. Soc. 48. 1849. Pp: 493-496. Read Nov. 9, 1846 and May 7, 1847. Goode, H. On the Diag. and Relief of certain species of Amblyopia. Svo. Edin. 1848. Goulier, C. M. Surundefaut assez coramun.de conform, des yeux et sur les moyens de rendre la vue distincte aux personnes qui en sont atteint. Compt. rend.'de 1'Acad de Sc. 7. Aoat 1865. T. LXI. P. 266. Hamilton A case of astig. Month. Jr. Med. Sc. Edin. 1847. P- 891. Harkness. \Vm. Communicat on the monochrom. aberrat. of the h. eye in ajjh- akia. Arch, of Ophth. XII. No. i. 1883. Harlan, G. C. Two cases of astig. Phila. Med. Times. IV. P. 183. 1873. Hasner, v. Artha Asymmetric d. Cornea. Klin. Vortrage ueber Augenheilk. 2 Abt Pp. 141-5- Credner, Prague, 1866. Hay, G. A case of astig. Boston M. and S. Jr. LXXV. Pp. 513-15. 1867. Helmholtz Ueber die Accommodat. d. Auges. Graefes Arch. B. I. Abt. 2. P. 3- '854. Helmholtz, H. Optique physiologique. Trad, par E. Javal et Th. Klein. Paris. 1867. Javal, E. Sur. 1'astig. Arch. gen. de Med. Aout 1867. Javal, E. Bibliog. de 1'astig. Ann. d'oculist. T. LV. P. 104. 1866. Jones, Wharton Analys. of my sight with a view to ascertain the focal power of my eyes for horizontal and for vertical rays, and to determine whether they possess a power of adjustment for different distances. Proc. Roy. Soc. V. X. Pp. 380-5. 1860. Kaiser, H. Ein Fall von Anisometrop. und allgemeine Beleucht. dieses Gesich- tsfehlers. Graefes Arch. B. XIII. Abt II. P. 3153. 1867. Kaiser, H. Die Theorie des Astig. Graefes Arch. B. II. Abt. 3. P. 186. BIBLIOGRAPHY. 53 Knapp, J. H. Die Kriimmung der Hornhaut des mensch. Auges. Heidelberg. 1859. (Habilitationsschrift.) Knapp, J. H. L'asym. de 1'oeil d. les different merid. Cong, period, [internatl. d'ophth. 1862. Knapp, J. H. Ueber die Asymmetrie des Auges in seinen verschied. Meridian- ebenen. Graefes Arch. B. VIII. Abt. 2. Pp. 185-241. Kelch, H. H. Astig. Phila. Med. and Surg. Rep. March 19, 1881. Knauthe, Ph. H. Ueber Astig. Dissert. Leipzig. 1863. Kohlrausch Ueber d. Messungen d. Radius d. vorderflache d. Hornhaut am leb- enden mench. Auge. Okens Isis. 1840. Landesberg, M. Regl. Astig. Med. Bulletin. Phila. P. 251. 1881. Landolt, E. and Nuel Versuch einer Bestimmung des Knotenpunktes fur excent. in das Auge fallende Lichstrahlen. Graefes Arch. B. XIX. Abt. 3. P. 301. 1873. Laquer Ueber d. Hornhautkriimmung im normal Zustande u. unter pathol. Ver- haltniss ophthal. Untersuchen. Graefes Arch. XXX. Abt. I. Pp. 99-134. Laurence, J. Z. Astigmatism. Med. Times and Gazette. Feb. 28 and May 2. 1863. Laurence The optical defects of the eye and their consequences, asthenop. and strabis. London. 1865. Leroy Sur la theorie de Pastig. Rev. gen. d'Ophth. Pp. 1-129. 1882. Mauthner, L. Vorlesungen iiber die optisch. Fehler des Auges. Wien. Brau- miiller. 1873-6. Matthiessen, L. Ueber den Aplanatismus der Hornhaut. Graefes Arch. B. XXII. Abt. 3. P. 125. 1876. Middleburg, H. A. De Zitplaats van het'Astig. Acad. Proef. 8vo. Utrecht. 1863. Mooren, A. Ftinf Lustren ophth. ^Wirksamkeit (Astig.). Wiesbaden. P. 274. 1882. Miiller, A. Ueber das Beschauen der Landschaften mit normaler und abgeand- erter Augenstellung. Poggd. Annal. B. LXXXVI. Pp. 147-52. 1852. Murdoch, Russell The retina an asymmet. surface. Trans. Amer. Ophth. Soc. P. 93. 1871. Nagel, A. Histor. Notiz ueber Hyperopie u. Astig. Graefes Arch. XII. 25-30. 1866. Nordenson, E. Rech. Ophthalmomet. sur 1'astig. de la cornee chez des ecoliers de 7 a 20 ans. Annal d'Oculist. Mars Avril. 1883. Pope Eine neue Art. der Assymmet. des Auges. Graefes Arch. B. IX. Abt. I. P. 43. 1863. v. Reuss, A. Untersuch. ueber die optisch. Constanten ametrop. Augen. Graefes Arch. B. XXIII. Abt. IV. P. 183. 1877. Rothmund, Jr. Ueber Weit u. Uebersichtigkeit u. ueber Astig. Bayer Aertz. In- tellbl. P. 19. 1863. Schirmer Contrib. a 1'hist. de 1'astig. et d'hypermetropie. Ann. d'Ocul. Brux. LXII. Pp. 201-10. 1869. Senff Sehen. Wagner Handwortbuch. d. Physiol. B. III. P. 271. 1846. Smith, P. Abst. of 29 cases of Astig. Birmingh. M. Rev. V. Pp. 202-9. I ^7 I> Theobald, Sam'l Notes on three cases of progressive astigmatism. Amer. Jrl. Oph., July, 1885, and Trans. Amer. Oph. Soc. 1885. 54 BIBLIOGRAPHY. Verbandlungen d. vom 3-6 Sept, 1859, in Heidelberg versammelten Augenarzte. Berlin. H. Peters. 1860. Wecker L'astig. et 1'osteogenese du crAne. Communicat a Seance, I5juiilet, 1869, de la Soc, d'Antrop. T. 66. P. 245. 1871. Wilde Cylind cornea. Dublin Jr. Med. Sc. XXVIII. I Se. P. 105. 1846-7. Young On the mechanism of the eye. Philos. Trans. Pp. 23-88. 1801. Zdllner, F. Beitrage zur Kenntniss der chromat. u. monochrom. Abweichung des mench. Auges. Poggd. AnnaL B. CXI. Pp. 329-36. 1860. CHAPTER IV. DIAGNOSIS OF ASTIGMATISM DETERMINATION OF ITS FORM AND DEGREE, AND THE DIRECTION OF THE PRINCIPAL MERIDIANS. 44. When a case of supposed astigmatism presents itself for examination there are four points to be settled : a, whether any astigmatism exists ; b, if it does, the direction of the prin- cipal meridians ; c, the special form of the anomaly, and d, its degree. 45. For simplicity of illustration we will assume that in the case under consideration there does not exist any turbidity of the refracting media, any affection of the nervous appara- tus, or any of the complications which we shall consider in detail later on, but will regard it as a purely optical difficulty. 46. In order to determine the first point, we place the pa- tient, as we always do when examining the static refraction of an eye, at a distance of 15 or 20 feet (4 to 6 metres) from the well-known test types of Snellen. The acuteness of vision of each eye is then taken separately ; and if we find that all the letters in No. xx (6), are clearly made out at a distance of 20 feet, the existence of astigmatism in any abnormal degree can be excluded. 47. If, however, V does not reach 6 / 6 we may be sure of the existence of some error in refraction, which may be either myopia, hypermetropia or astigmatism. In order to determine which kind of ametropia is present, we place in front of the eye first, a+i spherical lens. If this does not render the vision worse, or if it, on the contrary, im- proves it, we are sure hypermetropia exists, and the strongest -\- (55) 56 DETERMINING THE PRESENCE OF ASTIGMATISM. lens, through which No. 6 is seen clearly and distinctly, marks the degree of the hypermetropia, and, as V='/i we ma y De sure that astigmatism does not exist. If -}- lenses do not improve, but, on the contrary, impair vis- ion, then we try spherical concave glasses, and if we find one which gives V= M / M we may safely conclude that it is a case of simple myopia, and the weakest concave glass, which gives a normal acuteness of vision, marks its degree. 48. But if spherical lenses, while improving V somewhat, do not bring the acuteness of vision up to the normal stan- dard of 20 / we may rightly consider that astigmatism, either regular or irregular, is present. 49. Persons affected with regular astigmatism usually give us an intimation of their peculiar refractive error by the mis- takes they make in naming certain letters of the test-types P and F, for example, are very likely to be confounded ; C is often called G, and both are sometimes mistaken for O, while such letters as L and T are readily recognized. Dr. W. S. Little has devised a " test-card l of words, made up of letters confusing to the astigmatic eye," on this princi- ple, which is useful for the purpose of indicating to us whether or not astigmatism exists. 50. Being satisfied that astigmatism is present, the next step is to determine the direction of the principal meridians. One of th*e simplest methods of ascertaining this is to turn a cylindrical glass of -j- or I D before the eye, noting the meridians with which the axis of the cylinder corresponds when the smallest test letters of Snellen that can be distin- guished are most and least distinct. These meridians, which will be found at right angles to each other, are the meridians of greatest and least refraction. 51. Another plan is to place before the patient a series of lines of equal thickness, radiating from a common centre, such as the wall-known fan of Snellen. These lines should be placed at such a distance that one or two running in one di- rection shall be seen clearly and distinctly. The direction of 1 Published by J. W. Queen;& Co./Phila. THE PRINCIPAL MERIDIANS. 57 these lines will correspond to one of the principal meridians, and the other meridian will be at right angles to it. There are other methods for determining the direction of the principal meridians, of which we shall speak later, but in simple, uncomplicated cases these will suffice. 52. The directions of the principal meridians are ex- pressed in degrees representing their inclination to the hori- zon. Thus : If we find that the line of Snellen's fan which is most distinct is the vertical or at 90, the corresponding me- ridian will be horizontal or at 180, and the opposing meridian vertical or at 90. If the axis of the cylinder which renders the test-types clearest is at 45 we know that it is the me- ridian at 135 which is affected by its refraction, for the axis of the cylinder is always at right angles to the meridian whose re- fraction it affects. It therefore becomes easy to express ex- actly in degrees of inclination to the horizon the direction of the meridians of greatest and least refraction. 53. Having in this way obtained the direction of the prin- cipal meridians, it remains to determine whether only one or both are ametropic, and the degree of the ametropia ; in other words, to define the form and amount of astigmatism. This will be most easily done by taking some cases repre- senting each of the three forms of astigmatism. \ 54. CASE I. The patient has V=-- 20 /i barely, and it is not brought up to 20 / x i by any + or glass. By rotating a -j-i cylinder before the eye, we find that when the axis is perpendicular or at 90 V= 20 / xxx and a few letters of No. XX are made out. When the axis is at 180, vision is very much worse, so that he can scarcely make out No. LXX. This shows that the principal meridians are vertical and horizontal, and also that the horizontal meridian which corresponds with the refracting merid- ian of the correcting cylinder is hypermetropic. We now place a -(-0.507 axis vertical before the eye, which, while improving vision somewhat, does not increase it as much as the +i. The hypermetropia of the meridian is therefore greater than i 1). We then try +1.5 cy, axis 90, and find that with this all the letters in No. XX are seen distinctly, while with +2 cy axis 90 they are less distinct. Diagnosis : Simple hypermetropic astigmatism in the horizontal meridian. Or we may express it thus : H. astig. 1.5 D axis 90; for it must always be borne in mind that the axis of the cylinder is at right angles to the direction of the meridian it corrects. \ 55. CASE II. The patient in looking at Snellen's fan placed at a distance of six metres, says he sees only one or two black lines to the right, all the others appear- ing blurred. You find upon examination that the line which is sharpest and black- 58 ILLUSTRATIVE CASES. est is at 125. You now place before the eye a -fi spherical lens and ask him whether this line still remains as distinct as before. If he answers "No," then you try minus spherical lenses in the same way and if the line is not more distinct with than without them, this meridian (35) is emmetropic. You then place plus glasses before the eye and ask their effect on the lines to the left which are most blurred, and if you find that they do not help, but on the contrary render them still more indistinct, you try minus spherical glasses With these you find the indistinct lines to brighten up, and finally with 2 spherical the lines at about 35 become very clear and sharp, while those at 125 are rendered gray and indistinct. This shows that the meridian with its axis at 35 has a myopia 2 D. If a cylindrical lens 2 D is placed with its axis at 35 the fan becomes even, all the lines having the same clearness and distinctness and with it V = /. This is a case of simple DIAGRAMMATIC REPRESENTATION OF THE DIRECTION OF THE Axis OK AN MATIC MERIDIAN. myopic astigmatism: M. astig. = 2 D axis 35, "and it may be recorded graphic- ally as in Fig. 20, where the line AB represents the axis of the faulty meridian. { 56. CASE III. Without any glass V = '/M, and none of the lines in Snellen's fan are seen with distinctness, all being a confused blur. Spherical glasses art- tried as in the other cases, beginning with the convex, and it is found after a number of trials that with a 1.5 all the letters in No. 18 are properly made out, with the ex- ception that P is called F, and with this lens the line in Snellen's fan at 60 is quite sharply defined. Those near the bottom to the right, however, are very indistinct. If this is the weakest concave glass through which the line at 60 is sharply defined, then the meridian with its axis at 60 is myopic to the extent of 1.5 dioptrics. It is found on further trial that the line at 150 is brought out clearly by 3. all the others appearing less distinct. This shows that the meridian whose axis lies at 150 is also myopic. Both meridians are therefore myopic, but one in a higher de- gree than the other. The difference in the degrees (3 1.5 = 1.5) of myopia in the two meridians constitutes the astigmatism of the eye. Because there is a spher- ical ametropia associated with the astigmatism, this form is called compound myopic astigmatism, and we record it thus: M. 1.5 D with M. astig. 1.5 axis 150. W r ith this combination of minus glasses the fan appears uniform and vision = 6 /s. ILLUSTRATIVE CASES, 59 \ 57. CASE IV. We find that the patient, who is a boy of 15, sees the line of the fan at 170 more clearly than any of the others. He can also see it clearly with a Vie or a +Vis spherical. This shows that there is hypermetropia in the corre- sponding meridian, and thai he overcomes the glass by means of his accommoda- tion, which is very strong at that age. A + Vie or + Vis blurs this line, therefore meridian with its axis at 170 has H = Vis- With this glass the indistinct lines on the left near the centre also appear brighter and with a +Vio they are perfectly clear, the blackest one being at 80 ; that at 170 is very much blurred. We have, therefore, a H. in the meridian 80 which is greater than that in the meridian at right angles to it. There being hypermetropia in both meridians but more in one than in the other, this is compound hypermctropic astigmatism, and as both have H. = Vis METHOD OF RECORDING A CASE OF COMPOUND ASTIGMATISM. in common, we write H. Vis with H. astig.=Vio-*-Vi8= 18 /i80 w /iati=^/iti increase it slightly and + glasses up to V2 do not make vision worse. On asking him to look at the fan we find that all is indistinct, but he thinks he sees a vertical line, though it is much blurred. We place spherical glasses in succession before the eye as usual, and after many trials find that the line at 90 comes out sharply with + J /22, while those at the bottom are so confused that they cannot be recognized as lines at all. We are now assured that 90 is the axis of the hypermetropic meridian. The meridian whose axis is at 180 we know is not hypermetropic, because the horizontal lines are more blurred through the convex lenses. We therefore try minus glasses for this meridian, and after a 6O ILLUSTRATIVE CASES. number oi trials find that the line at 180 is sharp and black with '/, the other lines appearing as a grey blur. There is therefore a M. of '/ ' n this meridian. There being H. in the horizontal meridian and M. in the vertical meridian we have to deal here with a case of mixed astigmatism and we write II. = '/w 9 with M. = '/ 1 80. The Mai astigmatism is therefore equal to the sum of these, that is VM + '/ = '/is* + */i = "/i = '/4-75. With this combination of lenses (+ '/n 90 O '/ 180) V = '/ and all the lines in the fan become of uniform clearness. 59. In simple, uncomplicated cases the methods employed in the foregoing examples are sufficient, if carefully followed out,to establish the diagnosis and the character of astigmatism, and, under all circumstances, by whatever method the diagnosis of the astigmatism may have been determined, it must be veri- fied by means of cylindrical lenses and the test-types. The best vision is what we aim at, and no method has yet been found which can dispense with this as the final arbitrament. 60. But, unfortunately, all cases of astigmatism are not uncomplicated, and there are many ways in which error, both on the part of the patient and surgeon, may creep in. The sources of these errors will be considered in the next following chapter. BIBLIOGRAPHY. Raudon Note sur un moyen prat, de reconnaitre. i. L'astig reg. 2. La nature de 1'astig h. ou m. 3. Le meridian astigmate. 4. Le degre de 1'astig. sans les verres cylind. par 1'emploi exclusif des verres spheriques. Rec. d'Ophth. P. 8l. 1878. Buckner, J. H. Astig., illust. cases from clinic, mem. Cincin. Lancet and Obs. Aug. P. 466. 1875. Carreras Del Astig. Compilador Med. Barcelona. IV. Pp. 283, 301, 389. 1868. V. Pp. 89, 91. 1869. Culbertson, H. Refract, of the eye as distinguished from accommodat. and esti- mated as an equivalent from the index of refract. Cincin. Lancet and Clinic. VIII. P. 451. 1882. Daumas, L. C. De 1'astig. 4. Paris. 1874. Derby, H. Four cases of astig. Am. M. Times. New York. VII. Pp. 277-78. 1863. Donders, F. C. L'astig. Arch. gen. de Med, I. Pp. 200-9. Paris. 1863. Fenner, C. J. A treatise on refract, and accommodat. Richd. and Louisville Med. Jr. P. 481. 1873. Ferguson, R. M. On a remark, case of astig. Louisvl. Med. Times. Dec. 1 5. 1883. BIBLIOGRAPHY. 6l Fravel, E. H. Anom. of Refract. Gaillard's M. Jr. New York. XXXII. P. 442. 1882. Frothingham, G. E. A case of mixed astig. with predom. myopia, diagnosed by its very peculiar ophth. appearance. Phys. and Surg. Ann Arbor, Mich. II. Pp. 14-16. 1880. Fulton, J. F. Astig.: a rept. of cases. N. W. Lancet. St. Paul, Minn. II. Pp. 3-6. 1882. Galezowski De quelques varietes d'astig. Rec. d'Ophth. Paris. II. Pp. 464- 1874. Grossmann, L. Die Accommodat. u. Refract-lehre. Med. Chir. Presse. Pest. Nos. 10, 11, 12, 14. 1873. Hafften, van, Wm. Die Bestimmg. des Astig. Utrecht. 1879. Harlan, G. C. Co. myop. astig. Phila. M. Times. II. P. 70. 1871. Hays, Isaac Astig. Tr. Coll. Phys. Phila. N. S. I. P. 418. 1850. Higgins, C. Astig. Med. Times and Gaz. II. Pp. 669-71. London. 1876. Hirschberg, J. Refraktion. Eulenberg's real Encyp. d. ges. Heilkd. XI. P. 379- 1882. Hough, J. B. On the detect, and estim. of astig. Cincin. Lancet and Obs. XVII. Pp. 262-4. 1874. Hulke, J. W. Summary of 192 cases of astig. Ophth. Hosp. Rep. VIII. Pp. 141-77. London. 1875. Imbert De 1'astig. Paris. 1883. Javal, E. De 1'astig. (Rap. de M. Gavarret). Bull. Acad. de Med. XXXII. Pp. 872-82. Paris. 1866-7. Javal, E. Nouvelle install, pour la determinat. de 1'astig. Ann. d'Oculist. T. LVII. P. 37. 1867. Javal, E. De ia lentille de Stokes. Ann. d. Oculist. T. LXI. P. 73. iF6g. Javal, E. Divers appareils pour la measure de 1'astig. Compt. rend, de la Soc. de Biolog. P. 302. 1873. Javal, E. Des variations de 1'astig. Compt. rend, de la Soc. de Biolog. 55. V. P. 270. 1874. Javal, E. Lentille de Stokes modifiee, Ann. d'Oculist. T. LXXX. P. 201. 1878. Kaiser, H. Die Theorie des Astig. Graeles Arch. XI. Hft. 3. Pp, 186-229. 1865. Knapp, H. Demonstrat. of the refract, of light by asymet. surfaces and the deter- minat. of astig. with glasses and the ophthalms. Trans. Am. Med. Ass. 1880. Knauthe, T. H. Ueber Astig. 8. Leipzig. 1863. Landesberg, M. Regl. Astig. Med. Bull. Phila. III. Pp. 256-8. 1881. Little, W, S. A tabl. rept. exhibit, the position of the axis of the cylind. in simpl. co. and mxd. astig., the m. and h. forms compared, with rmks. Trans. Amer. Oph. Soc. 1880. Magin Dell 'ipermetrop. e dell'astig. Riv. Clin. di Bologna. V. Pp. 85-9. 1866. Mauthner, L. Vorlesungen ii. d. optisch. Fehler d. Auges. Wien. W. Braumuller. 1876. Mengin Astig. mixte a droite ; hypermetrop. simple a gauche, Rec. d'Ophth. 3. S. II. Pp. 1 7-20. Paris. 1880. Meyer, E. De 1'astig. Gaz. des Hop. XXXIX. P. 342. Paris, 1866. Middleburg, H. A. De Zitplaats van het Astig. versl. Nederl. Gasth. v. Ooglig- 62 BIBLIOGRAPHY. ders. IV. Pp. 146-90. Utrecht. 1863. Also in Graefe's Arch. B. X. Abt 2 P. 83. Nagel Die Anomal. der Refract u. Accommodat. des Auges. Graefe u. Sae- mish. Hdb. d. gesmt Aughlk. B. VI. Cap. X. Nicalaysen, J. Om. Astig. Norsk, mag. f. Laegevidensk. XX. Pp. 721-41. Christian ia. 1 866. Noyes, H. D. Obs in Astig. Trs. Amer. Ophth. Soc. 1868. Noyes, H. D. A scheme to aid in recording and examining cases of asthenop. Trans. Amer. Ophth. Soc. Pp, 81-7. 1871. Perrin, M. Astig. J. d'Ophth. I. Pp. 54, 112, 148. Paris. 1872. Reeve On optic, defects. Trs. Canad. Med. Assoc. I. P. 192. 1877. Risley A case of hypermetrop. astig. N. Y. Med. Jr. V. XL. No. 5. Salen, E. Om Astig. Upsala Lakaref. Forh. III. Pp. 457-8'- 1867-8. Schirmer Contrib. & 1'hist. de Pastig. et de 1'hypermetrop. Ann. d. Oculist. T. LXII. P. 201. 1869. Schweigger, C. Bemerk. ttber die Diag. u. Correct des Astig. Graefe's Arch. B. IX. Abt I. P. 178. 1863. Schweigger Hdbch d. spec. Augenhlk. 1871. Seely, \V. W. Experience in refract, cases. Trs. Amer. Ophth. Soc. 1884. Snellen, H. De Richtung der Hauptmerid. des astig. Auges Graefe's Arch. XV. 2 Hft. Pp. 199-207. 1869. Also Versl. Ned. Garth, v. Oogligjders. X. Pp. 151- 173. Utrecht. 1869. Tetzer, M. Beitrage zur Kenntniss des Astig. Med. Jahrb. XII. Pp. 145-51. Wien. 1866. Thilesen, P. Om Astig. 8vo. Christiania. 1873. Unger Lunette d'essai pour 1'astig. Ann. d'Oculist. T. LXXXI. P. 89. 1879. Weil, J. Essai sur 'a determinat. clin. de 1'astig. Ths. de Paris. 1875. Wolfskehl, P. Ueber Astig. in Thieikaug. u. d. Bedeut. d spaltform. Pupille. Ztschr. f. vergleich. Augenhlk. 1882. CHAPTER V. DIFFICULTIES AND OBSTACLES IN THE WAY OF AN ACCURATE DIAGNOSIS OF ASTIGMATISM INFLUENCE OF ACCOM- MODATION THE USE OF MYDRIATICS. 61. As stated in the concluding paragraph of the last chapter, all cases of astigmatism are not so readily determined as might appear from the examples given. The inexperienced beginner will meet with many perplexities, and there are cases which test the skill even of the most expert. We shall endeavor in this chapter to point out the principal obstacles that lie in the way of a correct and speedy diagnosis and the best methods for overcoming them. 62. Most of the difficulties arise from the fact that we are not dealing with an optical instrument alone, but also with an anatomical organ having a physiological function. It is the office of the eye, as an organ of sense, to interpret impressions made on the retina, and the judgments formed from these im- pressions are not always correct. It is astonishing how often otherwise intelligent persons will make statements as to what they see, which we know are not true, and which, upon further questioning and coaching, they reverse. As a matter of ex- perience, we find that most astigmatic patients have to be, to a greater or less extent, educated in the right method of observ- ing and of correctly reporting what they see, and it often re- quires the exercise of much patience on the part of both ex- aminer and patient to arrive at the exact truth. The answers to questions are frequently misleading, and much tact is fre- quently necessary to extract the true meaning from statements which, though honestly given, are incorrect. And besides, the answers are often of such a vague and general character that (6 3 ) 64 SOURCES OF ERROR IN DIAGNOSIS. opposite interpretations might be given to them, and it is never safe to trust to the results of a first examination. Sev- eral trials should be made with different lenses with their axis at various degrees until there is found one which, when placed at the same angle, always gives the same and the best result. When, in a compound myopic astig., the common M. being 3D, a minus spherical lens of that strength is held before the eye and the patient is told to look at the fan he will most likely say that he sees nothing. Upon close questioning, however, we find that he does see a single line, and this single line is perhaps the key to the situation. And when, on the other hand, in simple astigmatism of either form, a cylindrical lens of the proper kind, but under or over-correcting, is so placed before the eye that its axis shall correspond with that of the faulty meridian, the patient may exclaim, "Now I see all the lines." That may be true, but it may not be all we want. It is neces- sary not only that he see them all, but that he see them all with equal clearness and distinctness. Other cylindrical lenses of the same character must be tried until one is found with which the fan is said to appear uniform. But even this should not be entirely trusted. The test-letters must be the final resort, and glasses weaker and stronger than the one selected must be tried to see whether vision is made better or worse by them. 63. We find, under certain circumstances, an improvement with cylindrical glasses when there is no astigmatism present. A person having M = ! /i with V = *%, will find vision so much improved by a '/is cy. that some letters in No. L can be made out. This improvement does not come from the cor- rection of an astigmatism, but is due to a correction of the myopia in one meridian, thus transforming a M. of Vis mto a M. astg. of/is, in which one meridian is emmetropic; and an ametropia in a single meridian is much better for vision than an ametropia in both. Under these circumstances, too, vision remains the same when the lens is rotated with its axis in va- rious meridians, which is not the case in astigmatism. In making examinations by these methods, therefore, trials INFLUENCE OF THE ACCOMMODATION. 6$ with spherical glasses should always be made first, and if they do not bring vision up to the normal standard then search should be made for astigmatism. 64. It is believed by some that astigmatics used by pref- erence the centre of their focal interval, or rather that portion whose section is a circle, as shown in E, Fig. 12. This can hardly be, for the eye instinctively seeks to have a distinct image, if it is possible, of some part of an object, rather than a confused image of the whole. It is natural, therefore, that they should use one or the other focal line when it is possible for them to do so. Which focal line they prefer when they have both at command has not been determined definitely, but it would seem that theoretically they would select the anterior focal line, because here the circles of diffusion are smaller than at the posterior focal line ( 19). Certain ob- served cases appear to corroborate this view. I have seen several cases of simple hypermetropic astigmatism with the axis at 90 which had been converted by a tonicity of the ciliary muscles into a simple myopic astigmatism axis 180, thus rendering 90 emmetropic. I accounted for it by sup- posing that they preferred to always have vertical lines dis- tinct. It may be stated, in this connection, that the small de- gree'of accommodation possessed by some aphakial eyes which enables them to have an amount of distinct vision with the same glasses at different distances, has been explained by an astigmatism which enables them to see one part of an object more clearly at one distance and another part at another. Their range of A would be expressed by their degree of astig- matism. 65. But aside from these sources of error there is another still more important, which arises from the power possessed by the eye of changing its refractive condition at will. This faculty of "accommodation" (A) resides in the ciliary mus- cle, and the change is brought about by its action on the crys- talline lens, causing it to become more convex, thus increas- ing its refracting power. It will be seen, on a moment's con- sideration, that the accommodation becomes an important 66 INFLUENCE OF THE ACCOMMODATION. factor in determining the static refraction of the eye that is the refractive condition when in a state of absolute repose. In examinations of the eye as regards its optical properties its dynamic refraction must always be held in mind as a possible element, and its influence allowed for. This is not the proper place to consider the influence of the accommodation on all the forms of ametropia, so we shall limit ourselves to the ef- fects as we find them in astigmatism. 66. Since the effect of the accommodation is to increase the refraction of the eye, we know in what direction to look for its influence. Such an increase of refracting power would di- minish the degree of a hypermetropia, convert it into an em- metropia,"or even into a myopia. It would change an emme- tropia into a myopia, and where myopia existed increase its degree. It would in the same manner change not only the de- gree, but also the form of an astigmatism. A compound hy- permetropic astigmatism can be changed by the act of accom- modation into the simple hypermetropic form, into the simple form, or, it may be, into the compound myopic form. Mixed astigmatism may be masked by the accommodation, being converted into the simple or the compound myopic form. Take for example, H = 3 ^ H. astig. = 2 axis 90. An amount of A equal to 3 D would convert this into a H. astig. = 2 D ; that is to say, an increase of refraction of 3 D would render the meridian with its axis at 1 80 emmetropic and leave a H = 2 D at 90. If A = 5 D, then the meridian with its axis at 90 would be rendered emmetropic while that at 1 80 would be myopic by 5 3 = 20, converting it into a case of simple M. astig. Should A = 6 D it would be a com- pound myopic astig.: M = i ^ M. astig = 3 axis 180. In testing for astigmatism, therefore, due care must be ex- ercised in eliminating any complications on the part of the accommodation. It is for this reason that we use, by prefer- ence, those methods of examination in which the patient is re- moved to 5 or 6 metres from the test objects. Under these circumstances the emmetropic eye is in a state of repose and adapted to the parallel rays which come from objects at that USE OF ATROPINE. 6/ .< r distance, and there is no incentive for the exercsie of the accom- modative power ; while in the case of myopia the accommoda- tion would be of no avail, since the myopic eye has al- ready an excess of refraction, and its far point is nearer than 20 feet. So we have, in this method, to take only a possible hypermetropia into consideration. Under ordinary circum- stances, and where there is no actual spasm or undue to- nicity of the ciliary muscle, there need be no important error from this source, if proper care is exercised and sufficient time is given to the investigation. 67. Examinations should always begin with convex . lenses ; and myopic conditions should never be accepted unless there is an improvement with concave glasses, which no other glasses give. When, for example, we find that I cy. with the axis at 1 80 brings vision from 20 / 50 to 20 / 20 , we must not conclude that we have to do with a case of simple myopic astigmatism, particularly if the patient be a young person with an active ac- commodation. It might be that the I cy. 180 had con- verted a simple H. astig. of I D 90 into a simple hypermetro- pia ot i D, which the accommodation could readily overcome. In this instance it is true the astigmatism would have been cor- rected, but at the expense of the accommodation power. So before concluding a diagnosis of M. astig. we should try the effect of a + i cy. 90, and if with this V = 20 / 20 we know positively that it is H. astig. of I D axis 90. 68. There is a way by which we can with certainty get rid of the errors that arise from the accommodotion. By par- alyzing the ciliary muscle by some of the mydriatics such as atropine, duboisine, homatropine, etc., we eliminate its active or dynamic refraction, and place the eye in a condition of static refraction, though, as we shall see later, this is not al- ways its normal optical state of repose. When a drop of a 2 or 4% solution of atropine is put in the eye, in from twenty minutes to half an hour there is great dilatation of the pupil, followed some minutes later by a loss of the whole or a greater part of the power of accommodation. When there is spasm or undue tonicity of the ciliary muscle it frequently requires NORMAL OPTICAL STATE OF REPOSE. several instillations practiced at intervals of an hour or so to produce a complete relaxation of the muscle, and some- times it takes several days, with from four to six instillations each day, to obtain the full effect of the drug. 69. But while this paralysis of the ciliary muscle gives us a relief from disturbances on the part of the accommodation, it is in itself not entirely free from disadvantages, inconveni- ences, and even errors. One of the chief inconveniences attendant upon paralysis of A is that the effect of the mydriatic does not pass off fully within a week, and often ten or twelve days elapse before the ciliary muscle regains its normal tone. During this time the patient, unless highly myopic, is deprived of the use of the eyes for all close work, such as reading, writing, etc., and this, to the large majority of our patients, is a matter of great mo- ment. We have no right to deprive a patient of all use of the eyes for a week if it can be avoided. Besides, the result obtained by an examination under this condition does not represent always the actual and normal static refraction of the eye. A paralyzed state of a muscle is not its normal condition. There is a certain amount of to- nicity inherent in every muscle which disappears when it is paralyzed, and it is unquestionably a varying quantity in differ- ent individuals. As a result of this, we find that when the A of young people is paralyzed there is a diminution of static refraction varying from 0.5 D to 2 D. It is the custom to re- fer to this as the latent hypermetropia, and so, in a certain sense, it is, but it is doubtful whether we should under ordi- nary circumstances, and when it is low in degree look upon it as pathological or abnormal. The result of an examination of the refraction of a large number of children, ranging in age from a few hours to 10 and 12 years, seems to point to the fact that in the human eye we have from infancy to adult life a gradual evolution from the hypermetropic to the emmetropic and myopic condition. 1 Dantel, from the results of an exam- 1 It is a significant lact in this direction that the eyes of most lower animals are hypermclropic some of them very highly so. LATENT HYPERMETROPIA. 69 ination of a large number of persons of all ages as to their manifest and total hypermetropia, finds that only l / 3 of the to- tal H is manifest from 6 to 15 years; l / 2 from 16 to 25 ; 2 /3~V* from 26 to 35, and the two are equal only after the 36th year. He finds also, as a matter of experience, that in eyes other- wise sound a correction of manifest H is quite sufficient. With the rarest exceptions, all infants are hypermetropic, and few children of even 10 years, but show much decrease of their refraction on paralysis of the accommodation. This hy- permetropia is overcome, as a rule, by the normal tonicity of the ciliary muscle, which I do not think we have a right to regard in the light o( a pathological muscular spasm. When the ciliary muscle is paralyzed by a drug its natural tonicity is of course lost, and we have a correspondingly di- minished refraction, but when the effect passes off, the tonicity returns and with it increased refraction, and the eye resumes its previous optical state. That there is such a tonicity in the external muscles of the eye which is lost in paralysis, is clearly demonstrated by the ex- ophthalmus, often very marked, which accompanies a paraly- sis of all the external muscles of the eye. We have no means of measuring the amount of muscular tonicity, normal to the eye in any given case, for it is a ques- tion of physiological dynamics and we aje not dealing with a constant quantity. The actual power resident in the ciliary muscle does not seem, in some cases, to^bear any definite rela- tion to the muscular power of the other parts of the body. We sometimes find it weak in strong persons, and occasionally disproportionately strong in weak persons, though, as a gen- eral rule, it participates in a general muscular debility. It is apparent from this that, in young people particularly, we should not, as a rule, accept the refraction found under the full effect of a mydriatic as the normal optical state of the eye. When, therefore, there is ametropia present with the astigmatism which requires correction, the final glasses should not be ordered until a careful examination is made after the effect of the drug has passed away, for in the majority of cases JO SPASM OF THE CILIARY MUSCLE. in young persons, the glasses which correct while under the mydriatic, over correct when the eye returns to its natural state, and at the beginning, almost without exception, the glasses giving full correction prove unsatisfactory, for one rea- son, among others, that the equilibrum between the external and internal muscles to which the eyes have accustomed them- selves is destroyed, and it requires often a considerable time for them to become adjusted to the new order of things. 70 As to the frequency of true spasm of the ciliary muscle, the opinions of clinicians are somewhat divided. Most of the continental authorities do not consider it at all common, and, therefore, except on rare occasions, do not follow the practice of atropinization before taking the refraction. Mauthner (opt. Frh. d. Aug., p. 736), contends that the eye invariably shows its true static refraction under the ophthalmoscope. Hirsch- berg says ( CentralbL f. prak. Augenheilk. June, 1884, p. 169) that in the many thousands of cases that he has examined by the direct ophthalmoscopic method and with glasses, he has never met with a case of spasm. Furthermore, he says that he has never found the objective refraction different before and after atropinization, either in hypermetropia or in myopia. Landolt (Traite d* ophthalmol. par Wecker et Landolt Tome 3) says he rarely has recourse to atropine for the determination of astigmatism. In America, however, it has become a custom with quite a number to resort to atropinization as a routine practice in all cases. It should be the aim of the ophthalmic practitioner to at- tain such skill in the determination of refraction that he shall have accuracy in his results at a minimum of inconvenience to his patients. The best method, it seems to me, is to obtain the best results possible by the methods already described, or such a combination of those that will be described later as may be deemed necessary, and give the glasses thus indicated for trial. If these should not prove satisfactory, we have still atropinization left. And as we study our different methods more closely and acquire by experience a greater skill in their use, we will find less and less need for the mydriat/c. PARTIAL SPASM OF A. 71 71. My own guide to the use of atropine,! find in the di- rect method of examination by the ophthalmoscope. (See Chap. VII.) If I find the patient to persistently refuse + glasses, and yet there is a hypermetropia manifest under the ophthalmoscope, or if, while looking at the fundus through -f- glasses, I see the vessels becoming alternately clear and indis- tinct, indicating an alternate relaxation and contraction of the ciliary muscle, I know that there is an excessive tonicity of the ciliary muscles which masks a hypermetropia, and then I usually use atropine in order to discover to what extent the tonicity reaches;, not necessarily for its full neutralization, but as a guide in the selection of glasses that can probably be worn with comfort and advantage. For the beginner, however, particularly when the case is complicated and the answers given by the patient are confus- ing and unreliable, and where the results by one method of ex- amination do not correspond with those by another, an imme- diate paralysis of A may be the shortest way to a solution of the difficulty. 72. What has been said in the foregoing paragraphs in re- gard to the accommodation, has reference to the contraction of the ciliary muscle as a ivhole, and to its influence on the ame- tropia which may accompany astigmatism. The accommoda- tion in its entirety cannot affect the amount of astigmatism, though it greatly modifies its general character. It would seem however, from the reports of Drobowolski, Javal and others, that there can be a partial contraction of the muscle of accom- modation producing a lenticnlar astigmatism, the effect of which would be either to create a new or increase an existing astigmatism, or to a greater or less extent to neutralize that of the cornea. According to Javal the latter would appear to be the most common effect, for he has found corneal astigmatism as discovered by means of the ophthalmometer, overcome by an unequal accommodation, and made manifest only on com- plete paralysis of the ciliary muscle. To this unequal contrac- tion of the ciliary muscle he refers those cases of astigmatism which make their appearance in adult life and which give no 72 DISADVANTAGES OF A WIDE PUPIL. evidence of their existence in childhood. The unequal A seems to pass away with the increasing stiffness of the muscle and the hardening of the lens which are the accompaniments of advanc- ing years. 73. In treating of refraction by triaxial ellipsoids in Chap. II. it was shown in Figs. 7 and 8 that the monochromatic abe- rration of the cornea increased from the apex towards the periphery, and from this arises another disadvantage attendant on the use of a mydriatic. A wide pupil opens up the passage for a larger number of rays refracted nearer the periphery of the cornea, and in addition to increasing the circles of diffusion in all meridians, will in most instances also increase the differ- ence in the refraction in the two principal meridians. As a re- sult of this the astigmatism as determined in this condition will be apt to differ from that obtained with a pupil of normal size. 74. We repeat in conclusion, therefore, that what we wish to obtain is the static refraction of the eye in its two principal meridians when the organ is in its normal condition and not when its instrinsic muscles are in a state of spasm or paralysis. BIBLIOGRAPHY. Ayres The use of atrop. in detenu, glasses and the influence of the vasomotor sysL on the accommod. of the eye. N. Orl. Med. and Surg. Jr. XI. No, 8. 1884. Bjerrum, M. F. Ueber d. Refrac. d. Neugeb. Internal. Cong, zu Copenhagen. 1884. Bumstead, S. J. The unequal contraction of the ciliary muscle. Archiv. of Oph. XII. 2. 208-212. Dantel, Louis Ueber den Einfluss d. Lebensalters auf das Verhalt d. manifst. zur, totalen Hypermetrop. Cntbl. f. p. Augenhlk. juli-Aug. 1883. Dobrovolskii, V. Orazlichnikh izmaineniyakh Astig. (some modificats. of Astig). Voyenno Med. J. III. PL 3. 34-104. St Petersbg. 1868. Dobrowsky, W. Ueber verschied. Veranderung d. Astig. unter dem Einfluss d. Accommodat Graefe's Arch. XIV. 3 Hft. Pp. 51-105. 1868. Donders, F. C. Ueber scheinbare Accommodat. bei Aphakie. Graefe's Arch. B. XIX. Abt. I. P. 56. 1873. Ely, E, T. Refraction in the eyes of newly born children. Archives of Oph. VoLIX. P. 29. Germann, Theodor Beitrage zur Kentniss der Refractionsverhaltnesse der kinder im Sanglingsalter sowie im vorshulpflichtigen Alter. Graefe's Archiv. XXXI. 2. Pp. 122-146. BIBLIOGRAPHY. 73 Cradle, H. Act. of the ciliary msl. in astig. Am. J. M. Sc. N. S. LXXVII. Pp. 109-11. Phila. 1879. Hansen Untersuch. iiber die refract. Verhaltnisse in 10 bis 15 Lebensjahre u. das Wachsthum der Augen in diesen Jahren. Inaug. Diss. Kiel. 1884. Horstmann Beitr. z. Entwickelung d. Refractions verhaltnisse d. mensch. Auges wahrend d. ersten 5 Lebensjahr. Graefe's Archiv. 1884. Horstmann Refrac. an 40 atropinozirten Augen von Neugeboren. Tagbl. d. 53 Vers. Deut. Naturfor. u. Arz. zu Danzig. 1880. Horstmann Ueber verhalt. Refract, v. Kindern. Ber. d. Ophth. Ges. zu Heidel- burg. P. 239. 1878. Javal, E. Des variat. de 1'astig. Compt. Rend, de la Soc. de Biolog. 1873. Javal, E. Astig. chez les enfts. Gaz. hebd. P. 145. 1879. Javal, E. Sur la theorie de 1'accommodat. Compt. Rend, de la Soc. de Biolog. 1882. Kaiser, H. Bestim. der sogenannten optic. Constant, der Accommodat. u. des Astig. der beiden in Betracht gezog. Augen. B. XIII. I. 354. Knapp, J. H. Ueber die Lage u. Kriimmung der Oberflachen der mensch. Kris- tallinse u. den Einfluss ihrer Verand bei der Accommodat. auf die Dioptrik des Auges. Graefe's Arch. B. VI. Abt. II. P. I. 1860. Koenigstein Untersuch. an d. Aug. neugeborenen Kinder. Wien. Med. Jahrbuch. I. 1881. Landesberg, M. Ueber das Auftret. v. regelmassig. Astig. bei gewes. Refract, u. Accommodatanomal. Graefe's Arch. XXVII. Abt. II. Pp. 89-98. 1881. Pfliiger, Dr. Untersuchung. der Augen der Luzerner Schuljungend. Graefe's Archiv. XXII. 4. 63-117. Randall, B. Alex. The refraction of the human eye. Amer. Jnl. Med. Sci. July. 1885. Reuss, v. A. Beitrag zur Kentniss d. Refractverand. im jugendl. Auge. Graefe's Arch. B. XXII. Abt. I. P. 210. 1876. Schleich Die Augen von 150 Neugeborenen oph. untersucht. Mitt, aus d. oph. Klinik zu Tubingen. 1884. B. II. H. I. Ulrich, G. Refrac. u. Papilla opt. d. Aug. d. Neugeb. Inaug. Dess. Koenigsberg. 1884. Unterharnscheidt Ueber incomplt. oculomot. Lahmg. u. accommodativ Linsen- astig. Klin. Monatsbl. f. Augenhlk. XX. P. 37. CHAPTER VI. OTHER SUBJECTIVE METHODS OF EXAMINATION CHANGE IN THE FORM OF A POINT OF LIGHT ADAPTATION OF SCHEINER'S EXPERIMENT THE STENOPAIC SLIT MODIFICATIONS OF SNELLEN'S FAN OPTOMETERS. 75. In view of the difficulties and liabilities to error pointed out in the preceding chapter, it is apparent that there would be an advantage in having at command a number of different methods to which we could appeal in case of doubt and for verification. Fortunately we are not without such resources. 76. The various means used in the diagnosis of astigma- tism can be divided into two general classes ; the subjective and objective. 77. In the subjective methods we rely entirely on the state- ment of the patient as to how the test objects appear and base our diagnosis on these alone. 78. In the objective methods we are independent of the statements of the patient, and rely solely on our own observa- tions. 79. For errors in the first method the patient is mainly responsible. For errors in the second the observer is himself accountable. The methods described in Chap. IV belong to the first named class, and before going on to consider those of the ob- jective class we will give an account of other subjective meth- ods which have been found useful. 80. CHANGES IN THE FORM OF A REMOTE POINT OF LIGHT. This method, which was suggested first by Airy and was used very extensively by Bonders in the beginning of his (74) KYAMINATION WITH A POINT OF LIGHT. 75 studies of astigmatism, gives us directly a very correct idea of the direction of the faulty meridians. Bonders' plan of using it was as follows : In front of a window-pane of ground glass he placed a black board abo_ut_ thirty- five inches square, in the x < middle of which was a perforated metallic plate. In front of this perforation can be brought a diaphragm with openings vary- ing in size from l /. 2 to 10 mm. The patient is required to look at one of these openings, having a diameter of from 2 to 4 mm., *]/* Fig. 22. THE FORM OF A DISTANT POINT OF LIGHT AS SEEN BY AN ASTIGMATIC EYE. at a distance of from 10 to 15 feet. By means of-}- and glasses, if necessary, we produce alternate M and H, when if there be any astigmatism present the point will be observed to be drawn out in opposite directions in the two different .conditions, indicating the meridians of greatest and least refraction. 8 1. But even without the aid of the spherical lenses it is easy to determine the direction of the meridians when astigma- tism is present. In simple astigmatism either myopic or hypermetropic, and in the compound hypermetropic form the spot of light instead of appearing round and sharply defined, as at A, Fig. 22, will appear at a distance of four meters drawn out, say at 90, as at B. In the simple 76 EXAMINATION WITH A POINT OF LIGHT. forms the ametropic meridian will correspond in direction with this, because while the rays falling in the vertical planes of the meridian at 180 are brought to a focus on the retina, those falling in the horizontal planes, in meridian 90, unite_ either in front of or behind the retina and form circles of diffusion whicli spread the image out in an upward and downward direction. If the round spot is not seen clearly at the usual distance of twenty feet, indicating the compound myopic form, then the patient should be brought nearer until there is a distinct elon- gation in some direction, say at 45, as at C, Fig. 22. We then know that this is the direction of one faulty meridian, and, of course, the other must be at right angles to it. 82. But while this gives us the direction of the principal meridians, it furnishes no information as to the form of the astig- matism, the light spot being drawn out in the same di- rection in M and H. As the circles of dispersion, however, are formed in a differ- ent manner, according as the retina lies in front of or behind the focus of the refracting media, we are enabled in any case to determine, in a very simple way, to which category the eye belongs. When the spot is drawn out in a vertical direction, for ex- ample, in the case of H, the dispersion circles are homonymous , that is to say, those belonging to the upper part of the image are formed on the retina above, those belonging to the lower part of the image, below. The upper retinal impression is, un- der these circumstances, projected downward, and the lower one upward. In the case of M we have an opposite state of affairs ; the upper rays, after crossing, form circles of dispersion on the retina below, and these are projected above, while the upper dispersion circles formed by the lower rays are pro- jected downward. When, therefore, a diaphragm is brought from above downward to the edge of the pupil, so as to cut off the upper rays forming the dispersion circles, the lower portion of the diffusion line disappears in case of H, and the upper part gives way first in case of M. The same principle holds good, of PURVES APPARATUS. // course, whatever the direction in which the spot is drawn out ; if, in using the cutting-off diaphragm, the end of the line oppo- site to the direction from which it advances disappears first, then it is H ; if the dispersion circles of the same end disap- pear, it is M. 83. Laidlaw Purves has devised a contrivance by which the inclination of the line can be determined with precision. He draws a semicircle on the screen with the round opening as a center, which is marked off in degrees. The degree to which the diffusion line points gives of course the direction of the meridian that is at fault. In order to facilitate still further this reading, he has a second screen movable behind the first, with a hole in it, which is seen through a semicircular open- ing in the first, made just below the semicircle bearing the de- grees. To the astigmatic eye both light spots appear drawn out in the same direction, and if the opening in the movable diaphragm be turned until its diffusion image is on a line with that of the center opening, the degree under which it stands marks the astigmatic meridian. 84. But we have still no idea of the degree of the astig- matism, except that in cases where the dispersion line is long we know that it is higher than when it is shorter. For its more accurate determination we try cylindrical glasses, with their axes at right angles to the direction of the line of dif- fusion, and when we find one, be it -f- or , which makes the light spot again round, it measures the degree and gives us the form of the astigmatism. Snellen's and Dennett's modifications of Stokes' lens are very handy for this purpose, since, by rotating the disks, we obtain a number of different cylinders in rapid succession. Purves also employs this same method for determining the ametropia that may be associated with astigmatism in the com- pound forms. This he does by finding the cylindrical glass which reduces the dispersion circles in each meridian sep- arately. Having this, it is easy to find the ametropia com- mon to both, and that which is in excess in one meridian. 78 SCHEINER S EXPERIMENT. Example : The spot of light is generally diffused in outline, but is drawn out at 90 (vertically). A 2 cy axis 90 causes the lateral dispersions to disappear and gives the vertical line sharply defined edges. The horizontal meridian is, therefore, myopic 2D. With 3.5" 7 axis 180 the spot is drawn out at 180 and has clean cut horizontal edges. M in the vertical meridian therefore = 3.5, and the case is one of comp. myopic astig.: 2 ^ (3-5 2= ) I -5 cr ax i s 180. 85. Strawbridge, of Philadelphia, has also made a modifi- cation of this method. He has a semicircle of radiating slits like Snellens' fan cut in the diaphragm around the light spot, and these are marked in degrees. The line in the direction of which the light spot in the center is drawn out shows the in- clination of the faulty meridian. Fig. 23. SCHEINER'S EXPERIMENT FOR DETERMINING HYPERMETROPIA AND MYOPIA. 86. ADAPTATION OF SCHEINER'S EXPERIMENT. The experi- ment first described by Scheiner is well known. When a small illuminated object as a candle-flame is looked at through two small holes in a diaphragm, placed so close together that both shall fall within the area of the pupil, only one image is pictured on the retina when it lies at the focus of the refract- ing surfaces of the eye, as at E, Fig. 23. If the retina, how- ever, is found either in front of ( H) or behind ( M) the focus, two images are formed, and two candleflames will be seen. On the distance separating these two images and their relation to each other is based a diagnosis of the refractive condition of the eye. SCHEINER'S EXPERIMENT. 79 When the retina lies at H, images are formed at a and b and these, when projected outward, will be crossed or heterony- moiis that is, the image corresponding to the upper hole will be referred below, and. that belonging to the lower opening will be projected upward. When therefore, the upper hole is covered by a card brought in front of it, the lower candle will disappear ; and when the lower hole is covered, the upper im- age will go. When, on the contrary, the retina lies back of the focus (M ) the two images, a' and b' , will be projected homonymously , and the upper image will correspond to the upper hole and the lower image to the lower t hole ; and when the light coming through the upper hole is cut off, the upper image will disap- pear, and the lower image will disappear when the lower hole is covered. The existence of myopia or hypermetropia can, therefore, be determined with great readiness by simply covering one of the holes. If on covering the upper hole, for example, the lower candle disappears, there is hypermetropia ; if, on the other hand, the upper candle disappears, there is myopia. The distance separating these images will furthermore give us some idea of the degree of ametropia ; the greater the distance be- tween them, the greater being the amount of myopia or hyper- metropia. The ametropia, however, can be measured exactly by placing in front of the holes a -f- or glass which fuses the two images. The number of this lens giving the degree of M or If. 87. This principle can be employed in testing for astig- matism. Since the distance between the two flames varies with the degree of ametropia, when the holes are placed suc- cessively before the different meridians of the eye there will be a variation in the distance between the images in case there exists a difference in the refraction of these meridians. In turning the holes before the eye one meridian will be found where the images are farthest apart and another where they are closest together. These are the principal ^meridians, and the direction of the line uniting the two holes in these posi- tions respectively, gives us the direction of these meridians. 80 THOMSON'S APPARATUS. We determine the form of the astigmatism in the same man- ner as we do that of the general ametropia, by observing which flame disappears when one of the holes is covered. If the flame on the same side disappears, it is myopia, if the op- posite one goes, it is hypermetropia. The degree of astigma- tism is expressed by the cylindrical lens which, when its re- fracting surface corresponds to the faulty meridian, makes the distance between the images the same when the holes are brought before all the meridians. 88. Thomson, of Philadelphia, has devised a plan and invented an apparatus based on these phenomena, for the di- agnosis of the various forms of ametropia without the aid of glasses. For this purpose he employs two small flames whose dis- tance from each other can be varied. To the emmetropic eye these two flames appear sharply defined in outline, and are united only when one passes behind the other. With the ame- tropic observer, however, the case is different. To him each flame is an area of diffused light, whose extent is proportioned to the degree of his ametropia. In making an examination,' the patient is placed at a distance of 5 meters from the two flames and they are gradually approached until the edges of these areas of diffusion touch. Thompson has calculated the size of these diffusion areas for all degrees of Ma.nd H for the distance of 5 meters, and you read off on the arm of his in- strument the amount of departure from the emmetropic con- dition. In the instrument he has described each space of 2.5 cm. corresponds to one dioptry of refraction. While the degree of the ametropia is thus arrived at with tol- erable precision you have not as yet the form. This you ob- tain by passing a card partially across the pupil, when, as explained in the preceding paragraph, one side of the diffusion areas of both flames will be cut off. On the principle we have already explained, if the cutting off is homonymous it is a case of M, if heteronymous it is H. In making use of these diffusion images for the diagnosis of astigmatism, advantage is taken of the modification in the form THE STENOPA1C SLIT. 8 1 of the area of diffusion, as in Donders' method, and of the abil- ity by means of his instrument to place the flames in a line corresponding to any chosen meridian. In simple M or H the diffusion areas are round, and when their edges are in contact they remain so in whatever meridian they may be brought, by a movement of the bar of the instru- ment. In astigmatism, on the other hand, the diffusion areas are no longer round, but oval, and the two do not remain in contact when the arm is placed in all meridians. The direction in which the elongation takes place shows the inclination of the principal meridians. The arm is moved until the blurred images are in contact at their shortest diameters and its inclination to the horizontal is noted, and the amount of ametropia in that meridian read off on the scale. The bar is then turned at right angles to this and the long axes of the images are brought in contact. The position of the movable flame on the scale gives the ametropia in this meridian, and the difference between the two gives, of course, the amount of astigmatism. 89. EXAMINATION WITH THE STENOPAIC SLIT. When a diaphragm, having a slit a millimeter in diameter, is rotated before an astigmatic eye looking at test objects, placed at a distance of 5 or 6 meters, it will be found that when the slit corresponds to one certain meridian, vision is best, and when it is at the meridian at right angles to this it is worst. This gives us the direction of the principal meridians, and we can easily find the refractive condition of each separately. When the slit is at 90, for instance, all the rays which would pass through the other meridians are cut off by the diaphragm, and by testing in the usual manner with -f- and spherical glasses we can find with considerable exactness the state of refraction of the meridian open to the passage of rays ; and so for any other meridian whose refraction we may wish to deter- mine. Example : V = */ 36 . When the slit is at 130 V= */, when at 50 it is less than */ 60 . The slit being at 130, on trying, in the usual manner as de- 82 TEST-TYPES OF PRAY. tailed in Chap. IV., various spherical glasses, we find that with 1.5 V = */; therefore meridian 130 has M = 1.5. Turn- ing it now to 50 we find that it takes 4.5 to bring V - = l / 6 ', Fig. 24. **' If' JOS' 30' "7! O " iilinll fyfj// '////// ^S KKi f*2 y^w TEST TYPES BY PRAY. hence 50 has M = 4.5. The amount of astigmatism is there- fore 4.5 1.5 = 3: But with this there is combined a myopia, which is common to both meridians, of 1.5. The case is one CLOCK FACE OF GREEN, AND OF OLIVER. 83 of compound myopic astigmatism: 1-5 O 3 ax is I 3- The disadvantage of this method is that visual acuteness is con- siderably reduced by the exclusion of so much light by the diaphragm, and by the circles of dispersion, small it is true, but still appreciable, which come from the few rays which pass through the slit in the other meridian. 90. THE TEST LETTERS OF PRAY. A very useful and con- venient modification of the principle of Snellen's fan are the test letters of Orestes Pray. These letters are formed by a series of parallel lines which are inclined, for each separate letter, at a different angle to the horizontal, as shown, reduced, in Fig. 24. To the astigmatic eye the lines composing one of the letters, as P for example, will appear most distinct in outline, while those of another, as B, running at right angles to these, will appear most indistinct. The patient, being placed at such a distance that the letters as a whole are distinguished (20 feet), is able to tell us which let- ters these are, and we, knowing the inclination of the lines in each, are at once informed as to the direction of the principal meridians remembering always that the most and least dis- tinct lines are at right angles to their respective meridians. 91. John Green, of St. Louis, devised a set of lines drawn from a common center on a clock face, as in Fig. 25. The pa- tient indicates the lines which are most distinct by the figure on the clock with which they correspond, and the examination is conducted in the same way as when made with Snellen's fan. He has also designed many other figures, but they are all modi- ifications of this general plan, and are used in the same man- ner. 92. Oliver, of Philadelphia, has devised a modification of these methods which consists of a disk with three concentric series of radiating lines corresponding in size with three visual angles. Two of Fray's letters are attached to a rotating disk- perimeter, one at an angle of 90, the other at 180. The pa- tient must designate which of the radiating lines he sees most distinctly. The disk is then rotated until the lines of one of the letters appears most distinct, which will mark the direction of 8 4 OPTOMETERS. one principal meridian ; the other principal meridian will of course be at right angles to it. The examination is then con- ducted as in the usual way with Snellen's fan. 93. Culbertson has used the doubling of an object when looked at through two prisms with their bases together as a Fig. 25. THE CLOCK FACE OF GREEN. means of diagnosing ametropia. When the object is of a defi- nite size and at a certain distance the images touch at their op- posite edges. The degree of ametropia is determined by the glass, which when placed before the eye gives this touch- ing for the standard size and distance of the object. The re- fraction of the separate meridians can be taken by this means as well as that of the eye as a whole. 94. Nearly all of the various optometers can' be used for the determination of astigmatism. An objection to their use, however, is that with them it is even more difficult than in the examination with test-objects at a distance to control the ac- commodation; and to obtain anything like accurate results it is necessary to paralyze the ciliary muscle. 95. The apparatus of Bravais, of Lyon, since it employs a ZEHENDER'S APPARATUS. 85 principle somewhat different from the others, merits a short description. It consists of a tube of convenient length, at one end of which is a convex lens with a focal distance shorter than the length of the tube. The other end of the tube is closed with a diaphragm having a small round opening in its center. The patient looks through the tube with the hole turned to- ward a lamp or window, and if astigmatism be present the round light spot will appear oval as in Bonder's experiment (81) with its long diameter in the direction of the most strongly re- fracting meridian. In the interior of the tube there is another spherical lens which can be rotated on its axis in any desired meridian, and thus made to act as a cylinder (see 25). An index on the outside shows the degree of inclination of this lens when the light spot again becomes round, and a table shows the number of the cylinder to which this inclination cor- responds. 96. Zehender has adapted the method first employed by Young into the form of an instrument which he uses for esti- mating the degree of astigmatism and the direction of the prin- cipal meridians. He has a few fine threads stretched parallel to each other across one end of each of two tubes, one of which is inserted, telescope fashion, into the other. When the tubes are so placed that the threads of one lie close against and at right angles to the other,a non-astigmatic eye sees them all with equal distinctness when the tubes are rotated to any position on their common axis. When the inner tube is withdrawn, separating the two bands of threads to any considerable distance, however, it is no longer possible for the eye not astigmatic to see both bands distinctly at the same time. When the eye is astigmatic this, of course, is not always true. When the bands are at right angles and the tubes are revolved on their long axis there is one position in which the threads of one band are seen clearest and those in the other least so. The bands then lie in the direction of the principal meridians. Spherical glasses are now placed before the eye, one after another, until one is found which brings out the indistinct band clearly. The number of this glass expresses the amount of astigma- 86 JAVAL'S ASTIGMOMETER. tism in the meridian at right angles to the direction of the band. 97. Javal's Astigmometer : As stated in 94, one of the principal defects inherent in all the methods of opto- metric measurement where the test object is within a finite distance and close to the eye, is the almost unavoidable tendency to the use of the accommodation. We have always been accustomed to use the accommodation when the object is near us and when we know that it is at the other end of a short tube we instinctively accommodate for that distance. When the visual axes are parallel, however, as when we look at infinity, the ciliary muscle is usually relaxed. Javal has taken advantage of this fact in the construction of his astigmo- meter. As a test object he uses a circle with lines drawn through its center at every 15 degrees. This circle is looked at through a convex lens having a focus of about five inches. To the eye free from astigmatism, of course, all the lines appear of the same distinctness. The astigmatic eye sees some more clearly than others, and the card on which the circle is drawn is moved back and forth until one line becomes sharply defined. This line will lie in the direction of the meridian of greatest refrac- tion. Concave cylindrical lenses are then placed successively before the eye, beginning with the weakest, with their axes at right angles to the distinct line until one is found through which all the lines appear with uniform sharpness of outline. We thus obtain the direction of the principal meridians and the degree of astigmatism. The ametropia that may be asso- ciated with the astigmatism is determined subsequently. In order to avoid any interference on the part of tfie" accommoda- tion, he has a second circle drawn on the card, with its center at the same distance from the center of the circle with the lines as separates the visual axes of the eyes in a state of parallelism. When the two eyes look at these circles, therefore, there will be two circles seen unless the visual axes are parallel. 'When the patient sees only one circle with both eyes open, the eyes are adapted for distant vision and the accommodation is re- laxed. BIBLIOGRAPHY. BIBLIOGRAPHY. Anderson, T. New instrument for estimat. astig. Lancet. II. P. 415. 1880. Bravais Nouv. appareil pour diagnost. 1'astig. Lyon Med. X. Pp. 478-81. 1872. Culbertson, H. A method of determ. ametropia by prism, refraction. Cincin. Lancet and Clinic. X. P. 49. 1883. Farley, C. H. A method of discover, and correct, astig. Bost. M. and S. J. LXXXVI. Pp. 381-3. 1872. Gavarret Astig. optometre de M. Javal. Gaz. d'Hop. XL. P. 326. Paris. 1867. Green, J. On the detect, and measurement of astig. Am. J. M. Sc. n. s. LIII. Pp. 117-27. 1867. Green, J. On a color-test for astig. Trs. Amer. Ophth. Soc. N. Y. P. 130. IV-V. Green, J. On an optic, demonstrat. of the characterist. phenom. of astig. vis., by the cam. obscur. and by the magic lantern. St. Louis M. and S. Jr. N. S. V. Pp. 107-9. l868 - Green, J. An optic, demonstrat. of the character, phenom. of astig. vis; Trs. M. Ass. Mo. 1869. Pp. 170-81. St. Louis. 1870. Green, J. On a new syst. of tests for the detect and measur. of astig., with an analys. of 64 cases of refract, anomal. obsd. by the aid of this method. Trs. Am. Ophth. Soc. Pp. 1343. Tr. Am. Ophth. Soc. N. Y. 1867-8. IV-V. 1869. Green, J. Test-diagrams for the detect, and measur. of astig. Trs. Am. Ophth. Soc. 1878. Heymann Astig. Tafeln nach Dr. Pray. (2 Tafeln). Leipzig. Engelmann. Javal, E. Ueber ein neues Instrmt. zur Prtifg. des Astig. Klin. Monatsbl. f. Augenhlk. P. 334. 1865. Javal, E. Sur un nouvl. instrmt pour la determinat. de 1'astig. Ann. d'oculist. T. LVII. P. 39. 1867. Javal, E. Sur les applicat d'un appareil nouveau destine a determ. 1'astig. visuel. Bull. Soc. d'anthrop. de Paris. 2 S. XII. Pp. 149-58. 1877. Morosini, D. Determinaz. di miop., ipermetrop. astig. Sassari. 1833. Laidlaw Purves. Eine Methd. z. Bestim. der Refrctanoml. Graefes Arch. B. XIX. Abt. I. P. 89. 1873. Oliver, C. A. Descript. of a rotat. disc for test, for astig. Med. News, Oct. 6, 1883. Pray, O. M. Test-type for astig. Arch. Ophth. and Otol. N.Y. I. No. I. Pp. 17-21. 1869. Prouff, J. M. De la sclerotoscopie. Methd. a suivre pour les observat. ayant trait a la "keratite" pretendue "astig." Rev. clin. d'oculist. No. 2. P. 25. 1884. Schoen Apparat z. Bestim. d. Astig. besonders in seitlch. Sehrichtungen Graefes Arch. XXIV. Abt. I. P. 91. 1878. Strawbridge, G. An addit. method for the determ. of Astig. Trs. Am. Ophth. Soc. VIII. Pp. 100-4. N. Y. 1871. Thomson, W. Determinat. of degree of ametp. Am. J. M. Sc. Pp. 414-20. 1870. Thomson, W. A pract.and rapid method with an instr. for the diag. of the refract. Trs. Amer. Oph. Soc. V. II. Part 4. 88 BIBLIOGRAPHY. Thomson, W. An addit test for the diag. and correct for the optic, defects of the eye. Am. J. M. Sc. P. 76. 1870, Tweedy, J. On an improved optometer for estim. the degree of abnorm. reg. astig. London Lancet II. Pp. 604-6. 1876. Zehender; W. Ueber die Brewster. rnethd. z. Bestim. der Brechungsexponenten flUssigoder fetweich. Substanzen. Graefes Arch. B. III. Abt I. P. 99. 1857. Zehender, W. Zur Astigmonietrie. Bercht a. d. 15 versam. d. ophth. Gesellsch. P. 29. 1883. Weil, J. Essai sur la determ. cliniq. de 1'astig. 4. Paris. 1875. CHAPTER VII. OBJECTIVE METHODS OF EXAMINATION THE OPHTHALMOSCOPE AS A MEANS OF DIAGNOSIS IN ASTIGMATISM. 98. In the objective methods of examining for astigma- tism we do not rely, as in the subjective methods just de- scribed, on the statements of the patients for the data of diag- nosis, but trust entirely to our own observations. The ad- vantage of the plan is very great, since it makes us indepen- dent of the patient, and eliminates the most potent sources of error. For a satisfactory examination by the subjective meth- ods a certain in fact a very considerable amount of intelli- gence on the part of the patient is necessary. This, unfortu- nately, on account of age or mental condition, we do not al- ways have at command, and had we not some other means of getting at the facts it would be often impossible to arrive at any intelligent or definite idea as to the refractive state of the eye. The special advantages, as well as the defects and short- comings of the various objective modes of examination, will be pointed out when we come to a consideration of each plan in detail. 99. THE OPHTHALMOSCOPE IN THE DIAGNOSIS OF ASTIG MATISM. When Helmholtz invented the ophthalmoscope he not only gave to the profession an instrument by means of which the condition of the interior of the eye could be exam- ined in minutest detail, but, what is hardly less valuable, put into their hands an apparatus for testing its optical state. The ophthalmoscpe, as an optometer, has now, become one of our most important and reliable means of diagnosis. IOO. There are two ways of making an examination with the ophthalmoscope. One is the direct method, giving an (89) 90 DIRECT METHOD OF EXAMINATION. erect and virtual image of the fundus of the eye ; the other is the indirect method, in which the image of the fundus is in- verted and actual. The manner in which these two kinds of images are obtained is essentially different in the two methods. For the fundamental principles of ophthalmoscopy we shall have to refer the reader to general treatises on the subject. 101. The Direct Method of Examination. In this method we look directly into the eye to be examined and see the fun- dus in its proper position, but under the magnifying power of its refracting media. It will simplify our study somewhat if we remember that when we employ the ophthalmoscope as an optometer in ame- tropia, we are only using one optical instrument to neutralize the action of another, in the same way as we determine the strength of a + lens by the lens necessary to overcome its refraction and reduce its optical properties to zero. As in the determination of general ametropia by glasses, it is the object to so alter the course of parallel rays that they may appear to come from the far point of the eye under ex- amination, so, in making a diagnosis with the ophthalmoscope by the direct method, it is the purpose to render the rays which come out of the ametropic eye, and are directed to its far point, parallel. In both cases the glass which does this gives the amount of deviation of the eye from the emmetropic con- dition. IO2. This principle, as applied to the direct method of ophthalmoscopy, is shown in Fig. 26. The eye V is myopic, and the rays e f coming from a point o of the illuminated fundus, after passing out of the eye converge towards its far- point situated at a, six inches in front of the cornea. The eye E of the emmetropic observer is not adapted for converging rays, and in order to have the rays e f brought to a focus on his retina they must be rendered parallel. This can be done by placing a concave lens having a negative focus of five inches behind the ophthalmoscopic mirror and one inch in front of the eye to be examined. The rays e f directed to the negative focus of the lens, also at a, will then be made parallel, DIRECT METHOD OF EXAMINATION. 9 1 and the emmetropic eye E being in a state of repose and adapted for parallel rays, will unite them on its retina, and they will form there a clear and distinct image of the point o. This same lens, acting in a contrary sense, will render parallel rays coming from distant objects divergent as though they Fig. 26. DIRECT METHOD OF EXAMINATION WITH THE OPHTHALMOSCOPE. Alteration in the course of the rays by concave lenses in the principal meridians in compound my- opic astigmatism. came from the point a, five inches in front of it (that is the far- point of the eye). Therefore, the same concave lens through which an emmetropic observer can see the fundus of a myopic eye distinctly expresses the degree of myopia of the observed eye, and will adapt it to vision at an infinite distance. In the example we have taken the rays ef belong to one merid- ian the vertical but if the refracting surfaces are the same in all meridians, as in ordinary simple myopia, the law applies to the others as well, and through all points situated in every meridian there will proceed rays convergent towards a which which will be rendered parallel by the same lens ( 1 / 5 ) and be again united on the retina of E. Under these conditions, 92 DIRECT METHOD IN DIAGNOSING ASTIGMATISM. therefore, the emmetropic observer E will be able to see with distinctness all the details at the fundus of V, and the fine retinal vessels running in one direction will be made out as clearly as those running in any other. 103. The state of affairs is very different, however, when we come to deal with an eye having a different curvature in each meridian, as in regular astigmatism. Here the far-point to which the emerging rays converge, in the case of compound myopic astigmatism, will be in a differ- ent position for the two principal meridians, being nearest to the eye in the most strongly refracting, and farthest from it in the weakest. Letting V and H, Fig. 26, represent the two meri- dians of greatest and least refraction respectively, a will be the far point of V, 6 inches in front of the cornea, and b that of H, 9 inches in front of the cornea. It would not be possi- ble, therefore, for any one spherical lens to render the rays coming through these two meridians parallel so that they would be united at the same place on the retina of E, and as a consequence the observer could never obtain, by such a lens, a uniformly distinct image of the details of the fundus. If the delicate vessels running in the vertical direction were seen sharply with l / Bt those running in the horizontal direction and corresponding to the opposite meridian, V, would be blurred. When, on the other hand, a l / 6 lens is used which renders the fine vessels, running horizontally and correspond- ing to the vertical meridian V, sharply defined, those running in the opposite direction are indistinct. 104. On this principle and in consonance with these facts is based one of the methods of diagnosing astigmatism by means of the ophthalmoscope. The refraction of each principal meridian is taken separately, just as if it were a case of simple ametropia. The mirror of a refraction ophthalmoscope is brought close to the observed eye and the disk containing the correcting lenses is turned un- til one lens is found through which the finest retinal vessels running in one direction appear sharply defined. Let us say, for example, that the delicate vessels running horizontally over DIRECT METHOD IN DIAGNOSING ASTIGMATISM. 93 the outer edge of the optic disk are clearly made out with 3. The fine vessels running almost vertically in the region of the macula lutea will, through the same lens appear blurred and in- distinct (the accommodation of the observer remaining, of course, in a state of complete relaxation). The converging rays coming from these horizontal vessels and passing through the vertical meridian of the eye are rendered parallel by the 3 and thus become adapted to the emmetropic observer. The vertical meridian has therefore M = 3. The small verti- cal vessels near the macula are seen distinctly with I, while, with the same lens, the horizontal vessels at the edge of the disc appear blurred. The horizontal meridian which refracts the rays coming from these vertical vessels is myopic to the extent of I D. The case is one of Comp. My. Astig. J O 2 axis 1 80. The same principle applies, of course, to all the other forms of astigmatism. The direction of the vessels which are seen most distinctly gives the direction of the prin- cipal meridians, and the lenses +,or ,through which they are thus seen gives the degree of ametropia for each respectively. The degree of astigmatism is expressed by the difference in the refraction of the opposing meridians. 105. The defects of this method are two. There is, first, the impossibility of determining in all cases the exact direction of the faulty meridians. The fine vessels of the retina which we employ as test-objects do not spread out regularly in all di- rections like a Snellen's fan, and frequently there is no one which follows the exact line of the axis of either one of the principal meridians. Our estimate of the direction of the me- ridians is, therefore, only approximative, and cannot be made certain, except by some one of the other methods. Neverthe- less, we can always obtain an idea of their general direction, and this is frequently of the utmost importance as furnishing a key to the situation. The second defect applies equally to the determination of general ametropia by this means, and that is the want of ex- actness in estimating the degree of ametropia in each meridian. My observations and experience as a teacher have convinced 94 LIMITATIONS OF THE METHOD. me, that it is not given to all men to be good ophthalmoscop- ists. particularly by the direct method. A perfect result in de- termining refraction in this way requires, in the first place, an absolute control over the accommodation on the part of the observer, and this cannot be acquired by every one. A very slight change, one of which we are not at all conscious, in the tension of the ciliary muscle will make a difference of 0.5 or 0.75 D. Then, again, if the media are not quite clear and the pupil is small, as we have it nearly always in advanced life, it is not possible to distinguish within 0.75 D, between the lenses which give the clearest outline to a particular vessel. It is to be remembered, also, that particularly in M, the vessels which serve us as test-objects are not all on the same level. Those at the edge of the disc are in advance of those at the macula, and it is the refraction of the meridians at the latter place we want. Where the pupil is so small as to seriously diminish the illumi- nation of the fundus, a mydriatic should be used. Of these, hydrochlorate of cocaine and hydrochlorate of homatropine are best, since their effect on the accommodation is more transient than that of atropine. While acknowledging that there are some brilliant excep- tions to the general rule, I yet believe that, taking ophthalmo- scopic observers in the mass, it is not possible in an average of cases, to determine within 0.75 D of the actual refractive condi- tion of the eye, by means of the ophthalmoscope. But notwithstanding this, ophthalmoscopic examination by the direct method is, and will probably always remain, one of our readiest and most reliable aids in the diagnosis of astigma- tism ; and all students of ophthalmoscopy should diligently practice the method and endeavor to acquire the greatest amount of skill possible in its use. 1 06. The general appearance of the fundus of the astigma- tic eye is very striking, particularly in the high degrees of the anomaly and, when once seen and understood, is not likely thereafter to be mistaken for anything else. With the excep- tion of keratometry, to be considered later, I know of no other method which gives us so promptly such important informa- INACCURATE REPRESENTATIONS OF THE ASTIGMATIC FUNDUS. 95, tion as to the existence of these high degrees of astigmatism which are so puzzling when tested by the subjective methods alone. A single glance is often sufficient to reveal to us the direction of the principal meridians, and furnish an indication as to the special form of the anomaly. Fig. 27. DIAGRAM REPRESENTING JAEGER'S INACCURATE DRAWING OF THE FUNDUS OF THE. ASTIGMATIC EYE AS SEEN BY THE DIRECT METHOD. There does not exist, to my knowledge, a drawing represent- ing the fundusof the astigmatic eye with any approach to faith- fulness. Jager has in his well-known atlas (Fig. 31 of the smaller edition), a, drawing which purports to give the appear- ance of the fundus as seen in the direct method,but it is far from a true picture. That so faithful a delineator as Jager should com. mit such an error is indeed wonderful. 1 Fig. 27 is a diagrammatic 1 In Loring's text-book of ophthalmoscopy which has appeared since the MS. of this chapter has been in the hands of the printer, there is a representation of the fun- dus of the astigmatic eye. While more nearly accurate than Jager's, it yet fails to- give that marked contrast which exists between the distinctness of the vertical and horizontal vessels. 96 APPEARANCE OF THE FUNDUS IN ASTIGMATISM. copy of this drawing and a glance at it will show that it could not by any possibility be the fundus of an eye as seen through an astigmatic refracting system. The fine retinal vessels are seen running in all directions with equal distinctness which, as we have shown, could not be the case in an astigmatic eye. The only part of the drawing which has any semblance of truth is the appearance of the optic disk. This does give a very good picture of the disk as it appears when the meridian is adapted to the eye of the observer. The vertical outlines are sharp, while the horizontal outlines are blurred and indistinct. But under the optical conditions producing this effect it would not be possible to see the delicate retinal vessels running horizon- tally over the edge of the disk as they are represented in Jager's figure. So far as I know attention has not before been called to the falseness of this representation. Even so good and able an observer as Nettleship has copied it into his text- book without any allusion to its inaccuracy. I have endeavored to give in Fig. 28 a more nearly accurate representation of the appearance of the fundus of an astig- matic eye when examined by the direct method. It was sketched from a case of simple myopic astigmatism of 6 D axis 1 80, and it is given as seen without any correcting lens. The horizontal meridian being emmetropic, and the eye of the observer being emmetropic also, the parallel rays which pass out through this meridian are focused properly on the retina of the observer, and consequently all vertical outlines are distinct. The large retinal vessels passing upward and . downward over the face of the disk are seen sharply defined with the light reflex along their center very clear. As soon, however, as the vessels become defle*cted to one side and as- sume an oblique or horizontal direction out of the axis of the emmetropic meridian their outlines become blurred, the reflex is lost, and their course is marked only by an ill-defined band whose outlines merge into the surrounding red of the fundus. Wherever in their course, they again assume a vertical direc- tion, their outlines become once more sharply defined; all light points are converted into vertical light lines, and all black - .'"'i "; s^ALr APPEARANCE OF THE FUNDUS IN ASTIGMATISM. 9/ points or masses become vertical black lines, giving the fundus a striking appearance of vertical " streakiness." The vertical sides of the optic disk are sharp in outline while superiorly and inferiorly they are "fuzzy" and indistinct, and, as a whole, the disk appears vertically elongated. Such an ap- Fig, 28. APPEARANCE OF THE FUNDUS OF AN ASTIGMATIC EYE AS SEEN BY THE DIRECT METHOD OF EXAMINATION. pearance could easily be mistaken by a novice for a patho- logical condition a retinitis or neuro-retinitis. I distinctly remember in my first workings with the ophthalmoscope, be- fore I had studied astigmatism, making such an error in diag- nosis, which was, however, promptly corrected by one whose experience in such matters was greater than mine. 98 APPEARANCE OF THE FUNDUS IN ASTIGMATISM. A very good idea of these appearnces may be obtained by looking at a drawing of a normal fundus in any ophthahno- logical atlas through a -f cylindrical lens of six inches focus placed with its axis vertical, close to the eye and at six inches from the drawing. If the accommodation of the observer is then relaxed the rays coming from the vertical vessels and passing through the horizontal meridian will be rendered par- allel by the lens, focused by the observing eye on its retina, and seen clearly, while the others, coming from the horizontal and oblique lines and passing through the other meridians will unite, if at all, behind the retina, and give images with blurred outlines. 107. The same principles apply, of course, to every form of astigmatism with the principal meridians lying in all possi- ble directions. If, in the case taken as an example, the my- opia of the vertical meridian is corrected by a 6 spherical behind the ophthalmoscopic mirror, rendering the horizontal meridian hypermetropic, the horizontal vessels will come out clear and distinct, and all the vessels running vertically will appear blurred, since the rays coming from them cross behind the retina, while the disk will seem to be drawn out horizon- tally, with its superior and inferior borders sharply defined. If the meridians are oblique, the disk will be elongated in corre- sponding directions when the ametropia of each is corrected, and those portions of the vessels which run in these direc- tions will be sharply outlined. 108. In examining for ametropia by the direct method care should be taken to so arrange the relative position of the head of the patient to the light that the ophthalmoscope shall be as nearly as possible at right angles to the optical axis of the eye under examination. If this precaution be not taken and the correcting glass behind the mirror is inclined to the direction of the rays coming from the eye, there will be a cyl- indrical action on the part of the lens, as demonstrated in 25. It was for the purpose of obviating this source of error, among others, that the various " tilting " ophthalmoscopic mirrors were invented, (Loring, Wadsworth, DeWecker, and others). OPHTHALMOSCOPES WITH CYLINDRICAL ATTACHMENTS. 99 109. Dennett, Uhtoff and Parent have described modifi- cations of the refraction ophthalmoscope by which it is possi- ble to examine the fundus of the astigmatic eye through cor- recting cylinders. Uhtoff 's (Shoeler's) instrument consists of a disk with ten cylinders (-)- and ) which is fixed to one side of the instru- ment back of the mirror, the disk containing the sphericals being fastened at the other side. The glasses contained in these disks can be brought by rotation, as in the ordinary in- struments, behind the perforation in the mirror, superposed if necessary. The disk containing the cylinders can, in addition, be so turned, as a whole, that the axis of the cylinder behind the perforation can be placed in any desired direction. Parent's instrument is constructed on the same principle. Dennett used a small Stokes' lens behind the opening in the mirror. He tells me, however, that he has ceased to use it for some time. Such instruments I do not consider of any great value for making a first diagnosis of astigmatism, for there are many other means easier and more ready and reliable. It is, how- ever, often of great importance to be able to examine in detail the fundus of an astigmatic eye, to determine the presence or absence of pathological changes there. In an eye even mod- erately astigmatic this is not possible by the direct method. Some means by which this can be done is, therefore, im- perative. The instruments above mentioned would enable us to do this, but they are more or less cumbersome and somewhat expensive. It occurred to me, therefore, that some modifica- tion of the ordinary ophthalmoscope was possible which would enable us to use for this purpose the cylindrical glasses in our cases of test lenses. Such a modification I have devised, and a back view of it is represented in Fig. 29. It consists in the addition of a clip, behind the disk holding the lenses, into which a cylindrical lens can be placed. This clip moves in- dependently of the large disk, and has attached to it a section of another disk holding two lenses, + 3.5 and 3.5, which IOO OPHTHALMOSCOPES WITH CYLINDRICAL ATTACHMENTS. can be brought behind the .sight-hole in the mirror when needed. The degree of inclination of the axis of the cylinder is read off on a scale marked at the edge of the back of the mirror. REFRACTION OPHTHALMOSCOPE WITH A CLIP FOR THE INSERTION OF CYLINDRICAL LENSES. Though the instrument may not be of great value for the first determination of astigmatism, it is very useful for verifying the findings by other methods, and I believe will be found very convenient for that purpose, after some practice in its use. The instrument has, too, other advantages which I think will commend themselves for its general use. By the use of the two lenses in the superposed segment a large number of lenses are obtained for the determination of general ametropia. We can get. in all, fifteen plus and seventeen minus lenses, as follows : -f- 0.5; i; 1.5; 2; 2.5; 3; 3.554; 4.5; 5; 5.5; 6; 6.5; 7.5; u; and 0.5; i; 1.5; 2; 2.5; 3; 3.5; 4; 4.5; 5; 5.5; 6; 6.5; THE INVERTED OPHTHALMOSCOPIC IMAGE. 101 7.5 59.5; ii ; 13. These are all that are ever needed in prac- tice, and the interval between the numbers is sufficiently small for the finest diagnosis. Compared with other instruments of good workmanship and equal usefulness the price is very moderate 1 . no. Examination by means of the inverted ophthalmoscopic image. As already stated, the indirect method of ophthalmo- scopic examination differs essentially from the direct method. By the latter we look immediately upon the illuminated fundus itself, whereas with the former, we see its actual inverted im- age formed in the air by an auxiliary lens placed in the path of the emerging rays. Fig. jo. a FORMATION OF THE ACTUAL INVERTED IMAGE IN THE INDIRECT METHOD OF. OPHTHALMOSCOPIC EXAMINATION. The size and position of this aerial, image varies with the optical condition of the eye from which the rays proceed, the strength of the auxiliary lens used, and under certain cir- cumstances on the distance of this lens from the cornea. The problems in connection with this method of observation are therefore, somewhat more complicated than in the direct method. They are easily solved, however, when we bring to our aid a few of the fundamental principles of optics. Let us examine briefly into the manner in which this inverted aerial image is formed. In Fig. 30 E is an emmetropic eye 1 The instrument is made by A. Meyer's Sons, 93 William street, New York. Its price is $17.00. The clip behind the mirror can be made by them to fit the cylin- ders of any particular trial-case. IO2 THE SIZE OF THE INVERTED IMAGE. whose fundus is already illuminated. From the points o and b there proceed rays which, in passing out of the eye, be- come parallel. These rays, falling on the convex lens L., hav- ing a focal distance of 3 inches, are brought together and form at the focus of the lens an inverted image, a c, of o b. The eye of an observer at will see this image a c clearly when it is accommodated for vision ai that distance. The power of the lens L governs the size of the image a c and its position in re- spect to L. ill. When the eye is emmetropic, a c is always found at the focus of L, no matter at what distance from the observer's eyes the auxiliary lens is held, because the rays come from the eye parallel and remain so indefinitely, and will consequently always fall thus on the lens at whatever distance from the eye they may strike it. If a -t- 1 /* ls use d, the image will always be 3 inches in front of it: if a -\- l /-> is employed, it will be 2 inches, and so on. This being the case, with the same lens the size of the im- age a c must always be the same in emmetropia, at whatever distance from E the lens is held. This is true of the actual size of the image, but not strictly so as to its apparent size to the observer at O. The effect of removing L away from E would be to cause an approximation of the image a c to O. As a consequence of this it will be seen under a constantly increasing visual angle and as it is seen with only one eye and is always referred to the same position in space, its apparent size increases as it is brought closer to O. It is not strictly true, then, as stated by many authorities in ophthalmoscopy, that in emmetropia the size of the inverted image remains unchanged in all positions of the auxiliary lens. 112. In myopic and hypermetropic eyes we have an entire- ly different set of conditions to deal with. The rays coming from the illuminated fundus of these eyes do not emerge in a state of parallelism, but are either convergent or divergent. The size and position of the image produced by the auxil- iary lens, under these circumstances, must be determined by the laws of conjugate foci. VARIATION OF SIZE OF IMAGE IN H. 103 By applying these laws to the two abnormal optical condi- tions of myopia and hypermetropia we can know the position, and relative size of the image to its object in any given position of the auxiliary lens on the common optical axis. 1 13. Let us take the case of 'hypermetropia first. Here the rays emerge divergent, and those coming from the point o, Fig. 31, CHANGE IN THE SIZE AND POSITION OF THE REAL IMAGE OF THE HYPERME- TROPIC EYE IN THE INDIRECT METHOD OF OPHTHALMOSCOPIC EXAMINATION. after passing out of the eye assume a direction as though they cd.me from a point a behind the eye, which is the virtual and .eTect image of o formed by its refracting media. This point a is the far point of the eye, and in this case negative. The point a, therefore, and not o, becomes one of the two conjugate foci and gives the position of the object, whose real inverted aer- ial image is to be formed by the auxiliary lens placed in front of the eye. When this lens is at 3, (3 inches in front of the cornea) the image of the object at a will be formed at f, a dis- tance greater than the focus of the lens, When it is removed two inches farther to 5, the image will be formed at ^, since in bi-convex lenses the object and the image are displaced in the same direction, and being closer to the lens will be smaller. As the lens is still further removed from a the image will be brought closer to the lens and diminish correspondingly in size until it reaches a point where the emergent rays become prac- tically parallel, when the image will be formed at the focus of the lens, and will then remain of the same size, even though the lens were removed to infinity. 114. In myopia the conditions are the reverse of those in IO4 VARIATION OF SIZE OF IMAGE IN M. hypermetropia, and there is a corresponding change in the ef- fect on the position and size of the image formed by the aux- iliary lens. Here again we can assume, for the sake of uni- formity, that the object is not at the point o (Fig. 32) from which the rays emanate, but at the far point a, where the emerg- 32. A s n SHOWING HOW THE REAL IMAGE OF THE MYOPIC EYE VARIES IN SIZE ON REMOVAL OF THE AUXILIARY LENS IN THE INDIRECT METHOD OF OPHTHAL- MOSCOPIC EXAMINATION. ing rays meet and form a real and inverted image of the ob- ject at o. The image, formed by the auxilliary lens placed in the path of these rays, will be real and on the same side of the lens as the object, when the lens is found at any place between a and the eye M. When the lens is at I (i inch in front of M) the image which is seen by the observer will be at/, nearer the lens and smaller than the object at a. When the lens is ad- vanced towards the object and is found at 2, according to the law of conjugate foci, the image advances toward the lens, is found at e, and is increased in size. As the lens is still further removed towards a, the image gets nearer and nearer the lens and increases more and more in size, but still remaining real, until it is found at 7, and occupies the same position as the ob- ject. The image and object will then be of the same size, one lying at the first nodal point of the lens, /, the other at the second nodal point, k' . On a still further removal of the lens a is left between it and the eye, the image becomes virtual, is found between the lens and the eye M, and is larger than the object at a. It continues to increase in size on further removal VARIATION OF SIZE OF IMAGE IN M. 10$ of the lens until the lens is found at 9, when the object lies at its focal distance. The rays will then emerge from the lens parallel, / n, m i, and the image will lie at infinity and be in- finitely large as compared with the object. When the lens gets beyond its focal distance from the object at a, as at 1 1, the rays s t, r p emerge from it convergent, and will form, somewhere beyond, an inverted and real image of the object at a, being a real and erect image of o. As the lens is still further removed this real image approaches the lens and becomes smaller. 115. This variation in the size of the real image of the myopic eye on removal of the auxiliary lens, can be demon- strated by taking, as one of the conjugate foci, the actual object at o ; but in that case we should have to do it with a constantly varying compound optical system of the eye and the lens, mak- ing the problem much more complicated. We have taken the images (virtual and real), formed at the far points in the two states of ametropia, for the sake of uniformity and for ease of demonstration and comparison in the two conditions. 116. It is apparent from the foregoing, that it cannot be strictly true, as has been commonly stated in a general way without qualification, that the inverted image of the myopic eye is smaller than that of the hypermetropic eye when both are formed by the same lens. The relative size of the inverted image, as we have seen, depends entirely on the place occupied by the auxiliary lens on the optical axis, and there are some positions of the lens in myopia when it is near the far point of the eye under examination where it will be, not only rela- tively, but actually larger than the image of a hypermetropic eye of the same degree produced by the same lens in the same position as regards the eye. 117. These general rules in regard to the size of the in- verted image of the myopic and hypermetropic eye are equally applicable to the myopic and hypermetropic meridians of the as- tigmatic eye. The effect upon the image caused by the dis- placement of the auxiliary lens is of a peculiar character and different in the different forms of the anomaly. An observa- IO6 VARYING SHAPE OF THE DISK IN ASTIGMATISM. tion of these changes is most useful in making the diagnosis of the form of astigmatism from which the eye may suffer, and gives us a general idea of the direction of the principal me- ridians and, in a rough way, of the amount of the astigmatism. 1 1 8. In the simple form of myopic astigmatism, when the lens is gradually removed from its ordinary position at from I to 2 inches in front of the cornea towards the far point of the eye, there will be a progressive enlargement of the optic disk in the myopic meridian, while the diameter of the disk which corresponds to the emmetropic meridian will remain un- changed. If, for instance, the vertical is the myopic meridian, the surface of the disk instead of being round will appear drawn out vertically, and the amount and the rapidity of the elongation will be in proportion to the degree of the myopia in that meridian. Should the myopic meridian be oblique, the inclination of the oval disk will correspond to the direction of the faulty meridian. It must be borne in mind, in this connec- tion, that owing to the inward rotation of the eye necessary to bring the optic disk into view in ophthalmoscopic examina- tions, the disk is seen somewhat in profile and in the normal eye does not generally appear round, but vertically oval. For the diagnosis of a myopia in the vertical meridian, therefore, the oval in this direction must increase as the lens is removed from the eye. When, on the other hand, the lens is brought very close to the cornea, the horizontal (emmetropic) diameter remains un- altered, while the vertical (myopic) diameter gradually dimin- ishes in size, assuming finally, if sufficiently close, a horizontal oval form. 119. In compound myopic astigmatism, we have, in accord- ance with the facts just stated, a general progressive enlarge- ment of the disk on removal of the lens,with a greater enlarge- ment and drawing out of that diameter of the disk correspond- ing to the meridian most strongly myopic, while there is a greater shortening of the same diameter when the lens is brought very close to the cornea. 1 20. We have, of course, an entirely different set of VPPEARANCE OF THE FUNDUS BY THE INDIRECT METHOD. IO/ cnanges in hypermetropic astigmatism. Example: As the lens is withdrawn from the eye, the vertical diameter remains essen- tially unchanged, while the horizontal diameter, corresponding to the hypermetropic meridian, becomes more and more contrac- ted. Diagnosis : Simple hypermetropic astigmatism, axis vertical. 121. In compound hypermetropic astigmatism there is, on withdrawal of the lens, a narrowing of the disk in all its diame- APPEARANCE OF THE FUNDUS OF AN EYE WITH MIXED ASTIGMATISM, WHEN THE AUXILIARY LENS is HELD CLOSE TO THE CORNEA. ters, but it is more rapid in the diameter corresponding to the most hypermetropic meridian. The result is an oval with its short diameter in the direction of the meridian of least refrac- tion, the same as in the myopic forms, but it is produced in a diametrically opposite manner. In the hypermetropic forms it is the result of contraction in the faulty meridian ; in the myopic forms it is due to enlargement in the direction of the faulty me- ridian. 122. The most marked picture, however, is that furnished by the mixed form of astigmatism. Let there be, for example, (as in the case from which the accompanying drawings were taken), hypermetropia of 3 D in the vertical meridian, and my- opia of 7 D in the horizontal meridian. We have here the con- IO8 APPEARANCE OF THE FUNDUS BY THE INDIRECT METHOD. ditions necessary for producing the combined effects of both these optical states in a very pronounced manner. When the lens is held very close to the cornea the enlargement in the hy- permetropic (horizontal) meridians is at its greatest, while the APPEARANCE OF THE FUNDUS OF AN EYE WITH MIXED ASTIGMATISM, \YHKN THE AUXILLIARY LENS IS AT A GREAT DISTANCE FROM THE CORNF.A. contraction in the myopic (vertical) meridian is at its minimum. As a consequence the disk is elongated horizontally, while the retinal vessels are drawn together and take a more horizontal direction (Fig. 33). As the lens is gradually removed from this position the horizontal (hypermetropic) diameter progres- sively contracts, the vertical (myopic) diameter progressively enlarges, and the vessels turn, as it were, on a pivot, becoming KNAPP'S, SCHWEIGER'S AND BRAVAIS' METHODS. 109 more and more vertical until a point is reached where we have the appearances given in Fig. 34 in which the enlargement in the vertical (myopic) meridian is greatest, and the diminution in the hypermetropic (horizontal) meridian approaches its minimum. 123. These examinations should be made with a lens of short focus two inches at most since a strong lens gives a large ophthalmoscopic field, which with a wide pupil, is al- most indispensable for a satisfactory diagnosis. 124. The chief defect of the method is the lack of accuracy in determining the degree of astigmatism. This, as well as the direction of the principal meridians, can be only roughly esti- mated by the rapidity of change in the form of the disk on moving the lens, and the direction of the long axis of the oval. Its value lies in the knowledge it gives us of the existence and form of astigmatism in those cases where the amblyopia or stupidity of the patient makes it difficult or impossible to ob- tain reliable data by any one of the subjective methods of ex- amination. 125. Knapp and Schweiger have called attention to the change in the form of the disk, when seen successively by the direct and indirect methods of examination, as a means of di- agnosing astigmatism. The erect image of the disk in both M and H is oval, with its short diameter in the direction of the meridian of least refraction ; in the inverted image, on the other hand, the short diameter coincides with the meridian of greatest refraction. This, however, is true only when the auxiliary lens is held at the ordinary position near the eye. When it is removed to any considerable distance from it, as we have seen, there is a change to the opposite condition, and the oval is the same as in the direct method. 126. Bravais, of Lyon, suggested a method based on the associated movements of the lens and image. When the disk is in the center of the lens and the latter is moved from side to side, if there is emmetropia the lens and image move together. In myopia the movement of the image is less than that of the lens ; in hypermetropia it is greater. By moving the lens in 1IC COUPERS METHOD. various directions perpendicular to the optical axis, and noting the amount of displacement of the image, some idea may be formed of the direction of the principal meridians and the kind of refraction in each. 127. In this and in all the methods of examination with an auxiliary lens, great care should be taken to hold the lens strictly at right angles to the visual axis, for otherwise we would have the cylindrical action resulting from an oblique position of the spherical, which might be misleading as to the optical condition of the eye. 128. Mr. Couper has suggested a method of examination by the mirror alone for the observation of the inverted and erect images, successively, which is available particularly for the detection of the mixed and simple forms of astigmatism. For this purpose he employs a mirror of 30 inches focus and places himself at a distance of 4'/ 2 to 5 feet from the pa- tient. He is then in a position to see an inverted aerial imaged of the fundus formed by the meridian having a myopia of iD or more. This image may be only a portion ol a vessel or a part of the edge of the optic disk, and will be larger and formed farther from the eye the lower the degree of the my- opia, while the direction in which the vessel or vessels appear to run will be at a right angles to the faulty meridian. If the other meridian is emmetropic or hypermetropic, of course no vessels or other details of the fundus lying in that direction can have their images formed at that distance, and, therefore, cannot be seen. These come into view only when the mirror is brought closer to the eye, when they will be seen directly and erect, while the vessels in the other meridian will have vanished. 129. Schmidt-Rimpler claims that his plan for estimating refraction by the inverted image is applicable for the diag- nosis of astigmatism. In this method of examination the ob- server does not look at the retinal vessels or other details of the fundus, but at the aerial image of a gas-flame or illumi- nated fret-work which serves as the source of illumination. The manner in which this image is produced is as follows : SCHMIDT-RIMPLER S APPARATUS. Ill A fret-work of small squares and triangles, made in a screen, is placed before the flame of gas or a lamp. With a concave mirror of short focus (20 cm.) an image of this brilliant fret- work is formed in front of the observed eye, and becomes the source of its illumination. An auxiliary lens of a certain focus (10 cm.) is held at a fixed distance (10 cm.) from the eye to be examined, and the combined power of the lens and the re- fracting apparatus of the eye form an image of this open work in its fundus. This retinal image of the fret-work will be sharply defined only when the trellis-work image in the air and the fundus are at conjugate foci, and when this relation exists there will be formed, according to the law of conjugate foci, at the source of illumination a sharply defined image of the retinal image, and this it is which the observer sees. Now, the distance from the lens at which this distinct aerial image will be formed depends, as we have seen in 107 (the auxiliary lens and its distance from the eye being constant quantities), upon the refracting power of the eye. It is farther from the lens in H and closer to it in M than it is in E. If we have a means of measuring this distance, the determination of the kind and even the degree of ametropia becomes easy. This has been made possible by Schmidt-Rimpler, through a very simple arrangement. The power of the auxiliary lens and its distance from the eye being always the same, and the image of the fret-work being always at 20 cm. from the mirror, it is only necessary to approach the mirror to the eye until the aerial image becomes sharply defined, measure the distance between the mirror and lens, and subtract 20 from the dis- tance, in order to have the distance of the image from the lens. If a lens of 10 cm. focal distance is used, the image will be formed in emmetropia at 10 cm. in front of it, since the rays emerging from the eye strike it parallel ; in myopia, the distance of the image from the lens will be shorter, in hyper- metropia, greater. For a lens of 10 D (10 cm. focus) it has been found that every variation of I cm. from this distance of 10 cm. corresponds to a difference in refraction amounting to iD. This measurement he makes by means of a roller tape, 112 SCHMIDT-RIMPLER S APPARATUS. the roller end of which is attached below the lens, while the free end is held at the mirror. The manner of making the observation is as follows : the auxiliary lens is fixed near the end of a small bar graduated in centimetres, and under it is the roller tape, which winds up with a spring. The free end of this bar is placed on the lower edge of the orbit, and when the lens is at 9.5 cm. it is about 10 cm. in front of the principal points of the eye. The mirror, to which the free end of the measuring tape is attached, is placed at 40 to 50 cm. from the auxiliary lens and the fundus of the eye illuminated in the usual manner. The aerial image of the fret-work will then be seen as an ill-defined bright spot. As the mirror is approached closer to the lens it becomes more and more clear in outline, and finally one position is found in which all the details are sharply defined: The distance of the mirror from the lens is then read off on the measuring tape and 20 taken from it. The remainder is the distance of the image from the lens. The difference between this number and 10 gives the amount of ametropia. If, for example, the distance between lens and mirror is 35 cm. the distance of the image from the lens is (35 20) 15 cm. and there is H of 15 10 = 5 D, each cm. corresponding to I D of refracting power. If it is 27 cm. the ametropia is M (27 20 = 7 ; IO - 7) = 3 D. In astigmatism, from what has already been abundantly demonstrated, it is apparent that in no single position of the mirror can the lines of the figures of the fret-work at right an- gles to each other be seen with equal clearness, since the im- age of one set of lines will be formed sharply at one place and that of the other at another. Taking advantage of this fact, we approach the mirror until the lines of the figure run- ning in some one direction are seen with the greatest distinct- ness and, read off on the tape-measure the distance of the mir- ror. This gives us the refracting power of the meridian of least refraction. The mirror is then brought closer to the eye until the lines at right angles to these are seen sharply ; the dis- tance of the mirror read off on the tape then gives the re- VALUE OF THE DIFFERENT METHODS. 113 fraction in the most highly refracting meridian, and the differ- ence between the two shows the amount of the astigmatism. Example : The lines running vertically are seen at 34 cm., those running horizontally at 31 cm.; there is compound hy- permetropic astigmatism. In the vertical meridian there is H (31 20 = II ; ii 10 i) of i D; in the horizontal H (34 20 = 14 ; 14 10 = 4) of 4 D ; H = i D with astig. = 3 D axis 90. 130. My own experience convinces me, however, and I believe the opinion will be corroborated by most ophthal- moscopists, that the two methods of examination by the erect and inverted images as usually employed, and as described in 99 to 126, if cultivated with the care which their importance in other particulars demands, are capable of furnishing us with all the information in regard to the refraction of the eye that the ophthalmoscope is capable of giving. The data thus obtained are often very accurate, but the lia- bility to error is too great for any one of these methods to be relied upon implicitly. Before ordering glasses, the findings with the ophthalmoscope should be verified by an examina- tion with cylindrical lenses and the test letters. BIBLIOGRAPHY. Bravais Du diag. ophthalmoscopique de 1'astig. Lyon Med. VII. Pp. 319-25. 1875- Carreras, Arago El oltalmsc. de refrac en los reconocimientos visuales. Rev. d. cien. Med. VIII. P. 3. Barcel. 1882. Cohn, H. Ein Augenspiegl. f. schnell. Refractbestim. Klin. Monatsbl, f. Au- genhlk. X. Pp. 307-9. 1872. Couper, J. On a new and simple meatis of detect, mxd. astig. by the ophth. Med. Times and Gaz. London. I. P. 114. 1866. Couper, J. The ophth. as an optometer in astig. Rep. Internat. Ophth. Cong. London. 1872. Pp. 109-19. 1873. Dennett, W. S. Astig.; the fundus of astig. eyes ; an attachmt. to the ophth. Arch. Ophth. and Otol: N. Y. V. Pp. 505-7. 1876. Dennett, W. S. Zur Untersuch. astig. Augen mit dem Augenspiegel. Arch. Ohr. u. Augenhlk. VI I. P. 55. 1877. Frothingham, G. E. A case of mxd. astig. with predom. myopia diag. by itspecul. ophth. appearance. Phys. and Surg. Ann Arbor, Mich. II. Pp. 14-16. 1880. Giraud-Teulon La vision et ses anomalies. Paris. 1881. 1 14 BIBLIOGRAPHY. Giraud-Teulon Theorie de 1'ophthalmoscope avec les deductions qui en decou- lert Gaz. Med. d. Paris. Nos. 7 et 8. 1859. Giraud-Teulon De 1'influence des lentilles positives et negatives et de celle de leur distance a 1'ooil sur les dimensions des images ophthalmoscopiques de la papille ou disque optique dans les anomalies de la refraction oculaire, et particulierement dans 1'astigmatisme. Mem. presente a 1'Acad. d. Sci. Aout 9. 1869. Hay, G. Apparent form of inverted ophth. image of opt. disc in Astig. Trs. Amer. Ophth. Soc. P. 86. 1870. Knapp, H. Demonstratof the refract ot light by asymmetric, surfaces and the de- terminat. of astig. with glasses and the ophth. Trs. Am. Med. Ass. XXXI. Pp. 669-74. 1880. Landolt, E. Le grossement des images ophthalmoscopiques. Paris. A. De- laharye. 1874. L'Hoest Du diag. des anomal de refract, de 1'oeil au moyen de 1'ophth. Arch. Med Beiges. XXI. P. 177. 1882. Loring, E. G. Text-book of ophthalmoscopy. Part I. N. Y. D. Appleton & Co. 1886. Mauthner, L. Lehrbuch der ophthalmoscopie. Wien. 1867. Parent Descript. d'un ophth. a verres cyld. (nouveau modelle). Ann. d'oculist. Sept. Oct. 1883. Perrin, M. Traite d'ophthalmoscopie et d' optometrie. Paris. 1870. (Astig). Stammeshaus Ueber eine methode dem aufrechten Bilde eine starkere Vergroes- serung zur erhielen. Zehend. Monatsbl. f. augenhsilk. Jan. 1874. Schmidt-Rimpler Zur ophth. Refractionsbestimmg. mil Hiilfe des umgekhrt. Bildes. Tagebltt d. Naturfsohrsors. zu Kassel. 1878. Schmidt-Rimpler Zur cbjct Refractsmsg. Centralbl. f prakt. Angenhlk. P. 260. 1878. Schmidt-Rimpler Ophth. Refrctsbestim. im umgekrt Bilde. Zeitschr. f. Instru- mentk. Nov. 1882. Also in Augenheilkunde und Ophthalmoscopie. Braunschw. 1885. Schweiger, C. Ueber die Groesse des ophthalmoscop. Bildes. Nachrichten d. Koen. Gesell. d. Wissensch. u d. G. A. Univ. et Goettingen. No. 9. April, 1870. Schnabel Ueber die Lage und Groesse des aufrechten Bildes in Augenhinter- grunde. Zehenders Monatbl. f. Augenheilk. 1872. P. 117. Snellen, H. and Landolt, E. Ophthalmometrologie. in Handbuch. d. gesammt. Augenheilk. von Grafe u. Samisch. B. II. I. 1874. Stilling Ueber ophthalmosc. Refractsbestim. Klin. Monatsbl f. Augenheilkd. B. XIII. P. 143. 1875. Stimmel Objct. Bestming d. Astig. Klin. Monatsbl. f. Augenhlk. XIII. Pp. 3902. 1875. Uhthoff Demonstrat. eines Refracts ophthalmo. zur Bestiming. des Astig. Ber. U. d. versamml. d. ophth. Geselsch. Stuttg. XIV. P. 167. 1882. CHAPTER VIII. SKIASCOPY. (THE SHADOW-TEST.) 131. In a foot note on page 490 of his treatise on the 'Anomalies of Accommodation and Refraction of the Eye," Bonders makes the following record : " My friend Bowman recently informs me that ' he has been sometimes led to the discovery of regular astigmatism of the cornea, and the direction of the chief meridians, by using the mirror of the ophthalmoscope much in the same way as for slight degrees of conical cornea. The observation is more easy if the optic disk is in the line of sight and the pupil large. The mirror is to be held at two feet distance and its inclination rapidly varied so as to throw the light on the eye at small an- gles to the perpendicular and from opposite sides in succession, in successive meridians. The area of the pupil then exhibits a somewhat linear shadow in some meridians rather than in oth- ers.' " This description is too short and indefinite to enable us to de- cide whether these experiments of Bowman held the germ of the method now known under the names of " keratoscopy," "retinoscopy," "pupilloscopy," "phantoscopy," etc., but at all events no extensive practical application was made of the changes observed in the pupillary area when illuminated from a distance by a simple mirror until the publication of an article on the subject by Cuignetinthe Recueil d' Ophthalmologie in 132. Most of the names given to the method do not con- vey any intelligent idea of the nature of the phenomena on which it is based. The appearances do not pertain either to the cornea, pupil or retina alone. They are due entirely to the refractive condition of the eye as a whole. As the principal and distinguishing feature of the method is the behavior of the OPTICAL PRINCIPLES OF THE SHADOW-TEST. shadowy edges of the bright image of the source of illumina- tion, " the shadow-test " would seem to be the most appropriate term by which it could be designated. If, however, we should wish to use a general scientific term, the word " skiascopy," as suggested by the celebrated Greek scholar, M. Egger, is avail- able. 133. The method is founded on the observed fact that when the light from a flame, placed in the ordinary position for ophthalmoscopic examination, is thrown into the eye by means of a mirror at a distance of from 3 to 5 feet from the eye, and the mirror is rotated about one of its axes, a shadow is ob- served to pass across the bright area of the pupil. The relative brightness of the pupil and the direction and rapidity with which the shadow moves serve as a basis for diagnosis, and on the following principles : fig- 35- SHOWING THE OPTICAL PRINCIPLES ON WHICH SKIASCOPY is BASED. 134. When the light from the flame F, Fig. 35, is thrown by a concave mirror M in the direction of the eye P, from a dis- tance of from 3 to 4 feet, an image of the flame is formed, near the focus of mirror, at F 1 . This image then becomes the illum- inated object from which rays diverge and which, passing into the eye P, form an image on its retina at F*. The light is re- flected from this retinal image and passing out of the eye forms in its turn an image real or virtual at a certain place before or behind the eye, according to its refractive condition. 135. Let us suppose, for illustration, that F 1 is one OPTICAL PRINCIPLES OF THE SHADOW-TEST. 1 1/ meter from K the nodal point of the eye P. Then, if P is em- metropic, the image of F 1 formed on the retina at F 2 , which in this case will be blurred in outline, will send out rays that will be rendered parallel by the refracting media and an image of F- will be formed at infinity, behind the observer's eye at O. When the mirror is rotated to the position of M 1 , the source of illumination moves from F 1 to/ 1 and the retinal image moves from F* to/ 2 . To the observer's eye at O the movement of the image of/ 2 formed at infinity by the refracting media of P is in the sense contrary to the movement of the mirror, and the extent of this movement is infinitely large as compared to that of the mirror. If, however, the eye is myopic with its far point at F*, the retinal image F 2 will form a real and inverted image of itself at that point. When the mirror is rotated to M l the image of / 2 will move from F* to /* in the same sense with the mirror. The amount of movement will be measured by the distance from F* to/ 4 . Should the far point of the myopic eye lie at F 5 the image of F' 2 will be found there, and on rotation of the mir- ror, move to/ 5 , likewise with the mirror. The amount of move- ment is measured by the distance, F'f' 3 . It will be seen from this that the movement is less the greater the degree of myopia, and greater the smaller the degree. * 1 36. When, as in hypermetropia, the image of F 2 is virt and behind P, the character of its movements is changed. If it is found at **, for example, on rotation of the mirror to M l F 3 will move in an opposite direction to/ 3 and the extent of move- ment will be expressed, as before, by the distance F 3 / 3 . The farther F 3 is removed from K, that is the lower the degree of hypermetropia, the greater the amount of movement, until it reaches its maximum when the rays coming from it become practically parallel, and the eye essentially emmetropic. The closer F 2 approaches to K, that is the higher the degree of hy- permetropia, the less the amount of movement. 137. From the foregoing the following facts are estab- lished : i. That in emmetropia and hypermetropia the move- ment of the image is against that of the mirror. 2. That Il8 DIAGNOSIS OF AMETROPIA BY THE SHADOW-TEST. in myopia of degrees above iD, that is when the far point of the eye is within 3 feet, the movements are with the mirror. 3. That in both forms of ametropia the higher the degree the less the extent of movement. 138. But this is not all. The brightness of the image changes with the degree of ametropia. If F* coincides with the far point of the observed eye (there being M of iD), the image F 2 will be clear and distinct, and all rays proceeding from it will come back and be again united at F 1 . There will then be a maximum of brightness of the image seen by the observer O. If, however, F 2 should not be the conjugate focus of F 1 there will be circles of diffusion at F 2 which will be large in propor- tion to the departure in either way from this M of iD. Each individual point of F 2 will, therefore, have fewer rays coming from it, and there will be a diffusion of them over a greater ex- C- tent of surface, with a corresponding diminution in distinctness of the image. 139. Now, what we specially note in this method of exam- ination is the shadowy outline of this circle of diffusion which is so large in ametropia that the edges appear as almost straight lines, and its diagnostic value is summarized as follows : 1. Movement of shadow edge against the mirror, low degree of M, (less than i.D) emmetropia, or hypermetropia ; extent of movement less the higher the degree of hypermetropia. Bright reflex ; E. or low degrees of M. or H : dull reflex, higher de- grees of H. 2. Movement of shadow with the mirror ; M. above i D, its extent diminishing as the degree increases. Reflex duller in di- rect proportion to the degree of M. 140. There is one objection to this examination when made with the concave mirror, namely, that by it we are not able to distinguish between emmetropia and low degrees of hyperme- tropia and myopia, since in them all the shadow moves against the mirror. This is due to the fact that the source of illumina- tion, F 1 , is always at a finite distance and gives' out divergent rays, and if it is situated at a greater distance from P than one meter, only a limited number of its rays will enter the eye, and DIAGNOSIS OF AMETROPIA BY THE SHADOW-TEST. the illumination of the retinal image will be greatly diminished. This nearness of F 1 to P necessitates a near approach of to P. As a consequence of this, in all cases of M, where the far point lies behind 0, no actual inverted image of F 2 is formed in front of 0, but on the contrary, it tends to become virtual and erect and is classed with E. and H., and has the same move- ment against the mirror. In order to obviate this and have sharply defined diagnostic movements of the shadow, Story and others have suggested the use of a plane mirror, which would enable the observer to place himself at a distance of 12 feet or more from P. Under these circumstances the rays coming from the flame two feet behind P and fourteen feet from the mirror would approach parallelism and would be so reflected by the plane mirror into the eye P, without loss by dispersion. On emerging, the rays from F 2 could form a real image six feet from P which would be recognized by and a M. of o 5 D distinguished. When the plane mirror is used, however, it must be borne in mind that the movements of the shadow are the reverse of those observed when the concave mirror is used ; that is, in H and E, it moves with the mirror, in M against it. The reason for this is as follows : When the concave mirror is used, the source of illumination is an image of the flame at the focus of the mirror, and when the mirror rotates from right to left this image also moves from right to left, and con- sequently the retinal image F 2 moves in the contrary direction, with the results as we have seen. With the plane mirror, how- ever, the object furnishing the light is a virtual erect image of .F situated as far behind Mas the flame F is in front of it. When the mirror is rotated, therefore, from right to left, this image moves in a contrary direction and its retinal image, F 2 , in the same direction as the mirror. The image furnished by F 2 must move, in accordance with this, in a direction relative to the mir- ror exactly the opposite to that followed in the examination with the concave mirror. 141. The examination so far, however, has furnished us with no definite information as to the amount of ametropia. I2O DIAGNOSIS OF AMETROPIA BY THE SHADOW-TEST. We can know the higher degrees of M. or H., and if the plane mirror is used even the lower degrees, but we can only estimate the amount of departure from the normal optical con- dition in a rough manner by the greater or less dulness of the pupillary reflex, and the greater or less extent of shadow movement. It is possible, however, to obtain a quite accurate diagnosis by this method, by placing in front of the eye under examina- tion correcting glasses in succession until one is found with which emmetropic movements of the shadow are found. Let there be, for example, a short movement with the con- cave mirror and a dull reflex. This indicates, of course, M., and experience teaches us, of a moderate degree. We then put a 4. D in a trial frame, and placing it before the eye, make another observation and note the direction of the shadow. It is found to still be with the mirror: the M. is under-corrected. After trying 4.5 with the same result we find that with 5 there is large movement against the mirror, and a maximum brightness of reflex. This shows that there is a small amount of M. (about 0.5 D) remaining uncorrected. Adding this to the 5 D we have 5.5 D as about the degree of M. present. Should the plane mirror be used, we find before correction a movement against the mirror, and not until 5.5 is placed in the frame do we find a movement with the mirror. When one becomes skilful in the use of this method an approximation to within I D of the optical state of the eye can be made in the majority of cases. For its most satisfactory employment a wide pupil is essential, and it is necessary that the eye examined shall be protected thor- oughly from all light except that which comes from the mirror. Like most of the other methods of objective examination, it requires much practice to become expert in its use, and is, according to my experience, more consumptive of time than the ordinary ophthalmoscopic methods. 142. It will be seen at once how easy it is to use this meth- od in the diagnosis of astigmatism. We have, for this purpose, simply to determine, in accordance with the principles laid DIAGNOSIS OF ASTIGMATISM BY THE SHADOW-TEST. 121 down, the ametropia of the principal meridians in the same way that we examine for the general ametropia. Moreover, the direction of the principal meridians is, owing to some pe- culiarities of the phenomena, very readily discovered. If these meridians stand as they commonly do, vertically and horizon- tally, there will be a difference in the amount or character of shadow movement on rotation of the mirror in these directions respectively. But should the meridians lie obliquely one be- ing, say, at 45 on horizontal movement of the mirror, the Fig. 36. DIAGRAM SHOWING How THE SHADOW IN SKIASCOPY MOVES ACROSS THE PUPIL WHEN THE MERIDIANS IN ASTIGMATISM ARE OBLIQUE. shadow does not move in a horizontal direction, but at an angle of 45, and for the following reasons: We know, from the facts demonstrated in Chapter II, that both the diffuse retinal image of F l and the image of this im- age'as seen by the observer, 0, being formed by an astigmatic system are not circular as in general ametropia, but oval, with the long diameter in the direction of one of the principal meridians. The oval lying, as it does in our supposed case, with its long axis at 45, advances, when the image as a whole moves hori- zontally, its shadowy edge in a direction at right angles to its axis. Without going into any mathematical demonstration of 122 DIAGNOSIS OF ASTIGMATISM BY THE SHADOW-TEST. the matter it is easy to convince oneself of this fact by a very simple experiment. Take a circular opening (Fig. 36) and place behind it an object with a straight edge a c at an angle of 45. Now advance this object in a strictly horizontal direc- tion to b d; the apparent movement of the object will be, not from a to b and c to d, but in the direction of the line e /per- pendicular to a c. 143. In examining for astigmatism by means of the " shadow test " we first throw the light into the eye in the usual manner, and rotating the mirror in various directions note the brightness of the reflex, and the direction and extent of the shadow movements. If astigmatism is present, it reveals itself at once by the incongruity of movement explained in the preced- ing paragraphs, and the direction of the principal meridians is thus indicated. We then proceed to test the refraction of each meridian separately by placing in the trial frame before the eye various correcting glasses and rotating the mirror in the direc- tion of this meridian until one lens is found which gives emme- tropic motions. The meridian at right angles to this is then taken and the refraction determined in the same manner* Knowing then the refraction in the two meridians it is easy, in the way already sufficiently dwelt upon, to find the amount of astigmatism. When the correcting glasses thus indicated are placed in the frames with the axes of the cylinders at the proper angle, movements of the mirror in all directions should give emmetropic motions to the shadows. BIBLIOGRAPHY. Baker, A. R. Retinoscopy. Amer. Jr. Ophth. I. Pp. 116-19. 1884. Charnley, W. On the theory of the so-called keratoscopy and its practical appli- cation. Roy. Lond. Ophth. Rep. X. P. 344. ChiberL Determin. quantitat de la myop. par la keratoscopie (fantoscopie nitin.) a 1'aide de un simpl. mirror plan. Ann. d'oculist. LXXXVIII, P. 238. 1882. Cuignet Keratoscopie. Recuiel d' oph. 1873. Pp. 14 and 316.", Cuignet Astig. comp. et obliq.: keratoscopie. Rec. d'ophth. 35. I. Pp. 73-5. Paris. 1879. Cuignet Apropos de keratoscopie. Rec. d'ophth. P. 321. 1880. Forbes, L. On keratoscopy. Ophth. Hosp. Rep. X. P. 62. 1880. BIBLIOGRAPHY. 123 Hubert et Prouff Keratoscopie. Rev. Clin. d'Oculist. No. 5. P. no. 1884. Hartridge, G. The refraction of the eye. 2nd edition. London, 1886. Jackson, Edward The measurement of Refraction by the shadow-test, or Retino- scopy. Amer. Jnl. Med. Sci. April, 1885. Juler The applicat. of retinoscopy to the diag. and treat, of the errors of refract. Brit. Med. Jr. Pp. 116-70. 1882. Mengin De la keratoscopie comme moyen de diagnostic des differt. etats ametrop. de 1'oeil. Rec. d'ophth. P. 122. 1878. Morton, A. Stanford. Refraction of the eye, its diagnosis and the correction of its errors with a chapter on Keratoscopy. London, 1881. Morton, A. S. and Barrett, J. W. A clinical investigation of the various methods of practising retinoscopy. Brit. Med. Jnl. Jan. 1 6, 1886. Parent de la keratoscopie. Rec. d'ophth. P. 65. 1880. Parent Diagnost. et determ. object, de 1'astig. Rec. d'Ophth. 35. III. Pp. 229-52. 1881. Story, J. B. The advantages of the plane ophth. mirror in retinoscopy. Ophth. Review. II. P. 228. CHAPTER IX. KERATOMETRY AND KERATOSCOPY. 144. The fresh impulse given to the study of astigmatism in recent times was by measurements of the cornea in its vari- ous meridians, first made systematically by Knapp. And since the cornea has been found to play the chief part in the anomaly, the most convenient and proper method of investigation would seem to be by some kind of keratometry. And so it would be but for the fact that, until very recently, no rapid and accurate method of keratometry has been at the command of the prac- titioner. The ophthalmometer of Helmholtz is cumbersome, expensive, difficult to handle and very consuming of time ; all of which tend to exclude it from the consultation room. 145. The desirability of some practical method of kera- tometry being recognized, several attempts have been made to realize it, but up to 1881 none had been presented which offered theonerits of accuracy, facility of handling, simplicity of struc- ture and comparative cheapness. In that year, Javal exhibited before the International Medical Congress, at London, an in- strument constructed by himself in conjunction with Shiotz which fulfilled all these requirements, and in my estimation must be regarded as the most important, practical and exact means of diagnosis given to our science since the invention of the ophthalmoscope. 146. As regards the designation of this method of examin- ation we think the name "keratometry" more accurately descrip- tive than "ophthalmometry." The latter term could be applied to measurements of the eye in any or all of its parts, whereas, in the method under consideration, we simply measure the ra- dius of curvature of the cornea at any desired locality. Neither would " keratoscopy" be correct, since this means a simple in- spection of the cornea and does not necessarily imply any {124 > DIFFERENT METHODS OF DETERMINING THE RADIUS. 12$ measurements; a term quite appropriate, however, to the methods of Placido and DeWecker, to be described later. 147. The instrument of Javal and Shiotz 1 is constructed on the well-known fact that the image of an object of a certain size at a fixed distance from a convex reflecting surface grows smaller as the radius of curvature of that surface becomes shorter. There are several ways in which this principle can be ap- plied in determining the curvature of any given convex sur- face. (a.) A certain size of image may be taken as a standard and the distance between the object and reflecting surface varied until this standard size of the image is reached. It can then be de- termined, by calculation, what changes in radius of curvature correspond to a certain variations in distance ; or (b.} the distance separating the object and reflecting sur- face may remain the same while the size of the object is varied till the standard size of image is obtained ; or (c.) the distance and size of object being fixed the calcu- lation may be based upon the varying size of the image. 148. Of these plans the first and second are the most available, and of the two, Javal and Shiotz have chosen the second. The essential part of the instrument for ordinary use is a Wollaston's bi-refringent prism of such a power that it shall give an exact doubling of an object 3 mm in diameter when it is at 27 cm from the prism ; or, expressed in another way,when the object is 27 cm from the prism and the edges of the double images touch, the diameter of the object must be 3 mm. The object to be measured in this case is the corneal reflection of some suitable object placed in front of the eye. The accessories of the instrument are the optical appliances for seeing this double image to the best advantage and from a convenient distance,and a means for measuring the varying size of the object which furnishes the corneal image. 1 Made by M. Laurent, rue de 1'Odeon, Paris. The net price of the instrument is 350 francs. It can be obtained through J. W. Queen & Co., Philadelphia. 126 CONSTRUCTION OF JAVAL AND SCHIOETZ INSTRUMENT. In the construction of the objective W (Fig. 37) the birefrin- gent prism is placed between two convex lenses having each a focus of 27 cm. At the focus of the second lens, found between E and 0, a fine spider's web is stretched across the tube. By Fig. 37- THE OPHTHALMOMETER (KERATOMETER) OF JAVAL AND SCHIOETZ. means of these two lenses and the prism an inverted double im- age of the reflection from the cornea, which is situated 27 cm from the first lens, is formed at the spider's web, and this double image is seen through the ocular whose focus also lies at the spider's web. This double image is seen clearly, only when the eye of the observer is' accurately adjusted by means of the ocular to that distance. This inverted double image of the corneal reflection is not magnified. The reflection and its im- age are at conjugate foci, and the distance of the cornea from the first lens being the same as the distance of the spider's web CONSTRUCTION OF JAVAL AND SCHIOETZ INSTRUMENT. I2/ from the second lens, the two images must be of the same size ; in other words, the reflection image is simply transferred from the cornea to the focus of the ocular. The only thing now needed to furnish the necessary means for an examination is an object whose size can be regulated at will. All that is essential of such an object are two opposing sides, in order that we may know when the edges of the dou- ble images are in contact. This is obtained by having two white bands MM' moveable on an arc A, that is fixed on the tube Wat about 35 cm. from the cornea which serves as its center of curvature. The outer edges of these two bands con- , stitute the lateral limits of the object. As these bands are moveable it is easy to form an object of any desired size which can be accurately measured on the arc. The instrument has now only to be properly mounted to be ready for use, and the manner in which this is done is well shown in Fig. 37. 149. In making an examination the head of the examinee is placed in the head rest and the eye not to be examined is cov- ered with the shade P. The optical part of the apparatus is moveable, as a whole, backwards, forwards and laterally on the foundation board, and the elevation of the tube is regulated by the thumbscrew V. The ocular O must first be accurately adapted to the spider's web for the eye of each observer. The tube is then brought into line with the cornea and by movements back and forth so adjusted that a clearly defined double image of MM' shall be formed at the spider's web, where it is seen by the observer through the ocular 0. When this is done the prism is 27 cm. from the cornea, and when the double images of the corneal reflection formed by it touch by their opposing edges, each im- age has a diameter of 3 mm. When the instrument is thus adj usted, one of the white bands is moved along the arc until the inner edge of its image, as seen through the ocular 0, touches the outer edge of the image of the other band. Then, as stated above, the diameter of the corneal image of MM' is 3 mm. The size of the object MM' 128 LIMITATIONS OF THE INSTRUMENT. can then be measured off on the arc A. Knowing now the size of the object, the size of the image and the distance sep- arating the object from the reflecting surface, we have all the data necessary for calculating the radius of curvature of the convex surface of the cornea. 150. Thus far the instrument has no special practical ad- vantage over the ophthalmometer of Helmholtz, for it is the coritplitations from the observed data that are so tedious and time-consuming. But Javal and Shiotz have so arranged the various parts of their apparatus that a certain size of object when the instrument is properly adjusted shall correspond to a certain radius of curvature, which can be read off on the arc in millimetres or expressed in refracting power by dioptrics. A variation of 6 mm. in the size of the object 35 cm from the cornea corresponds to a change of I D in refracting power and a variation of 36 mm. in size (6 D) corresponds to a difference of about i mm. in the length of the radius of curvature. As it is comparatively easy by this instrument to approach to with- in 0.25 D of the actual refracting power, an estimation of the radius of curvature is possible up to l /, mm., which is all that could be demanded in the practical determination of refrac- tion. 151. As it is not possible with this instrument to examine with any degree of accuracy the lenticular surfaces, and as these form important elements in the general optical condition of the eye, the apparatus is of limited advantage in obtaining the refraction of the eye as a whole, except in cases of aphakia. Its usefulness for estimating general ametropia is still further diminished by the fact, which the instrument itself has done so much to establish, that the conditions of myopia and hypermetropia are not due, except in rare instances, to variations in the refracting surfaces of the eye, but to changes in the antero-posterior diameter of the eye-ball. 152. Since, however, it is a fact demonstrated more than twenty years ago in the physiological laboratory, and now fully corroborated by this very instrument in the consultation room, that the much larger part of astigmatism is corneal, and since METHOD OF USING THE INSTRUMENT. 1 29 it is as easy with it to measure the cornea in one meridian as in another, the value of this keratometer in the diagnosis of astigmatism can hardly be over-estimated. In fact, it might with great propriety be called an "astigmometer." The tube W can be turned on its axis, carrying with it the arc and the white bands MM', and any departure from its in- itial position is shown by a pointer moving over the fixed grad- uated disk E. It thus becomes possible to measure the cor- neal curvature in any desired meridian and to know the exact direction of that meridian. We have, therefore, only to meas- ure the cornea in the manner above described in its various meridians, read off on the arc the radius of each and take the difference between the strongest and weakest in order to have the amount of astigmatism expressed in difference in radius (r) or in dioptrics. The inventors have facilitated this determination in a most ingenious manner, whereby it is possible to see in the double image itself, and without the necessity of reading on the arc, the difference in the refraction of the principal meridians. One of the sides of the band M, instead of being straight is made in the form of five equal steps, as shown in A, Fig. 38. It is the lateral edge of the lower step which must be brought in contact with the edge of the other band M' in order to have the image of the required size of 3mm. 153. In making examinations with the instrument for as- tigmatism the tube is turned on its axis and the band M' moved on the arc, ^"remaining stationary, until one meridian is found in which the bases of the two bands form a continuous line, when their sides are in contact. The refraction of the cornea in this meridian (indicated by the pointer on the disk E) is then read off on the arc in r or in dioptrics and noted. The tube, with the arc, is then rotated to the opposing merid- ian, when it will be found, should astigmatism be present, that the sides have either separated or overlapped. If they have overlapped, the amount of crossing is shown by the number and portions of the steps of M covered by M', which is readily rec- ognized by the fact that these steps and parts of steps are just I3O METHOD OF USING THE INSTRUMENT. twice as bright (for obvious reasons) as the remaining steps of the band. Now, the size of these steps has been so regulated that each one shall represent I D of refracting power. If, therefore, one of these steps is covered, there is a difference of I D in the two meridians ; if two are covered (B, Fig. 38) we fig. 38. APPEARANCE OF THE CORNEAL IMAGE OF THE BANDS IN THE KERATOM- ETER WHEN THERE IS A DIFFERENCE IN THE REFRACTION IN THE T\VO MKKIDIANS OF THE CORNEA. A, meridian of greatest curvature ; B, the meridian of least curva- ture (longest radius). know the difference is 2 D and the necessity of reading the difference on the arc is obviated. If, however, it is desired to know the radius of curvature exactly in this meridian, indica- ted by the pointer on the disk E, the band M' is moved on the arc until its edge is just in contact with the lower step of the graded band M. Its position on the arc will then give the de- sired information. Moreover, the meridian in which there is a crossing of the bands is the less refracting. The fact of the two images over- lapping shows that they have a diameter greater than 3 mm. and consequently the surface giving them must have less cur- vature than that giving them with edges in contact, and in or- der to have them thus in contact the object must be made smaller by moving M' on the arc towards M. If the images of the bands separate in moving the arc from its initial position ITS LIMITATIONS. 13! where they were in contact, it shows that the first meridian is the less refracting with a larger radius of curvature. The cur- vature of the meridian where the separation is greatest is de- termined by moving the band M' along the arc away from M until the edges again touch. The refraction can then either be read off on the arc and the difference taken between that and that of the other meridian, or the arc can be turned again to the opposing and less refracting meridian, when the number and parts of steps overlapping will show at once the difference be- tween the two meridians, expressed in dioptrics and fractions thereof. 154. We have now ascertained the amount of the astigma- tism and the direction of the meridians of greatest and least refraction, but the data furnish no clue as to the form of the anomaly. The measurements give no information as to wheth- er the astigmatism is simple or compound, myopic or hyperme- tropic, or mixed. When, for instance, the horizontal meridian is found to be least refracting, it may be that (a) it is emmetro- pic, while the vertical meridian is myopic simple M. astig.; or (fr) it may be myopic also but less so than the vertical comp. M. astig ; or (c] it may be hypermetropic, the vertical being emmetropic H. astig ; or (d] it may be that both meridians are hypermetropic, this one being more so Comp. H. astig.; or (e) it may be hypermetropic while the other is myopic mixed astig. The differential diagnosis of the form must therefore be made by some of the other methods of examination. The only other defect of the method is that it leaves us in ignorance of the amount of the lenticular astigmatism. One important fact has been developed by the use of the instrument in this connection and that is that in at least one half the cases it is neutralizing in its character. When the individual is be- yond 40 years of age, however, it is rare to find any important difference between the total and the corneal astigmatism. In the following table are recorded 15 cases taken as they came from my note-book showing the difference between the astigmatism as determined by glasses and that found on meas- 132 DIFFERENCE BETWEEN CORNEAL AND TOTAL ASTIGMATISM. urement of the cornea. The excess of corneal refraction is des- ignated by -f, the deficiency by . TABLE VI. No. Name. Age. Astig. by Glasses Astig. by Keratome- ter. Difference. i Mr. N. 48 L I Rl. S I i-5 2 Mrs. H. 50 Li. 5 Ri '5 i. 3 Mrs. C. 52 L2 R2 2-5 2-5 +0.5 4 Mrs. M. 21 4 Ri-5 4- '25 0.25 5 Miss S. 28 L 1.25 K3 1.25 3-25 -0.25 6 Miss C. 17 Lo-5 0.75 -0.25 7 Mrs. M. 38 Ri.25 1.25 8 Mr. L. '9 K 0.5 nil -0.5 9 Mr. G. 8 Ro 0.5 +0.5 10 Miss G. ,8 Ro-5 0.5 it Miss C. 36 L3 *3 3-25 3-25 +0.25 +0.25 12 Mr. G. 5 L4-S K4-S 4- 4-25 0.5 0.25 '3 Miss L. 18 L none Ko-5 0.5 i. -0.5 +0.5 H Mrs. C. 33 L 3 R4-5 3- 4- 0.5 '5 Mr. M. 27 L none R 0.25 0.5 1-25 -0.5 + 1- These cases well represent the average of my examinations by this instrument which now number more than 100. I have PLACIDO S KERATOSCOPE. 133 never found a greater difference than iD, and the direction of the principal meridians has always been found to correspond essentially with the corneal meridians as determined by the keratometer. 155. The apparatus, for its most satisfactory employment, requires a good illumination of the white bands. I find that in this climate the light from an unobstructed window is quite sufficient. But for dark days and consultation rooms not well lighted, the instrument is provided with argand gas-burners and reflectors which make it possible to use it under all circum- stances. 39- THE KERATOSCOPE OF PLACIDO. 156. PLACIDO'S KERATOSCOPE. In 1880 Placido, of Porto, de- scribed an instrument for noting changes in the form of the cornea by means of the reflection from its surface of a series of concentric circles. This is the simplest form of keratoscopy and is available to any one at the cost of very little trouble. Take a board of any inflexible material wood, sheet-iron or stiff paper 25 or 30 cm. square, and draw on its white surface 5 134 ITS VALUE IN REGULAR ASTIGMATISM. concentric black circular bands I cm in width and 1^2 cm. apart from each other (Fig. 39). Make a hole in the center of the disk through which to look, and you have all the essential parts of the instrument. The patient is to be placed with the back to a good light and the board held at right angles to the visual axis at from 8 to 12 inches from the eye under ob- servation. If there is no astigmatism, the reflex from the apex of the cornea is circular and there is no irregularity in the course of the circles. Should regular astigmatism be present, the corneal reflex will be oval with its long diameter in the di- rection of the meridian of least refraction. For the purpose of enlarging the image, as well as for relieving the accommoda- tion of the observer a convex lens can be placed behind the hole in the disk. 157. Javal has added one of these disks to his ophthalmo- meter. The principal value of this disk is, as we'shall see, in examining for irregular astigmatism. It is of comparatively little use in the determination of the regular forms. At least I, after considerable experimentation with it, have not been able to satisfy myself of the existence of astig. below 3D. The variation between the meridians of least and greatest refraction is represented, as Javal's instrument shows, by a difference in radius of curvature of about */ of a millimeter for one dioptre of refracting power. It requires a most expert eye, to detect in the corneal reflection a difference of l / 3 of a millimeter in the radii of two opposing meridians, as expressed by the departure of the figure from a strict circle. For a simple rough estimation of the higher degrees it is, however, of some value, particularly in the way Javal has adapted it to his instrument. DE WECKER'S SQUARE. Fig. 40. 135 WECKER'S SQUARE FOR TESTING FOR CHANGES IN CORNEAL CURVATURE. Fig. 41. FIGURES FOR DETERMINING THE AMOUNT OF CHANGE IN THE CORNEAL REFLEC- TION OF WECKER'S SQUARE. 136 THE FINAL TEST OF DIAGNOSIS. 1 58. The same may be said in a general way of De Wecker's modification of Placido's idea. This consists of a square in- stead of a circle (Fig. 40) whose cornea! image is to be ob- served. He has made an addition to the method in furnishing a standard of comparison for the corneal image of the square by placing on a black surface (Fig. 41) the parallelograms which correspond to the different degrees of astigmatism expressed in dioptrics. This is held near the eye under observation and a direct and simultaneous contrast of the two outlines is thus furnished, which enables the observer to judge the more readily as to whether there has been any departure from the strict form of the square and, if so, to estimate roughly how much. 159. We have now completed a description of all the im- portant methods for the diagnosis of astigmatism. Some, it has been seen, have an advantage in one particular and some in another, while all have certain insufficiencies. A preference for one over the other will generally be due to the fact that the individual has practiced it more assiduously than the rest and thereby attained greater skill in its use. 1 60. But no one method should be relied upon exclusively; and no diagnosis of astigmatism should be considered as fixed until it has been verified by an examination with cylindrical glasses and test-types as described in Chapter III. The highest visual acute- ness must always be the final test of a diagnosis. BIBLIOGRAPHY. Angelucci, A. Sulla refrazione e correzione della cornee coniche ed ectatiche. Ann. d.OtL XIII. Fas. I. P. 35. Astigmometrie dc DeWecker et Masselon. Ann. d' Oculist. LXXXVIII. Pp. 44-6. 1882. Berger Ein modifict Keratoskop. Wien. Med. Presse. No. 46. 1882. Berger Ueber d. Diag. d. Kriimmungsanom. d. Homhaut mil d. Keratoskop. Wien. Med. Wchnschft. No. 51. 1882. Berger Der Hornhautspiegel (Keratoskop) u. seine pract Anwendung. Deutsch. Med. Ztg. Hft. 6, 1884. Bergmeister Demonst d. Keratskops v. Placido. Anzeig d k. k. Gesellsch. d. Aertz in Wien. No. 2. 1882. BIBLIOGRAPHY. 137 Berlin, E. Zur Berech. d. Astig d. Hornhaut Klin Monatsbl. f. Augenhlk. IX. Pp. 217-9. 1871. Burnett, Swan M. Ophthalmometry with the ophthalmometer of Javal and Schiotz, with an account of a case of keratoconus. Archives of Oph. XIV. Pp. 169-176. Fonseca Astigmatoscope. Arch. Ophth. de Lisbon. Jan.-Feb. 1882. Gavarret Astig. et Ophtalmom6trie. Rev. Scient. XXX. Pp. 74-80. Paris. 1882. Hasner Ueber Placidos Keratoskop. Prg. Med. WchnschrfL No. 13. 1882. Hirschberg Das stabile Keratoscop. Centralbl. f. Augenhlk. P. 30. 1883. Javal et Schiotz Un ophthalmometer practique. Ann. d'Oculist Juil. Aout. 1881. Javal Contrb. a 1'ophthalmomet. Ann. d'OculisL Mai-Juni. 1882. Javal Seconde Contrib. a POphthalmomet. Ann. d'Oculist. Jul.-Aout. 1882. Javal Troisieme Contrib. a 1'ophthalmomet Descpt. de quelques images kerato- scop. Ann. d'Oculist. Jan. Feb. Mars. 1883. Javal Quatrieme Contrib. a 1'ophthalmomet. Ann. d'Oculist Sept. Oct. 1883. Javal Prioritats Reklam. beziiglich des Keratoscops. Centbl. f. Augenheilk. 1882. P. 122. Landesberg The Keratoscop. Phila, Med. Times. XIII, P. 784. 1883. Laqueur Ueber d. Hornhautkriimmung in normalen Zustande u. unter pathol. Verhaltnissen, ophthalmomet. Untersuch. Graefes Arch. XXX. I. Pp. 99-134. Leroy, C. J. A. De la Keratoscopie ou de la forme de la surface corneenne deduite d. images apparentes reflech. par elle. Arch. d'Ophth. IV. No. 2. P. 140. 1884. Mayerhausen Notiz zur klin. Veranschaulich. d. Winkels y (mittelst d. Keratos- kops. Centralbl. f. Angenheilk. 1882. P. 123. Montardit Optometro-Astigmometro. Revis. d'Cienc. Med. Juli. 1881. Nordenson, E. Rech. ophthalmomet sur Pastig. de la cornee chez des ecoliers de7a2oans. Ann. d'Oculist. LXXXIX. Pp. 110-38. 1883. Pfalz Ophthalmometrische Untersuchungen u. corneal-Astigmatismus mit dem ophthalmometer von Javal u. Schiotz, etc. Graefes Archiv. XXXI. I. Pp. 201-228. Placido Astigmatoscope explorateur. Period d. oftal. pract. Sept. Nov. 1880. Also Centralbl. f. prakt. Augenhlk. VI. P. 30. Placido Nouv. Instrument de esploracas da cornea ; astigmatoscop. explor. advr. Period de ophth. prat II. No. r. P. 30. Lisb. 1881. Reich, M. Result, einiger ophthalmomet. u. mikro-optomet Messungen. Grae- fes Arch. XX. P. 207. 1874. Schiotz Mensur. ophth. de I'astig. Cong, d'ophth. de Milan. Compt Rend. P. 12. 1881. Schiotz Ophthalmometer de Javal et Schiotz. Norsk. Magaz, for Lagevid. R 3 Bd. 13. P. 214. 1882. DeWecker et Masselon Un nouveau astigmometre. Gaz. Med. de Paris. 6 S. IV. P. 398. 1882. DeWecker et Masselon Astigmometre. Ann. d'Oculist. Juil. Aout. DeWecker et Masselon La Keratoscopie clinique. Ann. d'Oculist XC. P. 165. (1883). 138 BIBLIOGRAPHY. DeWecker et Masselon, Modifct apportee a 1'astigmometre. Ann. d'oculist LXXXIX. Pp. 138-43. 1883. DeWecker et Masselon La Keratoconometrie. Rev. clin. d'Ocul. No. i. P. 5. 1884. Wicherkiewicz, B Keratoskopie, Przeglad lekarski (Polish). No. 7. 1884. CHAPTER X. SYMPTOMS OF ASTIGMATISM. 161. From what has gone before it will be readily under- stood that one of the most prominent, in fact a characteristic, subjective sign of astigmatism is diminished visual acuteness; and so it is when we come to examine these eyes in a scien- tific manner. But it is not always impaired vision which brings astigmatics as patients to the surgeon. A very consid- erable amount of bad vision often escapes the notice of ordi- nary patients suffering from astigmatism. Having never seen well at any time in their lives they have no stand- ard of comparison in their own experience and a careful edu- cation of the sense of vision has made up largely for indistinct retinal images, and so it happens that they not infrequently flatter themselves that their visual acuteness is above the normal. " My eyesight is very good ; I can often see things other people can't," is an expression heard almost every day in the consultation-room, and great is the astonishment of these patients when a rigid examination by the test-types shows a reduction of vision to 1 / 3 or 1 / 3 of the normal. 162. Persons with degrees of astigmatism even above the medium may reach middle life without being conscious of their defect, and then their attention is only called to it when their presbyopia drives them to an examination for glasses. An in- stance of this is the following : Mrs. G., aged 49, came to my office one day recently with her daughter who was under care for an asthenopia associated with hypermetropia, and mentioned casual- ly in conversation that she had given up reading in the evening because she could get no glasses to suit her. She attributed this to age and had resigned herself to the situation. Upon my suggesting that probably some glasses might be found which would give her good vision she submitted to an examination. It was found that in either eye unaided by glasses V=*/24- In the left with -[-0.75 spherical it was some- what improved, but with no other spherical glasses was it materially benefited. The (139) I4O ABSENCE OF ASTHENOPIA IN SOME CASES. only line in Snellen's fan that she could see without glasses, as a line, was the hori- zontal, and this was also seen with -(-0.75. Other -(- and glasses made it more indistinct It was only when a +5.25 spherical was placed before the eye that the center line came out sharply, and then the other lines approaching the horizontal became totally indistinguishable. With a -f O-7S O +4-5 cr axis 9 vision came up to nearly 4 /4 and the fan was uniform. An examination of the R. E. made in the same manner showed an obliquity of the axis of the meridian approaching the hori- zontal of 10 to the outer side, and this was confirmed by the keratometer of Javal- This instrument showed, when the arc was at 100, R=8'/i mm.; when it was at 10, R=9 mm. and in the latter position there was an overlapping of the double images of 4 l /a steps on the graded band. With 4-0.75 C +45 axis IOO > V=*/s- The keratome- ter also confirmed the diagnosis of the astigmatism of the L. ., both as to degree and direction of the meridians. She had never suffered from asthenopia and during her life had done a great deal of fine needle .work. A new world was opened up to her by means of her correcting glasses, she being then for the first time aware that she did not enjoy ordinarily good vision and could hardly be convinced that most people saw as well without glasses as she did with them. With +2* added to her correction for distance she was able to read the finest print in the evening for any length of time. 163. Cases as extreme as the above are exceptional, but it is not at all uncommon for the lower forms of astigmatism, from 0.5 D to I D to make themselves felt first when the ac- commodation begins to fail. Young himself said, speaking of the influence of his astigmatism of l / u on the acuteness of vision that "he believed he could examine minute objects with as much accuracy as most of those whose eyes are differently formed." Javal is of the opinion that in childhood and youth there is very commonly a masking of the corneal astigmatism by means of a partial accommodation, believing that when lenticular astigmatism is present, it is, in the majority of cases, neutralizing in its character. When age begins to affect the plasticity of the lens and the activity of the ciliary muscle, this power of unequal accommodation is lost and the latent astigmatism becomes manifest. How far this is true will be shown by a more extensive use of the keratometer, and a com- parison of the corneal with the total astigmatism before and after paralysis of the accommodation. 164. But a complaint of astigmatics more common than dimness of sight, though generally associated with it, is asthe- nopia, or painful vision. When the eyes are used for close ASTHENOPIA. 14! work, such as reading, writing, fine sewing, etc., for any con- siderable length of time, there is pain accompanied frequently with a sudden indistinctness of vision when the effort is pro- longed. This asthenopia may be of all degrees of intensity from a slight feeling of fatigue to a pain so severe as to prac- tically make any use of the eyes for near work impossible. The asthenopia of astigmatism is of two kinds, which are usually denominated muscular and nervous. The first named form has its seat in the muscle of accom- JL-- modation, being sometimes called accommodative asthenopia, and the fatigue comes from the irregular and spasmodic con- tractions of the ciliary muscle. The eye instinctively en- deavors to have as clear and distinct retinal images as is pos- sible. An image distinct in all its parts is impossible in astig- matism, but by a kind of "see-saw" action of the ciliary mus- cles, first one part of the object and then the other can in the majority of cases have its image properly focussed on the retina. So long as it possible to see more clearly and satisfactorily by this kind of muscular action there is an irre- sistible temptation to use it ; and, as is well known, nothing is more wearing on the muscular energy. A regular systematic contraction of a muscle may be continued for an almost indefi- nite time without fatigue, but convulsive-like movements soon exhaust its power. When general hypermetropia is present, and sometimes when it is not, this fatigue of the muscle is often followed by a suspension of its action with consequent indistinct retinal images. In the highest degrees of astigmatism where no amount of accommodation can give distinct retinal images of any portion of objects there is no temptation to strain it, and as a conse- q uence we do not find asthenopia of this kind so often a symptom in the higher degrees as in the lower. 165. As is the case in the other forms of accommodative asthenopia, the pain is not usually referred to the eyes them- selves, but manifests itself under some form of headache. The pain may be localized in any or all of the branches of the fifth pair of nerves, but in a majority of cases the headache is fron- 142 NEURALGIA FROM EYE-STRAIN. tal with a sense of constriction across the brow. It may, how- ever, be general, and in some instances purely occipital, and its connection with the eyes remain for a long time unsus- pected. The irritation may be reflected to other parts of the body and manifest itself under many curious forms, nausea being a not uncommon one. The relation of headaches and anomalies of refraction as ef- fect and cause has been long known to ophthalmologists, but the profession at large in this country were not impressed with its importance from the point of view of general medicine un- til Dr. S.Weir Mitchell called their attention to it in 1876. The general practitioner to whom these patients first appeal for the relief of their persistent headaches is very liable to overlook their real cause and will, of course, fail to give the desired relief, as the following case well shows : Mrs. P., aged 40, had been affected with severe headaches for many years and suf- fered much at the hands of many physicians for its relief. The attacks would oc- casionally come on without any assignable cause, but would always follow any at- tempt to use the eyes. Her indistinctness of vision was not such as to call the at- tention of her medical attendants to her eyes, and the pain in them was considered as a part of the "neuralgia." It was impossible for her to read for more than ten minutes without bringing on an attack. Finally, owing to the death of her husband, it became necessary for her to enter as clerk in one of the departments where she would be compelled to use her eyes for eight hours a day. This, under the then ex- isting circumstances, was impossible. In her despair she applied to still another physician who, suspecting that the refractive condition of the eye might have some- thing to do with the trouble, sent her to me for examination. I found a simple hy- permetropic astigmatism of VH axis of the correcting cylinders, R 45, L 135. \Vith these V = ""/so, and she was able to read with them with proper correction of pres- byopia without any considerable inconvenience or pain. She obtained her place in the Department and went immediately to work, and for more than six years has con- tinued to use her eyes at very trying work from 9 a. m. to 4 p. m. without any ma- terial discomfort, and her headaches have entirely ceased. Occasionally when run down by work in the hot weather her eyes trouble her somewhat, but a few days rest brings her back to a condition of ordinary comfort. There is no ophthalmic surgeon of experience but can produce cases as severe in their character followed by relief as speedy as this one from the proper adaptation of glasses. 166. The other form of asthenopia is nervous. The term is a broad one, but it must necessarily be so in order to cover the vagueness of our knowledge concerning it. The pain is VARIOUS OTHER NERVOUS DISTURBANCES. 143 not muscular in its character and is not always dependent upon close application of the eyes in near work. Moreover, it is most commonly found in persons of neurasthenic tendencies. The fatigue is a mental one if we may so express it. Indis- tinct images are abhorent to the visual consciousness in the same manner as discordant sounds are abhorrent to the audi- tory consciousness, and there is an instinctive tendency to get away from them. Something of this feeling may be experi- enced by the emmetrope on rendering himself artificially astig- matic by means of a pair of cylinders. The manifestations of this asthenopia are frequently feelings of general discomfort, associated, it may be, with dizziness, nau- sea and even vomiting. But often it is one of actual pain re- ferred not uncommonly to parts not connected directly with the eyes. As in other forms of neurasthenic asthenopia, there may be intolerance of artificial or glaring light, and all kinds of abnormal sensations referable to the eyes and their adnexa. Chorea and other nervous disturbances of a general nature are laid at the door of astigmatism. 167. These symptoms as well as those of muscular asthe- nopia sometimes make their appearance suddenly after a severe illness or as the result of some depressing causes operating to lower the tone of the nervous system, and may be the first in- timation to the patient of the existence of an astigmatism. They continue in a greater or less degree in some cases, after the refractive anomaly has been corrected, necessitating most careful and systematic use of the eyes. 168. Both forms of painful vision as well as the complaints of diminished visual acuteness are more common when the meridians are oblique than when they are horizontal and verti- cal. The reason of this most probably is, that when . the meri- dians lie near the horizontal and vertical, it is possible by using one or the other focal plane to see clearly at least a part of the letters whose strokes run usually in these directions ; when the meridians are oblique the lines forming the majority of the let- ters are blurred. 169. Objectively there is little to be seen different from the 144 SOME OBJECTIVE EVIDENCES. 4 normal. There is, however, sometimes found a persistent frown associated with a narrowing of the palpebral aperture. This is the result of the habit the astigmatic has acquired of cutting off some of the circles of diffusion by means of the lids, thereby diminishing the indistinctness of the retinal images. 170. Persistent blepharitis and chronic hyperaemia of the conjunctiva are frequent accompaniments of astigmatism as well as of the other refractive anomalies, and when found on examination of a patient should always lead to an investigation of the optical condition of the eye. It often happens that these conditions when associated with errors in refraction dis- appear as if by magic when correcting glasses are worn. Dr. Martin of Marseilles ascribes a form of keratitis to astig- matism, but it seems to us that sufficient data are not at hand to establish a positive connection between the two as cause and effect. 171. It is quite common for astigmatics, even those hav- ing the hypermetropic form, to consider themselves myopic, because they have to bring fine objects close to the eye in or- der to see them distinctly. The true explanation of this near- sightedness is that on a near approach of the object the increase in the size of the retinal image makes up to some ex- tent for its indistinctness of outline. 172. Astigmatism has also been considered as an active factor in the production of true myopia, and quite a num- ber of cases have been cited in which simple myopic or hy- permetropic or comp. hypermetropic astigmatism have been observed to pass over into the myopic forms. As the same can be said of general hypermetropia, it would seem that as- tigmatism could hardly be charged with this per sc. It is quite possible, however, that the close approximation of the work mentioned in the preceding paragraph as the result of bad vision might ultimately lead, with an existing predisposition to myopia, to the development of a true axial myopia, and it is also possible that under these circumstances some of the as- thenopia complained of is due to the unusual strain on the internal recti muscles. BIBLIOGRAPHY. 145 BIBLIOGRAPHY. Badal Etudes sur 1'etiolog.des maladies des voies lach. et en partic. sur une cause freqnt. de ces malades meconnue jusqu 'a ce jour. Ann. d'oculist. T. LXXVIII. P. 547. Bailey. W. A. Astig. considered in its relation to headache and to certain morbid conditions of the eye. Guys' Hosp. Rep. P. I. 1878. Bull The connect, bet. chorea and errors of refrct. of the eye. N. Y. Med. Rec. P. 648. 1878. Businelli Un cas d'astig. Giorn. d'oftalmol. Ital. T. VII. P. 10. 1864. Cuignet Un cas d'astig. avec ses consequen. myop., keratoscop., retinoscop. et. fonctionelles. Rec. d'Ophth. 33.11. Pp. 5204. Paris. 1880. Donders, F. C. Ueber einen Spannungsmesser, (ophthalmotonometer). Ueber Glaucom. Astig. u. Sehscharfe. Graefes Arch. Arch. B. IX. Abt. II. P. 215. 1863. Giraud-Teulon, J. Geurin, et Warlomont, Polemique. Astig et asthenop mus- culaire. Ann. d'oculist. T. XLVIII. P. 296. 1862. Giraud-Teulon Lettre sur quelques points relatifs a 1'asthenop. et & 1'astig. Gaz. Med. de Paris. XVII 33. Pp. 781-4. 1862. Green, J. On astig. as an active cause of myopia. Trans. Amer. Ophth. Soc. Pp. 105-8. 1871. Green, J. On astig. considered in its relations to defect, vision, asthenop. and myopia. Amer. Jr. Med. Sc. LIV. Pp. 82-94. 1867. Hall, L. B A contrib. to the study of blepharitis ciliaris from ametropia. Med Rec. N. Y. XXI. P. 399. 1882. Hewetson, H. B. The relation between sick-headache and defective sight chiefly resulting from astigmatism ; their pathology and treatment by glasses. Med. Times and Gaz. March 1885. P. 375. Hocquard, E. Etude clin. sur un cas d'asthenop muscul. par astig. myop. simpl. Rec. de mem. de med. milit. Sept. and Oct. 1877. Javal, E. De 1'astig. au point de vue de 1'hygiene. Rev. de hyg. II. Pp. 990-9 Paris. 1880. Keyser, P. B. Blepharitis and ametropia. Phila. Med. Times. P. 266. 1877. Korner, V. Influenzia de los vicios de refract, i de la estroflex. de los puntos lacrimales como causas de conjunct, cronica. Rev. med. de Chili. 2 X. P. 315. 1881, Kugel, L. Ueber Schiefsehen bei Astig. Wien. med. Wchnschr. XIII. Pp. 420-35- 52. 1863. Kiigel, L. Ueber Sehscharfe bei Astig. Graefes Arch. B. XI. Abt. I. P. 106. 1865. Martin, G. Sur le rapport qui existe entre une variete de la .keratite 'grave dite scrofuleuse et 1'astig. de la co rnee. Ann. d'oculist. T. XC. P. 14. 1883. Martin, G. A propos de la keratite astig. j,Rev. gen. d'ophth. T. III. No. ,4. _ P. 145. 1884. Martin, G. Deux, contrib. a 1'etude de la keratite astig. Ann. d'oculist. /T.~XC I. P. 44. 1884. 146 BIBLIOGRAPHY. Martin, G. Quat contrib. a 1'aude de la keratite astig. Ann. d'oculist. T. XCII. P. 37- 1884. Martin G. Blepharospasme astig. Ann. d'oculist. T. XCI. P. 231. 1884. Masson Etude sur 1'astig. corneen et la percept, des couleurs chez les opres de cataracte. These LyOn. 1883. Matlie wson. A. On asthenop. and the use of glasses. N. Y. Med. Gaz. Mch- II. 1871. Mengin Note sur un phenomene subjct produit par un astig. myop. compose. Rec. d'ophth. 3 S. IV. Pp. 7-9. Paris. 1882. Mitchell, S. W. Headaches from eye-strain. Am. Jr. Med. Sc. April. P. 374. 1876. Moore, W. O. Astig. causing severe headache. Planet. Pp. 1-88. N. Y. 1883. Murrell, J. E. Errors of refract of the eye. Richd. and Louisville Med. Jr. Sept P. 218. 1877. Peschel, M. Ueber den Astig des indirect Sehens. Arch. f. d. ges. Physiol. XVII. Pp. 504-10. Bonn. 1878. Prouff, J. M. De la sclerotoscopie. Methode a suivre pour lesobservaU ayant trait a la keratite pretendue astig. Rev. clin. d'Ocul. No. 2. P. 25. 1884. Reynolds, D. S. Clinic, observat on astig. Tr. Am. Med. Ass. XXXII. P. 231. 1882. Roosa, D. B. St. J. The relats. of blepharitis ciliaris to ametropia. Am. jr. Med. Sc. P. 92. 1877. Savage, G. C. Sick-headache, its cause its cure etc. Phila. Med. and Surg. Jr. P. 117. July 29, 1882. Schweigger Ueber Amblyopia levis congt durch Astig. Deutsche Klinik. 1863. Stevens, G. F. Some remarks upon the relations bet anomal. refract of the eyes and certain nervous diseases. N. Y. Med. Jr. P. 561. Sept 2. 1876. Thomson, W. On the connect bet staphyl. post, and astig. Am. Jr. Med. Sc. CXL, Pp. 383-97. 1875. Thomson, W. Can staphyl. post be indcd. by astig. Trans. Amer. Ophth. Soc. Pp. 310-18. 1875. Thomson, W. On astig. as a cause for persist headache and other nerv. sympt Med. News and Libr. XXXVII. Pp. 8 1 -8. Phila. 1879. Vossius Beitrag zur Lehre von angeborenen Coni. Zehend. Monats Bl. f. Aug- enheilk, Mch. 1885. P. 137. Webster, D. A case of astig. without asthenop. or conscious, of imperfect vision. N. Y. Med. Rec. XIV. P. 249. 1878. Weiss, L. Beitrage zur Entwicklg. d. Myop. ueber eine leicht ausfiihrbare Mes- sung d. Augenspiegelbildes und die Bedeut dieser Messg. fur die Beurtheilg. des dioptrisch. Apparats des Auges. Graefe's Arch. B. XXII. Abt III. Pp. 1-124. 1876. Worrell, J. P. Diseases of the Conjct and errors of refract Amer. Practitioner P. 34. 1877. CHAPTER XL CAUSES OF ASTIGMATISM LENTICULAR ASTIGMATISM. 173. Astigmatism maybe congenital or acquired. With rare exceptions regular corneal astigmatism is congenital and in quite a considerable percentage of cases hereditary. It is by no means uncommon to fiftd several members of the same family affected with astigmatism, though it may be of different kinds and in various degrees. 174. As all eyes are more or less astigmatic, and abnormal differs from normal astigmatism only in degree, it is a rational inference that the manner in which the eye is developed has something to do with this peculiar formation of the cornea. Moreover, we should expect its shape to be influenced, to some extent, by the manner in which the tissues surrounding it lids, orbit, etc. are developed. Dealing now in what we ac- knowledge to be pure speculation, it seems probable that the formative influences at work on the eyeball, would result, if left alone, in the production of a spherical form of the cornea ; but from some cause, inequality in pressure, unequal traction or the like, the sphere is compressed and the result is a spheroid such as we find it. Javal, among others, has attempted to trace a connection between the general shape of the skull and the shape of the eyeball as expressed in its astigmatism. In fact he has for- mulated a law which he thinks warranted by the facts in the case, which is : " The meridian of greatest refraction corres- ponds to the shortest diameter of the skull." This law has not, we believe, been fully verified by the observation of others, though there is unquestionably something of truth in his general proposition. Further observations are needed on this point which has also a high ethnographic interest. (147) 148 ASTIGMATISM FROM CORNEAL WOUNDS. " 175. Regular astigmatism may also be acquired. Any form ^ of traumatism affecting the anterior portion of the eye-ball may have, as a result of its cicatrization, an altered curve of the cor- nea. The most common of these traumas is the extraction of cataiact. That so extensive an incision as that employed in the various forms of extraction, should leave behind it some change in the corneal curvature is not at all astonishing. It can only be exceptionally that the coaptation of the wound would be so perfect as to leave no trace on the form of the cor- neal surface. These suppositions have been fully confirmed by measurements of the cornea before and after the operation. When the cornea is measured within ten or fourteen days after the operation, the meridian of least curvature is found, with rare exceptions, to be at right angles to the direction of the incision, and as the section is generally made upward or downward, the less refracting meridian is the vertical. The amount of astigmatism at this period is sometimes enor- mous. In one of my cases, where I had reason to suppose a tardy union of the wound, it amounted to 15 D., and Laquer reports one of 16 D. minus refraction. Such great differences should always lead us to suspect some interference with prompt healing. When the progress of the case is normal,the astigmatism commonly begins from the tenth day to diminish, and occa- sionally a complete cicatrization may bring about a shortening of the radius in this meridian, rendering it the most highly re- fracting. In one case under my observation, the refraction in the vertical meridian passed over from 1 1 D. fourteen days after the operation to 20 D. eight weeks after. Further obser- vations and examinations may lead us to the discovery of that form of incision and its position which is less likely to leave an important permanent deformity of the corneal curve. All kinds of perforating wounds and ulcerations of the cornea, par- ticularly at its margin, very frequently leave behind them, in addition to the usual irregular astigmatism, a greater or less amount of the regular form which can often be corrected with decided benefit to vision. 176. Keratoconus, keratectasia and other similar alterations REGULAR ASTIGMATISM IN KERATOCONUS. 149 in the general form of the cornea, while giving in the majority of cases a very irregular refraction may yet oftentimes have an associated regular astigmatism which can be corrected with most decided benefit to the patient, as the following case shows: Mrs. JR., 34 years old, saw well up'to her sixteenth year. V then began'to fail and at her twenty-first year was st its worst. Since that time it has remained stationary. At the present time V is less than Veo- An examination showed the existence of keratoconus (in which aspect it will be considered under that heading), but meas- urements with JavaPs keratometer also revealed a regular astigmatism. In L at 5 to the outer side of the apex, 180 R=5 mm. (39.5 D), 90, R=6 mm. (34 D), with a crossing of the bands of 6 steps; in R, at the same place, 180 R=6 3 /* mm. (30 D) ; 90 R=5'/ 2 mm. (36 D), with a crossing of the bands to the amount of 6 1 / steps. With +4 180 C 3,9o in R, Vr=*/2 ; with 7, 90 in L V=*/. In the investigation of such cases the ophthalmometer of Javal is of the highest value, and many cases which have here- tofore been confined to the stenopaic slit or subjected to op- eration will find a measure of relief at least from properly adapted cylinders. 177. Lenticidar Astigmatism. The first case of regular astigmatism of which we have an accurate history was lentic- ular in its character. As a matter of historic interest, I give the exact words in which Young describes his condition as found in Trans. Phil. Soc. of Lond. 1801 (not 1793 as stated by some), pp. 39-40, and contained in his paper on the " Mechan- ism of the eye." " My eye, in a stale of relaxation, collects rays which diverge vertically from an ob- ject at a distance of 10 inches from the cornea, and the rays which diverge horizon- tally from an object at 7 inches distance. For if I hold the plane of the optometer (fine wires) vertically, the images of the line appear to cross at 10 inches ; if horizon- tally at 7. The difference is expressed by a focal length of 23 inches. I never experienced any inconvenience from this imperfection, nor did I ever discover it until I made these experiments ; and I believe I can examine minute objects with as much accuracy as most of those whose eyes are cliffei ently formed. On mentioning it to Mr. Gary he informed me that he had frequently taken notice of a similar cir- cumstance, and that many persons were obliged to hold concave glasses obliquely in order to see with distinctness, counterbalancing by 'the inclination of the glass the too great refractive power of the eye in the direction of that inclination (cor. 10. Prop. IV), and finding but little assistance from spectacles of the same focal length. I5O LENTICULAR ASTIGMATISM. The difference is not in the cornea, for it exists when the effect ol the cornea is re- moved by a method to be described hereafter. The cause is without doubt the obliquity of the uvea and of the crystalline lens which is nearly parallel with it, with respect to the visual axis ; this obliquity will appear from the dimensions already given to be abont 10. Without entering into a very accurate calculation the differ- ence observed is found (by the same corollary) to require an inclination of 13 and the remaining 3 may be easily added to the greater obliquity of the posterior surface of the crystalline opposite the pupil. There would be no difficulty in fixing the glasses of spectacles or the concave eye-glass of a telescope in such a position as to remedy the defect" Young, eliminating the refraction of his cornea Jt>y immersing it under water, demonstrated that the astigmatism of his own eyes was resident in the lens. This was its commonly ac- cepted seat until the ophthalmometric measurements of Knapp suggested that the cornea might also play a part. As already stated in Chapter III it is now a well demonstrated fact that the cornea is the principal seat of the anomaly. The lens, however, not unfrequently adds its quota to the making up of the total astigmatism of the eye ; sometimes by increasing and sometimes by diminishing that of the cornea. 178. The lens may effect an astigmatic action in two ways; (a.) by a malposition and (.)by a change in the refraction of its meridians. A dislocation of the lens in order to produce an astigmatic effect must so change its position on the optical axis that it shall lie obliquely to the direction of the rays striking its sur- face, as considered in 2$ ; a simple displacement perpen- dicular to the optical axis will not give rise to astigmatism. Young, as already stated, attributed his astigmatism to such an oblique position of the lens. Regular astigmatism has also been found after iritis and after an operation for pterygium. Also in cases of pyramidal cataract and in membrana pupillae perseverans. Some of the cases of astigmatism following blows on the eye are in all probability due to such a dislocation of the lens. The/0rw of the lens is so subject to the action of the ciliary muscle that it is only in exceptional instances that we can consider the lens curvature apart from the influence, active or FIG. B. The Eye Ball Showing the Coats &c. of the Eye. 'j FIG. C. Longitudinal Section of the Eye and Orbit through the Dotted Line on FIG. A. 35 order on a separate piece of paper from that used for 3 ;tuJy of the following explanations will be of value to the dealer in optical & business generally and are worth remembering. DUTIES. It will be noticed that we show different qualities of the same styles of fn 1 good goods, all steel goods being well tempered, the quality being of the class of , a finer grade of the sarfle style, it may be depended upon, that the difference n tier class of trade, will find that it pays to handle the finer grades, as the differ JS NUMBERING. All of our lenses, except those in the cheapest rubber and ste i, and numbered in both the inch and dioptral systems, a comparative table of w PTRAL SYSTEM. The entire discontinuation of the inch system will be found to gre; misleading system of no value whatever, falsely indicating the necessity of ca: there is ever use for ; for instance, the difference between a 38 and 52 inch lens is i 12 and 13 inch lens. In the dioptral system, the lens of i meter '(39rVfr)i f i dioptre; a lens of half the power (twice the focal length,) is called YT. d tour times the focal length), is # dioptre and numbered 0.25 ; one-eighth is numb he best way to became acquainted with the dioptral system, is to totally ignore t :ES FOR PRESCRIPTION WORK. Prescription work and all goods of a special i ne price list for prescription work on page 408, instead of at prices quoted throi FEM OF STOCK NUMBERING. We have adopted the system of numbering stock it is generally known and will be more convenient to the trade than a new syster STEEL SPECTACLES FOR GOLD, SILVER, GOLDOIN ALLOY. GOLD FILLED, SILVERINE AND the last figure of the number is ALUMINUM SPECTACLES t temple wire. If the next to the last figure of the number is npin temple. o indicates Ffat eye wire, flat temple. ind temple. i " oval eye wire, flat temple. If round temple. 2 " " ' round temple, grooved lenses. 3 " " " half round temple, ing temple, usual joints. 4 beveled eye wire, flat temple. If riding temple. 5 for grooved lenses, riding temple. (irt end piece solid temple.. 6 " riding temple, usual joint, round eye wire. * - LENTICULAR ASTIGMATISM. 15 I passive, of this muscle. Alteration in density of the lens sub- stance which would change its refracting power are so irregu- lar in their nature that we are compelled to look upon lenticu- lar regular astigmatism as due, probably without exception, to alteration in the curvature of the lens-surfaces, brought about by an unequal contraction of the ciliary muscle. I must confess to an inability to understand how some fibres of this circular muscle can contract through the same nervous im- pulse more strongly than others, and in just such a way as shall give a regular astigmatic form to the lens surfaces. Nev- ertheless, from the experiments and observations of Dobowozki, Javal, Laquer and others, the fact seems estab- lished, and we must accept it whether we can satisfactorily ex- plain it or not. 179. As in the other form of lenticular astigmatism so in this, the total astigmatism of the eye may be the result of its addition to or subtraction from the corneal astigmatism. Javal, as already stated, is of the opinion that in the 'major- ity of cases it is neutralizing in its effect, for in the greater part of the cases examined by him before and after paralysis of the ciliary muscle, the total astigmatism was greater after paraly- sis, and corresponded more nearly to the corneal astigmatism as determined by his keratometer. He thinks also that in youth many cases of corneal astigmatism are masked by an un- equal action of the ciliary muscle. Laquer in his measure- ments found that in thirty-four cases where the total differed from corneal astigmatism, in nineteen the corneal was greater, and in fifteen it was less, and the differences were, without ex- ception, in the lower grades. My own experience with the keratometer, so far, would seem to show that where there is a difference the corneal is, as a rule, greater than the total astig- matism (see table VI). Of course it is to be remembered in this connection, that in those cases where the total astigma- tism is the greater the assisting lenticular astigmatism may be due to the oblique position of the lens, and that a paralysis of accommodation is essentiarto its positive exclusion. 1 80. A partial action of the ciliary muscle may also be 152 ASTK.MAilS.M 1-ROM STK Ali ISM US OPERATION. due to a trauma which paralyses some of its fibres or the nerve filaments, just as we see an irregular dilation of the pupil as a result of the same cause. i8r. It has been supposed that the operation for strabis- mus might exercise some influence on the corneal curvature, and Dr. Noyes has reported one case in which, after three strabotomies, the meridian of maximum curvature underwent a rotation of 25. The existence of such an action on the part of the operation for strabismus, has not, however, been demon- strated by keratometric measurements, and it is doubtful whether the corneal curvature is changed except, perhaps, in some very rare instance. BIBLIOGRAPHY. Amadei, G. Sulla craniologia delle anomalie de refraz. dell 'occhio. Ann. di Ottalm. XI. P. I. 1882. Berlin Ueber traumatisch linsen Astig. Ber. ii. d. Versamml d. Ophth. Gesellsch. P. 174-8. Heidelberg 1877. Bono, G. B. Del rapporto tra la forma del cranio e la refraz. oculaire. Gior. d. Soc. Ital. III. P. 133. Milan 1881. Bono Dell 'astig. negli operat. di cataratt. p. estraz. Gior. della R. Accad. di Med. de Torino N. 3. 1883. Bresgen Zur Entwicklg. v. Refrcts. u. Stellungs-Anomalien d. Auges in Folge v. Nasenerkrankung. Deutsch. Med. Wochenschr. No. 9. 1884. Emmert, E. Auge u. Schaedel. Hirschwald. Berlin, 1880. Francke, E. Zur Lehre von der memb. pupil, perseverans. Grafe Archiv. XXX. 4. Gosette L'asthenop. sua patologia e cura. Annal. de Ottalm. XII. 3-4. 1884. Hirschberg, J. Zur Prognose der Glaucomoperation. Grafe's Archiv. XXIV. I. 161-194. Jaesche Ueber die Beziehungen gewisser Augenubel zum Bau d. Schaedels- Dorpat. Med. Ztschr. V. P. 163-6. 1873. Kneis, Max Ueber Spindle-staar u. d. Accommodation bei demselben. Grafe's Archiv. XXIII. I. 211. Kaiser Die Theorie d. Astig. Graefes Arch. XL 3. P. 186. 1865. Knapp, J. H. Ueber die Erfolge der Scheiloperation. Zehend Monatsbl. f. Augenheilk. B I. P. 471-484. 1863. Landesberg, M. Ueber das Auftreten v. regelmassig. Astig. bei gewis. Refract u. Accommodationsanomal. Graefes Arch. XXVII. 2, also in Centralbl. f. prakt. Augenhlk. P. 362. I ec. f 1883. Lamlolt Sur les causes d. anomal. de la refract. Gaz. Hebdon. No. 39. 1877. BIBLIOGRAPHY. 153 Landolt Relat. bet. conform, of the cranium and that of the eye. Brit Med. Jr. I. P. 507. 1880. Laqueur Ueber die Kriimmungsverand. d. Hornhaut nach Operat. u. unter pathol. Verhalt. Ophth. Gesell. Heidelberg. XV. Leroy Theor. de 1'astig. Arch, ophth. I. P. 220. 1881. Landesburg M. Bericht ueber 123 Staaroperationen. Grafes Archiv. XXIV. 59-126 Leroy Optique physiolog. Arch, d'ophth. T. I. No. 3-4. Loring, E. G. An astig. glass for catarct. patients with some remks, on the sta- tistics ofvis. in catarct. operat. Trans. Amer. Ophth. Soc. P. 108-18. 1871. Martin, George Etudes d'ophthalmometrie clinique. Ann. d'Ocull. Mai-Juin. Masson, A. Etude sur Pastigmatisme corneen et la perception des couleurs chez les operes de cataracte. These de Lyon. 1883. Noyes, H. D. Astig. produced by tenot. of the rect. msls. Tr. Amer. Ophth. Soc. II. Pt 2. Pp. 128-31. N. Y. 1874. Pfalz Ophthalmomet. Uentersuch. ii corneal Astigmatismus met dem Ophthalmo- meter von Javal u. Shlotz. Grafes Archiv. XXXI. I. 201-228. 1885. Pomeroy Case of acquired astig. Tr. Amer. Ophth. Soc. 1867-8. IV-V. P.3O. N. Y. 1869. Prouff, J. M. Pathogen, de 1'astig. reg. produit par lacornee. J. Soc. de Med. e* Pharm. de la Haute Vienne. II. Pp. 66-8. Limoges. 1880. Prouff Antag. entre la myop. progres. et les forts degres d' Astig. conform a la regie. Rev. clin. d'ocul. du S. O. IV. No. 6. P. too. 1883. v. Reuss Ueber Astig. nach Staar Extract. Klin. Monatsbl. f. Augenhlk. VII- Pp. 473-6. 1869. v. Reuss Untersuch. ii. den Einfluss des Lebensalter auf die Kriimmung d.Horn- haut nebst einig. Bemerk. ii. die Dimension, d. Lidspalte. Grafes Arch. XXVIII. P. 27. 1881. v. Reuss u. Woinow Ophth. Studien ueber d. Astig. nach Staarextract. Wien- 1869. Roeder, W. Ueber d. gemeinschaft. Ursach. v. Glaucom, Myopic, Astig. u. den meisten Catarct. Arch. f. Augenhlk. IX. Pp. 164-83. Wiesb. 1880. Roder, W. Ueber Kapseldurchschneidungen und dadurch bedingte Krummungs- anderungen der menslichen Hornhaut. Grafes Archiv. XXIII. 4. 29-56. Schelske, R. Ueber d. Verhalt. d. intraocul. Druck. u. der Hornhautkriim. d . Auges. Graefes Arch, X. II. P. I. 1864. Schmidt- Rimpler Zur Kennt einig. Folgezustande v. Contusio bulbi. Arch. f. Augenhlk. XII. 2. P. 135. 1883. Schiotz. Hj. Ein Fall von hochgradigem Hornhautastigmatismus nach Staarex- traction. Besserung auf operativen Wege. Archiv. f. Augenheilk. XV. 2. P. 178. Sczelkow Verand. d. Hornhautkriim. mit zunehm. Alter. Centralbl. f. d. Med. Wiss. P. 819. 1880. Theobald, S. Notes of three cases of progressive astigmatism. Trans. Amer^ Oph. Soc. 1885 and Amer. Jnl. Oph. July, 1885. Webster, W. A case of mxd. astig. supposed to have been caused by the sucking of the eye by an infant. Med. Rec. XVIII. P. 38. N.Y. 1880. Wecker, L. Sur 1'astig. d. ses rapports avec la conform, des os du crane. Bull. 154 BIBLIOGRAPHY. Soc. d'anthrop. de Paris. 28. IV. Pp. 545-9. 1869. Also in Klin. Monatsbl. f. Augenhlk. VIII. P. 161-4. 1870. Weiss, L. Ueber den nach d. Weberschen Hohlschnitt entsteh. Cornealastig. u. die Ursache d. nach Extract, entsteh. Astig. iiberhaupt. Arch. f. Augen u. Ohrenhlk. VI. P. 58-84. 1877. Woinow, M. Falle wo nach Staar-ExtrcL ein anderer Grad. v. Astig. vorhand, war, als sich nach d. Hornhaut asymmet. berech. liess. Mosk. Med. Zeit. No. 42. i87a Woinow Astig. bei Staar-operat Klin. Monatsbl. f. Augenhlk. P. 466-8. 1871. CHAPTER XII. CORRECTION OF ASTIGMATISM. 182. When a differential diagnosis of astigmatism is once accurately made, all the optical data are at hand for its correc- tion. We have only to apply a cylindrical glass, which ex- presses by its refracting power the amount of astigmatism, with its axis in the direction indicated in the diagnosis, and the eye is rendered non-astigmatic. A knowledge of the exact inclination of the axis of the cyl- inder is, therefore, of the utmost importance in writing orders for glasses, and it is necessary that we have some mode of measuring its degree. It can be done by drawing on a sheet of paper a series of radiating lines like Snellen's fan at inter- vals of 5, and laying the trial frame straight on them with the center of the glass over the center of the radiating lines and noting with which line the axis marked on the cylinder corres- ponds, taking care always to read the degrees from \^& patient's left to his right. A much more efficient and satisfactory method, however, is to have the degrees marked on the trial-frame itself. Several trial frames of this kind have been made, the best of which, in my opinion, is the one manufactured by Meyrowitz, of New York, and shown in Fig. 42. The frame is constructed to hold two lenses on each side, and one of them can be turned by means of the two little knobs shown in the drawing. When in an examination the position of the cylinder where vision is best is found, the axis of the cylinder marked on the glass points to the exact degree of inclination. This frame is further use- ful for determining the distance between the pupils and the (155) 5 6 DESCRIPTION OF AIRY S CASE. height of the nose, two important factors in the proper fitting of spectacles. Fig. 42. MEYROWITZ'S TRIAL-FRAME.' \ 183. The first full account given of the correction of astigmatism by cylinders is that by the Royal Astronomer Airy, in 1827. For this reason and also to show that the correction was based on a scientific study of the optical condition, and to give the history of the term astigmatism as applied to this condition, I subjoin an account of this case taken from the last English edition of Mackenzie's classical treatise on the eye (London, 1854, p. 926). " Mr. Airy discovered that in reading he did not usually employ his left eye, and that in looking at any near object it was totally useless, in fact the image formed in that eye was not perceived unless attention was particularly directed to it. Suppos- ing this to be due entirely to habit, and that it might be corrected by using the left eye as much as possible, he endeavored to read with the right eye closed or shaded j but found that he could not distinguish a letter, at least in small print, at whatsoever distance from the eye the characters were placed. Sometime afterwards he observed that the image formed by a bright point, such as a distant lamp or star, in his left eye, was not circular as it is in the eye which has no other defect than that of being near-sighted, but elliptical, the major axis making an angle of about 35 with the vertical and its higher extremity being inclined to the right. Upon putting on con- cave spectacles, by the assistance of which he saw distant objects distinctly with his right eye, he found that to his left eye a distant lucid point had the appearance of a well-defined line, corresponding exactly in direction and nearly equal in length to the major axis of the ellipse above mentioned. He found also that if he drew upon paper two black lines crossing each other at right angles and placed the paper in a proper position and at a certain distance from the eye, one line was seen per- fectly distinct while the other was barely visible ; while upon bringing the paper 'The price of this trial-frame is $15.00. AIRYS CASE. 157 nearer to the eye the line which was distinct disappeared and the other was seen well defined. All these appearances indicated that the refraction of the eye was greater in the plane nearly vertical than in that at right angles to it ; and that, conse- quently it would not be possible to see distinctly by the aid of lenses with spherical surfaces. Mr. A. found, indeed, that by turning a concave lens obliquely, or on looking through a part near the edge, he could see objects without confusion ; but in both cases the distortion was such that he could not hope to make any use of the eye without some more effectual assistance. Mr. Airy's object was now to form a lens which should refract more powerfully the rays in one certain plane than those in the plane at right angles to it ; and his first idea was to employ one whose surfaces should be cylindrical and concave, the axes of the cylinders crossing each other at right angles and their radii different. To show that this construction would effect the purpose, it is only necessaiy to imagine such a lens divided into two lenses by a plane perpendicular to its axis ; thus it is easily seen that the refraction of the one will not be perceptibly altered by that of the other and the whole refraction will be a combination of the two separate refractions. The rays in one plane will be made to diverge entirely by the refraction of one lens, and those in the other plane by that of the other lens. This construction was then suffi- cient ; but for the facility of grinding and for the diminution of the curvatures, it appeared preferable to make one surface cylindrical and the other spherical, both concave. To discover the necessary data for the formation of the lens, Mr. A. made a very fine hole with the point of a needle in a blackened card, which he caused to slide on a graduated scale ; then strongly illuminating a sheet of paper, and holding the card between it and the eye, he had a lucid point upon which he could make observations with ease and exactness. Resting the end of the scale upon the cheek-bone, and sliding the card on this scale he found that what was seen as a point when close to the eye, at a distance of six inches appeared a well-defined line inclined to the verti- cal about 35 and subtended an angle of (by estimation) 2; at the distance of 3 l /2 inches it appeared a well-defined line at right angles to the former and of the, same apparent length. It was necessary, therefore, to make a lens which, when parallel rays were incident should cause those in one plane to diverge from the distance 3 x /2 inches, and those in the other plane from the distance six inches. Having procured a sphero-cylindrical lens 1 of which the radius of the spherical measured 3^2 inches and that of the cylindrical surface 4 ! /2 inches, Mr. A. found that he could read the smallest print at a considerable distance with the left eye as well as with the right. He found that vision was most distinct when the cylindrical lens was turned from the eyes ; and as when distant from the eye the lens altered the apparent figure of objects by refracting differently the rays in the different planes* he had the frame of his spectacles made so as to bring the glass pretty close to the eye. With these precautions he found that the eye which he had once feared would become quite useless, could be used in almost every respect as well as the other." ***** "Having occasion 20 years after the first account of the malformation of his left eye was submitted to the Cambridge Philosophical Society (1849) to explain that a change had happened in the state of the eye, Mr. Airy took an opportunity of men- 1 This glass was made by Fuller, of Ipswich. 158 ORIGIN OF THE WORD ASTIGMATISM. tioning that as the nature of the effect of that malformation was, that the rays of light coming from a luminous point and falling on the whole surface of the pupil did not converge to a point at any position within the eye, but converged in such a manner as to pass through two lines at right angles, the Rev. Dr. Whewell had affixed to this phenomenon the term Astigmatism" All knowledge acquired since this account was published has added nothing to the theory of the astigmatic condition or to the philosophy of its correction. Astigmatism, however, had been corrected independently, it would seem, by a number of individuals during the years between Young's discovery of the condition and the beginning of the new era inaugurated by the investigations of Knapp and Bonders. The optician Gary informed Young that he had found many myopes who saw better when their concave glasses were tilted. It also appears that the painter Cassus noticed some peculiarities in the work of his master, Gros, at Paris, in 1818, which he referred to a defect in sight, and that this defect was corrected by cylinders made by Guscipi, of Rome, in 1840-44, and these were afterwards duplicated by Soliel, of Paris. In 1852 Goulier sent to the French Academy of Science a sealed communication with the request that it be not opened until 1865. When it was examined it contained a good account of astigmatism (given in Abstract in Javal's article on the history and bibliography of astigmatism in Am. J'Ocu/., 1866) and manner of its correction by cylinders. A Swiss priest, Snyder, of Luzerne, also detected in himself an astigma- tism which he corrected by cylindrical glasses in about 1849. Dr. Isaac Hays in his American edition of Laurence on the Eye (1854), relates in full a case which had been successfully fitted with cylinders by the Philadelphia op- tician. McAllister, in 1825, and two others which had in that year (1853) come under his own observation in which the same optician had improved vision by the same means ; but no accurate account of these last was given. 184. Easy, however, as it may appear theoretically to cor- rect astigmatism, when we come to deal with the question practically it is not always so simple as it seems. We are dealing here in part with positive science and it is essential that our methods should be exact if we expect our results to be perfect. 185. In the first place, it is necessary that the diagnosis be in all respects correct. We must not only know the inclina- tion of the faulty meridian to within 5 (or even less in some cases) but the exact state of the refraction in each meridian separately. To obtain these in the majority of cases, as we have already seen, requires the expenditure of much time and patience, and the practitioner who hopes for uniform success and satisfaction in his astigmatic cases must grudge neither. In many cases it is only by examining and reexamining and METHOD OF RECORDING CASES. 159 testing and proving by many methods that the true condition is revealed, and sometimes it is necessary to give glasses to be worn for a time, in order that the close observation of the patient may throw some light upon an obscure point. 1 86. The methods of dealing with astigmatism after a cor- rect diagnosis has been established may be best shown by some cases illustrative of the various forms to be dealt with. CASE I. It has been shown by the various tests that there is simple myopic astig- matism in the vertical meridian. With 2 axis 180 V= 4 / 4 and Snellen's fan is uni- form and clear. You order: L. R. 2 axis 1 80. 2 axis 1 80. And if he is a young man of 18 and a student, or employed where he uses his eyes constantly for close work, you order him spectacles which he is to use constantly. If he thus early makes them a part of his eyes he places himself in the condition of an emmetrope and runs much less risk of trouble in future. 43- DIAGRAM FOR RECORDING ASTIGMATISM AND FOR ORDERING GLASSES, REPRESENT- ING THE PATIENT'S EYES AS SEEN FROM THE FRONT. We should always in recording diagnoses and ordering glasses follow a uniform system in order to avoid a trouble- some confusion and liability to error which would otherwise inevitably occur. We must always consider the glasses as the patient looks through them, and in counting the degrees of in- clination of the axis of the cylinders, proceed always from his left to his right ; and it is well to have this diagrammatically represented as in Fig. 43. Such diagrams are also useful for l6o CLINICAL CASES. recording graphically many other morbid conditions and in- juries of the anterior portion of the eye-ball and of the lids. The method of using this diagram is shown in Figs. 20 and 21. CASE II. A lady of 30 is found to have compound hypermetropic astigmatism with V=*/u. She is unable to read the evening paper with comfort and her fine needle-work tires her eyes even in the daytime. There is a general H of 1.5 with H. astig. of 0.75 axis at 45 in L and at 135 in R. With this correction V= 4 / and No. I is read with ease and comfort at ten inches. She is ordered : L. R. + 1-5 C + 0.75 45- + 1-5 C + 0.75 135. You insist upon the importance of her wearing these glasses constantly in order to save her from a possible future break-down ; but she objects so strongly that you feel perfectly certain she will not do it, particularly as she says her distant vision is as good as she cares about She also rebels at spectacles and wants to know why nose-glasses won't do as well. This is the battle that goes on in the consultation room daily, and the surgeon will commonly find it wise to effect some sort of compromise, particularly at the begin- ning. It is much more satisfactory and much less trouble to the patient to have cyl- inders set in spectacle frames since the axes are there always at the same angle and require no adjustment ; but young women are, as a rule, so opposed to wearing them, particularly in public, that they will often suffer rather than use them. They find nose-glasses less objectionable, and most opticians can now fit cylinders in them so that they can be adjusted properly on the nose with little trouble after patients have become accustomed to their use. You therefore have one pair of glasses set in spectacle frames for use at home when she is doing continuous work or reading, and another pair in pince-nez for reading the hymns in church, the programmes at con- certs or the theatre, for picture galleries, shopping, etc. In the course of time she will find her distant vision so much improved by the nose-glasses that she will wear them pretty constantly, and finding in the end that the spectacles are much less troublesome will most probably come to substitute them for the nose-glasses for all purposes. 187. Another condition which comes in as a complication is that of presbyopia. When the accommodation begins to fail its effect must be taken into consideration, since the same glasses will no longer do for far and near vision. CASE III. A gentleman of 48 complains of his inability to read with comfort in the evening. His distant vision has been sufficiently good for him as a professional man, though he has always considered himself somewhat " near-sighted." On test- ing it is found that there is myopic astigmatism of V in the vertical meridian, and correction brings V up from M Jy> to ^/M. With '/ &x ^ s l ^ f r DOtn eyes, he is not able to read No. i at 12 inches, but with a +7*8* placed in front of the cylin- ders he reads it with facility at from 10 to 1 8 inches. Instead however, of ordering CLINICAL CASES. l6l him a compound lens with a V^s on one face and a -\- l /& B on the other we sim- ply write for L. R. +1/48.90 +V.90, thus giving the optical result of the combination , for the spherical . -f 1 /^ neutralizes the J /48 cylindrical axis at 180 leaving a +V*8 action at 90, thus practically ren- dering the eye myopic Vis in all its meridians. This relieves the accommodation sufficiently for a time and gives satisfaction. CASE IV. A lady, 50 years of age, has had great difficulty in getting glasses for reading. She has gone from one optician to another and has accumulated a store of glasses of various kinds, but they are all unsatisfactory, and she has at last settled down to the belief that there are no glasses that will fit her eyes, particularly as she considers them "weak," her distant vision never having been good. She has at last, however, been pursuaded to have her eyes examined by an oculist and you find after a careful investigation that there is compound hypermetropic astigmatism. In L -MCH-J-S ax i s 7 gives V= 4 / 6 ; in R +2CH-O.75 axis 60 gives V 4 / 5 , and no other glasses or combinations do better. With both eyes corrected V= 4 /4 nearly, and with them the fan is clear and uni- form. Javal's keratometer verifies the degree of astigmatism and the direction of the principal meridians. This case offers departures from the usual in that the general ametropia is different in the two eyes (anisometropia), while the degree of astigmatism is not the same for each eye, and the direction of the faulty meridians is not symmetrical. When the meridians are oblique, as a rule, they stand at the same angle outward or inward for each eye very seldom is one outward and the other inward, a fact which would seem to point to a common formative cause at work for the production of the mal- formation. With these glasses, however, she cannot read ; her presbyopia has to be corrected. It is found that by adding +2.5 S to the distance glasses she can read the finest print with ease. You therefore order correction for distance, and give her the following for reading : L. R. +3-5 C + I -5 oy axis 7- +4-5 C +-75 cy axis 60. With her glasses life assumes a new and decidedly more cheerful aspect. She can see at a distance as she never could before, and the long hours of the evening are passed pleasantly in reading, something that before was impossible. CASE V. This is a young man of 21. His vision is very bad, being only 4 /eo> and a long and careiul examination with sphericals and cylindrical fails to bring it up to more than 4 /i 2 and he is benefited by both -+- and lenses. The keratometer of Javal showed an astigmatism of 4.5 D at 180 in L, and the same at 25 in R. In the trial by lenses, however, the answers and statements are so contradictory and un- certain that it is considered expedient to paralyze the ciliary muscle in order to get rid of the interference of the accommodation. So a drop of a 4 gr. solution of atropia sulph. is ordered to be put into each eye four times a day for three days when he is to return for another investigation. His eyes are examined now by the oph- thalmoscope, and in the left eye the fine vessels running horizontally over the sides of the disk are seen in the erect image only when 2.75 is brought behind the hole in the l62 CLINICAL CASES. mirror. Through this lens all the other vessels are dimmed in outline and the finer vertical vessels near the macula are not distinguished at all. These last are seen only when a -(-2 is behind the mirror. This gives at once a clue to the condition. On trying by the inverted method the disk contracts in its horizontal diameter and enlarges in its vertical diameter as the lens is removed from the eye, and the vertical diameter contracts and the horizontal enlarges as it is brought closer to the eye, and the ovals are vertical and hoiizontal. There can be no opinion now but that the case is one of mixed astigmatism, and proceeding, on the indications thus furnished, to a reexamination with glasses we soon find that with 2.75 axis 1 80, combined with -}-2 c axis 90 V= 4 /5- In the R eye the examination with the direct ophthal- moscopic method is not so satisfactory, but the disk appears an oval standing obliquely, and when a 3.5 or 4.5 is used behind the mirror, those parts of the vessels running obliquely upward and inward are most distinct ; and when -}-i or +1.5 is used those parts of the vessels running upward and slightly out- ward are sharpest in outline. In the inverted image the disk, instead of being a ver- tical oval when the lens is removed from the eye, is oblique with its top inclining outward. Turning now to the directions of the corneal meridians, as given by the keratometer, we find that the meridian of greatest refraction has its axis at 25, and the meridian of least refraction its axis at 115. A very few trials with glasses now show us that with 3.5 axis 25^ + 1.5 axis 115 V=*/. In ordering glasses for mixed astigmatism two plans can be followed. One is to have one surface of the lens ground as a cylinder, giving correction to one meridian, and the other as a cylinder correcting the other meridian, with their axes at angles crossed cylinders as they are called. For the above case, therefore, we write : L. R. 2.75 180 C +2, 90. 3.5, 25 C+i-5, 150. This is the form of astigmatic lens which, as we have seen, Airy first conceived for his own eye, and it is considered by many to be the best in some- particulars. Among other ad- vantages it is thought to give a flatter field. But it is an ex- pensive lens to manufacture for the trade, and there is more risk of an error in the direction of the axis than in the other form. The other plan is to convert it into a sphero-cylindrical lens, in which there is only one cylinder to be made. This is done in the following manner : If we take, for the left eye in above case, a 2.75 piano-spheri- cal and grind on the other side a +4.75 cylinder we have practic- ally the formula given above, for the +4.75 cylinder overcomes DIFFICULTY IN WEARING CORRECTING GLASSES. 163 the 2.75 in the meridian corresponding to its curvature and gives in addition a -(- cylindrical action of (4.75-2.75) 2 D,while the action of 2.75 of the sperical lens in the meridian at right angles to it is unaffected. Applying the same principle to the construction of the lens for the right eye, we would order : L. R. 2-75' G +4-75 c ' v 9- 3-5" C +5 cy US - This method can be 'modified in many ways and often to the advantage of the patient's pocket. Suppose, for example, that both eyes of the patient were affected with the mixed astig- matism of the left eye of the case just considered. When he arrived at 50 or 53 years his reading glasses could be made in the form of simple cylinders +4.75, 9O,thus rendering the whole eye myopic 2.75 D, and relieving his accommodation to the de- sired extent. Plane cylinders are not so expensive as sphero- cylinders, and we should not be above considerations of this kind, particularly for persons of limited means who lose or break their glasses frequently. 1 88. It is a fact, however, which occurs with an unfortu- nate frequency in our clinical experience, that the glasses which give perfect optical correction, particularly if this is deter- termined under atropine, cannot be worn with comfort and sometimes not at all. Such cases are to be found, as a rule, in persons who .have passed their youth with their anomaly uncorrected. Of this condition the following case is an illus- tration. CASE VI. Mrs. P., set. 30, has suffered from asthenopia and bad vision for a long time, for neither of which has she found any glasses beneficial. On examination I found V= 4 /is in L, 4 /24 in R. Plus glasses gave no improvement, but minus spher- ical glasses from I to 3 did increase the visual acuteness somewhat With 2.25 axis 180 V= 4 /6 in L, l fg in R. An opthalmoscopic examination by the direct method showed no myopia in the vertical meridian, but on the contrary, a hyperme- tropia in the horizontal meridian. This discrepancy in the findings by the subjective and objective methods being to me always an indication for the paralysis of accom- modation, I ordered her to apply a 4 gr. solution of atropine three times a day and re- port for reexamination at the end of three days. Under the mydriatic it was found that V= 4 /eo in R, */ 3 6 in L, and with +2.5 axis 90, V= 4 /9 in R and */e L. This condition was confirmed by the ophthalmoscope. As is my custom I allowed the effect of the mydriatic to pass off before ordering glasses. At the end of ten days when the pupil had regained its normal size, I found that the + cylinders gave 164 DIFFICULTY IN WEARING CORRECTING GLASSES. her no improvement for distant vision, but on the contrary, the concave cylinders did. She was given, however, +2.5 90 for each eye, with instructions to gradually accustom herself to their use. These instructions she followed faithfully for three months, but at the end of that time loi nd herself in no better condition than before. Her vision for distance had not improved, and while she could see better for close work with them, her asthlnopia was not relieved ; in fact, the discomfort was greater with the glasses than without them. She could see well with 2.y 180, and she was now ordered these for experiment. Distant V was more satisfactory, but she could not use them for near work. She was in despair, when happening one day to pick up her husband's glasses that I had prescribed sometim^ before for a H of 0.75 in the horizontal meridian, she found comparative comfort in reading, and these are the only glasses that we have found up to this time which are of any material ad- vantage. We hope, however, in course of time to be able to educate her up to the use of full correcting glasses, by gradually increasing their power. The case was first examined before I had any means of keratometric measurement,but lately I examined her with Javal's instrument, and found in both ^=8'/i mm. at 180 and 8'/4 at 90, with a crossing of the bands of a'/z steps at 180, thus verifying the diagnosis made by the other methods. Cases so extreme as this are not common, but lesser degrees are frequently met with. I can only account for them on the supposition that the eyes have been accustomed for so long to the astigmatic state as to make the abnormal, in a certain sense,the normal condition and that the cerebral center for vision resents an interference with the established order of things. It must be remembered, in this connection, that in dealing with the human eye we have to do not with an optical instrument alone, but with an organ of sense as well. All of our senses are, in a measure, affected by education, and after a certain habit has been once firmly fixed it is with difficulty changed in any important particulars. It is a fact now generally ac- knowledged that when strabismus has existed for a great while, binocular vision is not obtained even after the optical axes are correctly placed by an operation. It has seemed to me, therefore, not only unwise, but useless to attempt to force eyes back to our conventional standard, and to insist on patients wearing glasses giving full correction, when a fair trial has proven their unsatisfactoriness. Under these circumstances, it would appear best to find the glass, generally a weak one, which gives most comfort and tenta- tively increase the strength. The case just related also well demonstrates the condition DIFFICULTY IN WEARING CORRECTING GLASSES. 165 commonly called " spasm of accommodation." There was a much higher refraction manifest before the action of the atropine than after, and this is usually attributed to a spasm of the ciliary muscle. If by " spasm " is meant a permanent tonic contraction of the muscle, the term is certainly misap- plied, since when there is nothing to call the accommodation into play the muscle is relaxed, as shown by the direct ophthol- moscopic examination. The unusual contraction of the cil- iary muscle in this case is, in my opinion, a voluntary act, and is due to the fact that the patient from custom or preference has always used her anterior focal plane, which would necessi- tate such a contraction of the ciliary muscle as shall convert a H. astig. axis 90 to a M. astig. of the same degree axis 180. The use of this plane has become a fixed habit with her and the probabilities are that, at her time of life, it can be broken up with difficulty or not at all. Such difficulties as these are much less frequent in younger people who can more readily adapt themselves to altered conditions. Another aggravated case of this character is the following : CASE VII. A lady, 42 years old, had been treated for asthenopia by Dyer's method for some months, without,however,the discovery being made of any refractive anomaly. A Philadelphia surgeon, to whom she applied later, worked out, under atropine, a high degree of astigmatism which I found to agree essentially with that diagnosed by myself. The data obtained by the keratometer of Javal were: L, 15 /f=7 3 /4 mm. i85 = 8 1 /4 mm. with a crossing of 3*1/2 steps; R. 75 K= l / t mm. i6o=7 1 /2mm. with "a crossing of 4*/2 steps. V without glasses = 4 /eo in L., less than that in R. With 3.5"* 15, L V=Vis, with 4.5 70 R V=Vi- The Philadelphia surgeon had ordered correcting glasses, with instructions to persevere in their use. This she had done, but the longer she wore them the more uncomfortable they became. They made her so dizzy that she was utterly unable to wear them in the street, and she could not read with them at all. She was then ordered glasses which would combine a +1.5 with the correction above indicated, with the hope that thereby she would be able to use her eyes for near work at least, and in time work her way gradually" to full correction for distance. It was because she found that after several months' trial it would not be possible to use either of these with benefit or even comfort, that application was made to me. With this experience before me I had not much hope of benefiting her by means of glasses, particularly as I suspected that a large part of the asthenopia was nervous. I gave for experimental use, L -(-3.5 105, R +4.5 160, to be used for near work. She could read with comfort for a somewhat longer time with these than without them, but the benefit was not at all encouraging. i66 DEFICIENCY IN CORRECTING BY CYLINDERS. 189. Do cylinders give an absolute correction of the as- tigmatic condition ? They can not, from the fact that the re- fraction of an elliptical surface cannot be neutralized by a surface which has equal radii of curvature. Fig. 44. A EFFECT OF A CYLINDRICAL LENS ON THE REFRACTION OF THE SHARPER KM> OF AN ELLIPSOID WHEN THE PERIPHERAL RAYS OF THE TWO MERIDIANS ARE BROUGHT TOGETHER. 190. Where the cornea, as it usually does, represents a triaxial ellipsoid, we have a different set of conditions accord- ing to the special character of the curvature ; and the action of cylindrical lenses on the refraction of the principal meridians will not be uniform in all cases. Let us take, as an example, that form in which the cornea represents the sharper end of an ellipsoid with three unequal axes. It is plain from what has been demonstrated in Chapter II that the meridian of greater curvature, should it pass a certain point, will suffer from the greater aberration. A in fig. 44 represents the meridian of less, and B the meridian of greater cuivature. In A, the peripheral ray d crosses the principal axis XX' at e and the more central ray b at a, while in B the corresponding ray d' crosses at /, and b' at k. If we place a cylindrical lens before the refracting surface with its curvature corresponding to the meridian B, and of such DEFICIENCY IN CORRECTING BY CYLINDERS. i6 7 strength that the peripheral ray d' is carried back and made to cross the axis in the same point e as the peripheral ray d of the meridian A, the relation between k and z, though they are both carried back from their original position,remains unaltered at c and e, since the regular refraction of the cylinder does not counteract the aberration of the elliptical surface. The result would be that the rays crossing at a and c, would form figures of diffusion on the focal plane passing through e. 45- I a r, ANOTHER EFFECT OF A CYLINDRICAL LENS ON THE REFRACTION OF AN ELLIPSOID WHEN THE PERIPHERAL RAYS OF THE Two MERIDIANS ARE BROUGHT TO- GETHER. / If we bring the more peripheral rays, d and d ', of the two meridians, A and B, to cross at the same point c, moving them forward from a, z, as in fig. 45, we have the same result; for the central rays b, b' , which cross the axis at e and k, would form figures of diffusion on the focal plane passing through c. 191. We would have, of course, an analogous state of af- fairs in dealing with the blunter end of the ellipsoid ; for while it would be possible, by means of a cylindrical lens, to bring corresponding peripheral or central rays to cross the axis at the same point, it would not be possible to bring both the cen- 168 DEFICIENCY IN CORRECTING BY CYLINDERS. tral and peripheral rays to cross it in one point ; and it we should have to deal with a surface in which one meridian rep- resented the blunter end of an ellipse, while the other repre- sented the sharper end, the diffusion figures would be still more confusing. Fig. 46 represents such a surface where the peripheral rays, d, d', are brought, by means of a cylinder, to cross the axis at the same point e. The more central ray b of the flatter ellipse A, will cross the axis at c, behind the focal plane, passing through e, while the more central ray b' of the sharper ellipse B, will cross it in front at a, thus forming two sets of diffusion figures. Fig. 46. REFRACTION BY THE BLUNTER AND SHARPER ENDS QF AN ELLIPSOID COR- RECTED BY A CYLINDER. 192. Under any of these forms which the cornea may as- sume, 1 the retinal image must have its distinctness of outline impaired by the circles of diffusion which fall on it.- This dif- 1 In all the measurements that have been made up to the present time, the cornea has never been found to assume in either of its principal meridians the form of the blunter end of ellipse, but we see no reason to doubt the possibility of such an occurrence. *We do not take into consideration here the rays passing thu ugh the intermediate meridians. These require a separate investigation. EFFECT OF CYLINDERS ON THE NODAL POINTS. 169 fusion being greater in the higher than in the lower forms of astigmatism, we should expect to find the visual acuteness, after all possible correction, less in the former, and such I be- lieve is the experience of all practitioners. We should also expect that the vision of astigmatics, after correction, would be less than that of myopes and hypermetropes of the same grade after their neutralization by spherical lenses. As a matter of statistics, I find that out of about 2,000 as- tigmatic eyes of all degrees, only about \/ {0 have V=i, after the best possible correction. 193. It is apparent that this aberration in the principal meridians will be greater, the greater the angular aperture which in the eye would be represented by the pupil and con- sequently the larger the pupil the larger the figures of diffu- sion, and the more indistinct the retinal image. This is an additional reason for not accepting the examina- tions made under atropine as absolute, since the effect of the diffusion images on the retina will be different with a large pupil and with one of normal size, and this difference is likely to be strongly felt in the final'correction. 194. Another point in the action of cylinders to be taken account of in this connection is their influence on the position of the nodal points in the meridian of their action. While the cylinder in correcting the abnormal refraction brings the focal points of the two meridians together approximately, it ad- vances the nodal points of the meridian it affects when it is con- vex, and causes them to recede when it is concave. Now, the size of the retinal image is governed by the position of the nodal points in relation to the retina. This image is larger for the same object the farther the nodal points are removed from it. We should, consequently, expect to find a diminution of the image on account of the recession of the nodal points, when a concave cylinder is used, in the direction of the faulty meri- dian, and an enlargement of it in the direction of the hyperme- tropic meridian when a convex cylinder is used. As a result, there would, theoretically, be an enlargement of an object in the direction of the meridian corrected by a + cylinder, and a I7O HOW LOW A DEGREE OF ASTIG. IS TO BE CORRECTED. diminution of it in the direction corrected by a cylinder. 195. How low a degree of astigmatism it is necessary to correct? This is not purely a question in optics, but one in answering which many considerations must enter. Cylindrical glasses should not always be prescribed simply because distant vision as tested by the test types is thereby rendered better, for some persons with an as- tigmatism of 0.75 D have a sharpness of sight for distant ob- jects, on account of their better interpretation of retinal impres- sions, superior to some whose eyes are emmetropic. If such per- sons are satisfied with their distant vision, and do not suffer, no good can result from forcing on them the constant use of glasses. The use of glasses is a great inconvenience, many persons are strongly prejudiced against them, and they are more or less expensive. The wearing of weak glasses should, therefore, not be made imperative, if decided objection is urged, unless the surgeon is satisfied that undoubted benefit will follow their use. But when there is a complaint of asthenopia,even when the eyes are not used at close work, and particularly in nervous women, the correction of even low degrees of astigmatism is usually attended with great benefit. The constant use of cylinders of O.5D is often sufficient to transform misery into com- fort. And in almost all cases the addition of a 0.50 cyl- inder, where it is required, to presbyopic glasses makes reading much more comfortable, in the evening especially, or where close application for a considerable time is necessary. It occasionally happens, too, that the correction of astigma- tism as low as 0.25 D is found very beneficial. Such cases are usually iound in persons whose nervous systems are below par, and on restoration to health the glasses can be laid aside. When the amount of astigmatism after cataract extraction exceeds iD there is always an advantage from its correction; for less degrees it is hardly worth while. 196. We would call attention here to a fact in the correc- tion of astigmatism which has not yet met with a satisfactory HOW TO PROVE GLASSES. 17! explanation, and that is the improvement in vision given by the tilling of a spherical lens superior to that afforded by a cylin- der equivalent to that amount of inclination of the spherical. It is a matter of common observation that persons operated on for cataract often see better when their spectacles are held ob- liquely. This difference in effect may be due to some differ- ence of action on the rays passing through the intermediate meridians, a subject which has not been fully examined into on account of the great difficulty in obtaining formulae of gen- eral application. It may also be stated, in this connection, that some astigma- tics can correct their anomaly appreciably by making pressure at the proper place on the sclera* to give the correcting curva- ture to the cornea in that meridian. 197. When a prescription for glasses has been given, the case should not be summarily dismissed. The patient should be instructed to bring the glasses back for examination, for it is of the greatest importance that the optician shall have fol- lowed strictly the instructions of the surgeon. An approxima- tion to the glasses ordered will by no means suffice. A small error in the number of the lens, or a change of 2 or 3 in the position of the axis of the cylinder will often mar an otherwise good result. The mistake, moreover, may not always be the opticians. In the hurry of many examinations the surgeon himself may have put down the wrong number or the wrong degree, or put L for R. The necessity of some method of proving glasses is therefore apparent. 198. There are several methods by which this may be done but the one which is most rapid and best adapted to the con- sultation room is that of neutralization. When a -f- and lens are placed together the action of the one, as is well known, tends to neutralize that of the other, so that the combined power of the two is always equal to the difference in their refraction. When the strength of the two is the same, their optical action will be nil, the same as a bit of plane glass. When, therefore, we find, for example, a lens whose power we know which completely neutralizes a + lens* 1/2 HOW TO PROVE CYLINDERS. the power of which we did not know, the number of the one gives us the number of the other. How shall we know when the one neutralizes the other? One very simple method is that of watching the paralactic move- ment of objects through them. When a convex lens is moved back and forth a few inches before the eye, and at right angles to the optical axis, objects seen through it are observed to move in a direction opposite to that of the lens. Through a concave lens the movement is in the same direction as that of the lens. Let us have, for example, a lens whose number we are ig- norant of and the exact refracting power of which we wish to find. If the large types of Srrellen are very indistinct through it, we know at once that it is a strong glass, and begin by plac- ing on it a strong -f- glass, say No. 4. With this most of the letters of the test-types are seen, but there is still a movement of objects " with " the lens. With a + 5, there is a slight movement of the letters ' against " that* of the lens, showing an excess of -(- action. No. 4 is, therefore, too weak, and No. 5 too strong. We now try + 4.5 and find that in whatever di- rection the combined lenses are moved objects remain station- ary. It is possible by this test to tell to within 0.25 D the pow- er of any spherical lens, and this is sufficiently accurate for all practical purposes. 199. The question becomes somewhat more complicated, however, when cylinders are to be dealt with, because in them we have to determine not only the strength of the lens, but also the direction of its axis. In this examination we employ the fan of Snellen. Example : The lens whose power is to be determined, is a sphero-cylindrical convex. Through it the whole of Snellen's fan is indistinct. But by holding in front of it concave spheri- cals, one after the other, a lens is finally found which shows the line at 20 clear and sharp. The concave lens which gives the neutralization is of course the weakest one through which this line appears with clearly defined edges and which gives no paralactic movements. If this is 2.5, then we know that the HOW TO PROVE CYLINDERS. 1/3 meridian of the sphere-cylinder whose axis is at 2O is + 2.5. But with this, the lines to the right of the center of the fan are still blurred and offer paralactic movements. We now try the addition of concave cylinders with their axis at no , that is in the direction of the blurred lines, until one is found which renders the fan uniform and clear. When these lenses are moved together there will be no paralactic action if the correc- tion has been complete. Should there be a movement of objects it must be noted whether it is in the direction of the cylinder's axis or at right angles to it or in both directions, and of course also whether " with " or " against " the lenses. If there is a movement when the lenses are moved parallel to the direction of the axis of the cylinder, then the spherical lens is not right. If there is no movement in this direction, but only at right angles to the axis of the cylinder, then the cylinder is at fault, and the lens in either case will have to be increased or dimin- ished in power according to the direction of the movement, un- til one is found with which all movement ceases. 200. Dr. E. Gruening, of New York, 1 employs a method of "simultaneous contrast" which he has found very convenient, and which he prefers, as being more accurate, to the one just described. When a narrow stripe of a marquetry floor or carpet is looked at through a convex lens, that part seen through the lens appears wider than the part lying to either side of it; when viewed through a concave lens it appears narrower. As the margins of the stripe inside and outside the lens are seen at the same time coming up to the edge of the lens, a small differ- ence in magnitude can be readily detected. In applying this principle to the testing of spherical glasses we have only to hold the lens to be proven horizontally parallel with the floor and, looking down through it at the stripe, observe whether the part seen through the lens is larger or smaller than that lying out- side of it. If it is larger the lens is convex and we apply con- caves, as in the preceding experiment, until the stripe is con- 1 Verbal communication. 1/4 HOW TO PROVE CYLINDERS. tinuously of the same size from both sides through the lens. If the part seen through the lens is narrower, there is an excess of minus action, and we apply convex lenses until one is found which gives a uniform stripe. The same principle holds good, of course, for cylinders when their axes lie in the same direction as the stripe. In the meri- dian perpendicular to the stripe they act, to all intents and pur- poses, as sphericals, and may be so considered. If, therefore, the stripe is seen through the cylinder, in this position, to be enlarged, there is a plus action, and it is corrected by placing a concave cylinder on it with its axis coinciding with the stripe and the axis of the lens to be tested ; if it is diminished in size there is an excess of minus action, and the correction is made by convexes, applied in a similar manner. But the method is likewise useful in determining the direc- tion of the cylinder's axis. The portion of the stripe seen through the cylinder and the portions outside of it do not run in the same direction except when the stripe and the axis of the cylinder coincide or are at right angles to each other. Any deviation from these two positions causes the two portions to lie at angles to each other. Knowing the angle at which the axis of the cylinder should be, and finding the angle at which it is necessary to place the lens to be determined in order that the parts within and without the lens fall in the same direction, we here have the necessary data for determining whether the axis is properly placed. BIBLIOGRAPHY. Airy, George Biddell On a peculiar defect in the eye and a mode of correcting it Trans. Camb. Philos. Soc. V. II. 1827. P. 267-271. (Read Feb. 21, 1825). Airy, G. B. (Cylindrical glasses). Ed. Jour, of Sci. No. XIV. P. 322. Bagnesis Emploi d. verres correcteurs en ophthalmol. Ths. de Paris, 1883. Burnett. S. M. Refract, in the principl. mends, of a triax. ellipsoid, with rrnks. on the correct, of astig. by cyld. glasses, and an histor. note on corn, astig. with a com- municat. on the monochrom. aberrat. of the hum. eye in aphakia. by Prof. \V. Hark- ness. Arch. Ophth. XII. Pp. I-2I. N. Y. 1883. Carter, R. B. On defects of vis. which are reined, by optic, appliances. Med. Times and Gaz. I. VI. July, Aug. and Sept 1877. BIBLIOGRAPHY. 1/5 Bonders, F. C. Anomalies of the accommodation and refraction of the eye. New. Syd. Soc. Lond. 1864. Bonders, F. C. Astig. en cylindrsch. glazen. Utrecht, 1862. Germ, transl. by Schweiger. H. Peters. Berlin, 1862. Fch. transl. by H. Bor. Paris, 1863. Bonders, F. C. Prakt. Bermerk. ueberden Einfluss v. Hulfslinsen auf die Sehsc- harfe. Graefes Arch. XVIII-1I. P. 245. 1872. Farley, C. II, A method of discover, and correct, astig. Bost. Med. and Surgjr. June 13. 1872. Galezowski Tabl. synopt. de la refract, de 1'oeil; choix des lunettes. Paris 1865. Gosetti L'asthenop. sua patogen. e cura. Annal. di. Ottalm. XII. Pp. 3-4 1884. Green John On spectacle lenses of asymmetrical curvature. Amer. Jnl. Oph. Mch. 1886, pp. 53 59. Homberger, J. Astig. and cylnd. glasses. A review of Bonder's theories. Am J. Ophth. II. Pp. 21-65. N - Y - l86 4- Hay, G. Befcts. of ocul. refract, accommod. and converg. and their treatment by spectls. and otherwise. Bost. Med. and Surg. Jr. Oct. 20. 1870. Imbert, A. Nouveau precede de verification des verres cylindriques. Ann. d'Ocul. Mai. Juni. 1885. Javal, E. Sur le choix d. verres cylind. Ann. d'Oculist. LI 1 1. P. 50. 1865. Javal, E. Be la neutraliz. d. 1'ache de la vis. Ann. d'Oculist. LIV. P. 9. 1865. Javal E. Sur le choix d. verres cylind. Ann. d'Oculist. LV. P. 5. 1866. Javal, E. Sur les applicat. d'un appareil nouveau destine a measur. 1'astig.; an- alyse mathemat. de 1' act. d. verres cylind. Cong, internat. de Geneve. 1877. Knapp, H. Ueber d. Einfluss d. Brillen auf die optisch Constanten u. die Seh- scharfe des Auges. Arch. f. Augen. u. Ohrenhlk. I. 2. 1870. Knapp, H. On the designation of the meridians in the determination of glasses and of the visual field. Archives of Oph. XV., pp. 207 210. 1886. Konigstein Bie Anomal. d. Refct. u. Accommodat. Practische Anleiting zur Brillen bestimmung. Wien. 1883. Laurence, J. Z. On astig and its correct, by cylind. lenses. Med. Mirror. I. Pp. 4-11. London. 1864. Levi, M. Saggio pratic. sull 'astig. e metodo facile per trov. la correz. Ann. di Ottal. VII. Pp. 232 47. Milan. 1878. Loring, E. G. An astig. glass for catarct patients. Trans. Amer. Ophth. Soc. Pp. 108-18. 1871. Mauthner, L. Vorlesungen ii d. optisch. Fehler d. Auges. Wien. W. Braumiil- ler. 1876. Motais I 'ince-nez pour verres cylindriques. Ann. d'Ocul. Mai. Juni. 1885. Noyes, H. B. Note respect, the first recorded case of astig. in this country for which cylind. glasses were made. Am. Jr. Med. Soc. N. S. LXIII. Pp. 355-9- 1872. Raehlmann, E. Ueber die optische Wirk. d. hyperbol. Linsen. Ber Anwend. derselb. als Brillen. Zehenders Monatsbl. XX. P. III. Raehlmann Glaesercorrect. bei Keratocon. Ber. ii d. versamml. d. Ophth. 1/6 BIBLIOGRAPHY. Gesellsch. XII. Pp. 50-2. Stuttg. 1879. Reusch, F. E. Theorie der Cylinderlinsen, p. 35. Leipsig, 1868. Reynolds, D. S. The prolate lens of Dr. Fox. Mr. Borsh's sphere-cylinders on one surface. Amer. Jn'l Oph. April, 1886, pp. 95 98. Roberts, P. F. Prescrip. de lente* en un caso de astenop. acomodat. pra astig. compust y. anisometroe. Rev. Med-quir. XVI. Pp. 198-204. Buenos Ayres. 1878-9. SchiStz A case of astigmatism of the lens after iridectomy. Archives of Oph. XV., pp. 200203. 1886. Schidtz, H. On the most suitable metho 1 of recording optometric examinations. Archives of Oph. XV., pp. 203 207. 1886. Schweigger, C. Bemerk. ii. die Diag. u. Correct d. Astig. Arch. f. Ophth. IX. Hft. I. Pp. 178-91. Berlin. 1863. Stilling, J. Sphaerold. Glaeser. gegen Astig. Centralb. f. prakt. Augenhlk. IV. Pp. 273-5. Leipzig. 1880. Woinow Ein kurze Bemerk. zum Brillen gebrauch. Graefes Arch. XVIII. Abt. II. P. 49. 1882. Woinow Zur Lehre U den Einfluss d. optisch Glaeser auf die Sehscharfe. Graefes Arch. XVIII. Abt I. P. 349. 1872. CHAPTER XIII. IRREGULAR ASTIGMATISM CONICAL CORNEA. 20 1. Regular astigmatism, as we have seen, is a condition of the eye in which its refraction approaches that of a triaxial ellipsoid where the principal meridians are ellipses and at right angles to each other. All other departures from a strictly spherical refraction are classed under the general term irregu- lar astigmatism. 202. IRRE.GULAR ASTIGMATISM can have its seat in either one of the refracting media of the eye and may, consequently, be lenticular or corneal. 203. With very rare exceptions all eyes are affected with a certain amount of irregular astigmatism, but when it is not sufficient to reduce V below 20 / 20 , it is considered as normal. Normal irregular astigmatism is for the most part lenticular and is the result of a want of homogenity in the lens substance. This want of uniformity of structure is due, mainly, to the manner of the lens's growth. The development of the lens is not symmetrical in its entirety, but in parts or sectors inde- pendent of one another and these are afterwards joined to- gether to constitute a whole. It is seldom that the union of these sectors is so perfect as to leave no trace of their separ- ate existence. 204. This peculiarity in the construction of the lens is dem- onstrated by dissection and by entoptic experimentation. Anatomical investigation shows not only a gradual increase in the density of the lens substance from the circumference to- wards the center, but also the remains of its sectorial evolu- (177) 1/8 SECTOIRAL CONSTRUCTION OF THE LENS. tion. Fig. 47 is a meridional section of the lens of a young infant in which this sectorial character is well represented. This structure of the lens is also often apparent in the liv- ing eye under oblique illumination, and particularly so in some cases of cataract, where the line of union of two adjacent sec- tors is plainly visible. 205. The refractive unevenness of the lens caused by its anatomical structure is shown by means of a simple entoptical experiment. Make a fine point of light by holding a strong convex lens, such as the ocular of a "microscope, at ten or Fig -47- w ^-4 A \ \ ' .'''" THE SECTORIAL CONSTRUCTION OF THE HUMAN CRYSTALLINE LENS. twelve feet from a gas jet. In this manner a fine pencil of rays is obtained which we can use for casting on the retina shadows of such opaque objects in the refracting media of the eye as lie in its path, while variations in density will manifest themselves by brighter or darker lines or spots. As this bright focus is approached to the eye we see first, the shadows cast by the ob- jects on the surface of the cornea, such as tears, meibomian se- cretions, etc. As it is brought closer, the diffraction of the pupillary edge of the iris is seen, and then the inequalities of the lens structure, those on the anterior face being first brought to view, afterwards those at the center and on the posterior face SPECTRUM OF THE LENS. 1/9 successively ; and finally the objects in the vitreous humor and on the inner layers of the retina. A " spectrum" of the crys- talline lens thus obtained shows such a want of homogeneity of structure as would not be tolerated in any optical instru- ment of man's construction. Bonders gives at page 200 of his "Treatise on the Anomalies of Refraction and Accommodation of the Eye " a very elegant spectrum of the crystalline lens of his right eye. In Fig. 48 is given a diagram of the spectrum of my right eye, showing the remains of the lines of union of the sectors ; the minor irregularities in the structure of the lens are not recorded in the diagram. Fig. 48. A SPECTRUM OF THE AUTHOR'S CRYSTALLINE LENS, SHOWING THE LINES OF UNION OF THE SECTORS. 206. It is a legitimate inference that such optical imperfec- tions should seriously impair visual acuteness, and this un- doubtedly is the case. It is certain that our conventional standard of visual acuteness would be much higher than 20 / 2 o if it were not for these defects in the lens, and it is most proba- ble that to a freedom from them is to be attributed that super- normal acuteness possessed by some persons amounting often to 2 % . We have, however, become so accustomed to many of the manifestations of these defects, that we either ignore them or no longer regard them as abnormal. ISO CAUSE OF THE RADIATIONS OF A STAR. 207. The most common of these appearances are the lines seen radiating from bright stars or distant points of light. We are perfectly well aware that the stars are in reality not rayed, but round, and yet so wide spread is this fault of vision that the conventional typical representation of a star has become to be a central bright spot with radiating bright streaks. Fig. 49. THE APPEARANCE OF A DISTANT POJNT OF LIGHT TO THE AUTHOR'S RIGHT EYE. Only a very few persons are recorded as seeing the stars without these rays, from which we may infer the extreme ra- riety of a perfectly homogeneous crystalline lens. To my right eye a distant street lamp has the appearance shown in Fig. 49. On comparing this with the spectrum of the lens (Fig. 48) it will be seen how nearly they agree. There are eight rays to the star, and clear indications of eight sectors to the lens, and the directions of the rays coincide perfectly with the positions of the sectors. . 208. Another manifestation of this irregular astigmatism of the lens is polyopia monocularis, though it is seldom present as a normal condition sufficiently marked to attract atten- tion. It can be experimentally demonstrated in the following manner : Take a small black dot on a white ground, or better still, a small white point on a black ground, such as can be ob- POLYOPIA MONOCULARIS IN IRREGULAR ASTIGMATISM. l8l tained by scraping the enamel from a visiting card on a piece of black velvet, and arming the eye with a strong convex lens (6 or 8 D) in order to render it myopic and avoid the contrac- tion of the pupil associated with accommodation, bring it close to one of the small white scales having a diameter of about l / 3 mm. When the bright spot is brought very close to the eye and passes within the point of distinct vision, it does not become a broad even circle of diffusion, as it would do were the crystalline lens perfectly homogenous, but breaks into a series of grayish figures around a darker center. Each one of these figures is the image of the bright spot formed by its corresponding lens sector. Fig. 50, which is borrowed from Helmholtz, shows the polyopia produced by the lens in the right (a) and left (b) eye of that great scientist. fig- 50- POLYOPIA MONOCULARIS (HELMHOLTZ). In neither of my own eyes is the polyopia so marked as that represented in these figures, from which I judge that my lenses, though far from homogeneous, are yet more free from inequalities of refraction than is usual. Each one of these images shows, likewise, fringes of colors, demonstrating the ex- istence of a chromatic aberration as well. I find this chromatic phenomenon quite marked in my own eyes. 209. Monocular polyopia is one of the most marked features of abnormal irregular astigmatism of the lens, and is most frequently found associated with incipient senile cataract. The sclerosing process in the lens does not commonly affect the different sectors equally, and the result is such a difference 1 82 OTHER CAUSES OF IRREGULAR ASTIGMATISM. in their refraction as leads to two or more images of the same object. Sometimes the first indication of the formation of cat- aract is the appearance of two or more horns to the moon and multiple images of a distant street lamp. 210. Dislocation of the lens, in addition to producing in certain instances a regular astigmatism, gives rise also to the irregular form, and a certain part, probably, of the normal ir- regular variety comes from a want of centering of the cornea and lens. Injuries to the capsule and zonula which allow the lens to become irregularly curved will also have the same effect. 211. Mauthner is of the opinion that the lenticular variety of irregular astigmatism is increased on accommodation for near objects. He accounts for this by supposing that the cap- sule on relaxation of the zonula falls into folds which would, of course, mar the uniformity of the lens surface and lead to ir- regular refraction. This wrinkling of the capsule he claims to have demonstrated as an actuality. 212. If we make exclusion of the monochromatic oberra- tion in the principal meridians demonstrated by Prof. Hark- ness, ( 29) and that demonstrated by myself ( 14) neither of which are correctible by cylinders, there is no corneal astig- matism of the irregular form which we can consider as normal. And while, as we have seen, in the majority of instances lenticular astigmatism is congenital, with few exceptions irreg- ular corneal astigmatism is acquired. We meet, however, sometimes with a class of cases (and they are getting more numerous since we have now at command the proper means in keratoscopy for their easy detection) in which there are ine- qualities on the surface of the cornea that is still transparent, and where there is no history of a past inflammatory affection. In such cases there was, in all probability, an ulceration of the cornea during intra-uterine life. It would appear from this that the formative processes in the cornea are much more regular and constant than those of the lens. 213. The most common causes of irregular astigmatism in DIAGNOSIS OF IRREGULAR ASTIGMATISM. 183 the cornea are inflammations and injuries of its substance. The reparative processes following these pathological conditions are seldom so perfect as to leave the curvature or homogeneity unaltered ; and even a slight change in either of these particu- lars will be sufficient to affect in an appreciable manner the distinctness of the retinal inage. The amblyopia under such conditions does not depend solely on the opacity due to the effusion and organization of inflammatory material in the cor- neal substance, but results mainly from the distortion and blurring of the image caused by the irregular dispersion of the light rays, and this distortion and indistinctness of the image are quite as marked when the defect is unattended with any opacity, as, for example, in resorption ulcers with clear bot- toms and edges. The condition of vision in these astigmatics is very well imitated by looking through a pane of very bad window glass which has irregular surfaces and inequalities in its substance. 214. DIAGNOSIS OF IRREGULAR ASTIGMATISM. Abnormal irregular astigmatism of the lens is readily determined in the following manner : The patient is caused to look with each eye separately at a small distant point of light, such as Bonders used in his original method for determining regular astigma- tism ( 80), and if it does not appear single, but on the con- trary, broken up into two or more spots, the diagnosis of ir- regular astigmatism is fixed ; and if on further examination the cornea is found to be regular in curvature, its seat in the lens is placed beyond doubt. This kind of astigmatism being most commonly met with in commencing cataract, the opacities of the lens associated with the change in the sectorial refraction can be seen by the oblique method of illumination or by simple illumination with the ophthalmoscopic mirror ; in the latter case revealing them- selves as dark or black lines or spots against the red back- ground of the fundus. 215. If there be a dislocation of the lens leaving its edge in the area of the pupil, the margin will be seen as a bright curved line on oblique illumination and as a curved black line 184 KERATOSCOPE IN DIAGNOSIS OF IRREGULAR ASTIGMATISM. on direct observation of the fundus by the mirror alone. The bright line in the first instance is due to the reflection of the incident light from the edge of the lens, having, of course the color of the light used, being yellow if it is artificial and white if day light. The black line in the other method conies from a total reflec- tion of the light coming from the illuminated fundus along the edge of the lens, leaving a narrow unilluminated space in striking contrast to the otherwise brilliantly lighted background. It often happens that two images of the fundus visible at the same time can be obtained in the indirect method of ophthalmoscopic examination, one through the lens and one through the pupillary space which is free of the lens. 216. Irregular corneal astigmatism is most easily diagnosed Fig- 5i- o p KERATOSCOPIC APPEARANCE OF THE CORNEA w A CENTRAL CORNEAL OPACITY. by keratoscopy, and best by means of the disk of Placido de- scribed in 156. Wecker's square ( 158) can also be used, but it is much inferior to the concentric circles. In making the examination, the patient is seated with the back to a win- dow and the figures are so held as to get a good reflection of them from the corneal surface. Any irregularity of curvature is then at once manifest in a distortion or unequal thickness of one or more of the circles, or a distorted form of the square. The shapes which they assume are sometimes quite fantastic. They will be best illustrated by the actual appearances in some cases selected from my case-book. Figure 51 represents in A the appearance of Placido's disk, KERATOSCOPIC APPEARANCES IN IRREGULAR ASTIGMATISM. 185 and in B that of Wecker's square, as they were reflected from a cornea having an opacity near its center, the result of an ulcer. It will be observed that in this case there is also some regular astigmatism as shown by the drawing out of the circles and square from above inward downward and outward,a not unusual consequence of corneal ulceration. Fig. 52. KERATOSCOPIC APPEARANCE IN A SMALL CORNEAL INFILTRATION. Figure 52 shows the reflection from a cornea in which there was a small circumscribed opacity resulting from an infiltra- tion, the rest of the cornea being clear. V could not be brought to more than 4 / 60 even after a correction of the myopia that was present. 53- 217. Should neither Placido's disk or Wecker's square be at command, the reflection of a window sash with its rectangular figures will show any irregularities that may be on the corneal surface. In this examination, of course, the patient must sit facing the window. 1 86 EXAMINATION BY OBLIQUE ILLUMINATION. 2 1 8. The reflection figures in any one of these methods of keratoscopy are not the same from all parts of the cornea. The changes in form as the eye is moved in different directions, while the object is stationary, are quite kaleidoscopic in their character. Fig. 53 gives two forms of Placido's disk in a case of cystoid cicatrix situated at the upper inner sclero corneal margin; one, A, from over the center of the pupil, showing the extreme flattening of the cornea in the direction of the scar, and the other, B, when the eye was turned IO inward. 219. Irregularities of the corneal surface, even where there are no opacities, can often be detected by direct inspec- tion, and particularly when oblique illumination is used. The appearance of an ulcer with a clear bottom, for instance, is quite characteristic when the light is concentrated on it by a convex lens. The edge appears as a bright ring, the sides darker, on account of the reflection of the light out of the line of the observers' vision, and the center as a bright spot of light. The same appearances will be found also in a transparent cir- cumscribed elevation of the surface. These ulcers and eleva- tions, whether transparent or not, cast shadows on the anterior face of the iris. In the case of a transparent elevation, the shadow will have a bright center surrounded by a dark ring, while in the case of a depression there will be dark center with a brighter rim. The surface of the iris seen through these ir- regularities often presents a wavy appearance which changes as the point of view is changed. 220. All these circumscribed alterations of curvature and opacities reveal themselves as dark spots on a red back-ground when the fundus is illuminated by the ophthalmoscopic mirror, the light from the bottom of the eye being either reflected or refracted by them in such a manner that little or none of it which should pass through them reaches the eye of the ob- server. 221. A certain and often a considerable amount of irregu- lar astigmatism of the cornea is manifest during the healing of the wound after cataract extraction, and particularly when it is complicated with inflammation either of the cornea itself or of the anterior portion of the uveal tract. IRREGULAR ASTIGMATISM AFTER CATARACT EXTRACTION. 187 I extracted an opaque lens from the R eye of John O'N by means of Weck- er's incision and an iridectomy. The operation was perfectly smooth and normal and no symptoms of irritation showing themselves he was allowed to leave the hospital at the end of the ninth day. Three days after, he presented himself again with a pronounced iritis. The wound which at the time of his discharge appeared well united showed signs 'of separation, and the lips were infiltrated and gray. I made measurements with the keratometer and found 115 r = 10 mm. 10 r = 7 3 /4 mm., a difference in refraction amounting to 13 D. Fig- 54- KERATOSCOPIC IMAGE AFTER CATARACT EXTRACTION. A keratoscopic examination with the disk of Placido showed an amount of wrink- ling ot the cornea as exhibited in Fig. 54. The iritic inflammation was most per- sistent, and it was six weeks before there was any evidence of abatement. He was examined with the keratoscope and keratometer from time to time and there was no alteration observed until the inflammation began to subside. But evn when ihere was no longer any inflammation going on, there was quite an irregularity in the course of the rings, and it was only after I had made a discision of the secondary cataract that the figure became regularly oval. This case shows quite conclusively that the contraction of the capsule especially when accompanied with inflammatory deposits is capable of drawing on the base <5f the cornea in such a manner as to wrinkle its surface. 222. The operation of iridencleisis now seldom performed the operation for iridectomy, and, in fact, any traumatic in- jury to the cornea, or sclero-corneal margin is liable to be followed by a greater or less amount of irregularity in curva- ture which will mar the distinctness of the retinal image. In all cases of injury to the anterior portion of the eye where re- duced visual acuteness follows, a keratoscopic examination should be made to determine how far irregularity in corneal curvature is the cause. 223. Changes in the tension of the eye-ball hypo-and 188 SYMPTOMS OF IRREGULAR ASTIGMATISM. hypertony often affect very markedly the character of the corneal curvature. The evenness of the corneal surface is not often affected by an increased tension, but where the tension is reduced some irregularity is seldom absent. Fig. 55 shows the reflection image of the disk from the left eye of Mrs. C., which was affected with ophthalmo-malacia in consequence of a chronic uveitis following a dislocation of the lens. The ball was much smaller than the other, and the tension was re- duced to 3. 55- KERATOSCOPIC IMAGE IN OPHTHALMO-MALACIA. 224. The symptoms of irregular corneal astigmatism are es- sentially the same as those found in the same form of lenticu- lar astigmatism. These are : a dazzling sensation which comes from the diffusion of light .over the retina caused by the dis- persion of the light rays by the semi-opaque spots, depressions, elevations and irregularities of curvature ; diplopia or polyopia arising from the different images formed by the different parts of the same refractive surface ; distortion of the outlines of ob- jects from an unequal refraction in the same plane making a straight line, for example to appear crooked ; amblyopia from the indistinctness of the principal retinal image due to the causes just stated ; and frequently an asthenopia, the expres- sion of muscular strain from the necessity of holding work close to the eyes or of mental fatigue in attempting to obtain definite sensations from indistinct impressions. 225. The regular form of astigmatism which is frequently TREATMENT OF IRREGULAR ASTIGMATISM. 189 found associated with these corneal changes must be treated in the manner described in the chapter devoted to that subject. 226. In the treatment of the irregular form the indications are to cause the light to pass through the most regularly curved part of the cornea and to cut off that which passes through the portion which only serves, by its diffusion, to ren- der the image indistinct. 227. One way of accomplishing this is to place a small hole or a narrow slit, I to 2 mm. wide, in an opaque disk such as Bonders used in his first investigation of regular astigma- tism, opposite the most evenly refracting portion of the cor- neal surface. By this means all rays are cut off except those going through the part corresponding to the slit, and this then represents practically the refracting surface of the cornea. We can then proceed to examine this part of the refracting media of the eye in the same way as when the whole cornea is ex- posed, and determine the character and degree ofitsametropia should any be present. In some cases we find a very considerable augmentation of visual power, particularly for near objects by this means, but it is not so applicable to distant vision on account of the nar- rowing of the visual field. And as a matter of my experience, the improvement, after the correction of whatever ametropia (including regular astigmatism) that may be found on a careful examination, that is produced by the addition of the stenopaic apparatus, is not sufficient to justify its employment except in rare cases. 228. Another method is to remove the pupil, either by making an iridectomy or by the operation of iridencleisis,to such a position that it shall lie behind the most regularly curved portion of the cornea. It frequently happens that there is a central opacity of the cornea which covers the pupillary area, and we have a choice of several positions at which to make the artificial pupil. We should, of course, under such circumstances, choose that place where there is least irregularity of corneal curvature. This we are enabled to do by means of the concentric circles or the KERATOCONUS. square. We get reflections successively from the various parts of the surface until one part is found which offers least irregu- larity of outline and make the pupil to lie under that. Such iridectomies as should all iridectomies made for visual pur- poses must be small. 229. KERATOCONUS. The cornea, as a result of inflamma- tory changes in its substance may become very much dis- tended in all directions and assume somewhat the shape of a globe (kerato-globus) ; or it may become bulged out at a cer- tain locality (keratectasia) ; or it may assume the form approx- imating that of a cone (keratoconus). All of these conditions will give rise, of course, to the phenomena of irregular astig- matism. These consequences of inflammation are most com- monly associated with opacities which still further mar the dis- tinctness of the retinal images. But there is one form of keratoconus which is developed in a clear cornea without any changes in the transparency of the tissue. It was known among the earlier writers as " staphy- loma pellucida." There are some reported cases in which the change was probably congenital, but for the most part it is one of gradual development. 230. The precise nature of these changes and the pathology lying at the root of them have not been definitely settled, but there is scarcely any doubt that the tissue of the cornea is thinned at its apex and thickened at its base, and that it is not the result of an inflammation of the substance of the cornea at least in the ordinary acceptance of the term inflammation. It usually commences about the fifteenth year and stops about the twenty-fifth, though it is not always progressive during that period. It occurs with much greater frequency in women than in men. | 231. The first of the more modern writers to describe this condition was Scarpa, in his treatise published in 1802. As a matter of historic interest I quote the case re- corded by him. 1 1 From the French edition translated from the Italian by Foumier-Pescay and Be- gin. Paris. 1821. Tome 2. P. 214. FIRST DESCRIPTION OF KERATOCOMUS. 19! "Not long ago it happened to me to observe a peculiar affection of the cornea, which I am not able to classify unless it be under the heading of staphyloma. In a woman 35 years of age, with naturally prominent eyes, the centers of the two cornese were protruded without any apparent cause, in such a manner that this membrane no longer formed the segment of a regular sphere affixed by its base to the sclerotic, but assum ed exactly the shape of a pointed cone. Viewed laterally the cornea had the appearance of a small transparent funnel applied by its base to the sclerotic. During some movements of the globe the point of the cone seemed somewhat less transpar- ent than the base ; in other movements this effect was not apparent. Yet at the places where this transparency was least, there was sufficient to oppose a remarkable obstacle to vision. On placing the eye directly in front of a window the apex of the cone reflected the light to such an extent that it appeared as a brilliant point ; and as this occurred directly in front of the pupil, already contracted, the woman could only see distinctly in a subdued light which allowed the pupil to dilate sufficiently; when the light was strong she could see only a little, and confusedly." It appears, however that Beer 1 had noticed some condition similar to this, for he says. "There is a kind of staphyloma worthy of remark, which I have seen in more than one case of hydrophthalmia. The cornea in such cases is inconceivably distended, but it does not lose its transparency. The patients, notwithstanding the transpar- ency of the cornea, saw little or none at all." The conical character of such a cornea seems to have escaped his notice. Among the older writers mention is made of the "pellucid cornea" by St. Yves (1722), Manchart (1748), Taylor (1750), who gave it the name "Ochlodes;" Himly (1819), who gave it the name of "Keratosis," and v. Ammon (1831) who called it "Keratoconus.' 2 The first thorough examination of the optical phenomena presented by the coni- cal cornea, I find in Wardrop. 1 The examination was made by Dr. (afterwards Sir David) Brewster, and I add his account of it in full as given in a letter to Mr. Wardrop, (p. 119-20). It is interesting among other things from the fact that it is, perhaps, the first attempt at the em- ployment of keratoscopy in the diagnosis of abnormal curvature of the cornea. "When you first mentioned to me the case of Miss , I was much surprised at the number of images which she observed round luminous objects. As this multipli- cation of images could arise only from some irregularity in the cornea or crystalline lens which gave their surface the form of a polyhedron, it was completely inexplica- ble from the shape of the cornea itself which your drawing represented (Fig. 56) as a regular surface, resembling very much that of a hyperboloid ; for the only indistinct- ness occasioned by a cornea of this kind would arise from the concentration of the rays before they fell upon the retina. When I had the pleasure of examining the eye itself, the difficulty of explanation was in no respect diminished. In every aspect in which the cornea could be viewed its section appeared to be a regular curve, increasing incurvature toward the vertex . a form which could produce no derangement in the refraction ^of the incident rays. 1 Prakt Beobactungen ii. d. grauen Starr u. d Krankheit. d. Hornhaut. Wien. 1791 2 Essays on the Morbid Anatomy of the Human Eye. Edinburgh. 1808. FIRST ATTEMPT AT KERATOSCOPY. As the disease was evidently seated in the cornea, which projected to an unnatw ' distance, it did not seem probable that there was any defect in the structure of the crystalline lens. I was therefore led to believe that the broken and indistinct images which appeared to encircle luminous objects arose from some eminences in 'he cornea which could not be detected by a lateral view of the eye, but which might be rendered visible by the changes which they produced upon the image of a luminous object that was made to traverse the surface of the cornea. I, therefore, held a candle at the distance of fifteen inches from the cornea, and keeping my eye in the direction of the reflected rays, I observed the variations in the size and form of the image of the candle. The reflected image regularly decreased when it passed over the most con- vex parts of the cornea ; but when it came to the part nearest the nose, it alternately expanded and contracted and suffered such derangements as to indicate the presence of a number of spherical eminences and depressions which sufficiently accounted for the broken and multiple images of luminous objects." A LATERAL VIEW OF A CONICAL CORNEA. (WARDROP). 232. The diagnosis of this condition is oftentimes a matter of no difficulty, a simple inspection of the cornea in profile be- ing sufficient to show the conicity quite plainly. There is also very frequently a bright reflex at the corneal apex as if a tear had fastened itself there. This, however, is in the higher forms of the anomaly. In the lower developments these gross changes are not so apparent, and we must then resort to other methods of examination, when keratoconus is suspected. 233. For this purpose there is nothing better than a careful and systematic examination by means of the keratoscope. In this way we get, through the changes in the form of the reflec- tion figures at various localities, a very good idea of the general form of the surface, as well as of the changes at particular por- tions. The figures are small at the apex and generally in- crease in size as they approach the periphery. It occasionally happens that this increase is very regular, showing how nearly perfect the cone is. The following is an illustration of this : OPHTHALMOSCOPIC CHANGES IN KERATOCONUS. 193 CASE I. It is the case of Mrs. R. a part of whose history relating to regular as- tigmatism was given in Chap. XI, \ 175. She reports that up to her sixteenth year she saw well. At that time her vision began to fail and gradually got worse till her nineteenth year, since which time it has remained about as it is now. On October 6, 1884, the time of my first examination, V = 2 - 5 / 60 . With 6s she saw with either eye No. 60 at 4 meters ; no other spherical glasses giving further improvement. As is my habit, I then made an ophthalmoscopic examination before trying cylindrical glasses, since I often obtain thereby important indications as to the directions of the meridi- ans, the form of the astigmatism, etc., which will materially shorten the examination and add to its accuracy. 57- DISK AND LARGE RETINAL VESSELS AS SEEN IN KERATOCONUS, WHEN EXAMINED BY THE DIRECT OPHTHALMOSCOPIC METHOD. I at once found that I liad to do with a case of keratoconus. Even in the inverted image it was not possible to see all parts of the disk clearly at once, and when the auxiliary lens was moved from side to side there was that paralactic movement of the vessels which is characteristic of keratoconus when this method of examination is used. When the light from a plane mirror was thrown into the eyes from a distance, as in examination by skiascopy, the peculiar unstable shadow crescent of conical cornea was beautifully shown. Examination by the direct method was in the high- est degree unsatisfactory. At no time and with no lens was it possible to get more than a small portion of two or three vessels in focus at once, and the slightest move- ment of the eye of the patient or of the ophthalmoscopic mirror would throw these out of view and bring others forward. Some idea of the peculiar distortion of the vessels may be obtained from Fig. 57, which represents diagrammatically the disk of the R eye and its immediate neighborhood as seen with a + 4 behind the ophthal- moscopic mirror. The black lines represent the parts of the vessels seen with dis- tinctness, the shaded portions the parts that were out of focus. 194 KERATOSCOPIC APPEARANCES IN KERATQCONUS. The radius of curvature of the cornea was measured by the keratometer in various meridians and in different parts of the same meridian. The most nearly regular por- tion was found, not directly in the line of vision, but about 5 outward in each eye. At this place in L 180 r $"* (^/ t D), 90 r = 6 mm (34 D) ; in R 180 r = 6 s / mm (30 D), 90 r = sVj mm (36 D). But even in these meridians there was a great change in the figures as soon as the place of measurement was removed a few degrees from this point The shape of the bands became very much distorted and it was impossible to take accurate measurements. It was apparent, however, that the corneal surface became flatter as it approached the periphery. This distortion began much sooner on the outer side in both eyes. I measured in L the meridian 2)ou-n. KERATOSCOPIC IMAGES AT VARIOUS PARTS OF A CONICAL CORNEA. at 180, 20 inward and outward from the apex, and found r inward = 7.5 mm ,outward 8 mm . The distortion was also greater in the upper than in the lower portion of the cornea. An examination with the concentric rings revealed an approach to regularity of curve which I do not believe is commonly met with in keratoconus. Fig. 58 shows the form of Placido's disk at the center, and at 20 upward, downward, inward and outward. It will be seen how pear-shaped it becomes when reflected from the sides of the cone, indicating a gradual flattening towards the base. The similarity in the shape of the four lateral reflections shows an approximation to uniformity in curva- ture at corresponding distances from the apex, resembling, somewhat, an ellipsoid of revolution, though we know from measurements that it is compressed laterally. The apex itself, however, offers a very considerable amount of irregularity. 234. Such regularity is quite exceptional, the majority of cases being more like the following: KERATOSCOPIC APPEARANCES IN KERATOCONUS. 195 CASE II. Miss L., set. 19, says she had fairly good vision up to three years ago. Since that time it has gradually deteriorated until now she can barely count fingers at 3 meters. In Fig. 59 are shown enlarged views of the reflections of Placido's disk from the corneal apex of both eyes. The image became larger as it approached the periphery in all directions, showing an increased radius of curvature. Not having a keratometer at command at that time no measurements of radii were taken. The reflection figures of Wecker's square are shown below those of the circles in Fig. 59. 59- KERATOSCOPIC IMAGES IN CONICAL CORNEA. The irregularity of these is in stril jng contrast to the uniformity of the disk in th case of keratoconus just described. No glasses improved distant vision. With the unaided eye she could read, L, No. 5 of Wecker's scale, and R, No. 7, at 6 to 8 inches. When a diaphragm, having a hole I mm. in diameter was placed before the eye, she could read, L No. I, R, No. 4, of the same scale at the same distance. Dis- tant vision was not materially improved through this stenopaic hole. 235. There are other methods of diagnosis, which, though less accurate than keratoscopy, are nevertheless of value and bring out very characteristic appearances. Among these the ophthalmoscope ranks first. When light is thrown into the eye with the mirror, as in examination by skiascopy, the center of the pupillary area appears bright, with an ill-defined dark ring or crescent separating it from the periphery, which is also bright, but usually less so than the cen- ter. This dark ring or cresent is not fixed, but very vacillat- 196 OPHTHLMOSCOPIC APPEARANCES IN KERATOCONUS. ing, moving with each change in the position of the eye or mirror. In the majority of cases, when the mirror is at a proper distance from the eye, an inverted image of a part of the fundus can be seen without the aid of an auxiliary lens, through the central part of the cornea. This image, which may often not be more than a portion of a single retinal vessel, moves in the same direction as the mirror and nearly always changes its shape with a change of its position. All these phenomena are due to the optic'al properties of the corneal cone. The central part, on account of its excessive curvature, is strongly myopic and concentrates the rays coming from the illuminated fundus at its far pojnt some inches in front of the eye, making a brilliantly illuminated area, together with an inverted image of the objects lying in that part of the fundus. Those rays which fall on the sides of the cone at a certain angle suffer total reflection, rendering this portion of the ophthalmoscopic field much darker in comparison with the central area. Those rays falling on the more peripheral and flatter parts of the cornea pass through, but, being more scat- tered than the central ones fewer of them reach the eye of the observer; hence this circumferential portion of the field is less brilliant than the central. Examination by the direct ophthalmoscopic method fur- nishes equally characteristic phenomena. It is impossible to get a clear and distinct view of all the parts in the entire ophthalmoscopic field at once. A vessel, for instance, will ap- pear with sharply-defined outlines at a certain part and then suddenly become blurred and thrown out of its course. The outline of the disk is not distinct in all its parts, and the ap- parent curvings and twistings of vessels are often quite fantas- tic ; the whole presenting an appearance which might easily be mistaken by a novice for a pathological condition. Fig. 57 is intended to give some idea of how the fundus ap- pears under these conditions. The most marked phenomenon, however, in connection with these appearances is its change- ableness. The slightest movement of the head or mirror throws some parts clearly in view out of the focus, and brings others, hitherto obscure, forwards. OPHTHAMOSCOPIC APPEARANCES IN KERATOCONUS. ip/ There are also appearances peculiar to this form of irregular refraction when the examination is made by the indirect method. Even when the inverted image is clear and distinct throughout, there are differences in the paralactic movements of the different parts which make the diagnosis certain. If the refracting media are symmetrical in their refraction as a whole, when the auxiliary lens is moved in any direction perpendicu- lar to the line of vision, the image moves with it as a whole, because all parts of the image are formed on the same plane ; but if there is such irregularity in refraction that parts of the image will be formed in several different planes, movements of the lens will be accompanied by unequal movements of these separate parts of the image, some moving much more rapidly than others. And in keratoconus where the different parts of the cornea have different refractions these parallax motions are sometimes very striking. 236. The subjective symptoms of keratoconus do not differ in any essential particulars from those of the other forms of irregular astigmatism. Vision is always impaired, and dis- tant V is much worse in comparison than near, and occasion- ally there is a complaint of polyopia monocularis. Metamor- phopsia or a distortion of images is also a not infrequent ac- companiment. 237. Treatment of Keratoconus. Keratoconus may be treated optically or by operation. The strictly optical treatment has not until quite recently found favor with the profession. Bonders gives in his treatise no suggestion of glasses, and the only mention Mauthner makes of them is to express an opinion of the worthlessness in general of cylindrical lenses in this class of cases. The stenopalc slit or hole was the only means, other than op- erative, which it was thought worth while to employ for the improvement of vision. This apparatus, by excluding all the rays except those going through a limited portion of the cor- nea cuts off a large amount of diffused light that is very de- structive to the distinctness of the retinal image. These patients 198 OPTICAL TREATMENT OF KERATOCONUS. almost universally, by instinct, make use of such an apparatus by narrowing the palpebral aperture. It is not always a matter of indifference over what part of the cornea the slit or hole lies, and it should be placed successively in different positions until that one is found in which vision is clearest; and it not infrequently happens that the addition of a spherical or cylin- drical glass contributes still further to the distinctness of the image. The advantage of the stenopaic apparatus is confined almost entirely to near vision, and this is often very markedly improved. It is seldom usetul for distant vision on account of the diminished illumination and the restriction of the visual field. 238. But a great improvement in vision can be effected in a large number of cases by means of spherical or cylindrical glasses alone. There are few cases in which there is not a greater or less amount of regular astigmatism; and in some instances the benefit derived from a correction of this by cylindrical glasses is very great as shown in the case reported in 175. The chief obstacle that has hitherto lain in the way of a more general employment of cylinders in such cases is doubtless the great difficulty usually experienced in unravelling the optical complexities inherent in the con jition. Few surgeons have the time or patience to work out the problem with lenses and test objects alone where there is so high a degree of amblyopia. The ophthalmoscope offers little or no assistance in the task. It is here that keratometry and keratoscopy find one of the fields for their most satisfactory application. A simple inspec- tion of the corneal reflection of the concentric rings is suffi- cient to give us the direction of the principal meridians, and if a keratometer is at hand, it is easy to find the difference in the refraction of these two meridians, expressed in dioptries, data which will render the further determination of the refraction of the eye comparatively easy. 239. We have seen in 1 86 et seq how cylindrical lenses fail to give complete correction to the corneal ellipsoid in reg- ular astigmatism. It is apparent that they will be much less effective in correcting the paraboloid curve in keratoconus. HYPERBOLIC LENSES IN KERATOCONUS. 19 ) Such a surface can be neutralized only by a lens which ap- proaches to a hyperbola in form. 240. Rahlmann, of Dorpat, was the first to use such lenses for the correction of conical cornea. At the meeting of the Hei- delbergCongress of Ophthalmologists in 1879 he exhibited these lenses for the first time with the report of a case in which they had been successfully applied. The best V to be obtained by concave spherical and cylindrical glasses was 1 / 10 5 with the hyperbolic lenses it advanced to l / 2 . Since then the subject has been further worked up by Rahlmann himself, and several others, and the advantage of such lenses now seems estab- lished beyond question. All cases, however, are not benefited in the same degree, and some are not benefited at all. Up to this time their selection has been somewhat empirical, but since we have now a ready means for measuring the corneal curvature at its various parts, it seems possible that we may be able to determine the proper correcting lens with greater scientific exactness. The principal difficulty at first will be in having the glasses manufactured with the curve found neces- sary by the measurements, but if further experience demon- strates the promising usefulness of these lenses, optical art will, as it has always done, keep abreast with the demands made upon it. Rahlmann employs two series of hyperbolic lenses, which differ from each other in the length of the hyperbola axis. Series "A " has an axis of l ji mm. .series "B" an axis of 2 mm. The different members of each series are numbered according to the size of the assymptote angle. The larger this angle is the less the surface is curved, and the weaker the refracting power and vice versa. When the assymptote cone with a base of 30 mm. has a height of I mm. (the height depending on the size of the assymptote angle) it is No, I ; when it has a length of 2 mm., with a smaller assymptole angle, it is No. 2, and so on. The members in series " A " having a shorter axis to begin with are much stronger than those in series " B " and are more pointed, and consequently better adapted to the sharper corneal cones. Angelucci has foun,d great advan- 2OO OPERATIVE TREATMENT OF KERATOCOUS. tage from a combination of these lenses with cylinders in the correction of keratoconus. 241. The operative treatment of keratoconus is of two kinds. One has for its object a change in the shape or position of the pupil ; the other aims at a reduction in the curvature of the cone. The operations on the pupil consist either in making an iridectomy (as small as possible) under the most regularly curved portion of the cornea or in removing the pupil by the operation of iridesis, as first done by Critchett, to the same desirable local- ity. This last operation leaves a slit-like pupil which offers the same advantages as a stenopaic apparatus. Bowman mod- ified it by making the operation at opposite sides (double iridesis) causing the slit to extend all the way across the width of the iris. This is, however, a questionable improve- ment, and is probably not now performed by any one. 242. It has also been thought by some that the performance of an iridectomy has stopped the progress of the corneal change during the period of its development. Others have noted an arrest of the process under the local use of atropine and of eserine. 243. The treatment of the cone itself is addressed to a flattening of its apex and a reduction of its curvature. This is accomplished by a removal of the top of the cone by opera- tion and the subsequent cicatrization of the wound. The cic- atrization is aided sometimes by caustic applications. Special forms of trephine have been been devised by Bowman and Wecker to remove a small circular piece from the corneal apex. For the manner of performing these operations and a description of the special instruments used, the reader must be referred to the chapter on operations in the text-books of ophthalmology and the various articles on the subject whose titles are to be found in the appended bibliography. It must be said, however, in regard to all these operative procedures that the opening of the anterior chamber to such an extent, is, at least, a hazardous undertaking, involving as it does the in- tegrity of both cornea and lens, and should never be under- taken until all optical means have failed. BIBLIOGRAPHY. Abadie, C. Trouble de la refract, du a un astig. irreg. de la corn6e efsimulant de 1'hemeralopie. J. d'Ophth. I. Pp. 21-3 Paris. 1872. Adams, J. E. Uniocul. diplopia. (Oph. Soc. of G. Br. 1882). Brit. Med. Jr. Pp- 667. Oct. 22. 1881. v. Ammon Hyperkeratosis, s. Ochlodes. .v. Ammon's Ztrschr. f. Ophth. B. I. P. 122. 1830. v. Ammon Neue patholog-anatom. Untersuch. einer Cornea conic. Deutsche Klinik. No. 45. P. 483. 1851. Angelucci, A. Contrib. all applicaz. delle lenti iperbolic. Quad. Stat e fram di Optalm. 1882. Angelucci, A. Richerche ottalmomet. per determin. lo astig. irreg. delle cornea coniche. An. di Ottalm. XII. P. 48. Pavia. 1883. Angelucci, A. Sulla refraz. e correzione delle cornee coniche ed ectatiche- Pavia. 1884. Also in An. di Ottal. XIII. I. 1884. Bader Treat, of con. cornea by removal of the top of the cornea. Lancet, I. P. 73- 1872. Benaky, N. P. Du Keratocone et de sa correct, par les verres coniques. Paris. 1881. Burnett, Swan M. Ophthalmometry with the ophthalmometre of Javal and Schiotz, with an account of a case of keratoconus. Archives of Oph. XIV. Pp. 169-176. Bowman Operative treat, of conic, cornea. Ophth. Hos. Rep. Oct 1859. Bowman Treat, of Keratoconus. Ophth. Hosp. Rep. 1872. Cappelletti Anatom. path. Untersuch. einer Corn, conica. Wien. Med. Wochen- schr. P. 14. 1852. Carter, D. B. On conic, cornea. Lancet. Feb. 6., Mch, 13. 1869. Chelius, Fr. Ueber das Staphyloma d. Hornhaut. Heidelberg. 1847. Chelius Zur Lehre v. d. Staphylomen d. Auges. Heidelberg. 1858. Cooper Conical cornea. Lond. Med. Jr. May, June. 1850. Critchett, G. Artific. pupil in keratoconus. Brit. Med. Jr. Mch. 31. 1860. Daguillon Contribution a Petude du staphylome pellucide conique de la cornee. Bull. clin. nat. oph. de 1'hop. de Quinze-Vingts. Paris. 1885. III. 60-68. Dor, H. Trait, du keratoconus (staphyl. coniq. pelluc.) par Pemploi des verres coniq. Lyon Med. XXXVI. Pp. 271-4. 1881. Fano Staphylome transpar. spheriq. de la cornee. Gaz. des Hep. P. 39. 1861. Fernandez, I. S. Astig. regl. a consequen. de un estafilom. esperic. ti anspar. de ambas corn, y al parecer debido a un gerontoxon. Anfiteatro anat I. P. 139- Madrid. 1873. (201) 2O2 BIBLIOGRAPHY. Fevre Basile Du keratocone et en partic. de son trait. These No. 146. P. 46* Paris. 1879. Frank Case of partial keratoconus with a remark, change in the refract, following an injury. Maryld. Med. Jr. Sept 1883. Giraud-Teulon Causes et mecanis. de certains phenom. polyop. monoc. Compt rend. T. LIX. Pp. 904-6. 1862. Graefe, A. von. Zwei FSlle v. Kerectasien. Arch. f. Ophth. I. P. 251. 1854. Graefe, A. von. Ueber Iridect bei Keratcon. Arch. f. Oph. IV-II. P. 271. 1858. Graefe, A von. Zur Heilung d. Keratocon. Arch. f. Oph. XII-II. P. 215. 1866. Graefe, A. von. Ueber Keratcon. Berl. kin. Wchnschr. No. 23. 1868. Gut, J. Ueber Diplop. monophthalmic. Zurich. 1854. Also in Henle u. Pfleu- gers Zeitschr. IV. Pp. 395-460. 1854. Hay, G. Two cases in which Raehlmann's hyperbol. lens improved vision. Trans. Amer. Ophth. Soc. 1884. Heyfelder Keratoconus. Ammons Ztschr. f. Ophth. IV. P. 189. Himly Zusammengestell. Beobachtg. iiber das Staphyl. conic. Himlys Biblioth* i. Ophth. I -2. P. 345. 1816. Higgins, C Two cases of conic, cornea treated by remov. of the apex of the cone. Brit Md. Jr. I. P. 623. London. 1880. Higgins, C. On eight cases of conic, cornea treated by elliptic, excis. of apex. Ophth. Hosp, Rep. Pp. 316-21. London. 1882. Hirschberg, J Zur Pathol. d. Keratocon. pellucid. Centrbl. f. prak. Augenhlk. Jan. 1885. Horner Zur Behand. d. Keratocon. Zehender klin. Monatsbl. VII. P. 49. 1869. Hulke Two cases of conic, cornea treated by iridodesis. Ophth. Hosp. Rep. No. 4. P. 338. 1862. Jaeger Untersuch. zweier mit Hyperkeratosis behaft Augen. Ammons Ztschr. L Ophth. I. P. 544. 1830. Jago, James. Entoptics with its uses in PhysioL and Medicine. ChurchilL London- 1860. Javal Trois. contrib. a 1'ophthalmometrie, descript de quelques imag. keratoscop. An. d'Ocul. LXXXIX. Jan. lev. 1883. Jones, Wharton Cornea conic. Med. Times and Gaz. No. 21. P. 389. 1857. Knapp, H. Coloring of the shining reflex at the edge ol lenses disloc. in the antr chamber ; a nice clin. expr. Arch, of Ophth. X. P. 456. Knapp Ueber die Diag. d. irreg. Astig. Klin. Monatsbl. f. Augenhlk. II. Pp. 304-16. 1864. Kuchler Eine neue operat. Methode der sammt. wahren Hornhaut Staphylom nebst Untersuch. ueberdie Form u. Bildungsweise dieser Staphylom. Braunschweig- Lawson Two cases of keratocon. with success, operat Lancet Sept 1860. Lyall De Staphylom. pellucid, conic. Diss. Petrop. 1816. Mandelstamm, L. Ein Fall v. monocul. doppelt u. binocul. Vierfachsehen. Cen- tralbl. f. prakt. Augenhlk. Juni. 1882. Marheinecke De Keratocone. Inaug. Dis. Berlin. 1863. Martin, A. De Keratoc6ne. Mouvement Med. XVI. Pp. 371-3. Paris. 1878. BIBLIOGRAPHY. 2O3 Masselon Fragts. d'ophth.-operat. du keratoc6ne- An. d'Oculist. T. LXXI. P. 121. 1874. Mauthner Ueber Keratoconus. Anzeig. d. k. k. Ges. d. Aerztein Wien. 4 April. 1873- Mohr, Ad. Noch einmal"Das Eserine." Groefes Archiv. XXIII. 2. P. 161-212. Nottingham Practic. obsvrs. of conic, cornea and on the short sight and ether defects of vis. connected with it. London. 1854. Noyes, H. D. The optic error of conic, cornea, (2 cases of operat.) Fifth Internat. Ophth. Cong. P. 72. 1876. Pickford Staphyloma cornea pellucid. Dublin Jrl.. January. 1844. Placido Cristallocon. polaire anter. Period de Oftalm. Lesbon. 1881. Raehlmann, E. Ueber die optische Wirk. der hyperbol. Linsen. bei Keratocon. u. unregelmass. Astig., sowie iiber die Anwend. derselb. als Brillen. Zehenders Monatsbl. XX. P.m. Raehlmann Glaesercorrect. bei Keratoconus. Bericht d. Ophth. Gesellsch. zu Heidelberg. P. 50. 1879. Raehlmann Hyperbol. Linsen. Klin. Monatsbl. f. Augenhlk. P. 303. 1880. Raehlmann Zur Frage die Correct, des Keratocon. durch Glaeser. Berl. klin. Wochenschr. XVII. P. 484. 1880. Rampoldi, R. Contrib. alia storia clinic, del cheratocono. An. di Ott. XII. Fas. 364. Rampoldi, R. Sulla ge'nesie del cheratocono. Annal. di Ott Anno XIV. Fasc. 4. 1885. P. 286. Renton, J. C. Case of conic, cornea ; trephining ; vision impd. Lancet. I. Pp. 7-8. 1880. Reuss Ophthalmomtr. Messung. bei Keratocon. Wien Med. Presse. 1873. Scarpa Saggio de osservaz. e d'esperienze sulle principali malatti degli occhi. P. 215. Pavia. 1801. Schmidt Diss. ueber hyperkeratosis. Erlangen. 1830. Schoeler Ueber hyperbol. Brillenglaeser zur Correct, d. Keratoconus. Berl. klin. Wochenschr. P. 377. 1880. Secondi, R. The operat. for Keratocon. Trans. Internat. Ophth. Cong. London. 1872. Sichel Abhand ueber die Entsteh. u. Behand. d. Staphylom. pelluc. conic, d. Hornhaut. mit einig. Bemerk. ueber die Staphylom. ueberhaupt. Walter u. Ammons. Jourl. B. in. H. I. 1843. Steinheim Ueber Keratoconus u. seine Behand. Arch. f. Aug. u. Ohrenhlk. TI. P. 212. 1871. Steinheim Zur Behand. d. Keratocon. mit eserin. Arch. f. Augenhlk. IX. Pp. 253-6. Wiesb. 1880. Stilling, J. Sphaeroid. Glaeser gegen Astig. Centralbl. f. prakt. Augenhlk. P. 273. 1880. Thomson, Wm. Three cases of conic, cornea correct, by suitable glasses. Trans. Amer. Ophth. Soc. 1874. Tweedy, Jno. On a visible stellat. of the normal and of the cataract crystal, lens of the human eye. R. L. Ophth. Hosp. Rep. VIII. P. 24. Walker Principls. of Ophth. Surgery. London. 1834. Walton Conical cornea. Brit. Med. Jour. June 20. 1863. 2O4 BIBLIOGRAPHY. Walther Beobacht. einer cornea conic, im chirurg. ophthalm. Klinicum zu Miinchen. Walther u. Ammons Jr. f. Chirurg. V. P. I. 1846. Webster, D. Ein Fall. v. Lenticonus. Arch. f. Aug. u. Ohrenhlk. IV. 2. Pp. 262-4. 1875. Weiss, L. Polyop. monoc. an einem Auge dessen Hornhaut abnorm gekriimmt ist (ein dem Keratocon. entgegen gesetztes Verhalten zeigt) Arch. f. Ophth. XXI- 2. Pp 187204. 1875. White-Cooper, W. On conical cornea. 8 London. 1850. \Vimmer De Hyperkeratosis. Lipsiae. 1831. Weber, Adolph Ueber Calabar und seine therapeutische Verwendung. Graefe's Archiv. XXII. 4. 224. Wimmer Drei neue Falle von sogenannten Hyperkeratosis. Ammons Ztschr. f. Ophth. II. P. 439. 1832. Wecker et Masselon L'arc keratoscop. son emploi comme keratoconometre, pu- pillometre ct strabometre. Rev. clin. d'Oculist. No. 9. P 201. 1884. Window, W. H Pseudoconical cornea. Hahnemann Monthly. II. Pp. 661-5. Phila. 1880. Withington, J. B. Double conical cornea, occurring during pregnancy; excision. Lancet I. P. 878. 1880. St. Yves, Carl De nouveau traite des maladies des yeux. Paris. 1722. NOTE TO SECTION 196 Pp. 170-171. Since the text of this work has been put in type, I have made a series of experi- ments which render intelligible some of the peculiar optical properties of spherical lenses when held obliquely to incident pencils of light. I used in these investiga- tions a Snellen's phakometer, where the sources of the pencils are seveial small holes near the periphery and at Ihe center of a disk 2.5 cm. in diameter, through which light, whose rays have been rendered parallel, passes. The lens to be examined is placed in the path of these rays, and turned on its vertical axis and its focus found by means of the image of these holes on a movable screen, for various degrees of in- clination. The investigations of Pickering and Williams have already shown the cyl- indrical action thus acquired by a spherical lens (see Table II, page 34), but their measurements only give the results of the rays passing through the central portion of the lens. My experiments were directed to finding if there was also a difference in the focus of the rays refracted by the edge of the lens nearest the object and that corresponding to the edge farthest removed from it. This I found to be the case and the amount of the difference was very decided for even medium angles of inclina- tion. / found that the cylindrical focal plane of a spherical lens placed obliquely to the incident pencils, lies obliquely to the optical axis, aud in a sense contrary to the inclination of the lens. In Table VII are given the foci of a spherical lens of +iD for every 5 of inclina- tion up to 45, beyond which accurate results cannot be obtained on account of the general diffusion of light. In the second column is given the increase of the gen- eral spherical refraction, and in the other two columns the foci expressed in dioptrics and decimals, at the side of the lens nearest the object (being the image of the hole on the opposite side) (F) and at the side farthest from it (F 1 ), the last, of course* being the image of the hole on the side of the lens nearest the object- NOTE. TABLE VII. 2O5 Degrees of Inclina- tion. Spherical Action. F. F.i 5 o Slight. Slight. 10 i.i i. 20 1.25 15 1.2 1.30 i-5 20 1.25 i-57 i-75 25 1.30 1-7 2.2 30 1.4 2.6 3- 40 1.6 3-6 5-i 45 i-75 5-2 6.8 I also experimented with other lenses, but will only add the results with a lens of +8 D., giving the focus at the center of the lens(F) in addition to the two at the periphery. Degrees of In- clination. Spherical Action. F. F. /?. 10 8.1 8-3 8.4 8-5 20 8.2 8.7 9- 9-5 30 8-5 10. 10.5 "3 40 9- 13-5 15- 17- The superiority of obliquely placed spherical to the ordinary cylindrical lenses, in some cases of cataract extraclion, is probably due to the correction of a difference in the refraction in the different parts of the same meridian, (generally the vertical, since the incision is always made above or below) by this len's whose refraction gradually increases from one extreme of a corresponding meredian to the other. In other words, it corrects a certain amount of irregular astigmatism resulting from the corneal wound. Keratometric measurements, in these cases of cataract extraction, at various points on this meridian should enable us to measure exactly the amount and character of this form of irregular astigmatism and furnish data for correction of the defect, either by a lens inclined to a certain degree, or a lens ground in such a manner as to give the same optical effect. I will also state, in this connection, that I found the same results as to character and degree when a cylinder was rotated on its axis. The cylindrical action as a whole was increased, thus confirming the views of Hay, and opposing those of Sous (see \ 26, pp. 34 and 35), butt here was also the same inclination of the focal plane as was found in the obliquely placed spherical lens. APPENDIX. A STATISTICAL RECORD OF 806 ASTIGMATIC EYES. I have collected in the following table the data furnished by 475 cases taken in the order in which they were recorded in my private case-book during the last five years, and which, I hope, may be of some value to the future student of astigmatism- These 475 persons had 806 astigmatic eyes, showing that in about $\% of the cases the anomaly was unilateral. In 291 of the eyes affected with all degrees of astigmatism the visual acuteness was brought, by correction, up to the normal standard of 4 /4 being about 36$. This is a better showing than that alluded to on page 168 where in 2,000 cases there was normal vision in only 10%. This computation was made principally from Snellen's and Van Haaften's statistics, and the difference between the two is probably due to the fact that I have corrected the lower degrees more frequently than they. My clientele is drawn largely from the clerical force in the various .departments at the National Capital, where the work is of such a nature as to cause small errors in re- fraction to be felt, particularly by women. To this latter fact is due the preponderence of women in my tables, there being 276 of them to 199 men. In the higher forms it will be seen on a consultation of the tables a normal visual acuteness is rarely found. In 504 of the 806 eyes the principal meridians were ver- tical and horizontal. The relative frequency of the various forms was as follows: Simple myopic astigmatism ----- 294 or yj-%. Compound myopic astigmatism ----- 162 or 20.^. . Simple hypermetropic astigmatism - 210 or 26.%. Compound hypermetropic astigmatism - - - 113 or 14. %. Mixed astigmatism - - - - - - - 27 or 3-Jfc. Total 806 100. (206) APPENDIX. 2O7 A STATISTICAL RECORD OF 806 ASTIGMATIC EYES. Num- ber. Name. Sex and Age. Correcting glasses and direction of axis of cylinder. '^ision after correction. I 3. F. M. VI., 40. L.-H/36 90- R.+VS6 90. 20 /20 M /20 2 :. M. M.,36- ^.+0.5 90. R. +0.25 90. % 3 R. D. D. M.-26. -H/ 90' ;/s 4 V. Me. F., 17. L. 1/30 1 80. R. 1/30 180. 4 /6 5 A. Me. F., 38. L. 1/30 180. R. 1/30 1 80. 4/ /6 6 H. H. H. F., 20. L. Em. R. 1/40 1 80. 4 /6 7 R. M. M., 23. L. 2.25 ;3 0.75 90. R. 2.25 C; 0-75 ^o - 4 A 8 M. S. F. F.,40. L. 1/40 1 80. R. 1/40 1 80. V* 9 E. T. F. F., u. L. Vio 1 80. R. 1/ 10 180. ;/9 10 C. M. M., 38. L 1/60 10. R. i/eo 170. % ii G. K. M., 24. L.+O.S 90. R.+o.s 90. J/4 12 S. W. B. M., 26. L. 0.75 1 80. R. 0.75 1 80. J/4 13 E. P. F., 10. L. i C 0.25 180. R. 2 C o-5 1 80. 4 /5 14 G. R. F., 42. L.+0.7S 140. R.+i-S 20. 4 /6 15 H. M. F., 14. L. 5 C 1-5 20. R- 5 C i-5 130. 4 /6 4 /6 16 A. C. F., 21. L.+2.25 90 C 3-5 1 80. R-+3-590C 1-75 180. 4 /6 4 /6 17 H. D. B. M.,2;. L 7 C r -75 r 5 - R. 7C 1 -75 160- 4 /6 4 /6 18 J. L. E. M.,3o. L.+2.5 90. R. Em. Vl2 208 STATISTICAL RECORD. Num- ber. Name. Sex and Age. Correcting glasses and direction of axis of cylinder. Vision after correction. '9 J. W. H. F.,49- L.+O.S 70. R. -t-o-s 120. */ V* 20 L. G. F., 12, L-+0-75 C 0.5 90. R-+0-75 C 0.5 90. V V 21 W. L. M., 14. L.+6 C 4-1.5 180. R.+6C+i-5i8o- 4 /5 v 22 L.B. H. M., 35- L. a75 70. R. 0.75 120. 4 / V* 23 0. D. W. M., 25. L.+0.75 90. R.-f-as 90. */4 V* 24 M. E. F.,24. L.40-5 90. R.+0-5 90- Vi V* 25 H. H. M. M.,34. L.+O.S 90. R.+0.5 90. 4 /4 V* 26 L.E. B. M., 28. L. 0.75 180. R. 0.5 180. */4 V* 2? E.W. N. F.,39- L. i C 2 ^S - R.+I 90. 4 /4 4 /4 28 T. A. F., 45. L. Em. R.+0.25 i8c. */ 29 H. A. H. F.,54. L. i 180 C + 2.5 90. R-+I-5 C +i 9- 4 / 4 /6 30 I. M. C. F., 22. L.+0-5 90. R.-|-o.5 90. 4 /4 V* 31 A. C. F., 45- L. 0.5 1 80. K. 0.5 1 80. 4 /4 4 /4 32 T. E. M. M., 25. L. 0.5 C 0.5 1 80. R. Amblyopic. 4 /4 33 A. M. M. M.,34. L. 0.5 1 80. R. 0.5 180. 4 /4 4 /4 34 B. D. F.,20. L. Amblyopic. R. 6 180. V. 35 S. F. T. M.,30. L. 6 C i 1 80. R. 3 C i 140*. 4 /4 4 / 36 T. T. M., 41. L.Em. R. i 1 80. */6 37 M. G. F., 18. L, 8. R. SO i 8o. 4 /6 4 /6 APPENDIX. 2O9 Num- ber. Name. Sex and Age. Correcting Glasses and direction of axis of cvlinder. Vision afli'- correction. \ 38 C. E. M., 46. L. E. R.+0-75 1 80. 4 / '/ 39 A. C. F., 64 M-i.75' R.+0.75 9,. */18 4 /!8 4? j. r. A.. M., 22. i- 4 '^ i-5 15". R- 5 C 1-75 5- '/ */5 4i C. C. N. F., 36. L-f 2 C + 2 9- R.+0.75 S. V 9 4 /9 42 O. DeF. M., 50. L.+0.75- R.+ I C +0.5 1 80. 4 /5 -"/ 43 E. H. F., 18. L. 0.5 1 8. R. 0.5 180. V* */ 44 J.R M., 33. L. 4 C i 1 80 R5- V* 4 /* 45 J. N. P. M., 46. L. 0.5 90. R. Em. 4 /4 '/ 46 C. H. B.. M., 58. L- 0-75 C 0-75 95- R. 0.5 C -5 9- 4 /5 4 /5 47 N. G. D. F., 30. L. 7 C i 90- R.-3-5- . 4 /18 4 /5 . 48 E. H. M., 50. L- 3.5 C 0-75 I 8o. R--3-5- <4 /12 4 /12 49 S. H. P. M., 35. L. 8 ^ i 180. R. 8C '-5 1 80. 4 /18 Vl6 50 M. W. F., 17. L. 2 C' -5 l8o - R. 2 C 0.5 70. 4 /4 4 /4 5 1 E. W. F., 50. L. 0.5 1 80. R. 0.5 1 80. 4 /4 4 /4 52 C. H. W. M., 21. L. 0.5. R-+I-5 C +i 9- 4 /4 Vl8 53 J. A. W. F., 38. L. 0.75 180. R. 0.5 1 80. 4 /4 4 /4 54 J. T. W. M., 40. L. 1.5 20 C + 2 -75 IIO - R. Em. 4 /6 4 /6 55 H. J. H. F., 36. L.+0-5 1 80. R.+I-75- :;;. 56 E. D. F., 38- L.+0-75 90 C 0-75 l8o - R-+0-75 90 C -75 180. % 210 STATISTICAL RECORD. Num- ber. Name. Sex and Age. Corteeting Glasses and direction of axis of cylinder. Vision after correction. 57 W. H. M., 31- L.7 C 2 1 80. R.-7C-I 1*0. 4 ll 58 C. H. F., 28. L.+I 1 80. k+i.25 10. /! 59 L.G. B. F.,48. L. j 180 0+0.7590. R i i.So J . 4 /s 4 /5 60 C E. F.,40. L.-fas 90 O -5 '80. R 075 180^. ;/* 61 M. D. F., 25. L. i 560. R. 1.5 120. v! 62 M. B. F., 14- L.+0-5 14... R.+a5 140. 4 /l 63 R.A.M. M..2& L.+I.25C+' '80. R.+2. 5 . 4 /5 4 /5 * II. \V. B. M., 31. L-+3-5C+' 90. R. Em. V. V 65 CS. E. M., 36- L. 2 1 80 C +0-75 90. R.-2. 5 . % 66 E.B.J. F.,40. L.+0-5 90 C 0.5 180. k. 0.5 90. J/l 6 7 G. H. M., u. i_ 0.75 180. R. as iSo. */; 68 J. W. H. F., 35- k. a$ 90. 4 /5 69 C.S.B. M., 36. L.+0-75 90. R.+O-S 90. :8 128 S. C. M., 42. L 3 C l 9- R. 4 C -5 90 */9 4 /9 129 T. W. H. M., 37. L.+2.25ii5. R.-J-0.75 120. 4 /9 */9 I 3 E. S. M., 61. L. 1.5 1 80. R. Em. 4 /8 Vl2 131 F. D. F., 21. R. 0.5 1 80. L. Em. 4 /4 I 3 2 A. G. F., 1 8. I,. 3C 0-75 1 80. R. 4. 4 /4 4 /4 STATISTICAL RECORD. Num- ber. Name. Sex and Age. Correction Glasses and direction of axis of cylinder. Vision after correction. '33 I.T. F., 13. L. 3Oo.75i8o. R. 3O0-75 '80. ; '34 M. B. F.,8. L-+2-5 O +2.25 90. R.+2 O+2-5 90 . 4 /w '35 J.S F., 22. L. 1.25 180. R. 3.5 180. ;/ 136 J.C. F.J* I- 0.5 1 80. R. 0.75 180. 4 /! 137 M. P. B. M., 23. R-+4 O+3-590 . L-+4O+3-590 ' 7- '38 W. M. M,2,. L.+3 O +1.5 90. R-+3 O +i-5 90. 4 / v. '39 P.O. M., 18. L. 1.25 180. R. 0.75 180" ;/ 140 M T. F.,40. L. loOi-S '80. 4 /. 4 / w 141 M. D. F., 40. L+i90. R+i.25 90. ;/ 4 142 T. D. M.,5'- L. 10 O '-5 20. R ioO ' "0. 4 / J43 A. H. F,48. I-+o.75O+o.5'5o. R-+0.75 O+0-5 40. 4 /. 4 /. '44 F. H. M.,14. L, i. 5 40 0^-2.75 120+. R. i 1 80 O+2-5 90+. 4 /S '45 A. H. F. M.,37- L.+0-5 140. R.+0590 . 4 /6* 146 J.S. F-.39- L.+O 5 90. R.+0.5 90. v! '47 F. E. M., 1 6. L.- 8 O '-75 '80. R. 8. 4 /'j 148 D. W. P. M., 3 8. L. 4.530.540. R. 4-5 O '-5 '80. 4 /5 4 /6 149 E. P. F., 13. L. atrophy of o.n. R. 0.75 180. 4 / 'So L.F. F., 16. L.-0.7545 - R 075'35- V. */ 15' K.I. M., 26. ; ()-> (amblyopia). R+ 0+0.75 75. V. APPENDIX. 215 Num- ber. Name. Sex and Age. Correction glasses and direction of axis of cylinder. Vision after correction. 152 T. J. M. VI., 22. L. 0.75 1 80. R, 0.75 i So . v 53 R. M. M.,2 3 . L. Fm R.-i , .5 yo- */4 '54 E. C. F., 51. L. 0.5 1 80. R. 0.5 180. 4 /5 V5 '55 G. S. P. M-, 45. L.+ I 75 R. 0.75 1 80. v 4 / 156 R. H. M., 21. L. 2 C 1-5 90. R. 2 C 2. 95. 4 /4 */* '57 W. H. P. M., 28. L.-3C-;.55; o R. 2.5 C i 1 60 . 4 /5 4 /5 '58 S. P. S. F., 51- L.+0.75 135. R.-f 0.75 45 , 4 /4 4 /5 '59 W. C. S. M., 27. L. 3 1 80. R.3 1 80. 4 /6 4 /6 160 P. C. M. M.,29- L.+I. K.-f-O-S 90. 4 A 4 /4 161 E. S. M., 27. I- 4 C I 45- K. i C r '^o. 4 /5 V. 162 T. B. M., 54- L. r.niblv. R.+0.5 45- 4 / 63 F. L. F., 24. L.+4 C +3 1 8o- R.+2 C +3 180. 4 /24 4 /. 164 A. M. F., 25. L.+o 5 90. R.+O.S 90. 4 /5 4 /5 ,65 A. W. H. M., 40. LH-o.5 i35- R.+0.25 45- V* 4 /4 1 66 J. C. P. M., 30. L.+3- R.+2.25 C +o-5 9- 4 /4 4 /5 167 J.S. M., 16. L. atnblyopic. R.+0.75 90. 4 /5 1 68 S. R. F., 26. L.+0.5 90. R.+ i. 90. Vi */4 169 S. C. F., 14. L 3-5 C 0-75 90. R- 3-5 C 0.75 90. 4 /5 4 /5 170 J. McE. M., 21. L. 4 '0. R3C-I- '70. 4 /u 4 /b 216 STATISTICAL RECORD. Num- ber. Name. Sex' and Age. Correction glasses and direction of axis of cylinder. Vision after correction. 171 D. McE. M., 21, L.+I.25 C +3-5 5. R.+2 C +4 105. '/ Va 172 L. M. M., 50. L. 6 C 2-5 90 R. 7C 3 1 80. V Vu 173 T. C.S. M., 46. L. 0.75 1 60. R. Em. 4 /4 V4 174 E.T M. >4 8. L.+075 90. R. Em. 4 /9 */ '75 L.P. F., 30. L.-f as 1 10 C 0-75 20. R. 1.25 160. */5 4 /6 176 F. G. D. F., 38. L.+0.75 70. R.+0.75 1 10. I 177 M. M. F., 16. L.+I-75 90. R.+ I. 1 80. * 178 A. A. F. F., 15. L.+3- R.+o 75 90. 4 /. V. 179 A.B. S. M., 45. L. i C 2-5 180. R. 0.75 180*. Vu 4 / i So S. A. F.,42. L-+5-5 '35. R-+I-75 45 4 / 4 / 181 E.N. W. M.,29. L. 9C 1-25 1 80. R. 9 C 1.25 180. V. 4 / 182 A.W. F.,9- L.+5.5 180. R-+5 C +3-5 90. 4 /M Via 183 J, li. M. M.,2 5 . L. 0.75 1 80. R. 0.75 1 80. 4 /4 v 184 M. C. F., 70. L. i 1 80. R. E. (Com. Cat.) 4 / V* 185 A. P. F., 31. L. i C +i 160. K- 3-5 C 2.5 1 80. 4 /. V. 186 M. G. F.,23. L. 2.25 C i 90. R- 3-5 C i 90. 4 /5 4 /6 187 M. W. F.,39- L. i 1 80. R. 0.75 1 80. 4 / 4 /5 1 88 E.S. M., 26. L. 0.5 1 80. R. 0.5 180. 4 /4 V 189 C.C.B. M., 38. L-+7C-fi90. R.-t-bC-fi 90. 4 /~ V* APPENDIX. 217 Num- ber. Name. Hex and Age. Correction glasses and direction of axis of cylinder. Vision after Correction. 190 L. J. D. F., 39- L.+ I.5 90. R-+I-5 C +5 90. V5 4 /5 191 V. E. P. F., 54- L. Amblyopia. R-+I C+075 1 80. 4 /5 192 R. G. M., 21. L. Atrophied. R.-fo.5 1 80. V. 193 L,. L F., 12. L. 0.73 1 80. R. 0.5 1 80. V* /< 194 S. S. W. M., 26. L. 2.25 ;3 0.5 90. R. 2.25 ^ 0.5 90. V4 V* 195 J. R. M. M., 33- L. 0.5 10, R. 0.5 100. % 196 C. T. F., 40. L.+I 115. R.+0.75. 1: 197 A. I. D. M., 57- L.+I C +-5 9- R-+I C +0.5 90. */5 4 /5 198 D. P. G. M., 15. L.+I C +0.75 9- R-+I C +-75 90- 4 /5 4 /5 199 A. J. G. F., 50. L. 1.5 O -75 I2 o. R. Amblyopia. 4 /5 200 M. J. S. M., 63. L. 5 C i 9. R. 5 C i 9. 4 /12 Vl* 2OI J.H. M., 43- L. 0.75 45. R.- 9 . 4 /9 /M 202 J. S. B. M., 36. L. 0.75 C 1-5 "S ' R. 0.5 50. 4 /!8 4 /9 203 H. C. F., 40. L. 0.5 90. R. 0.5 90. 4 /5 4 /5 204 M. E. M. F., 50. L.-I 135. R. i. 4 /12 Vl2 205 R. D. K. F., 40. L-+I-25 C+ r -5' IIO - R. Em. 4 /9 V* 206 H. B. C. M., 29. L. 4 C 2-5 165. R. 6 C 2 1 80. 4 /6 */6 207 II. C. H. M., 53- L.+0.7S 10. R.+o.75ii 5 . V* V* 208 H. L. M., 28. L. 2 C 2 15. R. 7 s C o-S 1 80. 4 /6 4 /9 218 STATISTICAL RECORD. A'um- ber. Name. Sex and Age. Correction glasses and direction of axis of cylinder. Vision after correction. 209 C. F. B. M., 32. L. Em. R.+0.5 170. 4 /I 210 J. H. M. M.,48. L i 115. R. Em. (Corn. Cat) ;/;; 211 S. C. McD. M, S i. I-+2C+0-75 180. K-+0-75 C +0.75 180. v 4 / 212 M. W. R. K.,2,. 1. 1 C 2 l8o. R- '-25 C 0-75 180. 4 /4 V* 213 V.J. F., 22. I.. o.7s 1 80. R. 1.25 1 80. y. 2I 4 L.B. S. M.,I 3 . I.. i 180. R. i 1 80. v 4 /4 215 J. P. J. M.,24- L 0.5 180. R. 2.5. 4 /l 216 J. P. H. M.,43- L.+O.S 90. R. 0.5 1 80. y* 217 A. D. R. M.,45. [-+0.5 45. R.+o. 5 135. % 218 G. M. D. M.,52. L.-I.5'. R. i C 0-75 1 80. vl 219 R. N. B. M., 40. L. emmetropia. R. 0.75 1 80. 4 /4 4 /4 220 M. R. F., 24. I.. 1.25 1 70 C +3-75 80. U. 0.75 10 ^ +3.25 100. Vn 221 CD. F., 41. L. 3.5 ^ -5 1 80. R. 4 C o-S 1 80. A 222 W. F. M.,48. !>. Em. R. 0.5 90. y* 22 3 C C. G. M.,s.. L.+0.75 90. R.+O 75 90. */4 V* 224 W. H. B. M., 13. L. 0.75 90. R. amhlyopic. */* 22 5 E.E. W. F., 30. L, 2.5 4S o . y 226 H. T. M., 4 , I~ .1-5 C 0-75 R. 8\ ?i 227 M. E. M. F., 15- L. i ^ +0.5 90. R.-H C+28o. y* APPENDIX. 219 Num- ber. Name. Sex and Age. Correction glasses and direction of axis of cylinder. Vision after correction. 228 C. M. R. M., 26. L. amaurotic. R. 8 C i 1 80. 4 /6 229 C. T. F., 30. L. 0.75 180. R. 0.75 180. V5 4 /5 230 F. S. F, 12. L. 0.5 1 80. R. 0.5 1 80. 4 /4 V* 231 B. C . F., 12. L. 2.5 1 80 C +4 90- R.+4 90- Vn Vl2 232 A. H. W. F., 1 8. L. 45 C -i-5 85- R. 45 C 2 90. 4 /6 4 /6 233 N. G. F., 1 6. L. 2.5 C 0-5 80. R. 0.5 90. 4 /9 4 /6 234 J. H. McB. M., 40. L. i 90. R.-i.S 95. 4 /9 4 /6 235 A. R. F., 20. L. 0.5 90. R. 0.5 90. V* 4 A 236 B. P. F., 25. L. i 180. R. i 1 80. 4 A 4 /4 237 D. B. F., 1 6. L. 0.5 O 0.75 1 80. R. 0.75 C 0.75 180. 4 /5 4 /5 238 D. T. W. M., 33. L. 2.75 C 1-5 I00 . R. 3.5 C i I00 . 4 /5 4 /5 239 H. H. M., 1 8. L.-fo.75 1 80. R.+0.75 180. 4 /6 4 /6 240 E. P. H. M., 49. L. i C 0-5 180. R. amblyopic. V5 241 J. M. E. F., 34- L.+0.5 90. R.+0.75 90. 4 /9 4 /9 242 A. M. M. M., 38. L. 0.75 180 R. 0.75 1 80. V* 4 /4 243 R. K. M., 50. L.+I. 1 80. R. amblyopic. 4 /6 244 W. W. F., 38. L. 0.5 135. R.-O.S 45- 4 /4 4 /4 245 G.J. ' M., 38. L. 0.75 90. R. 1.25 90. */5 4 /5 246 M. M. F., 48. L.-0.75 135 C +0-75 45- R. 0.75 45 C +0-75 i35- 4 /6 4 /6 220 STATISTICAL RECORD. Num- ber. Name. Sex and Age. Correction glasses and direction af axis of cylinder. *ision after correction. 247 C. W. S. F., 30. L. 0.5 1 80. R. as 180. /4 v 248 F. L.G. F., 16. L. 0.5 1 80. R. 0.5 180. Vi /4 249 P. X.D. M.,4i. L.+.M 90. R.+2.5 90. v /I 250 L. H. F., 1 8. L. 0.5 1 80. R. 0.5 1 80. V* 4 /4 251 I. W. B. M.,40. L. 0.5 1 80. R. 0.5 1 80. */l */5 752 J. S. B. F., 48- L.+07535 - R.+0.75-. 4 /6 4 /6 253 D.B. F., 18. L. 3C 5 "80. R. 3 C o 5 1 80. '/ '/ 254 E. M. F., 25. L.+0-5 175. R.+0.5 180. / v 255 J. J. A. M.,40 L 0.5 40. R. Em. */. 2 5 6 E.S. F., 21. L. Em. R.-0.7S 90. V. 257 r. s. ?., 26. L. 0.75 50 R. 0.75 140. 4 / / 258 K. J. F. F., 40. L.+0.75 135. R.+0.75 45. 4 /5 4 /5 259 K. B. F. F., 40- L. a 5 1 80. R. 0.5 180. 4 / 4 /4 260 C E. P. F., 30. L. a 5 1 80. R. 0.5 15. 4 / 4 / 261 K. B. M., 3 i. L. i 70. R. i 110. */ V. 262 CS. F., 30- L. 05 180. R. 0.5 180. % 263 M. W. F., 65. L ioc. R. 6C i 90. ft 264 E.L. F., i& L.+OJ5 90. R.+0.5-. 4 /4 4 / 265 H. E. F., 18. L.+0.75 90. R.+0.75 9- 4 /5 4 /5 APPENDIX. 221 Num- ber. Name. ex and Age. Correction glasses and direction of axis of cylinder. r ision after orrection. 266 -H.. ., 29. u. 0-5 1 80. R.. 0.5 180. 4 /5 4 /5 267 .H. VI., 45- L. 0.25 135. R.. 0.5 45*. f ^ 268 R. G. ., 18. L. 0.5'. R. 0.5 1 80. ^ 269 .H. H. f 34- L-+I-75 C +i 90. R.+I-75 C +i 90. 4 /5 270 L. B. F., 21. L.+O.S 95. R.+O.S 85. 4 /4 4 /4 271 W. R. W: F., 25. L. 12 s . R. 12 C I- V 272 J. H. W. M., 28. L, 6 C I 90. R. 8 C I 90. 4 /6 4 /6 273 G. W. M., S I. L.+3 180. R.+2 1 80. Ve 274 A. L. F., 16. L. i.SC o-545- o 4 /4 275 F. S. P. M., 26. i ST^ 1 ; A 4 /5 4 /5 276 J. S. B. M.,50. L.+P. R.+I C +0.5 1 80. 4 /I 277 J.L. F., 20. L. 0.75 90. R.-0.75 90. v* 278 F. W. I. M.,2 7 . L.+0.5 90. R.+O.S 90. 4 /4 4 /4 279 C. A. P. M.,45- L-+I Q,+ -s- ;/ /; 280 C. A. N. F., 26. L. 0.75 180. R. 0.75 180. 4 /l 281 L. A. F., 21. L.+0.75 i35- R.+0.75 45 4 /4 */4 282 D. E. S. F., 30. L.-i.s 90. R. 2.5 90. 4 /4 4 /5 283 L. B. F., 12. L. 4. R. 3C 1-5 l8o - 4 /9 4 /9 284 M. V. F., 13. L.+i 100. R,+i 80. % 222 STATISTICAL RECORD. Num ber. 285 Name. Sex and Age Correction glasses and direction of axis of cylinder. Vision after correction. M. L.S. F., 40. L.+l8oC. R-+0.75 95 C - y* 286 S.C F., 36- L.+0.7S 9- R.+O.75 90. ;/ 287 W. F. R. M.,22. L. 0.5 1 80. R. 0.5-. % 288 E.M. F., 50 L.+0.75 l8o - R-+I C +0.75 180=. 4 /e 4 / 289 E.P. F., 3. L.+2-5 90. R.-J-2.5 90. ;/. 290 J. P. M. M.,53- L. 10 C * 175' R. 10 C i 10. y. 291 E S. P. M.,40. I 0.75 180. R. 0.75 1 80. 4 /5 4 /b 292 C.W. F. F., 3- L 0.75 180. R. o 75 180. 4 /l 293 J. H. W. F., 40- L.-J-25 C +o 5 100. R.+i C +i 90. ;/; 294 A. S. F., 21. L +0.75 180. R. Em. % 295 J. O. S. M., 48. L. Em. R.+2 25 ^ +0.5 100. 4 /s 296 1* -M . 1 '. F, 40. L-+I-75 C +0.5 9- R -+' 75 C +o-5 90. 4/5 4/5 297 C.A. H. M,30. L 0.75 C 0-75 60. R. 0.5 ^ -5 120. 4/5 4/5 298 K. S. F., 17. L 0.5 40. R. 0.5 180. 4/5 4/5 299 S. A. F., 42. - +0.75 100. R +0.75 180 . J/4 300 W. H. K. M., 23. L 3-5 C i -5 '55. R. 4-5 s . 4/J 301 E. W. N. F., 40. i.^5 C i 20. 4 / 302 J. B. B. M.,50. ..+2.25p +0.75 30. V; 33 D. E. S. M., 3 6. L 1.5 i So . R. i 170 . 4 /4 4 /4 APPENDIX. 223 Num- ber. Name. Sex an Age. Correcting glasses and direction of axis of cylinder. Vision after correction. 3<>4 H. W. G. F.,35- L. 0.75 180. R. 0.75 1 80. 4 /4 V* 35 W. A. K. M., 4 i. L. i C 2 180. R. 1.5 1 80. 4 /9 V9 306 T. B. M. M.,23- L. 0.5 90. R. 0.75 100. 4 /5 4 /6 307 R. R. W. M.,33- L. Amblyopic. R.-0.5 180. V* 308 E. C. F., 17. L.+0.75 90. R. 1.25 180. 4 A 4 /5 309 J. B. K. M., 14. L. <; 1 80. R. 5 1 80. 4 /l* 4 /12 310 T, C. M., 25. L. 0.75 1 80. R. 0.75 1 80. V' V* 3" J. F. K. M., 43. L. 0.75:180. R. Em. 4 /4 312 A. M. F., 21. L. Em. R. 0.75 180. V* v 313 M. L. F., 21. L. 2 C 2.5 130. R- 4 C i-5 130. Vl8 4 /24 3H S. M. B. M.,40. L. +2.5 70. R.Em. Vl8 4 /4 315 K. A. F., 12. L 4 10. R. 4 1 80. 'V 18 Vl8 316 L. J. B. M.,45. L.+3-5 C +I.2S 160- R.+4 C -f i 1 80*. */9 Vl2 317 H. C. L. F., 33- L+2C+' 165. R.+2 C +1 15 4 /5 4 /5 3i8 W. B. H. M., 23. L. 0.5 180. R. 0.5 i8o v . 4 /4 4 /4 3'9 C. N. F., 22. L. 2 1 80. R. 2 1 80. % 320 H.F. M.,33- L. 0.5 20. R--0.5 '55- % 321 S. P. T. F., 40. L. 4 140. R. 4 165. 4 /6 4 /24 322 M. W. F., 1 8. L.+6 105. R.+2 1 80. 4 /36 4 /9 224 STATISTICAL RECORD. Num- ber. Name. Sex and Age. Correcting glasses and direction of axis of cylinder. Vision after correction. 323 S. R. B. F.,40. L.-0.75. R. 0.5 100. ;/. 324 F. 0. F., 18. L. 0-5 35- R-+0-5 30. 4 / 4 / 325 A. P. F., 55- L.+3- R.+I-75 C +0-75 90. ;/; 326 M. L. F. F., 21. L.+O.S 180. K.+0.7S '80. j/t 327 J.C. F., 17. L.+I.25 120. R. +0.75 90. V; /; 328 D. M. O. M., 38. L. as 90. R. a25 90. v V* 329 N. H. F., 13- L. Em. R. 2.25 1 80. 4 /u 33 A.B. F.,30. L.-0.75 30. R. 2.5. V. V. 33i M. B. F., 14. L. 3-5 C 0.5 90. R.-3-5- % 332 M. D. F., 13- L. +10 0+0.75180. R.+IO C +0-75 1 80. v! 333 J.J.J- M.,47- L.4-I- R-+2-5 C +1 120. vl 334 B. A. P. F., 45- L. 12. R. 8 C i 145. ;/ 335 J. M. K. M., 26. L.4-0-75 105. R. 2. % 336 R. J. M. M.,32. L. 6 C i 180. R. 2. \u 337 W:F. M. M.,47. L.4-0.5 90. R.4-0.5 90. vl 338 D. B. S. F., 45- I 0.5 180. R. 0.75 135. 4 /4 4 /4 139 A.T. F., 19- L. Em. R.4-as 115. 4 /4* M. L.S.B. M., 23. I 1.75 170. R. 1.25. 4 /4 V* Hi M. F. F., 50. L.+3 '80 R.+2.25 C +0.75 180. 4 /o Vs APPENDIX. 225 Num- ber. Name. Sex and Age. Correction glasses and direction of axis of cylinder. ^ision after correction. 342 H. B. B. F., 4 6. -+!-5 C+-5 9- R.. Aniblyopic. 4 A 343 L. N. F., 20. L. 10 C 0-5 180. R. 9C 0-5 1 80. 4 /6 4 /9 344 E. R. B. F., 40. L-+I-5 C +0.5 90. R-+I. C +0.5 90. V 4 345 A. W. F., 19. L. 0.75 1 80. <.. Em. ;/4 346 E. B. F., 28. L.-I.5 135. R- 1-5 C 1-5 45- 4 /5 4 /5 347 D. S. M., 33- L.+2.25 O + !-5 I2 o. R.+2.5- 4 /9 2 348 S. C. F.. 38. L. 4. C o-75 180. R- 3-5 C 0.5 180. 4 /5 */ 349 E. F. F., 39- L-+2-5O+I 170. R-+2-5O+I 180. Vl8 35 G. C. K. F., 50. L.+445- R+o.sO + i 90. ;/i8 35- D. C. F., 41. L. 1.5 1 80. R. 2 1 80. ;/5 352 C. H. M. M., 40. L. 0.5 20. R. 0.5 140. \ 353 M. A. F., 18. L. 0.50 -75 1 80. R. 1.5 C 0.75 180. i 354 M. W. R. F., 40. L.+2 140. R.+i 10 C 1-5 100. 4 /5 4 /6 355 E. M. F., 48. L. 2 ioO+4-75 100. R 2 I70C+5 80. 4 /9 8 356 N. M. F., 50. L. 0.5 90. R. 4 O 0.5 90. 4 /5 4 /9 357 A. T. B. M..SI. L. 4O i 7o. R. 4O i 130. % 358 M. A. F-, 45- L 0.5 90. R.-4- 4 /u .159 M. W. F., 50. L. i O 0.75 60. R. r C 0.75 120. %- 360 B.C. F., 36. L.+2 O +0.5 QO- R. +0.75 90. ' ; /: 226 STATISTICAL RECORD. Num her. Name, Sex and Age, Correction Glasses and direction of axis of cylinder. Vision aftet correction. .#1 E.T. P. M.,48. L. Amblyopic. R.+0.5 90*. */ v 362 E.J. F., 50. I-+2 C +o 5 5 K.+2C+0-5 '75- V* v 363 L.P. F., 38- L.+2.5 C +o 5 i8oP. R-+2-5C+0.5 i84^ compound, - S 1 definition of, - I derivation of the term, 14 determination of its existence, 59 diagnosis of, - 55 forms of. 5 of the horizontal corneal meridian, - 39,40,41,42 influenced by accommodation, 66 mixed, 5 1 234 INDEX. name given by Whewell, 158 normal, 38 regular in the human eye, - 43, 44 simple, 50 Asthenopia, astigmatic, 143 astigmatic, illustrative case of, 142 illustrative case of, - 142 in astigmatism, 141 muscular, 141 on what it depends, - 141 nervous, 143 often absent in high degrees of ametropia, - 141 worse when the meridians are oblique, _ 143 Atropine, indications for the use of, 71 use of in diagnosis, 67 Aubert, on the form of the cornea - 43 Axis of cylinder, method of indicating its inclination, 155 at right angles to the faulty meridian, 57 B Blepharitis, in astigmatism, - 144 Blows on the eye producing astigmatism, - 150 Bowman on the shadow-test, 115 Bravais' apparatus, - 85 method of ophthalmoscopic diagnosis, 109 Brewster's description of conical cornea, - 191 Burnett's modification of the ophthalmoscope, 99 Cassus used cylinders in 1840, 158 Cataract extraction, a cause of astigmatism, 148 Chorea, said to be due to astigmatism, 143 Ciliary muscle, partial contraction of, - 71,151 varying power of, 69 inherent tonicity of, - - 68 INDEX. 235 Clinical cases, - 159, 165 Collecting optical systems, their office, 8 Congenital astigmatism, 147 Conical cornea, diagnosis of, 192 lateral view of, 192 Cornea, Aubert on the form of, 43 focal curve of, 41 normal astigmatism of, 44 Harkness on the form of, 39 its form a triaxial ellipsoid, - 42 Corneal and total astigmatism, table comparing, - 132 astigmatism, history of, 46, 48 ellipsoid, optical zone of, - 43 ellipsoid, scleral zone of, 43 irregular astigmatism, 183 Correcting glasses, sometimes unsatisfactory, 70 Correction of astigmatism by pressing on the sclera, 171 Couper's method of ophthalmoscopic diagnosis in astigmatism, 1 10 Cranium, shape of, influencing astigmatism, - 147 Crossed cylinders, - - 32, 162 Cuignet re-introduces skiascopy, - 116 Culbertson's prisoptometer, - 84 Curvature of convex surfaces, method of determining, 125 Cylinder, axis at right angles to its refracting surface, 30 increase in refraction of by rotation, - 35 Cylindrical action of spherical lenses, - 34, 204 Cylindrical lens, how formed, 30 focal lines of 23 refraction by 31 Cylindrical glasses may improve when no astig. is present, - 64 Cylindrical glasses in kerataconus, - 198 Cylindrical lenses, forms of - 32 Cystoid cicatrix, keratoscopic appearances of 185 236 INDEX. D Dantel on hypermetropia in childhood, 69 Deficiency in correction by cylinders, 166 Degree of astigmatism, the lowest requiring correction 1 70 Dennett, cylindrical attachment to the ophthalmo- scope, 99 Dennett's modification of Stokes' lens, 33 Diagnosis of astigmatism, illustrative cases, 57, 59 best vision, the final test of 136 errors in, caused by the accommodation - 65 Diagrams for recording astigmatism, - 58, 59, 159 the axes of the meridians, - 58, 59 Difficulty in wearing correcting glasses, 163 Dislocation of the lens producing astigmatism, 150 Donders' first papers on astigmatism, 48 Drobowolski on partial contraction of the ciliary muscle, - 71 E Egger, originates the term skiascopy, 116 Ellipse blunter end of 16 definition of 15 foci ot 15 major axis of 15 minor axis of 15 refraction by the sharper end of 17 sharper end of 16 Ellipses, refraction by 16 Ellipsoids, biaxial, - 20 focal lines of, curved, 23, 25 no general formula for their refraction, 26 triaxial, 2O Elliptical form of the cornea, 40 Emmetropic eye 49 and ametropic eyes compared, 49 Eye, office of, as an organ of sense, 63 INDEX. 237 F Focal curve of the normal cornea, - 41 distance, first, 4 second, - 4 Focal distances of a biconvex lens, - -7 Focal interval of Sturm, - 22 circular section of not in the center, 29 formation of - -28 Focal line of Sturm's interval, anterior shorter, - 29 cylinder straight, 23 Focal plane, astigmatics preferably use one, 65 choice of by astigmatics, - 65 of a triaxial ellipsoid, - 22 of obliquely placed lenses, - 204 Foci, principal, 4 Forms of astigmatism, relative frequency of, 206 Fundus of an astigmatic eye as seen by the direct method, - 96, 97 G Gavarret, work on optics, - 10 Gerson, on astigmatism, 46 Goulier's account of astigmatism, - 158 Glass, crown, 7 flint, 7 index of refraction of, 7 Green, John, clock face for diagnosis, 83 H Harkness on monochromatic aberration of the cornea, 39, 41 Hay, G., on shortening of focus of cylinder by rotation, 35 Hays, Dr. Isaac, observation on the correction of as- tigmatism, 158 Headache due to astigmatism, - 141, 142 Helmholtz's corneal measurements, - 46 ophthalmometer, 124 Hirschberg on spasm of A, - 70 238 INDEX. Hyperbolic lenses, - 199 Hypermetropic eye, - 50 Hypermetropia, the rule in childhood, 68 found constantly in most lower animals, 68 I Images, formed by convex surfaces, 10 how formed by a convex refracting surface, - 8 Inch system of numbering glasses, - 1 1 of numbering glasses, disadvantages of, 1 1 always expressed in vulgar fractions, 13 how to convert it into the metric, 12 Intermediate meridians, refraction by, 22 Inverted ophthalmoscopic image, apparent size of in Emmetropia - 102 in hypermetropic astigmatism, - 107, 108 its size and position, - - 101, 102 in mixed astigmatism, - 107 in myopia. 104 in myopic astigmatism, - 106 size and position of in hypermetropia, 103 Iridectomy in irregular astigmatism, 189 Iridencleisis, a cause of astigmatism, - 187 Irregular astigmatism, - 177 normal, 177 produced by accommodation, - 182 diagnosis of, - 183 by the ophthalmoscope, 183 treatment of, - 1 86 Irregular corneal astigmatism after cataract extraction, 187 J Jager's inaccurate drawing of the fundus of the astig. eye, - 95 J aval's astigmometer, 86 Javal on corneal astigmatism, - - 48 on the form of the cranium in astigmatism, 147 on lenticular astigmatism, - 71 INDEX. 239 Javal and Schiotz' ophthalmometer, 124 Jones on astigmatism, 46 K Keratitis said to be due to astigmatism, 144 Keratoconus, 190 case of 193 a cause of irregular astigmatism, 148 operative treatment of, 200. Keratometry, exact meaning of the term - 124 its value .in astigmatism 124 Keratoscope of Placido ; how made, 133 Keratoscopic appearances in irregular astigmatism, 184,185 images in keratoconus, - - 194,195 Keratoscopy, false, - 115 Keratoscopy in the diagnosis of irregular corneal as- tigmatism, 184 Keratoscopy, first attempt at, 192 its limitations in regular astigmatism, 134 meaning and application of the term, 124 Keratosis, 191 Knapp's combined method of ophthalmoscopic ex- amination, io9 Knapp, the first to demonstrate corneal astigmatism, 47 L Landolt, on the use of atropine in determining astig- matism, - 7 Lens, concave, action of on light, 7 convex, action of on light 7 Lenses, collecting - 3 different forms of, 2, 3 dispersing 3 methods of numbering, 1 1 negative, ' 3 positive, 3 spherical, 3 why so called, - 2 24O INDEX. / Lenticular astigmatism, 149 forms of, 150 neutralizing corneal - 71 causes of, 45 ,46 Little, W. S., test card of, - 56 Loring's drawing of the fundus of the astigmatic eye - - 59 M Mauthner on spasm of A, - 70 McAllister, made cylinders in 1825, 158 Meridians, intermediate, 22 Meridians, principal, - 21 the two principal at right angles, 20 Meridian, vertical the more strongly curved, 44 Metric system, always expressed in whole numbers and decimals, - 13 how to convert it into the inch, 12 of numbering glasses, 1 1 Mitchell, S. W., on headaches from eye-strain, 142 Monochromatic aberration, absence of, 18 Mixed astigmatism, two methods of correcting, 162 case of, 161 Myopia as a cause of astigmatism, - 144 Myopic eye, - 50 N Near-sightedness, apparent, due to astigmatism, 144 Neurasthenic asthenopia, - 143 Nodal points, effect of cylinders on, - 169 Nordenson on corneal astigmatism, - 48 Normal astigmatism, demonstration of, - 45 Normal to an ellipse, how to obtain, - 16 O Objective methods, advantages of, - 89 of diagnosis, - 74, 89 Objective signs of astigmatism, - 143, 144 INDHX. 241 Obliquely placed lenses, cylindrical action of, - 33, 204 Obstacles in the way of an accurate diagnosis, 63 Ochlodes, - 191 Oliver, C. A., disks for diagnosis, - 83 Ophthalmometer of Helmholtz, practical disadvan- tages of, - 124 of Javal and Schiotz, its construction, 125, 126, 127, 128, 129 method of using, - 129,130 its optical basis, 125 does not give general ametropia, 131 Ophthalmometry, objection to the term, 124 Ophthalmoscopes, with cyl. attachments, - - 99, 100 Ophthalmoscope in the diagnosis of irregular astigmatism, 183 in diagnosis, - 89 Ophthalmoscopic appearance in keratoconus, - 193,195 examination, defects of in diagnosing astigmatism, 93, 94 different methods of, - 90 direct method in astigmatism, - 92, 93 direct method of, 90, 91 indirect method of, 101 findings should be verified by glasses and test-types, 113 Optical appliances, function of, 2 Optical treatment of keratoconus, - 197 Optics, elementary principles of, I Optometers, - 84 Orbit, influence of in producing astigmatism, 147 Over-correcting combinations of sphericals and cylinders, 32 P Parallel rays of light, I Parent's cyl. attachment to the ophthalmoscope, - 99 Partial accommodation in childhood, 140 causing astigmatism, - 71,151 Phantoscopy, - - 1 15 Pickering and Williams' table, 34 Points, cardinal, 4. 7 242 INDEX. Points, nodal, 4, 6 Point of light, changes of, in astigmatism, - 75 Points, nodal and principal, coincide in a bi-convex lens, 7 Points, principal, 4 Placido's keratoscope, 133 Planes, focal, 4 principal, 4, 5 Polyopia monocularis, 180 Pray O., test letters of, 83 Presbyopia in astigmatism, - 160 Presbyopia sometimes first makes astigmatism felt, 140 Principal meridians, determination of the direction of 56 their inclination expressed in degrees, 57 points, same for a simple refracting surface, - 5 planes, same fora single refracting surface, - 5 Proving glasses, 171 by neutralization, 171 simultaneous contrast, 173 Pupilloscopy, - 115 Purves, Laidlow, apparatus for diagnosis, - 77 R Rahlmann's hyperbolic lenses, 199 Recording cases, method of 159 Refraction, laws governing, 2 Refracting-power of a lens, on what it depends, 7 Refracting media of the eye, 38 Regular astigmatism from keratoconus, case of 149 Retinoscopy, 115 s Schemer's experiment, in diagnosis of ametropia, - 78 astigmatism, - 79 Schoeler's cyl. attachment to the ophthalmoscope, 99 Schmidt-Rimplers' method of ophthaimoscopic diag- nosis, - - - no, 1 1 1 INDEX. 243 Schweigger's combined method of ophthalmoscopic examination, 109 Sectorial construction of the lens, - 178 Senf, the first to measure the cornea, 46 Shadow-test, 115 Skiascopy, 115 detection of principal meridians by, - 121 in diagnosis of ametropia, - 117 in the diagnosis of astigmatism, 121 diagnosis of hypermetropia by, 118 diagnosis of myopia by, 118 on what it depends, - 115 optical principles of, - '- Il6, 117 use of plane mirror in, 119 Sous, on diminished refraction of cyl. by rotation, - 35 Snellen's fan, 56 Snyder's account of astigmatism, - 158 Spasm of accommodation, illustration of, - 165 "Spectrum" of the lens, 179 Spherical aberration, excess of in ellipses, - 18 action of Stokes' lens, 83 glasses should always be tried first, - 65 lenses, how formed, - 3 Sphere-cylinders, - 32 Spheroid, characteristic refraction by, 20 compressed, - 20 lorm of 14 refraction by, 19 Staphyloma pellucida, 190 Star-rays, origin of, - 180 Static refraction, examination of, - 55 of the eye, - 66 Statistical record, - 206 Stenopaic slit in keratoconus, '197 in irregular astigmatism, 189 its use in diagnosis, - 81 Stokes' lens, 33 244 INDEX. Strabismus, operation for, a cause of astigmatism, - 152 Strawbridge's apparatus for diagnosis, 78 Sturm's interval, diffusion images greater on post, focal plane, 29 sections of, at various parts, - - 27, 28 Subjective method of diagnosis 74 Symptoms of irregular astigmatism, - 188 Table, comparative, of metric and inch systems, 12 Tension of Eye-ball, changes of corneal curvature in, 188 Thomson's modification of Scheiner's experiment, - 80 Tilted lenses in the astigmatism after cataract extrac- tion, - 171, 205 Tilting mirrors, 98 Trial-frame of Meyrowitz, - 155 Trial glasses, what a set should contain, II, 12 Trial lenses, - 1 1 Triaxial ellipsoid, model of, 21 normals to the meridians of, 21 "skew" surface of, - 21 u Unreliability of patients' statements, 63 V Vision, diminished, easily overlooked by patients, - 139 Vision, diminished, a subjective sign of astigmatism, 139 Visual acuteness in astigmatism, - 169, 206 w Wecker's square for testing for changes in corneal curvature, - - 135, 136 Whewell first gave the name astigmatism, - 158 Wilde, on the form of the cornea, - 46 Women, relative frequency of astigmatism in, 206 Wounds of cornea and sclera, causes of astigmatism, 148 INDEX. 245 Y Young's astigmatism lenticular, 45 Young's case of lenticular astigmatism, 149 z Zehender's astigmometer, - 85 TABLES. Table I. Inch and metric systems of numbering glasses 12 Table II. Pickering and Williams' tables showing the foci of a spherical lens when placed obliquely 34 Table III. Hay's table, showing the increase in refraction of a cylinder on rotation about its axis - 35 Table IV. Harkness' table comparing the focus of a normal with spherical cornea - 42 Table V. Showing the foci of the horizontal and vertical meridians in 21 eyes 44 Table VI. Showing the difference in the astigmatism as determined by Javal's keratometer and test-glasses 132 Table VII. Showing the cylindrical action of a spherical lens placed obliquely to incident rays, and the ob- liquity of the focal plane 205 Appendix. Statistical record of 806 astigmatic eyes - 206 :\vu umvcno/ IBRAfTi UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles This book is DUE on the last date stamped below. 130NY-S UBRAR i DdlTVD Form L9-Series 4939 F-CAIIF(W iiln /5JAE-UNIV 3 115800972 7966