CLINICAL USE OF 
 
 PRISMS 
 
 ;■:':. y.,,'A:r-A 
 
 GENEVA OPTICAL CO. 
 CHICAGO
 
 THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 
 OF CALIFORNIA 
 
 LOS ANGELES
 
 OPHTHALMOLOGICAL PRISMS.
 
 THE CLINICAL USE OF 
 
 PRISMS; 
 
 AND THE 
 
 Decentering of Lenses. 
 
 BY 
 
 ERNEST E. MADDOX, M.D. 
 
 Formerly Syme Surgical Fellozu, Edinburgh. 
 
 SECOND EDITION. REVISED AND ENLARGED. 
 
 Bristol : 
 
 JOHN WRIGHT AND CO. 
 Xotfton : 
 
 SIMPKIN, MARSHALL. HAMILTON. KENT AND CO., Limited. 
 HIRSCHFELD BROS., 82, HIGH HOLBORN. 
 
 1893-
 
 JOHN WRIGHT AND CO., 
 PRINTERS AND PUBLISHERS, BRISTOL.
 
 1213 
 
 PREFACE 
 
 TO THE SECOND EDITION. 
 
 A considerable amount of new material 
 has been added to this edition, consisting 
 partly of a fuller study of convergence, and 
 partly of a number of optical problems and 
 practical points worked out since the first 
 edition. The number of diagrams, too, has 
 been considerably increased. It has been 
 endeavoured to maintain the utmost sim- 
 plicity in the optics of the subject, and 
 while giving enough to afford interest and 
 precision, preference has been given to 
 graphic or mechanical demonstrations, so 
 that no unmathematical reader will, it is 
 hoped, experience any difficulty, unless per- 
 haps with two or three formulae, which can 
 be neglected without loss. My thanks are 
 due to Mr. Berry for being so kind as to
 
 vi PREFACE. 
 
 read the proof sheets, and for valued com- 
 ments thereon. Though the undoubted 
 value of strong prisms is confined to a rather 
 limited sphere, a knowledge of the principles 
 of convergence, and the decentering of 
 lenses is advantageous to all students of 
 refraction. 
 
 20, Alva Street, 
 
 Edinburgh, 
 
 July, ifyj.
 
 EXTRACT FROM 
 PREFACE TO FIRST EDITION. 
 
 The title of this little work indicates its chief 
 features, but does not cover its ground com- 
 pletely. Its first object was to communicate 
 a series of aids to precision in the use of 
 prisms, worked out during several years, 
 which it is hoped will be of some service in 
 this difficult by-way of ophthalmic practice. 
 They have, however, been introduced by 
 a sketch of the simplest properties of prisms, 
 and supplemented by a brief account of their 
 
 chief clinical uses It will not 
 
 be supposed that the precision aimed at in 
 these pages is necessary in the majority of 
 refraction cases. It is chiefly anomalies of 
 convergence, faulty tendencies of the ocular 
 muscles, and the needs of the increasing neu- 
 rasthenic class of patients that are kept in
 
 viii PREFACE. 
 
 view. In these last cases, spectacles cause 
 discomfort, however perfectly refraction may 
 be corrected, unless the lenses are also suit- 
 ably placed in respect of convergence, and 
 sometimes even then, for a time. 
 
 Part of the manuscript was kindly read 
 over by my friend, Dr. Poulett Wells, to 
 whom I am indebted for one or two valuable 
 corrections, and, indeed, for suggesting the 
 need of a book on prisms. 
 
 July, 1 8 89.
 
 CONTENTS. 
 
 CHAPTER I. 
 
 Geometrical Properties of Prisms - Pages 1—9 
 
 Rectangular Prisms — Circular Prisms — Apex and Base. 
 
 CHAPTER II. 
 Simplest Optical Properties of Prisms Pages 10 — 28 
 Refraction— Deviation— Relation between Deviating and 
 Refracting Angles— Construction for Deviation — Rules 
 and Tables — Dispersion. 
 
 CHAPTER III. 
 Prismetrv ... - Pages 29—35 
 
 Numeration of Prisms — Degrees — Centrads — Prism- 
 Dioptres. 
 
 CHAPTER IV. 
 Testing the Apex of Prisms - Pages 36—39 
 
 Marking the Apex. 
 
 CHAPTER V. 
 Prismatic Aberration - - Pages 40—46 
 
 Apparent Distortion of Objects by Prisms. 
 
 CHAPTER VI. 
 Rotating Prisms - - - Pages 47—5° 
 
 Herschell's— Cretes'— Risley's— Binocular. 
 
 CHAPTER VII. 
 Images by Internal Reflection - Pages 51—55 
 
 Guides to the Apex.
 
 x CONTENTS. 
 
 CHAPTER VIII. 
 
 Clinical Properties of Prisms - Pages 56—65 
 
 Angle of False Projection — Displacement of the Visual 
 Axis — Overcoming of Prisms — Production of Diplopia 
 — Adducting and Abducting Prisms. 
 
 CHAPTER IX. 
 
 Adjustment of Prisms in the Trial-Frame 
 
 Pages 66 — >o 
 Resultant Prisms —Clinical Strength of Prisms. 
 
 CHAPTER X. 
 
 Decentering of Lenses - - Pages 71 — 82 
 
 Combinations of Prisms with Lenses — Manufacture of 
 Prismatic Lenses — Virtual Prisms. 
 
 CHAPTER XI. 
 
 The Study of Convergence - Pages 83—106 
 
 Grades of Convergence — Tests for Convergence — Effect 
 of Lenses, Prisms, and Tenotomy — Adaptability of 
 Convergence to Accommodation — Latent Deviations. 
 
 CHAPTER XII. 
 
 Effect on the Fixation Lines of Displaced or 
 Decentred Lenses - - Pages 107— 115 
 
 Rules and Tables. 
 
 CHAPTER XIII. 
 
 The Clinical Application of Prisms in Diagnosis 
 
 Pages 116 — 137 
 
 Estimation of Punctum Remotum and Punctum Proximum 
 
 of Convergence — Relative Convergence — Dissociation 
 
 of Convergence and Accommodation — Hyperphoria — 
 
 Tests for Binocular Vision. 
 
 CHAPTER XIV. 
 
 The Use of Prisms in Treatment Pages 138—145 
 
 Corrections of Latent Deviations in Distant and Near 
 Vision — Hyperphoria — Prisms for Diplopia— Cosmetic 
 Prisms.
 
 COXTEXTS. xi 
 
 CHAPTER XV. 
 Analysis of Spectacles - - Pages 146—152 
 
 The Prism-Measure — The Analyser. 
 
 CHAPTER XVI. 
 Localising the Eyes - - Pages 153— J 57 
 
 Trial-Frame for Temporary Prisms — Maxims for Prescrib- 
 ing" Prisms. 
 
 Appendix - Pages 158—163 
 
 Resultant Prisms — Sines, Arcs, and Tangents — Table of 
 Sines and Tangents — Formulae for Refraction through 
 Prisms.
 
 PRISMS. 
 
 Chapter I, 
 
 GEOMETRICAL PROPERTIES OF 
 PRISMS. 
 
 OPHTHALMOLOGICAL Prisms are simply 
 wedges of transparent material, contained 
 between two plane faces, which are inclined to one 
 another at a moderate angle. The " strength " of 
 a prism depends on the size of this angle, which 
 varies therefore in different prisms, and also on 
 the refractive properties of the material from which 
 the prism is made. 
 
 Since the terminology of prisms in optics, and 
 especially in ophthalmology, is so different from 
 that of prisms in geometry and physics, it will be 
 well to notice in some detail the terms employed. 
 
 Refracting Surfaces. — By " refraction " is 
 meant the deflection, or sudden bending from its 
 former course, of a ray of light as it enters (other 
 than perpendicularly) the surface of a rarer or 
 denser medium. The body of a prism does not 
 refract light, since rays travel through its sub- 
 stance in straight lines. It is only as they enter or 
 leave the prism, and thus pass from one medium 
 
 to another that they undergo refraction. It is for 
 
 I
 
 PRISMS. 
 
 this reason that the two plane polished faces are 
 called the " refracting surfaces." In Fig. I they 
 are represented by the faces acfb and a deb. 
 
 Angle of Refraction. — We have seen that the two 
 plane faces of a prism are made to slope towards 
 each other so as to contain between them a mode- 
 rate angle. This angle is called the "angle of 
 refraction," because the total effect of the prism 
 on the direction of a ray of light depends on the 
 size of this angle, as well as on the refracting power 
 of the material from which the prism is made. 
 Until recently, clinical prisms have had the number 
 of this angle in degrees scratched upon them, so 
 that prisms marked, e.g., with i° or 2° were known 
 to have their refracting surfaces inclined to each 
 other by i° or 2° respectively. Trial cases used 
 generally to be provided with a series of prisms,
 
 THEIR GEOMETRICAL PROPERTIES. 
 
 marked in this way, from i° or 2 3 up to 12° or 24 . 
 The angle of refraction is the one item the optician 
 needs to know in order to grind a prism. He first 
 sets a pair of compasses so that their legs shall 
 enclose the prescribed angle, and then cuts and 
 grinds the piece of glass to the shape of a wedge 
 that will just fit in between the two legs. To 
 measure the refracting angle of a prism, or, as we 
 
 J 
 
 AT 
 
 ...M 
 
 Fig. 2. — Prism Measure : the index points to the required 
 angle when the teeth at its foot are pressed upon the prism. 
 
 may simply call it, " the angle " of a prism, we 
 may resort to the same manoeuvre, and after grasp- 
 ing the prism between a pair of compasses, measure
 
 4 PRISMS. 
 
 the angle they include on a protractor.* But if the 
 prism be mounted in a metal ring, this method is 
 impracticable, and the " prism measure " of the 
 Geneva Optical Company will be found useful 
 (Fig. 2). 
 
 What, however, is of interest to the surgeon, is 
 the optical power of a prism, and not its mere 
 physical conformation, and it is undoubtedly better 
 for trial prisms to be marked by their deviating 
 power over a beam of light, as described 
 later on. 
 
 Principal Section. — Any section made through 
 a prism at right angles to its refracting surfaces is 
 called a " principal section."! Such a section is 
 shown in Fig. 3. The two refracting surfaces are 
 
 <KrR~crKG.AHGl£ 
 
 atsc 
 
 Fig. 3. — The same prism in section. 
 seen to meet at the edge of the prism, enclosing 
 between them the " refracting angle." The third 
 side, opposite the edge, is called the base. 
 Rectangular Prisms. — In geometry, when we 
 
 * For a diagram of a protractor, put to a different use, 
 see Fig. 13. 
 
 \ To put it another way, it is any section made perpen- 
 dicularly to the axis of the prism.
 
 THEIR GEOMETRICAL PROPERTIES. 5 
 
 speak of a rectangular prism, we mean one which 
 has a rectangular section. Ophthalmological prisms, 
 however, are always triangular in section, as shown 
 in Fig. 3, so that when we speak of them as 
 " square," " rectangular," " circular," and so forth, 
 it must be understood that these expressions only 
 apply to the shape of the refracting surfaces. It is 
 evident that two plane surfaces may be of most 
 various shapes, and yet be inclined to each other 
 by the same angle, so that what we call the "shape" 
 of a prism, in no way affects its strength. A rect- 
 angular prism is shown in Fig. 4, of a kind not 
 
 C 
 Fig. 4. — A rectangular prism. 
 
 used clinically, but rather by students of optics. A 
 square prism, which is of course a variety of the 
 rectangular, is represented in Fig. I. In both 
 figures the " refracting surfaces " are lettered a cfb 
 and a d e b, meeting along the " edge " a b, and 
 enclosing the "refracting angle" d a c, which is 
 seen to be smaller in Fig. 1 than in Fig. 4. 
 The remaining surface d e f c is called the 
 " base." 
 
 For some clinical purposes square prisms are
 
 PRISMS. 
 
 extremely useful, since it is so easy to hold them 
 in any desired position. Their disadvantage is that 
 
 they will not fit into the 
 ordinary trial-frame, but 
 in every other particu- 
 lar this shape is prefer- 
 able. It would be well 
 for trial-cases to be 
 provided with at least 
 one square prism, having 
 a refracting angle of 
 about 12°. A conveni- 
 ent way of using square 
 prisms is that recom- 
 mended by Xoyes, in 
 which a series of in- 
 creasing strength are 
 joined together in a 
 frame, so that one after 
 another can be made to 
 pass before the eye. 
 Such a series is shown 
 in Fig. 5. 
 
 Circular Prisms. — 
 Clinical prisms are al- 
 
 Fig. 5.— A "bar of prisms" most universally cir- 
 (Gen. Opt. Co.). J 
 
 cular, to admit of their 
 
 insertion into the same trial-frame as clinical 
 
 lenses.
 
 THEIR GEOMETRICAL PROPERTIES. 7 
 
 One is shown in Fig. 6, and the hypothetical design 
 
 Fig. 6. — A circular prism. 
 
 in Fig. 7 is intended to show how a circular prism is 
 related to a rectangular one, as though it were cut 
 out of it. 
 
 Fig. 7. — A hypothetical illustration to show the relation of a 
 circular prism to a rectangular one. 
 
 Apex and Base. — The thinnest part of a circular 
 prism is called the apex. It is the point where the 
 two refracting surfaces meet, or most nearly meet. 
 The base of a circular prism is the thickest part of 
 it, exactly opposite the apex. It is not therefore a 
 surface as in the case of a rectangular prism, but 
 an imaginary line (b in Fig. 6) uniting the most 
 separate points of the two circular surfaces. An 
 imaginary straight line from the apex to the centre 
 of the base we may call, for convenience, the base-
 
 8 PRISMS. 
 
 apex line. All objects viewed through prisms appear 
 displaced in a direction parallel to the base-apex 
 line, as shown in Fig. 8, where a real object 
 appears displaced to e in a direction parallel to the 
 base-apex line af. 
 
 Edge of a Prism. — It is easy to understand what 
 is the edge of a rectangular prism, for, as already 
 explained, and shown in Figs. 4 and 7, it is the 
 line a b, in which the refracting surfaces meet. But 
 in a circular prism the surfaces meet only at a point. 
 A circular prism therefore has no actual edge, but 
 only an imaginary one, viz., an imaginary line 
 which passes through the apex at right angles to 
 the base-apex line, as b c in Fig. 8. It is the 
 
 h 
 
 o 
 
 Fig. 8. — To show how an object at O appears displaced, not in 
 the direction d towards the apex a, but in the direction e towards 
 the edge be, and parallel to the '« base-apex line," af. 
 
 line in which the two refracting surfaces would meet 
 if they were prolonged, and it coincides therefore 
 with the edge of the rectangular prism, out of which 
 we may imagine the circular prism to have been
 
 THEIR GEOMETRICAL PROPERTIES. 9 
 
 cut. The name is taken from the edge of a knife 
 in which the two polished faces of the blade meet. 
 Though the edge of a circular prism has no real 
 existence, it has a very real importance, for all 
 objects seen through prisms appear displaced 
 towards their edge.
 
 IO 
 
 Chapter II. 
 
 SIMPLEST OPTICAL PROPERTIES OF 
 PRISMS. 
 
 Refraction by Prisms. — In the case of a well- 
 made clinical prism, we have only two media to 
 take account of (both of which are practically homo- 
 geneous and isotropic), viz., air and glass. A 
 homogeneous medium is one of equal density 
 throughout. An isotropic medium is one that is 
 singly refracting, that is, when a ray of light enters 
 the surface of an isotropic medium, it continues as 
 a single ray after refraction. 
 
 A doubly refracting medium possesses certain 
 surfaces which have the property of dividing a ray 
 of light into two rays, one being refracted in a 
 different direction to the other. Rock crystal is an 
 instance, and though it is possible to cut weak 
 prisms out of this material in such a way that the 
 refracting surfaces shall not, to an appreciable 
 extent, refract doubly, crown glass is more desir- 
 able. Different media vary greatly in density, and 
 the denser a medium, the more it retards the 
 velocity of light. Thus when a ray of light, travel- 
 ling in air, reaches the surface of a piece of glass,
 
 SIMPLEST OPTICAL PROPERTIES. u 
 
 its velocity becomes instantly reduced by more 
 than one-third, and after travelling through the 
 glass at this lessened speed, it regains its former 
 velocity as it again emerges into air. 
 
 A consequence of this remarkable property of 
 media is, that whenever a ray of light enters a 
 medium of different density, other than perpen- 
 dicularly, it is bent or refracted from its former 
 course. If the medium be homogeneous, the ray 
 pursues a perfectly straight course through it, and 
 is only refracted at its surfaces. To show how this 
 refraction takes place, it will be necessary to touch 
 lightly on some of the elementary properties of 
 light, which, according to the undulatory theory, 
 consists of vibrations propagated in a hypothetical 
 substance, called " aether," which is supposed to 
 permeate the whole of space. These vibrations 
 occur transversely, or at right angles to the axis of 
 propagation of the ray of light : just as when a stone 
 is flung into a pond, though the waves travel rapidly 
 towards the banks of the pond, the actual particles 
 of water do not move towards the banks at all, but 
 only rise and fall, mounting to the summit of a wave, 
 and then sinking into the trough left behind it, 
 so that the motion of the particles is at right 
 angles to the direction in which the waves are 
 propagated. It is the same with light, only with 
 these differences, that in aether the tiny side-to -side 
 movements are not in one direction only, like the
 
 12 PRISMS. 
 
 perpendicular* movements of the water (except in 
 polarised light), but in all directions at right angles 
 to the axis of the ray. Moreover, while the waves 
 in a pond travel along the surface only, light .travels 
 in all directions from its source, so that we have to 
 do with three dimensions instead of two. When 
 light is generated at a point, it tends to travel out- 
 wards from that point, not as we have seen, in an 
 ever-widening circle, like the waves of a pond, but 
 in an ever-increasing sphere (unless hindered, as it 
 always is, in some directions by bodies in its way 
 which absorb, refract, or reflect it). The waves in 
 a pond are enlarging circles, those of light form 
 enlarging spheres, and in each we can speak of a 
 wave-front. The motion of the waves is always in 
 a direction perpendicular to the wave-front,-f- a 
 fact which, if grasped, will help us much. A 
 moment's reflection will remind us that this is true 
 
 * It is true that the motion of the particles of water is not 
 quite so simple as this, since they describe curves, sometimes 
 even ellipses or circles, which, being parallel to the direction of 
 propagation, spoil the illustration for light, where the circular 
 or elliptical motions of the particles of aether are perpen- 
 dicular to the direction of propagation. 
 
 f I do not trouble the reader by explaining why this is so. 
 It really depends on the principle of Huygens, that the 
 disturbance at any point of a wave-front is the resultant of 
 the separate disturbances which the different portions of the 
 same wave-front, in any one of its earlier positions, would 
 have occasioned if acting singly.
 
 SIMPLEST OPTICAL PROPERTIES. 13 
 
 in the waves of water. Imaginary lines, drawn in 
 all directions from the spot where the stone entered 
 the water, will be radii of the circles, and represent 
 the directions in which the waves advance. Now, 
 if the pond be perfectly circular, the waves gene- 
 rated by a stone dropped exactly into its centre will 
 break upon the shore with the direction of their wave- 
 fronts unaltered. If, however, the pond is not circular, 
 wherever the waves meet the shore obliquely, the 
 direction of the wave-fronts will be altered, as they 
 break upon it. Similarly with light ; when it falls 
 perpendicularly on the surface of a new medium, 
 the direction of its wave-front is unchanged, but if 
 it falls obliquely, the wave-front is altered in direc- 
 tion. There is this difference, however, that the 
 light waves are not like those of the water, broken 
 upon the shore, but go on travelling through the 
 medium in a new direction — a direction perpen- 
 dicular to the new wave-front. Let us now ask, 
 " How is it that the surface of a new medium can 
 alter the direction of the wave-fronts that meet it 
 obliquely ? " It depends on the fact already men- 
 tioned, that light does not travel with equal velocity 
 through different media, but that its velocity is 
 retarded in proportion to the density of the medium : 
 just as a column of soldiers, crossing a desert at 
 " quick march," when they come to a canal that 
 lies across their path, have their velocity retarded, 
 by progression through water not being so rapid as
 
 14 
 
 PRISMS. 
 
 progression through air. If the canal lie straight 
 across their path, so that all the men in the front 
 rank reach the bank and enter the water simultane- 
 ously, the column has the direction of its front 
 unchanged. When light comes from a considerable 
 distance, the wave-fronts may be regarded as linear, 
 so that the ranks of soldiers represent successive 
 wave-fronts. 
 
 If, as in Fig. 9, the same column of soldiers find 
 a canal crossing their path obliquely \ one man in the 
 
 Fig. 9. — To illustrate refraction of light. 
 
 front rank (b) reaches the water before his com- 
 rades in rank with him, and since he is retarded 
 before they are, they gain on him, and the direction 
 of the front of the column is altered. The same 
 may be said of all the succeeding ranks, and it
 
 SIMPLEST OPTICAL PROPERTIES. 
 
 15 
 
 illustrates how the successive wave-fronts of light 
 as they break obliquely on the surface of a denser 
 medium, become altered in direction. The same 
 man, however (£), who was first to enter the water* 
 will also be first to get out of it, and he will then 
 gain on his comrades (who are still in it) as much 
 as he lost before, so that the column resumes its 
 original frontage, and pursues its original direction, 
 being only displaced a little to one side, as shown 
 by the figure. If, on the other hand, the canal 
 were triangular in shape, instead of having parallel 
 banks, the original direction would not be resumed, 
 for the man who first entered the water might have 
 to leave it last, or, even if he left it first, he would 
 
 Fig. 10. — Refraction by a plate of glass. 
 
 not gain, on leaving it, as much as he lost on enter- 
 ing it. This is analogous to what happens in the case 
 of prisms, for we have seen they are triangular in 
 section. While the refracting surfaces of a pane of 
 glass are parallel, as in Fig. 10 those of a prism
 
 1 6 PRISMS. 
 
 are inclined to each other. The consequence is, that 
 when rays of light traverse a prism, they are bent 
 from their previous course, and emerge in a new 
 direction. An imaginary line, perpendicular to the 
 surface of a medium, is called a " normal " to that 
 surface. Thus in Fig. 10, which represents a pane 
 of glass traversed by a ray of light //', the dotted 
 line n is the normal at the point of incidence of 
 the ray, and the line n is the normal at its point 
 of emergence. It will be seen that on entering 
 the denser medium, the ray is bent (or " refracted ") 
 towards the normal (zz), while at its emergence from 
 the denser medium it is refracted away from the 
 normal (V). 
 
 Deviation. — The deviation from its former 
 course which a ray of light suffers by traversing a 
 prism is the combined result of the two refractions 
 which it has undergone at the two surfaces. The 
 denser the glass, and the greater the angle of 
 the prism, and the more obliquely it is traversed 
 by the ray, the greater is the total deviation 
 it produces. With prisms of ordinary crown 
 glass, the " angle of deviation " for a ray of light 
 passing through the prism (in the direction of 
 " minimum deviation," p. 24) is slightly more than 
 half the refracting angle of the prism, if it be 
 a weak prism, and increasingly more than half as 
 the refracting angle increases. In Fig. 1 1 a ray ( ef) 
 is seen traversing a prism. On entering the glass
 
 SIMPLEST OPTICAL PROPERTIES. 
 
 17 
 
 it is bent towards the normal (n), and on leaving it 
 away from the normal (#'), so that its course is 
 altered by its passage through the prism; the ray 
 (e), incident on the first surface, was pursuing a 
 course towards /, but it now proceeds towards f. 
 
 Fig. 11. — Refraction by a prism. 
 
 The angle d contained between the forward pro- 
 longation of the entering ray (e\ and the backward 
 prolongation of the emergent ray (/) is the 
 deviating angle, or, shortly, the " deviation " of the 
 prism. The amount of deviation suffered by a ray 
 is the same, whatever part of the prism it traverses, 
 provided it forms the same angle with the normal 
 at the first surface. Thus parallel rays as g, e, in 
 Fig. 11, also emerge parallel. In the figure, the 
 angle of deviation at the first surface is w, and that 
 at the second surface is v, and it is evident at a 
 glance that the total deviation at the prism is the 
 
 sum of these two deviations. The figure is so 
 
 2
 
 1 8 PRISMS. 
 
 constructed that the angle of incidence at the first 
 surface (z), and the angle of refraction at the second 
 {/ ) are equal, and in that case the deviations at the 
 two surfaces are equal, or v = w. When we speak 
 of the deviating angle of a prism, we assume the 
 deviation to be that of a ray subject to these con- 
 ditions, for, as we shall see, under other conditions 
 the deviation is greater. 
 
 Fig. 12 shews, in a very simple, yet quite exact 
 A 
 
 \ X ' ; / 
 
 \ i ■' / / 
 
 v \ ■ / / / 
 
 w 
 
 
 
 Fig. 12. — To shew the proportion between the refracting angles 
 (A), and the deviating angles (0) of prisms. 
 
 way, how the deviating angles of prisms increase 
 more rapidly than their refracting angles. Three 
 prisms are delineated, in principal section, with 
 their apices meeting at A. The dotted lines from 
 the base of each prism enclose between them the 
 deviating angle of that prism. A prism only a 
 trifle stronger than the largest in the figure would
 
 SIMPLEST OPTICAL PROPERTIES. 19 
 
 have a deviating angle equal to its refracting angle. 
 But since for clinical purposes we never approach 
 anything like this strength, and the smallest prism 
 in the figure represents about the largest we pre- 
 scribe, we have never to do with a deviating angle 
 much more than half the refracting angle. The 
 same figure shews us how easily we may find the 
 deviating angle of any prism by construction. 
 Draw any circle about a point 0, and take any 
 point A outside the circle, such that the distance 
 A shall be to the radius of the circle in the ratio 
 of the refractive index of the glass. Thus, with 
 crown glass, since its average refractive index is 
 1 "54, if we make the radius one decimetre we shall 
 make the distance A 0=i'S4 decimetres. Then 
 with A as apex, draw the prism so that its base 
 b c shall be a chord of the circle, and its refract- 
 ing angle A shall be bisected by a straight line 
 between A and 0. Then lines drawn from the 
 centre (0) to the extremities of the base, enclose 
 the deviating angle required. 
 
 With weak prisms, there will be only a small 
 error if we express the 'ratio of the deviating angle 
 to the angle of refraction, by the decimal figures in 
 the index of refraction of the glass. Thus, if the 
 glass have an index of 1*5, the deviating angle is 
 half (-5) of the refracting angle. If the index be 
 the usual one of 1-54, the deviating angle is rather 
 more than half ('54), and so on. For exact formulae,
 
 20 
 
 PRISMS. 
 
 the reader is referred to Appendix. Dr. Jackson 
 says that of late years the tendency has been to raise 
 the index of crown glass, and that many years ago 
 it was nearer 1*52. His proposal before the Ninth 
 International Congress, to have all prisms marked 
 by the deviation they produce instead of by their 
 refracting angles, has been generally approved. 
 The Committee, appointed to consider the proposal, 
 recommended, in 1888, that : — 
 
 (1,) Prisms ought to be designated by the number 
 of degrees, " minimum deviation," they produce. 
 
 (2,) Where intervals of less than one degree are 
 desired, half degrees and quarter degrees should be 
 used. 
 
 (3,) To indicate that degrees of deviation are 
 meant, the letter d should be used; thus prism 2°d 
 will indicate a prism that produces a minimum of 
 two degrees. 
 
 The following table shews the angle of deviation 
 for prisms of from i° to 12 by the ordinary 
 
 TABLE I. 
 
 Angle of 
 
 Angle of 
 
 Angle of 
 
 Angle of 
 
 Refraction. 
 
 Deviation. 
 
 Refraction. 
 
 Deviation. 
 
 1° 
 
 32' 
 
 r 
 
 3° 48' 
 
 2° 
 
 i° 5' 
 
 8° 
 
 4 20' 
 
 3° 
 
 i° 38' 
 
 9° 
 
 4° 54' 
 
 4° 
 
 2° IO' 
 
 IO° 
 
 5° 26' 
 
 5° 
 
 2° 42' 
 
 n° 
 
 5° 59' 
 
 6° 
 
 3° 15' 
 
 I2 P 
 
 6° 32'
 
 SIMPLEST OPTICAL PROPERTIES. 21 
 
 marking, if the refractive index be taken as i - 54. 
 It will be seen that with the highest of the series 
 there is an error of only half a degree in assum- 
 ing, as we are wont to do, the deviating angle to 
 be half the refracting angle; this being an error 
 of eight and a half per cent. 
 
 It must be confessed that the dioptric measure- 
 ment of prisms lays a great burden on the optician, 
 for whereas, formerly, he could test the correctness of 
 his angle at all stages of his work, it is impossible 
 to test the deviation of a beam of light until the 
 polishing process has begun, so that the earlier 
 processes have to be repeated. Perhaps the best 
 plan is that recommended by Prentice — to keep a 
 large number of prisms in stock, of all sizes, and 
 select the one whose deviation is nearest the 
 prescription. 
 
 In attempting to make a prism of definite diop- 
 tric power, an optician should have a good idea to 
 start with of the angle which, when imparted 
 to the glass, will be most likely to satisfy the 
 requirements, and to do this he should multiply 
 the prescribed angle by two, and subtract nine 
 minutes for each degree in the prescribed angle if 
 the prism is a weak one, or ten minutes for each 
 degree if the prism is a strong one (over 6°d). 
 
 Thus to produce a prism of 2 c d, he would cut 
 the glass to an angle of 3 42'; that is, to 2X2° 
 minus 9 x 2'. To make a prism of g°d, he would
 
 22 PRISMS. 
 
 cut the glass to twice nine degrees, minus ten times 
 nine minutes, or i6° 3c/. 
 
 To make, however, calculation of any kind un- 
 necessary, what we might call a deviation protractor 
 could easily be constructed ; so that the optician, 
 instead of adjusting the legs of his compasses to an 
 ordinary protractor (see p. 3) to get the refracting 
 angle, might adjust them to the deviation protractor, 
 knowing that a prism made to fit in between the 
 legs would then produce the deviating angle. All 
 that is necessary is to work, as it were, with an 
 ordinary protractor upside down, and place the 
 pivot of the compasses at a point whose distance 
 from the centre of the arc is 154 times greater than 
 the radius of the arc, as shewn greatly reduced in 
 Fig. 13. The legs of the compasses should be 
 
 Fig. 13. — To shew how a protractor could be used to make 
 prisms of definite deviations. 
 
 opened symmetrically with respect to a line join- 
 ing their pivot and the centre of the arc. Or, on 
 the same principle, a special instrument could be 
 made, as in Fig. 14.
 
 SIMPLEST OPTICAL PROPERTIES. 
 
 21 
 
 But as prisms are at present manufactured, it is 
 extremely difficult to make them with mathema- 
 tical accuracy. 
 
 Fig. 14. — A proposed deviation protractor. The distance of c 
 from the centre of the arc is 1-54 times the radius of the latter. 
 The arc is marked in ordinary degrees. 
 
 Duane has pointed out a disadvantage in the 
 dioptric measurement of prisms in the hands of the 
 oculist, just as the one last spoken of affects the 
 optician. It is that if prisms be combined by 
 apposition against one another, the deviation pro- 
 duced by the combination is not equal to the sum 
 of their several deviations, and indeed it would be 
 far easier to calculate precisely the effect of the 
 combination if the refracting angles were known,
 
 24 PRISMS. 
 
 than if only the deviating angles were "known. In 
 this particular the disadvantage is undoubted, and 
 " accordingly " he adds with truth, " in all problems 
 involving the use of several prisms together, the 
 old system is much more convenient than the 
 new." * 
 
 Minimum Deviation. — When the points of incid- 
 ence and emergence of a given ray are equi-distant 
 from the edge of the prism, the ray is said to 
 traverse the prism symmetrically \ because the 
 angles of incidence and emergence are then, as 
 shewn in Fig. II, equal. A ray under these con- 
 ditions suffers less total deviation than if it passed 
 through the prism in any other direction, and is 
 therefore said to traverse the prism in the "direction 
 of minimum deviation," or, to put it another way, 
 the prism is said to be (in reference to the ray) in 
 its " position of minimum deviation." 
 
 It is easily demonstrated by looking at a small 
 object through a prism, and then rotating the 
 prism about its axis,f when the apparent displace- 
 ment of the object will increase with each 
 increment of obliquity imparted to the prism. It 
 will be found that there is a certain position which 
 gives smaller appearance of displacement than any 
 
 * "Archives of Ophthalmology," Vol. XX., p. 321. 
 
 t The axis of a prism is an imaginary straight line parallel 
 to the edge, and mid-way between the edge and the base.
 
 SIMPLEST OPTICAL PROPERTIES. 25 
 
 other, and that when the prism is in this position 
 small rotations of it have no appreciable effect on 
 the amount of deviation. The position of minimum 
 deviation is that most suitable for measuring the 
 optical strength of prisms, because it is the position 
 in which slight accidental aberrations have least 
 effect. 
 
 The fact that a ray of light is more strongly 
 deviated when it passes through a prism in one 
 direction than in another, is an important one, 
 accounting as it does for " prismatic astigmation," 
 and for one or two varieties of the distortions 
 produced by strong prisms. For these the reader 
 is referred to p. 40. Meanwhile, a simple mechan- 
 ical method I have adapted for comparing the angles 
 of deviation with rays of varying incidence, may be 
 described. Let two circles be described about a 
 common centre {Fig. 15), with their radii in the 
 ratio of the refractive index. That is, if the radius 
 of the smaller circle be 1, that of the larger will be 
 1*54 in the case of crown glass. At the extremity 
 (/) of the smaller radius insert a pin perpendicularly 
 into the paper, and after cutting a triangular piece 
 of paper, a b c, to represent any given prism, lay it 
 down with its side ac touching the pin (/), and its 
 apex (a) touching the outer circle. The right hand 
 edge a b of the movable triangle will then mark 
 off on the smaller circle the arc of the angle 
 of deviation, while the angle (z), between the
 
 26 PRISMS. 
 
 margin (a c) of the triangle and the line Io from 
 the pin to the centre of the circle, represents the 
 angle of incidence for each position. 
 
 By rotating the triangle into various positions, 
 ever keeping the apex in contact with the outer 
 circle, and the left hand margin in contact with 
 
 Fig. 15. — Mechanical method of shewing how the deviation pro- 
 duced by a prism alters with the angle of incidence. 
 
 the pin, we can find in a moment the arc of the 
 deviation produced for any required angle of 
 incidence ; that is, for any value of i the deviation is 
 represented by d. It will be noticed that the 
 position of the paper triangle in which it marks off 
 least of the smaller circle, and therefore indicates 
 the smallest possible angle of deviation, is when the 
 line which bisects its angle A passes through the
 
 SIMPLEST OPTICAL PROPERTIES. 27 
 
 centre O. This is the "position of minimum devia- 
 tion." It may be said, in passing, that the size of 
 the angle of emergence is represented in every 
 position by the angle between ab and xo. 
 
 It is sometimes desired to find the deviation 
 suffered by a ray which enters one surface of a 
 prism perpendicularly, and which, therefore, is only 
 refracted at the second surface. Indeed, Prentice 
 recommends this position for the measurement of 
 prisms, as being most suitable for his " Prismo- 
 meter." To find what is the deviation to be 
 expected under these circumstances, we have only 
 to revolve the paper prism till the margin ac 
 coincides with the radius / 0, when the other 
 margin ab will mark off the arc of the deviation 
 required. 
 
 DISPERSION. — By dispersion, or " chromatic 
 aberration," is meant the breaking up of light into 
 its constituent colours. It is a property possessed 
 in greater or less degree by all prisms, since the 
 differently coloured rays, being unequally refran- 
 gible, are deflected through different angles, 
 the violet rays experiencing the greatest deflection 
 and the red the least, while the paths of the 
 rays of intermediate colours are spread out between 
 these two extremes. The whole solar spectrum can 
 thus be received upon a white screen arranged to 
 intercept a pencil of light which has traversed a 
 strong prism. This property of dispersion, so
 
 28 PRISMS. 
 
 valuable in spectrum analysis, is a serious dis- 
 advantage in the ophthalmological use of prisms, 
 from the coloured margins it appears to give to 
 objects, and the want of definition it occasions, 
 just in proportion to the strength of the prism 
 used. 
 
 It is only fairly weak prisms, therefore, that can 
 be clinically employed with much advantage. It is 
 not often advisable to exceed 3 or 4, though the 
 limits depend on the visual acuity, and habits of 
 observation, of the patient. In amblyopia from 
 corneal nebulae, stronger prisms can be borne. The 
 dispersive power of crown glass is so much less than 
 of flint glass that it is invariably employed for 
 clinical purposes. Achromatic prisms can be made 
 by cementing together two prisms, one of crown, the 
 other of flint glass, with the apex of one to the base 
 of the other, since the ratio between the refractive 
 and dispersive power is different in the two kinds 
 of glass.* But though suggested long ago, such 
 combinations have been precluded by their weight 
 from clinical use. 
 
 * The dispersive power of crown glass is to that of flint 
 glass as 33 to 52 ; whereas the refractive power is about as 
 31 to 32, though it varies greatly with different specimens, 
 and must be determined for each.
 
 ' 
 
 29 
 
 Chapter III. 
 
 PRISMETRY 
 
 APART from the question as to whether it is wise to 
 prescribe prisms by their deviating angles, it is cer- 
 tainly of advantage for the surgeon to possess means 
 of noting the optical strength of the prisms he uses. 
 This is especially the case in scientific enquiries. 
 
 As the measurement of the physical angles of 
 prisms has been known by the name of " gonio- 
 metry," I have chosen the name of prismetry for 
 the measurement of their optical power, to save 
 confusion. The simplest form of goniometer is the 
 " prism-measure " of the Geneva Optical Company. 
 
 But this acquaints us only with the geometrical 
 — not with the optical properties of prisms; what 
 the surgeon needs alone to know is not their 
 refracting angle, but their deviating power over a 
 beam of light. It has been noticed already that 
 this " angle of deviation " is in each case about half 
 the angle of refraction — with weak prisms incon- 
 siderably more, and with strong ones increasingly 
 more, than half, — but apart from this difference, 
 the refractive index of different specimens of crown 
 glass varies a little, so that Donders* truly observed 
 
 * "Accommodation and Refraction of the Eye" (Sydenham 
 Society, p. 132).
 
 30 PRISMS. 
 
 of the angles of deviation, "If we wish to know 
 these accurately, it is necessary to determine the 
 deviations for each glass separately." To do this 
 with certainty and ease I contrived two simple 
 methods some years ago, one most suitable for 
 practice, the other for demonstration purposes. The 
 first can be made without expense, and employed 
 without artificial light. It consists simply of a 
 strip of paper or cardboard suspended horizontally 
 on the wall, at such a height from the floor as to be 
 about level with the eyes of the observer. The 
 card itself is marked, as in Fig. 16, in tangents of 
 degrees* for this distance. All that is necessary 
 to measure the deviating power of a prism is to 
 
 Fig. 16. — First mode of prismetry. 
 
 hold it at this distancef with its apex to the left, 
 and so that its upper border appears just beneath 
 the line of degrees, as in the figure. The vertical 
 border of the card appears necessarily displaced 
 
 * For tangents of degrees, see p. 161. A scale of this kind 
 has been used since May, 18S6, by Curry and Paxton, to whom 
 I gave it, for measuring the deviating angles of their prisms. 
 
 f The distance of the observer's eye behind the prism 
 does not affect the result in any way.
 
 PRISM ETRY. 31 
 
 towards the edge, and points upwards to the 
 number which expresses in degrees, at once 
 and without calculation, the required deflecting 
 angle of the prism. In the figure this is seen to be 
 3 . One precaution alone needs to be observed : if 
 the lower edge of the cardboard seen through the 
 prism appears disjointed from the level of the rest, 
 as in Fig. 17, the apex of the prism is not pointing 
 exactly to the left, but is either too high or too low, 
 according as that part of the broken line seen 
 through the prism is above or below the remainder. 
 A slight rotation is therefore necessary to correct 
 this, till the lower border of the cardboard appears 
 at one level, as in Fig. 17. 
 
 Fig. 17. — A prism not held truly. 
 
 The distances between the degrees of the card 
 depend, of course, on the chosen distance at which 
 it is found most convenient to hold the prism, and 
 this would depend on the size of the room and 
 other conditions. The distance of the observer's 
 eye from the prism is of no consequence; anyone 
 can easily mark a piece of cardboard for himself 
 from the accompanying table which gives the
 
 3 2 
 
 PRISMS. 
 
 distances from the right-hand border of the card 
 at which the several degrees are to be marked 
 upon it, assuming the prism to be held at a uniform 
 distance of six feet (first column), or two metres 
 (second column). 
 
 TABLE II. 
 
 For marking a card in tangents of deg 
 
 rees at 6 ft. (column A) ; 
 
 or 2 metres (column B). 
 
 
 
 A 
 
 B 
 
 
 A 
 
 B 
 
 l° 
 
 1*25 in. 
 
 3*49 cm. 
 
 9° 
 
 1 1 '4 in. 
 
 31-68 cm. 
 
 2« 
 
 2'5 » 
 
 6- 9 8 „ 
 
 IO° 
 
 I2'6 ,, 
 
 35'26 „ 
 
 3° 
 
 37 „ 
 
 10-48 „ 
 
 n° 
 
 14-0 „ 
 
 38-88 „ 
 
 4° 
 
 5'° „ 
 
 I3-98 „ 
 
 12° 
 
 1 5*3 » 
 
 42*5 n 
 
 5° 
 
 6'3 » 
 
 ITS » 
 
 13° 
 
 1 6*6 „ 
 
 46-I7 „ 
 
 6° 
 
 7'57 „ 
 
 21-0 „ 
 
 14° 
 
 I7-9 » 
 
 49-86 „ 
 
 7° 
 
 8-8 4 „ 
 
 24-56 „ 
 
 15° 
 
 I9'3 „ 
 
 53*59 » 
 
 8° 
 
 IO-I2 „ 
 
 28-11 „ 
 
 16 
 
 20-64 „ 
 
 57 35 „ 
 
 For a different range, the measurements would 
 of course differ in proportion: thus, should it be 
 decided always to hold the prism at 3 feet, the 
 distances would be half as great as in the table ; if 
 at 12 feet, twice as great. 
 
 A second method of prismetry affords a much 
 prettier demonstration of the deviating angle of 
 prisms, but needs a more concentrated illumination 
 than diffused daylight. It consists of a strip of 
 wood, as in Fig. 18, laid flat on a table or counter 
 with a shorter strip fr, fixed at right angles to its 
 further end in such wise that its plane is vertical. 
 Upon the longer strip a cylindrical lens c, is fixed 
 erect, with its axis vertical, so as to throw a line of
 
 PRISMETRY. 
 
 33 
 
 light from the gas flame g upon the strip b, which 
 is marked in tangents of degrees ; so that a prism 
 held before the cylinder c t with its base-apex line 
 horizontal, at once makes the bright line move 
 to that degree which indicates the deviating angle. 
 
 Fig. 18.— Second mode of prisraetry. 
 The flame can either be fixed to the main strip 
 or be quite separate, and it is well, if the light is 
 poor, to combine with the cylindrical lens a 
 spherical one of such strength that the source of 
 light shall be at its principal focus. 
 
 Unit of Prismetry. Three proposals are in the field 
 as to the unit of measurement for the deviation of 
 prisms — the degree, the centrad, and the prism-dioptre. 
 I leave the decision as to which possesses greatest merit 
 to others, and will here only briefly notice some of the 
 peculiarities of each. 
 
 The degree is a familiar unit, and if "possession is 
 nine points of the law" should hold its own, unless some 
 
 3
 
 34 PRISMS. 
 
 really surpassing merit attaches to its rivals. We measure 
 every other ophthalmic angle in degrees, and it would 
 certainly seem strange to measure a deviation of the eyes 
 in one unit, and correct that deviation in another. 
 Perhaps when some other unit has established its 
 superiority sufficiently to replace the degree for all 
 purposes it will be time to accept it for prisms. 
 
 The second proposal is the " Centrad," by Dr. 
 Dennett, of New York. It possesses three advantages 
 over the degree. 
 
 i. — Being a new unit, and since it is only proposed 
 to use it for the deviations of prisms and not their 
 physical angles, it might lessen the possibility of con- 
 fusing the two methods of marking prisms. 
 
 2.— It is a smaller unit than the degree, and a prism 
 with a deviation of one centrad would answer roughly 
 to a prism with a refracting angle of i°. A centrad is 
 slightly more than half a degree ('57 • . . of a degree). 
 
 3. — It has a slight relation to the metre-angle, in that 
 half the number of centimetres between the pupils indi- 
 cates the number of centrads in one metre angle. 
 
 The centrad is taken from the well-known " circular 
 measure." It is the hundredth part of a " radian," a 
 radian being the angle subtended at the centre of a 
 circle by an arc which is equal in length to the radius. 
 Circular measure has a certain theoretical interest. 
 
 The third unit, proposed by Mr. C. F. Prentice, is the 
 " Prism-Dioptre." It has much to recommend it. The 
 size of a single prism-dioptre differs inappreciably from 
 that of a centrad, both being the departure of 1 in 100, 
 that is, a deviation of one centimetre at one metre 
 distance, but the centrad is measured on the arc, and the 
 prism-dioptre on the tangent. The relation to the metre-
 
 PRISMETRY. 35 
 
 angle of the P.D. is practically the same as the centrad, 
 though not quite so perfect.* Its chief recommendation 
 is the ease of measuring on the straight, and also its 
 beautiful relation to lenses, and their decentering. It 
 has the disadvantage, however, of not being theoretically 
 suitable in high numbers for multiplication : for instance, 
 two prism-dioptres form an angle less than twice times 
 one prism-dioptre. A prism-dioptre is 34' 35". 
 
 The measurement of prisms is as easy for one unit as 
 for another, and the scale recommended on p. 30 has 
 been adapted by Prentice to the prism-dioptre, by having 
 it marked in centimetres instead of in degrees, while a 
 beautiful instrument has been constructed by him called 
 the " Prismometer," to use where great refinement is 
 wanted. To measure in centrads, a short arc would 
 have to be used, marked in hundredths of its radius, 
 or a tangent scale could be made in tangents of centrads. 
 
 The adoption of the prism-dioptre would certainly 
 reduce the decentering of lenses to extreme simplicity, 
 and this is by far the strongest point in its favour. 
 
 A lens of iD displaced laterally one centimetre has 
 the effect of a 1 P.D. prism; displaced 2 cm. of 2 P.D., 
 and so on. A lens of 2D similarly displaced, has the 
 effect of a 2 P.D. prism. 
 
 We should have only to remember that the prismatic 
 effect is that of the decentering in centimetres, multiplied 
 by the dioptric strength of the lens. 
 
 * The metre angle is the angle whose sine is half the 
 inter-ocular distance in terms of metre. Since the centrad 
 is an arc measurement, and the prism dioptre is a tangent 
 measurement, the former approaches the sine more nearly 
 than the latter. Arcs lie between sines and tangents. (See 
 Appendix, p. 159.)
 
 36 
 
 Chapter IV. 
 TESTING THE APEX. 
 
 CIRCULAR prisms, as usually sold, have their apex 
 and base indicated by a slight scratch from a 
 diamond. On testing a series of prisms by a 
 simple plan, to be described immediately, much 
 inaccuracy was noted in a large proportion, and 
 experimental work may be sometimes vitiated on 
 this account An obvious consequence of in- 
 accurate marking, is that prisms may not be quite 
 squarely set in the trial-frame ; yet the slightest 
 departure from precision in this particular alters an 
 experiment. For example, if it be desired to see 
 
 Fig. 19. — Shewing the effect of setting a prism by a wrong mark. 
 The marked apex is towards /;, and the true apex is towards a, 
 so that the flame 0, which should appear at b, appears at a. 
 
 whether a patient can overcome a prism of 15 d, 
 with its apex exactly in or out, an aberration of 
 the base-apex line through only a ninetieth part
 
 TESTING THE APEX. 37 
 
 of a circle has the effect of not only lessening in a 
 trifling degree the desired horizontal deflection which 
 it is the aim of the prism to produce, but also of 
 introducing a new and unsuspected vertical deflec- 
 tion of more than i°. This is shewn in Fig. 19, 
 where the actual flame appears displaced to a 
 instead of b ; — the true base-apex line being a, 
 though the prism is marked as if it were b ; hence 
 a b is the angle of error in setting the prism. At 
 twelve feet distant the flame would appear more 
 than two and a half inches higher than it really is.* 
 Now it is well known that vertical diplopia greatly 
 embarrasses the neuromotor apparatus, and in some 
 persons it cannot be overcome at all when greater 
 than one degree, so the prism in the experiment 
 may be put down with the verdict that it is too 
 strong to be overcome, when really it is the con- 
 comitant accidental vertical diplopia created by it 
 which cannot be overcome, or at least the effect of 
 which alters the result. 
 
 If anyone will take the trouble to test the marks 
 upon his own prisms, he will find how frequently 
 
 * The vitiating vertical deflection of a ray of light by a 
 prism whose base-apex line is supposed to be horizontal, or 
 the vitiating horizontal deflection by a prism whose base-apex 
 line is supposed to be vertical, may be found in any particular 
 case, by the following formula, sin. x — sin. D + sin. rj 
 where x is the angle required, D is the deviating angle of 
 the prism, and r the angle of accidental rotation from exact 
 rectitude.
 
 38 
 
 PRISMS. 
 
 they are misplaced ; the test can be easily made by 
 the following simple device. Draw upon a sheet of 
 paper two fine straight lines intersecting each other 
 exactly at right angles, as in Fig. 20, and hold the 
 prism horizontally above them, so that on closing one 
 eye the supposed apex apparently coincides with 
 the point of intersection of the lines, and the prism 
 appears to touch the horizontal line only at that 
 point, and does not in the least overlap it on either 
 side. If the prism is correctly marked, the vertical 
 line appears unbroken, as in Fig. 20, but if not, the 
 part of the line seen through the prism appears 
 
 Fig. 20. — Mode described for Fig 21. — Appearance with a 
 testing the apex of a prism. badly marked prism. 
 
 disjointed from the rest and displaced, as in Fig. 21, 
 towards the side of the real apex. It only remains 
 to rotate the prism till the unbroken appearance of 
 Fig. 20 is gained ; then the point on the prism's 
 edge in apparent coincidence with the point of 
 intersection of the lines may be regarded with 
 confidence as the real apex. 
 
 Greater distance of the prism from the vertical
 
 TESTING THE APEX. 39 
 
 line magnifies the phenomenon, and makes the test 
 more delicate. The true base of a prism can be 
 found and marked in just the same way as the 
 apex, and if prisms thus manufactured come into 
 use, one of the many causes of experimental in- 
 accuracy will be removed. To those who manufac- 
 ture prisms in large quantities it may be permissible 
 to suggest a special apparatus to mark the apex 
 with mathematical accuracy. Each prism should 
 be laid on a horizontal glass plate, with cross lines 
 beneath, or, better still, one longitudinal line, the 
 use of the transverse line being replaced by two 
 pins in the glass plate, half an inch apart, to press 
 the prism against, while it is rotated till the 
 longitudinal line appears continuous, then a 
 diamond held in a sliding arm, and working midway 
 between the two pins, would mark the apex.
 
 Chapter V. 
 
 PRISMATIC ABERRATION. 
 
 With the exception of chromatic aberration (p. 27), 
 which prisms share in common with lenses, the 
 optical imperfections of prisms are chiefly due to 
 the fact that no constant ratio exists between the 
 angles of incidence and refraction, but only between 
 the sines of those angles (p. 162). We have seen on 
 page 17 that parallel rays, entering a prism, also 
 emerge parallel ; but with this exception, all homo- 
 centric light, that is, all light proceeding from, or 
 going towards, a single point, is, after traversing 
 a prism, no longer homocentric. The stronger the 
 prism, and the greater the departure of the beam 
 of light from the direction of minimum deviation, 
 and the more converging or diverging its com- 
 ponent rays, the greater is the prismatic astig- 
 matism. With weak prisms, as used in practice, 
 it gives rise to little more inconvenience than the 
 spherical aberration of lenses. 
 
 But it accounts for some phenomena, which are 
 apt to puzzle those who experiment with strong 
 prisms. The astigmatism of a prism is slightly 
 akin to that produced by a weak cylindrical lens, 
 in that a cone of light, after having passed through
 
 PRISMATIC ABERRATION. 41 
 
 a prism, is somewhat flattened, its section becoming 
 slightly elliptical instead of circular ; or, in other 
 words, two rays which enter the eye in one meridian 
 have a more distant focus than two which enter it 
 in another meridian. In Fig. 22, two rays proceed- 
 ing from a point enter the pupil of an eye in the 
 
 Fig. 22. 
 
 vertical meridian. The inferior ray (a) is drawn 
 so as to traverse the prism in the direction of 
 minimum deviation, and it therefore experiences 
 the least possible deflection with which any ray 
 can pass through a prism. 
 
 Since the superior ray (J?) has a different angle of 
 incidence, it experiences a greater deflection, so 
 that on their emergence the two rays are less 
 divergent than they were before. On this account 
 they enter the eye as if they came from a point (T) 
 a little further off than it would be if there were no 
 prismatic astigmatism. 
 
 Suppose now the prism were tilted a little round
 
 42 PRISMS. 
 
 its axis, so as to bring the superior ray, instead of 
 the inferior, into the direction of minimum devia- 
 tion. The conditions would then be reversed, for 
 the inferior ray would be most deflected, and the 
 two rays would enter the pupil more divergent, and 
 as if they came from a point nearer than they would 
 do if there were no prismatic astigmatism. We 
 see, therefore, that the nature of the astigmatism 
 is altered according as the apex of the prism is 
 moved (away from the position of minimum 
 deviation) towards the object, or away from the 
 object. The greater, too, the tilting, the greater 
 the astigmatism.* 
 
 One consequence of prismatic astigmatism is that 
 objects appear altered in shape when viewed through 
 a prism. If square objects are looked at through a 
 tilted prism, they appear oblong, being narrowed in 
 one dimension, if the base of the prism be anterior 
 
 * What about the rays which enter the horizontal meridian 
 of the pupil ? Even they are not simple in their behaviour, 
 but the more peripheral ones traverse the prism higher {i.e., 
 nearer the edge) than the central ones, so that they describe 
 an increasingly curved surface as they proceed from O till 
 they reach the prism, and after leaving it, this transverse 
 curve (with its concavity upwards) becomes less and less, 
 till they enter the pupil in the straight line of its horizontal 
 diameter. 
 
 This will be easily understood after the explanation of the 
 second form of prismatic aberration, since it depends on 
 the fact that the peripheral rays have, after leaving the 
 prism, a longer course than the central ones.
 
 PRISMATIC ABERRATION. 43 
 
 to the apex, and broadened if the apex be much 
 anterior to the base. If a scale of equi-distant 
 figures on the wall be viewed through a prism with 
 its apex to the right, the intervals between the right 
 hand figures will appear larger, and those between 
 the left hand figures smaller, than they should be.* 
 An undescribed form of prismatic aberration is 
 observed when a long straight line is looked at 
 through a prism. It appears curved, with its con- 
 cavity towards the apex of the prism. Let us 
 endeavour to give an explanation of this pheno- 
 menon, and in language which will make it in- 
 telligible to an unmathematical reader. Take a 
 paper triangle, as in Fig. 23, and draw a line bisect- 
 ing its acutest angle, such as af. Then, if we 
 imagine the base (b c) of the triangle to be the long 
 
 * It will be easy to understand this from Fig. 22, if the eye 
 there represented be imagined as the object looked at by an 
 observer's eye at 0. If the prism be in a position, such that 
 the most apical ray (b) is deflected more than the basal ray 
 (a), objects will appear vertically lengthened, while, if the 
 basal ray were most deflected, objects would appear vertically 
 shortened. In this use of the figure, the rays of light 
 represent " lines of direction," meeting at the nodal point of 
 the eye, and including between them the "visual angle." 
 The apparent size of objects depends on the size of the visual 
 angle, and it is evident that this would be larger when the 
 apical " line of direction " is bent most, and smaller when 
 the basal one is bent most. Each line of direction is of 
 course one ray of a cone of light, the base of which is the 
 observer's pupil, and the apex some point of the object.
 
 44 
 
 PRISMS. 
 
 horizontal line we are looking at, and a the position 
 of the observer's eye, the lines a &, a f, and a c re- 
 present three rays of light as they would reach the 
 eye were no prism in the way. We may, for our 
 purpose, suppose the size of the pupil to be in- 
 considerable, so that rays from every point of the 
 
 Fig. 23. 
 
 line travel to the eye at a in one plane — the plane 
 of the paper. Now bend the triangle at de over 
 the sharp edge of a table, and we have what at first 
 sight we might think to be the alteration in the 
 direction of the light to be introduced by inter- 
 posing a prism, edge up, in the position de\ for 
 the prism deflects every ray of light towards its 
 base, one as much as another. 
 
 The paper triangle does not, however, truly re- 
 present the case, for if it did we should not see the 
 line curved but straight, since the light would still
 
 PRISMATIC ABERRATION. 45 
 
 enter the eye in one plane, for the smaller triangle 
 ade is just as much a plane as the whole triangle 
 was at first. What, then, is the explanation ? It 
 is this, that the distances a d and a e being greater 
 than the distance ag, the gradient is less, as even a 
 horse knows who prefers to descend a hill obliquely. 
 A fly walking down e a would not have so steep a 
 walk as one walking down g a. The paper, there- 
 fore, does not represent the course of the rays 
 through a prism, for a prism imparts equal gradients 
 (that is, equal steepness) to all the rays. For the 
 rays d a and e a therefore to possess the same 
 gradient as g a, they must traverse the prism higher 
 up, just as a long hill is higher than a short one of 
 equal steepness. If we took a triangle of elastic 
 material, and stiffened the base of the triangle, and 
 then bent it at de over a curved edge, with its con- 
 cavity upwards, we would then represent the course 
 of the rays of light, and show why the line appears 
 curved. 
 
 So far we have only spoken of prisms held 
 before one eye, the other being closed. Bin- 
 ocular distortion results when both eyes are fitted 
 with prisms, and has received its partial explana- 
 tion, I believe, from Wadsworth, to whose paper* 
 I would refer those interested, since it is difficult 
 to give a just account of it without reproducing 
 
 * Trans. Amer. Oph. Soc, 1883.
 
 46 PRISMS. 
 
 his diagrams in full. It depends on the different 
 deviations produced with different angles of 
 incidence, as already described in speaking of 
 prismatic astigmatism, and accounts for the spherical 
 appearance of flat surfaces when they are viewed 
 through prisms. 
 
 Since tangents increase faster than their angles (p. 159), 
 it follows that when we look with one eye at a plane surface, 
 the details of that surface are more crowded together in the 
 peripheral portions of the retinal image than in the central 
 portions. But we have learned to disregard this, and 
 consider it normal. Prisms with edges out disarrange 
 this peripheral overcrowding, in binocular vision, in a way 
 which reminds us of a spherical or cylindrical surface. 
 Not only so, but the eyes in glancing from detail to 
 detail, make different excursions when viewing the 
 periphery of a ' spherical surface, than that of a plane 
 surface, in proportion as the tangent to the surface is 
 inclined to the visual axis. A similar alteration in the 
 excursions, when we turn the eyes from side to side, takes 
 place in consequence of wearing prisms. It is really 
 the altering of the motions of the eyes which accounts 
 most, I believe, for the illusion. It is most marked when 
 prisms are worn edge out ; a plane surface then appears 
 convex towards the observer. With prisms edge in a 
 plane surface appears concave.
 
 47 
 
 Chapter VI. 
 
 ROTATING PRISMS. 
 
 We are indebted to Sir John Herschel for show- 
 ing how, by placing two prisms in apposition, and 
 rotating them in opposite directions, we can produce 
 the effect of a single increasing prism. If two 
 prisms of equal strength be placed with the apex 
 of each against the base of the other, they so 
 neutralise each other as to have the effect of only 
 a thick plate of glass. The more they are rotated 
 from this position, the greater is the prismatic effect 
 of the combination, till it reaches its height, when 
 the two apices coincide. Cretes, of Paris, mounted 
 two such prisms in a circular frame with a handle, 
 so that on moving a button along the handle the 
 prisms revolved in opposite directions at equal 
 rates. This useful instrument is commonly known 
 as " Crete's prism," or the " prisme mobile." Each 
 prism has a refracting angle of 12°, and the instru- 
 ment is marked accordingly. Landolt has had it 
 marked in degrees of deviation, and metre angles. 
 If we wish to know how strong a prism can be 
 placed before one eye without creating diplopia, 
 we start at zero, and press up the button till double
 
 48 PRISMS. 
 
 vision commences, when the strength of the prism 
 can be read off. 
 
 By far the neatest form, however, in which 
 Herschel's prisms are put up, is that of the "Rotary 
 prism," designed by Dr. S. R. Risley, of Phila- 
 
 Fig. 24. — Risley's Rotary Prism. 
 
 delphia. It is small and circular, and can be placed 
 in an ordinary trial-frame. On turning the little 
 button the two prisms, each of 15°, rotate in oppo- 
 site directions. The diameter in which the button 
 lies coincides with the base-apex line of the virtual 
 prism, however much the actual prisms are rotated. 
 The virtual prism can be increased from o° to 30 
 (iS°d). The markings indicate the physical angle 
 of the virtual prism, not the deviating angle. If 
 the apex of the front actual prism be to the button 
 side of zero, the position of the button indicates the 
 apex of the virtual prism ; if the actual apex be to 
 the other side of zero, the button indicates the base
 
 ROTATING PRISMS. 
 
 49 
 
 of the virtual prism. Every form of Herschel's 
 prism, however, has some disadvantages. The 
 diminution in the visual acuity, occasioned by the 
 chromatic aberration and prismatic astigmatism, is 
 in one eye only, and thus the desire for single 
 vision is lessened more than if it were equally dis- 
 tributed over both eyes, as in the apparatus sketched 
 in Fig. 25, where one prism revolves in front of 
 each eye. This apparatus would only be of use for 
 testing convergence and divergence. To use it, we 
 would start with both prisms, apex upwards, and 
 rotate the apices towards, or away from, each 
 other. The plane in which both visual axes lie is 
 depressed in so doing ; but this is of no account, 
 while in addition we obtain the increased converg- 
 ence or divergence of the visual axes which would 
 
 Fig. 25. — Proposed rotary prismatic trial frame with prisms 
 before both eyes. 
 
 be produced by prisms with their apices inwards or 
 outwards. In the following table I have shewn 
 how much each prism needs to be rotated to give 
 
 4
 
 5° 
 
 PRISMS 
 
 the horizontal effect of i°d, 2°d, etc., supposing the 
 strength of each actual prism to be 8°d. 
 
 TABLE III. 
 
 Rotation Required. 
 
 Horizontal Effect. 
 
 Rotation Required. 
 
 Horizontal Effect. 
 
 7° 8' 
 
 I°d 
 
 38° 30' 
 
 5 e d 
 
 14 23' 
 
 2°d 
 
 48° 24' 
 
 6°d 
 
 2i° 53' 
 
 3 °d 
 
 6o° 53' 
 
 7 °d 
 
 29 50' 
 
 4°d 
 
 90 
 
 8°d 
 
 The table is made from the formula below, in 
 which H is the required horizontal effect for each 
 prism, D the deviating angle of each prism, and 
 r the rotation of the axis of each from the vertical. 
 Then 
 
 tan. H. 
 
 sin. r — 
 
 tan. D. 
 
 For sines and tangents, the reader is referred to 
 page 161. Since the second column in the table 
 gives the deviation imparted to each line of fixation, 
 it must be multiplied by two to give the total effect 
 on convergence, and to compare it with Crete's or 
 Risley's prisms it must again be multiplied by two, 
 since these are marked according to the refracting 
 angles and not according to the angles of deviation.
 
 5* 
 
 Chapter VII. 
 
 IMAGES BY INTERNAL REFLECTION. 
 
 HITHERTO we have only considered the refraction 
 of light by prisms, but at each surface a smaller 
 portion is also reflected. The more oblique the 
 incidence of a beam of light, the greater is the pro- 
 portion reflected, and the brighter is the image 
 produced by reflection. 
 
 Fig. 26. — Image produced by internal reflection within 
 a prism. 
 
 The light reflected from the first surface of a 
 prism is lost to the eye altogether, being returned
 
 52 PRISMS. 
 
 into space, but that which, after refraction at the 
 first surface, undergoes internal reflection at the 
 second surface, as at R in Fig. 26, is again reflected 
 internally from the first surface at R' (though at 
 each surface some escapes by refraction) before it 
 finally reaches the eye by refraction at r. Even at 
 r a portion is again reflected internally, and this 
 internal reflection from surface to surface goes on 
 till the base of the prism is reached, or till all the 
 light is, for practical purposes, lost by escaping from 
 the prism. With a weak prism we may, on 
 looking through it at a flame, see a series of images 
 from internal reflection, especially if we hold it 
 obliquely to increase their brightness, but each 
 becomes fainter than the last. They, and the 
 flame, all appear in one straight line, which is 
 parallel with the base-apex line of the prism. 
 Only the first of these images is illustrated in 
 Fig. 26. 
 
 When the incident ray (i) traverses the prism in the 
 direction of minimum deviation, the angle of reflection 
 at R is equal to the refracting angle (A) of the prism, 
 and each subsequent reflection is by an angle greater 
 than the last by twice the angle of the prism (3A, 5A, 7A, 
 etc.). It is under these conditions that the course 
 of the rays can be studied to most advantage, for one 
 finds by experiment that moderately tilting a prism away 
 from this position has very little effect on the apparent 
 position of the image. 
 
 Since the ray which escapes at r into the eye
 
 INTERNAL REFLECTION 53 
 
 determines the direction in which the faint image is 
 projected, the projection is indicated by the dotted 
 line/'. The ray/ is one which enters the eye by 
 refraction only, and is projected in the direction of 
 the dotted line p. The angle between the two 
 dotted lines p and p' represents, therefore, the 
 apparent visual angle between the bright image of 
 the flame seen by refraction only, and the first faint 
 image seen by reflection as well. Since the 
 imaginary line joining these two images is exactly 
 parallel to the base-apex line, we are provided with 
 a very beautiful way of setting a prism exactly 
 horizontal or vertical : we have only to see that 
 these two images are horizontal or vertical relatively 
 to each other. In other words, the faint image of a 
 flame viewed through the centre of a prism points 
 exactly to the apex of the prism, and it is curious 
 that so simple a guide does not appear to have been 
 hitherto utilized. Could we not utilize also the 
 distance between the bright image of a flame and its 
 faint image for measuring the strength of a prism ? 
 For the stronger the prism the greater their distance. 
 Nothing is easier than to say what figure of a scale 
 is covered by the faint image of a flame placed 
 at the zero of the scale and looked at through 
 a prism, and were the refractive index of glass 
 a constant quantity, this plan would provide us 
 with a more delicate test of the strength 
 of a prism than any in use. But unfortunately
 
 54 PRISMS. 
 
 there are slight differences in the refractive index, 
 and the visual angle depends not only on the angles 
 of reflection, but also on those of refraction. The 
 formula I have made, however, shows that the 
 figure on a tangent scale pointed out by the faint 
 image, indicates, without much error, that the angle 
 of the prism is nearly one-third, and the deviating 
 angle nearly one-sixth, of that expressed by the 
 scale. If we know the index of refraction, or have 
 such confidence in the uniformity of the glass as to 
 take its average for granted, we can find the exact 
 strength of the prism by a formula. The distance 
 of the scale should not be less than a metre, 
 preferably two or five, if great delicacy be 
 required. 
 
 I will endeavour to show how I constructed a formula. 
 Let a line be drawn from R, such that if it represented 
 a ray incident at R its refracted ray would be Rr. 
 Then the angle (S) between this line and the ray i\ is 
 the angle expressed by the figure on the scale covered by 
 the faint image, for it is evident that light proceeding 
 from n, and light proceeding from i enter the eye as one 
 in the beam from r. But the ray Rr forms an angle of § A 
 with the normal, therefore the angle of incidence of the 
 ray n is sin. ~ l (n sin. f A). This gives us the inclination 
 of n to the normal. The inclination of i to the normal 
 is evidently sin." 1 (/x sin. |) ; but these two angles to- 
 gether compose 5. So that 6* = sin. _1 (,«, sin. § A) + 
 sin. -1 (/A sin. |). From this a table could be easily con- 
 structed for any given index of refraction.
 
 INTERNAL REFLECTION. 
 
 55 
 
 In the table which follows, I have taken the 
 index of refraction as 1-54. 
 
 TABLE IV. 
 
 Refracting Angle of 
 Prism. 
 
 Projection of Faint Image 
 on a scale. 
 
 1° 
 
 3° 4' 
 
 2° 
 
 6° 9' 
 
 3° 
 
 9° 14' 
 
 4° 
 
 12° 21' 
 
 5° 
 
 15° 27' 
 
 6° 
 
 18° 34'
 
 56 
 
 Chapter VI II, 
 
 CLINICAL PROPERTIES OF PRISMS. 
 
 The only clinical use of prisms is to change the 
 direction of the rays of light, but this is fruitful in 
 its secondary applications. Prisms always produce 
 an optical illusion, for they make objects appear in a 
 different position from that which they actually 
 occupy. 
 
 Clinical prisms, as we have seen, are generally 
 circular, their thinnest point being called the 
 
 Fig. 27. — To shew how an object at (0) appears displaced, not in 
 
 the direction d towards the apex (a), but in the direction e towards 
 
 the edge (be), and parallel to the " base-apex line" (a /). 
 
 " apex," their thickest part the " base," while an 
 imaginary line between the apex and base may be 
 called the " base-apex line" All objects viewed
 
 CLINICAL PROPERTIES. 57 
 
 through a prism appear displaced in a direction 
 parallel to this line and always towards the edge. 
 It is customary to say that objects appear displaced 
 towards the apex, and in practice there is no harm 
 in using this convenient though less correct mode 
 of expression, provided it be not misunderstood. 
 Fig. 27 illustrates the difference, and shews that 
 the object does not appear displaced in the 
 direction d towards the apex a, but in the direction 
 e towards the edge b c, for while represents the 
 real position of the object, e represents its apparent 
 position as seen through the prism. If the prism 
 be rotated, its edge, of course, rotates with it, but in 
 all positions the object will appear displaced to the 
 same extent towards the edge, so that, in making a 
 complete revolution of a prism, the false image will 
 appear to revolve at an equal rate round the real 
 position of the object. 
 
 Lines viewed throngJi a prism. — If, instead of 
 using a small object, we look at a vertical line on 
 the wall, or the edge of a door, as xx in Fig. 28, 
 through a prism held several inches from the eye 
 with its apex at a, we observe that the part of the 
 line seen through the prism appears disjointed from 
 the rest in a direction towards the edge of the 
 prism, but the disjointed portion still appears a 
 nearly straight line. If another line, such asjj/jy, be 
 in view through the prism at the same time, its dis- 
 jointed portion will appear displaced in the same
 
 5^ 
 
 PRISMS. 
 
 direction, and to exactly the same amount as that 
 of the other line xx. It will be noticed too, that 
 movement of the prism from side to side will not 
 affect, in the slightest degree, the apparent position 
 
 Fig. 28. — To show the apparent displacement of lines 
 through a prism. 
 
 of the disjointed portions of the lines. Herein a 
 prism widely differs from a lens, for since the re- 
 fracting surfaces of any prism are of necessity 
 inclined to each other by the same angle in every 
 part of their area, it follows that the apparent 
 displacement of an object is the same through 
 whatever part of the prism it is viewed. It is true 
 that rotation of the prism will alter the apparent 
 position of the disjointed portions of the lines, but 
 they will still continue (if the prism be weak) vertical. 
 Herein again a prism differs from a spherical lens, 
 rotation of which has no apparent effect whatever, 
 while a cylindrical lens differs also from a prism, in 
 that when it is rotated, a line viewed through it 
 appears distorted from the vertical. When a prism
 
 CLINICAL PROPERTIES. 59 
 
 is rotated, the apparent displacement of the dis- 
 jointed portion varies in amount according to the 
 rotation. The maximum displacement is obtained 
 when the base-apex line is at right angles to the 
 line looked at, and the displacement becomes less 
 and less as this position is rotated from till the 
 base-apex line becomes parallel with the line 
 viewed, in which position the displacement is nil, 
 or, rather, it appears nil t for, in fact, there is just as 
 much displacement, but being in the direction of 
 the whole line, it is not evident.* 
 
 Angle of False Projection. — Since the ap- 
 parent position of an object in space is determined 
 
 I—. 
 
 Fig. 29. 
 
 by the direction in which the rays of light from the 
 object enter the pupil, it follows that, when viewed 
 
 * It will be noticed that a long straight line, viewed 
 through a prism, held about an inch from the eye, with its 
 base-apex line at right angles to it, appears curved, with its 
 concavity towards the apex. This is explained on page 43.
 
 60 PRISMS. 
 
 through a prism, the object will appear misplaced 
 by an angle which is nearly identical with the 
 deviating angle of the prism. 
 
 In Fig. 29 the real position of the object is at 0, 
 but it appears to be at /, because the pencils of 
 rays enter the pupil as though they came from I. 
 
 The angle by which an object appears displaced 
 ("angle of false projection") is always less than the 
 actual deflection of light by the prism, owing to the dis- 
 tance between the prism and the centre of rotation of 
 eye, as shown in Fig. 30, where the deviating angle of 
 
 Fig. 30. — To illustrate the discrepancy between the deviating 
 angle of a prism and the apparent displacement of an object seen 
 through it. 
 
 the prism (oi'F) is evidently greater than the angle of 
 false projection (ocF). But generally the distance of 
 the object is so great compared to the distance of the 
 prism, that the two angles may be taken as practically 
 identical. 
 
 Displacement of tlie visual axis by prisms. — We 
 have seen that prisms appear to displace objects in 
 the direction of their edge. Since an eye tends to be 
 diverted towards the (apparently) new position of 
 the object, it follows that the line of fixatio7i is also 
 displaced towards tlie edge, and in working with
 
 CLINICAL PROPERTIES. 
 
 61 
 
 prisms these two clinical properties are all that 
 need be remembered. Fig. 31 illustrates both : a 
 
 Fig. 31. — A prism before an eye, in monocular vision. 
 
 prism is placed before one eye, the otJier being 
 covered, and it is evident that the object O appears 
 displaced to F, and the line of fixation v is diverted 
 from to F, — both in the direction of the apex a. 
 The line F C in which the false image lies is called 
 the " line of projection," since it marks the direction 
 in which the picture on the retina is mentally 
 projected. 
 
 Overcoming of Prisms. — With binocular vision, 
 as in Figs. 32 to 35, the conditions are not quite so 
 simple. In all these figures the continuous lines 
 shew the actual course of the rays from the object 
 O, and the dotted lines are the lines of projection. 
 They almost explain themselves : in all it will be 
 seen that the object appears displaced towards the 
 edge of the prism, though in some (Figs. 32 and 35)
 
 62 
 
 PRJSMS. 
 
 there is diplopia, since the object is seen in its true 
 position O by the naked eye at the same time that 
 its false image F is seen by the other in the 
 
 0. 
 
 Figs. 32 and 33. — Prisms not overcome, and therefore causing 
 diplopia. 
 
 direction of the edge of the prism, which has its 
 edge in in Fig. 32, and its edge out in Fig. 33. In 
 these two figures the conditions are those in which 
 a prism is not " overcome,'' that is, the desire to 
 unite the true and the false image into one is not 
 great enough to cause the visual axis (v) of the 
 right eye (c) to accommodate itself to the new 
 direction of the pencils of light from the object; or, 
 to put it another way, the association between 
 accommodation and convergence is too strong for 
 the eyes to accommodate for O, and yet at the 
 same time, converge for a much nearer point 
 (Fig. 32) or a much farther point (Fig. 33). There
 
 CLINICAL PROPERTIES. 
 
 63 
 
 is, as a necessary consequence, double vision. The 
 eyes have, as it were, to choose between double 
 vision on the one hand, and the maintenance of an 
 abnormal relation between convergence and accom- 
 modation on the other. With weak prisms they 
 prefer the latter, but with prisms above a certain 
 strength they have to put up with the former. 
 In Figs. 34 and 35 the prisms are "overcome/' 
 
 <?F 
 
 \ 
 
 * 
 
 ■P 
 
 Figs. 34 and 35. — Prisms overcome ; no diplopia. 
 and there is no diplopia ; it has been corrected by 
 the desire for single vision, and the two images are 
 fused into one. Now, the united image appears in 
 a false position, though the angular displacement of 
 the line of projection, p F, is only half that of the 
 false image alone in the previous examples. The 
 diplopia is corrected by a rotation of the eye so as
 
 64 PRISMS. 
 
 to receive again upon its fovea centralis the picture 
 of the object which the prism had dislodged to 
 another part of the retina ; thus in these two 
 figures the line of fixation, v C, has come to be in 
 line with the rays of light coming through the 
 prism from the object, and since both eyes receive 
 a picture on the fovea, vision is single. In Figs. 32 
 and 33 there is no definite line of fixation for the 
 right eye, since it is fixing nothing, and it is clear 
 that the picture must fall on the retina away from 
 the fovea ; though with every effort to unite the 
 images and bring the axis of vision, v C, into the 
 line of the rays, the position of the picture on the 
 retina will vary, and the images will move towards 
 or from each other. 
 
 Prisms set with their edge inwards, as in Figs. 32 
 and 34, are called adducting prisms, and those 
 with their edge outwards, as in Figs. 33 and 35, are 
 called abducting prisms. The former, when vision 
 is binocular and without diplopia, by increasing the 
 necessary convergence of the eyes, make objects 
 appear nearer than they actually are, and the latter 
 make them appear too far away. Thus in 
 Fig. 34 the real object 0, appears to be at F* 
 As Hering has shewn, convergence occurs as if for 
 the cross, and both eyes are turned towards / by an 
 
 * Theoretically the combined image should be at /, were 
 convergence the only criterion, but accommodation remains 
 for a greater distance, and the "knowledge of distance"' 
 removes its apparent position from /to F.
 
 CLINICAL PROPERTIES. 65 
 
 impulse of the conjugate innervation which turns 
 the two eyes to the left : it is the mental cognizance 
 of this effort which imparts corresponding obliquity 
 to the line of projection,/ F. The prism, therefore, 
 does not test the strength of either rectus, since 
 convergence is a single action affecting both eyes 
 equally, but it estimates by how much convergence 
 can be made to exceed accommodation, or vice 
 versa. The two functions are so associated in daily 
 work that there are limits to the amount by which 
 either can be increased or diminished without the 
 other. Prisms should be placed as close as possible 
 to the eye, then their angles of deviation nearly 
 express the diplopia, or corrective squint, they 
 occasion, or the sum of both if both are present. 
 
 One of three events, therefore, may happen on 
 placing a prism before an eye. (1,) If vision is 
 monocular, one false image is seen, whose distance 
 from the actual position of the object is unvarying, 
 and dependent entirely on the deviating angle of 
 the prism, Fig. 31. (2,) With binocular vision the 
 prism may be too strong to be overcome, in which 
 case there is diplopia with an inconstant distance 
 between the images, which approach each other 
 spasmodically with every effort to overcome the 
 prism. (3,) The diplopia may be overcome and 
 the object appear single, though its position in 
 space is misjudged through an angle practically 
 equivalent to half the deviating angle of the prism. 
 
 5
 
 66 
 
 Chapter IX. 
 
 ADJUSTMENT OF PRISMS IN THE 
 TRIAL-FRAME. 
 
 If the apex and base of a circular prism are 
 correctly marked, there is no difficulty in setting it 
 with the base-apex line either exactly vertical or 
 horizontal. But if there should be any doubt about 
 their precise position, the following simple ex- 
 pedient will at once enable us to detect and correct 
 any malposition. If the base-apex line is wished 
 to be horizontal, as with the right hand prism of 
 Fig. 36, hold the trial-frame a few inches from the 
 
 Fig. 36. — Two prisms in a trial-frame. 
 
 eyes, so that, as represented in the figure, the upper 
 extremities m m m m, of its sockets coincide to all 
 appearance with a horizontal line a b c, upon the 
 wall, door, or window : if this line appears con-
 
 ADJUSTMENT IN TRIAL-FRAME. 67 
 
 tinuous, the prism is correctly set, but if that part of 
 it visible through the prism appears disjointed from 
 the rest, as d in Fig. 36, the apex is either too high 
 or too low, according as the apparent disjointment is 
 upwards or downwards. In the figure the apex is 
 too high, and the correction is therefore easily made 
 by rotating the prism so as to depress the apex till 
 the line appears continuous. If the base-apex line 
 is wished to be vertical, as with the left hand prism 
 of the same figure, the horizontal line on the wall 
 must be supplemented by another at right angles to 
 it, as ef'iVi the figure : again adjusting the frame as 
 before to the horizontal line of sight, the rectitude 
 of the prism is now indicated by the appearance of 
 the vertical line. If its course appears undeviating, 
 the setting is faultless, but if, as in the figure, the 
 part seen through the prism is dissociated from the 
 rest, the apex is shewn to be too much to the same 
 side, and it therefore needs readjustment. With 
 artificial light, the images by double internal re- 
 flection can be utilized to great advantage, as 
 described on page 53. The best way is to place 
 the trial-frame on one's own face, and rotate the 
 prism till the faint image appears level with the 
 flame, or vertically above it. 
 
 Resultant Prisms. — We sometimes wish to 
 combine the effect of a vertical prism of known 
 strength with the effect of a horizontal prism of 
 known strength. By vertical and horizontal prisms
 
 68 PRISMS. 
 
 are meant prisms whose base-apex lines are respect- 
 ively vertical and horizontal. It is true that we may 
 place the vertical prism before one eye, and the 
 horizontal one before the other. But as a rule it is 
 better to divide each prism between the two eyes to 
 equalise the weight. In that case, let R stand for 
 the deviating angle of the resultant prism before 
 each eye, and Fand H for those of the vertical and 
 horizontal prisms respectively for each eye ; and 
 let r be the angle from the vertical at which the 
 base-apex line of the resultant prism must stand. 
 Then 
 
 Fan. R = V Tan. 2 V + Tan. 2 H. 
 Tan. H 
 
 and Sin. r = 
 
 Tan. R 
 
 As Dr. Duane truly says, for the weak prisms we 
 prescribe, the sine, arc, and tangent may be taken as 
 identical without sensible error. Then the simpler 
 formulas suffice, 
 
 R = V V 2 + H* 
 
 and Sin. r = — • 
 
 I am indebted to Dr. Duane for correcting a slight 
 error which crept into this section in the first edition. 
 For the simplest proceedings of all, see Appendix, 
 page 158.
 
 ADJUSTMENT IN TRIAL-FRAME. 69 
 
 CLINICAL STRENGTH OF PRISMS. 
 
 The optical strength of a prism is invariable, but 
 its clinical strength, or physiological strength, 
 depends on the use that is made of it. For instance, 
 when a pair of adducting prisms are worn in the 
 usual way, their effect on convergence is least on 
 looking straight forward to a distance, and becomes 
 greater on looking to either side, and also on near 
 vision. This is due to principles already explained 
 (p. 24). When abducting prisms are worn, the effect 
 of the pair on convergence is also greater on looking 
 to either side than on looking straight forward, and 
 there is a certain distance, dependent on their 
 strength, beyond and within which their effect 
 increases. These really unimportant variations 
 may be lessened by placing the bases of adducting 
 prisms slightly in advance of their apices, and the 
 bases of abducting prisms slightly in advance for 
 distant and in arrear for near vision. 
 
 There is, however, one difference between the opti- 
 cal and clinical strength of prisms, which is of some 
 slight importance, and may perhaps be commended 
 to those who prescribe prisms for hyperphoria. 
 
 A vertical prism, which fully corrects a hyper- 
 phoria in distant vision, only partially corrects it in 
 near vision, for the clinical effect of a vertical prism, 
 on the separation of the visual axes, is greater in 
 distant than in near vision. This is shewn in Fig. 
 37, where the line O N represents the visual axis of
 
 jo PRISMS 
 
 the naked eye, and the lines n and n ', that of the 
 other eye, on looking, through a prism, at a distant 
 object, and a near object, in turn. 
 
 ___! 
 
 N 
 
 P*S> 37- — To shew that the clinical strength of a vertical prism is 
 greater in near than in distant vision. 
 
 For practical purposes, since the position of the 
 prism, and the direction of vision, are so incon- 
 stant, it will be better to make a simple approximate 
 rule than to give useless formulae, and the following 
 one will be found quite sufficient if any be needed. 
 
 Divide the deviating angle of the prism by the 
 distance in inches of the object from the centre of 
 the eye to find the reduction in the effect of the 
 prism in near vision. Thus, with vision for five 
 inches, the elevation of the visual axis by a prism 
 is one-fifth less than in distant vision, so that a 
 prism of 5 d would have an effect of 4 on the 
 visual axis. With vision for ten inches, the eleva- 
 tion of the visual axis would be one-tenth less, and 
 so on. It is well to know the fact thus treated of, 
 because, if a patient fitted with vertical prisms says 
 they suit him best in near vision, it may mean they 
 are too strong, whereas, if they suit him as well in 
 distant vision, they are probably not.
 
 71 
 
 Chapter X. 
 
 DECEXTERIXG OF LENSES; 
 
 AND COMBINATIONS OF PRISMS WITH LENSES. 
 
 INSTEAD of imparting sphericity to the surfaces 
 of a prism, and thus combining a prism and a 
 lens, where it is wished to obtain the effect of 
 both, it is possible to get the same result more 
 accurately by simply decentering the lens, a pro- 
 cess which, though already well known, may be 
 simply explained. 
 
 The "optical centre" of a lens is that point 
 traversed by all rays which, after entering the lens, 
 emerge from it in a direction parallel to their 
 former course.* All rays which do not traverse 
 the optical centre are bent from their former course 
 to a degree which depends on the distance from 
 this point, at which they pass through the lens — 
 the greater the distance the greater the deflection. 
 In other words, a lens, in every part other than the 
 optical centre, has the effect of a prism upon any 
 
 * This one "property" is all that is necessary for our 
 present purpose, hence it is mentioned, instead of giving 
 a correct definition. It is that point in the principal axis 
 of a lens, which divides the line joining the two centres of 
 curvature in the ratio of the radii of curvature.
 
 7 2 
 
 PRISMS. 
 
 single ray of light, — the effect of a weak prism near 
 the optical centre, and of a stronger and yet stronger 
 one with every further removal from it, and this 
 equally with concave and with convex lenses. It is 
 evident, therefore, that by shifting a lens so as to 
 bring a more peripheral part into use, a prismatic 
 effect can be obtained just as much as if a prism 
 had been combined with the lens in its former 
 unshifted position. We can alter the position of 
 the optical centre in one of two ways, the prismatic 
 
 QO> 
 
 Fig. 38. A decentred lens. 
 
 equivalent of which is identical, but each of which 
 possesses an advantage of its own. First, the lens 
 may simply be displaced as it is, rim and all, by 
 lengthening or shortening the spectacle-frame; or, 
 secondly, the frame remaining unchanged, the lens 
 can be decentred in its rim, as shewn in Fig. 38, 
 The focal length of this lens is exactly the same as 
 of that shewn in Fig. 39, inasmuch as its surfaces 
 have the same radius of curvature, but it is as 
 though it were cut peripherally, as shewn in Fig.
 
 DECENTERING OF LENSES. 
 
 73 
 
 40, a b from a larger lens cd, so that its optical (0) 
 
 £T>a 
 
 Fig. 39. A lens normally centred, 
 and geometrical (G) centres do not coincide as in an 
 ordinary lens. A brief study of Fig. 38, which 
 
 Fig. 40. Peripheric lenses cut out of a larger one. 
 
 gives the lens a b, of Fig. 40 in section, will show 
 that the effect of cutting it eccentrically out of a 
 larger lens is exactly the same as if a smaller lens 
 of the same strength had been split to admit a 
 prism between its two halves. Without altering 
 its focal length then, a prism has been virtually 
 introduced. The geometrical centre of a lens is 
 the point midway between all edges, as G in Figs. 
 38, 39, and 40. The optical centre, on the other
 
 74 PRISMS. 
 
 hand, lies in the thickest part of a convex lens and 
 the thinnest part of a concave one. For determin- 
 ing its position in any particular lens, methods will 
 be described further on. A lens is said to be 
 truly centred when the optical and geometrical 
 centres coincide as in Fig. 39 ; but to be decentred 
 when, as in Fig. 38, the optical centre (0) and the 
 geometrical centre (G) are apart, the amount of 
 decentration depending on their distance apart 
 The two points may be so far removed from each 
 other that the optical centre may come to lie out- 
 side the lens altogether. Such would evidently be 
 the case with the small lens ef'm Fig. 40, since the 
 optical centre is at O. Fig. 41 shews this small 
 
 Fig. 41. A lens with its optical centre 0, far outside itself. 
 lens in section, and it is evident at a glance that 
 opposite surfaces have nowhere parallel tangents, 
 and that one or both of the surfaces would need 
 to be prolonged considerably before any point 
 could be found in the one having a tangent 
 parallel to that of a point in the other; were this 
 done a line uniting the points would pass through 
 the optical centre O. 
 
 We have seen that the effect of decentering a 
 biconvex lens is equivalent to splitting it into 
 two halves, and inserting a prism between them
 
 DECENTERING OF LENSES. 75 
 
 (b a cm Fig. 38). The strength of this (virtually 
 interpolated) prism depends on, first, the amount 
 of decentration, and, second, the focal length of 
 the lens. A strong lens needs decentering to a less 
 extent than a weak one to produce the same 
 effect Table V. (p. 76) not only illustrates this but 
 enables us to find the exact prismatic equivalent 
 of decentering any lens. All that is required is to 
 fix on the number of millimetres (in the highest 
 horizontal row of figures) by which a lens is known 
 to be decentred, and the prismatic equivalent is 
 found in the column beneath, opposite the dioptric 
 strength of the lens. Conversely, should it be 
 required to know how much to decentre a given 
 lens in order to combine with it a certain prism, the 
 eye runs along the horizontal line of angles opposite 
 the known strength of lens till that angle is found 
 nearest to the strength of prism required, when the 
 number of mm. at the head of the column will 
 indicate the decentering necessary. 
 
 The word " decentering " is generally applied to 
 making the optical centre no longer coincide with 
 the geometrical centre of the lens, but we have 
 already said that the prismatic effect is the same if 
 the whole lens, rim and all, be simply displaced, as 
 by lengthening or shortening the spectacle frame ; 
 in other words, it makes no prismatic difference, 
 so long as the optical centre is moved, whether the 
 geometrical one remains in statu quo, or whether
 
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 DECENTERING OF LENSES. 7 7 
 
 it is shifted equally itself. How are we then to 
 decide between these rival modes, in any given 
 case? Decentering of any kind has the disadvan- 
 tage of being attended with proportionate increase 
 of weight, as much as if a prism were inserted : the 
 lens of Fig. 38 is very evidently heavier than that 
 of Fig. 39. This fault is entirely avoided by the 
 alternative of displacing the entire lens (instead of 
 only decentering the optical centre in the lens), 
 but, on the other hand, such displacing entails, 
 beyond certain limits, an unpleasant appearance 
 and, worse still, a limitation of the field of bin- 
 ocular fixation. It may therefore be laid down as 
 a practical rule, that the dislocation of the optical 
 centre should be effected only slightly by displacing 
 the whole lens, rim and all, leaving the remainder 
 (should any more be required) to be obtained 
 by decentration proper, that is, by decentering 
 the lens in its rim. 
 
 To take an example, let us suppose it is desired 
 to prescribe spectacles such that each optical centre 
 is 10 mm. nearer to the median plane than the 
 centre of the eye, and we have found that the 
 centre of each eye is 32 mm. from the median 
 (sagittal) plane. The effect of limitation of the 
 field of binocular fixation must be considered for 
 each case, for its inconvenience or otherwise 
 depends on the distance of the patient's occupa- 
 tion ; but, say that on consideration, 5 mm. of
 
 78 PKISMS. 
 
 displacing for each lens is all that is advisable ; that 
 will make each geometrical centre 27 mm. from the 
 median plane, and leave 5 mm. for decentering. 
 
 In prescribing the spectacles, therefore, some 
 such form as the following might be used : 
 
 R. 
 
 L. 
 
 Spherical. + 4 D + 4 D 
 
 Geometrical centre. 27 mm. 
 
 27 mm. 
 
 T-, * 5 mm. 
 Decentration. • D •, 
 
 inwards. 
 
 5 mm. 
 inwards. 
 
 The optician would have the choice of making 
 these lenses by decentration, or by imparting 
 sphericity to the surfaces of a prism. If by decen- 
 tration he would grind a large lens, of the focal 
 length ordered, find its optical centre (p. 147) and 
 mark it with a dot of ink, then make another dot 
 5 mm. distant and cut out the lens with the last 
 dot for its geometrical centre, placing it in a frame 
 made with the centre of the rim 27 mm. from the 
 middle of the bridge, so that the first dot (indicat- 
 ing the optical centre) shall lie to the inner side 
 of the second dot. This plan is more accurate 
 than that of making a prism, and is one to be 
 encouraged. Whenever great precision is required, 
 decentering should be chosen, unless indeed it be
 
 DECENTERING OF LENSES. 79 
 
 combined with the manufacture of a prism, 
 according to the second plan as follows. By 
 Table V. the strength of prism required in the 
 above prescription is easily found, for opposite 4D, 
 and under the column 5 mm. we find i° io'. This 
 is the deviating angle of the prism, and needs 
 nearly doubling for the physical angle (p. 18). 
 
 After grinding, therefore, such a prism, and 
 giving the prescribed spherical element to each 
 of its surfaces, he would proceed to find the optical 
 centre of the prismatic lens, by one of the methods 
 described on p. 147, marking it with a dot of ink, 
 and measuring the geometrical centre 5 mm. from 
 it in the direction of the apex of the prism, to 
 proceed thereafter just as before. In this way, 
 any inaccuracy in the first manufacture of the 
 prism is completely corrected. With weak 
 prisms, indeed, combined with lenses, the whole 
 problem of the difficulty of accurate manufacture 
 would be solved in this way. 
 
 With lenses too weak, or prisms too strong, 
 for the optical centre to lie in the combination 
 at all, the prism-measure of the Geneva Optical 
 Company comes to our aid. Placing a 
 prismosphere* under the teeth connected with 
 the index, and with its base-apex line parallel 
 to them, it is easy to find the position which makes 
 
 *This is a term used by Dr. Percival in series with 
 sphero-cylinder, to signify a "prismatic lens?
 
 8o PRISMS. 
 
 the index point to the required strength of prism. 
 The central tooth then points to the future 
 centre, which can be dotted with ink. The prismo- 
 sphere should now be rotated 90 to make sure 
 that when the tooth points to the dot, the index 
 is at zero. This is to guard against the introduc- 
 tion of any vertical prismatic effect. If it does not 
 point to zero, move the prismosphere laterally, and 
 with care, till it does, when the new point marked out 
 by the central tooth gives the true required centre. 
 
 When plain prisms are ordered, uncombined with 
 lenses, we lose the power of adjusting their strength 
 in this way. 
 
 In the case of cylindrical lenses, the effect of 
 decentering depends on the direction in which it is 
 made. Thus horizontal decentering of a lens, with 
 a horizontal axis, has no effect, and the effect is 
 greatest when the axis is vertical. With an oblique 
 axis we need to find the focal length of the lens in 
 the horizontal meridian. Here, though calculation 
 would be easy,* the lens-measure of the Geneva 
 Optical Company comes in most usefully to save us 
 from it. By pressing it against the horizontal 
 meridian of the lens, it records at once what we 
 need to know. Adding this to the strength of the 
 
 * To find the strength in dioptres, of the horizontal merid- 
 ian of an oblique cylindrical lens, we need only, I believe, 
 multiply the strength of the lens in dioptres by the sine 
 of the angle of rotation of its axis from the horizontal.
 
 DECENTERING OF LENSES. 81 
 
 spherical surface, if the latter be of the same sign, 
 or subtracting one from the other if the signs be 
 different, we then proceed as before. 
 
 As regards the distance of the optical centre 
 from the median plane, we must remember that for a 
 lens to have no effect on convergence, it must, at 
 reading distance, be displaced 2 or 3 mm. more in- 
 wards than for distant vision. This position there- 
 fore forms the zero, by departing from which in 
 either direction the visual axis is deflected. 
 
 As a rule, it is best for the geometrical centre to 
 be in front of the centre of the eye in spectacles for 
 distance, and 2^ mm. within this in spectacles for 
 reading purposes. 
 
 To relieve deficient convergence, prisms should 
 be set " edge out;" convex lenses should be displaced 
 inwards, and concave lenses outwards. 
 
 To relieve excessive convergence, prisms should 
 be " edge in," convex lenses displaced outwards, and 
 concave lenses inwards. 
 
 " Orthoscopic Spectacles " as described by Dr. 
 Scheffler, have been so long known that they must 
 not altogether escape mention. In these, accom- 
 modation and convergence are affected in equal 
 amount. The two lenses have but one optical 
 centre common to both, just as though they were 
 cut from opposite edges of one large lens. The 
 proof of their correct manufacture is that they 
 throw a single image of a flame upon a wall at their
 
 82 PRISMS. 
 
 focal distance. They have generally been pre- 
 scribed in a few standard strengths, but they can be 
 made for any patient by combining with each of 
 his lenses a prism, whose deviating angle is found 
 in Table V., opposite the description of lens, and 
 under the number of millimetres by which the 
 optical centre of each eye is distant from the median 
 plane. These spectacles undoubtedly may have 
 their place, but it is better to ascertain the condi- 
 tions of convergence in each case and prescribe 
 accordingly, rather than to adhere to any fixed 
 combinations. 
 
 In the absence of a table, we may, as Ward Holden* 
 suggests, remember that a lens of id, decentred 87 mm., 
 produces the effect of an added prism of i°. So that 
 we may, if not wishing great accuracy, multiply 87 mm. 
 by the number of any prism we wish to obtain the effect 
 of, and divide by the number of dioptres of the lens. 
 Thus : — Required the decentering necessary in a lens of 
 + 3D to produce the prismatic effect of 4 ? 
 
 Ans. 87 mm. x 4° -f 3 = n '6 mm. 
 
 In working with this rule, it is the refracting angles of 
 prisms that are dealt with. Table V. gives the deviating 
 angles. To produce the effect of a prism of 1 V, a lens 
 of id must be decentred 17*45 mm. 
 
 * Archives of Ophthalmology, Vol. XX., p. 21.
 
 33 
 
 Chapter XL 
 
 THE STUDY OF CONVERGENCE. 
 
 To prescribe prisms satisfactorily it is necessary 
 to know something of the physiology of conver- 
 gence, our knowledge of which, however, is still very 
 incomplete. According to Hering's well-proved 
 theory, both eyes move together as though they 
 were a single organ. No ocular muscle can in health 
 receive a nervous impulse without the transmission 
 of an equal impulse to some associated muscle of 
 the other eye. Thus there is one conjugate innerva- 
 tion which turns both eyes to the right, and another 
 which turns both eyes to the left. Besides these 
 lateral movements, there are, in all probability, two 
 other innervations, which turn both eyes respect- 
 ively upwards and downwards. By these innerva- 
 tions, which need not detain us, the visual axes can 
 be simultaneously moved in any direction, but were 
 there no other innervation, we would see all near 
 objects double, from inability to converge the visual 
 axes upon them. This want is supplied by the 
 innervation of convergence, which controls the 
 internal recti, one as much as another, and inde- 
 pendently of their control by the conjugate lateral 
 innervations. The efforts of convergence and
 
 PRISMS. 
 
 Fig. 42.- The three grades of convergence in vision for -25m. 
 1 o scale : half life size.
 
 THE STUDY OF CONVERGENCE. 85 
 
 accommodation are intimately intersusceptible, so 
 that the slightest impulse to either makes a 
 difference in the other, albeit the difference is not 
 necessarily equal in amount. If one eye be covered 
 while the other is fixing a near object, the occluded 
 eye will, in the majority of persons, deviate out- 
 wards 3° or 4 . This behaviour of a normal eye, 
 placed in the dark, was some years ago noted by 
 the use of the blind spot* V. Graefe had long before 
 shewn how by placing a prism, edge up, before one 
 eye, and looking at a dot on paper with a vertical 
 line through it, he could detect what he called 
 " muscular insufficiency " in many cases of myopia. 
 But his test did not appear to reveal that a lesser 
 degree of the same thing was a physiological con- 
 dition. Fig. 43 shews a slight modification of his 
 
 t 
 
 ysT 8'T6'S"4' X t 1'\ 7 
 
 10'2>° 8° T 6\f 4' f f 1\ f Z'S' 4° 5°6'7'S*3°1Q 
 
 10' 0' 8' 7° 6' 5°4'J°Z° V 
 
 T Z°J'4° ST GT 7° 8° 9' 10" 
 
 Fig. 43. — A tangent scale reduplicated by a vertical prism. 
 
 test, the results of which agree with the blind spot 
 method. It consists of a lithographed scale, gradu- 
 ated in tangents of degrees to right and left of a 
 central zero, from which rises a vertical arrow. The 
 
 * " On a new method of determining the relation between 
 Convergence and Accommodation of the Eyes.'' Trans. Oph. 
 Soc, Vol. III., p. 290.
 
 86 PRISMS. 
 
 scale is held -25m. before the eyes, and is redupli- 
 cated by a square prism of 12 , held vertically 
 before one eye. The lower arrow then points 
 upwards to that number which measures the devia- 
 tion of the eye. We call this a " latent deviation," 
 because it does not exist in ordinary vision, being 
 overcome by a subtle visual-reflex action which 
 protects us from seeing double. This action is 
 discontinued when the false image produced by a 
 prism is so far removed from the true one as to 
 make it hopeless to attempt their union by over- 
 coming the prism (cf. p. 63). The latent deviation 
 revealed by this test shews that the association of 
 convergence with accommodation is not complete 
 centrally, so that a supplementary action is needed 
 to supply the deficiency, and since the involuntary 
 motive for this action is afforded by the desire to 
 fuse two images into one, the proportion of con- 
 vergence thus kept up may be called the " fusion 
 supplement," or, better still, the "reflex con- 
 vergence." 
 
 In ordinary binocular vision there is perfect 
 concert between accommodation and convergence, 
 so that the two visual axes meet exactly at 
 whatever point is accommodated for, and the 
 visual-reflex is maintained in activity by the fact, 
 of which some cerebral centre is every moment 
 kept sensible, that were the effort abated, the united 
 mental images would immediately resolve them-
 
 THE STUDY OF CONVERGENCE. 87 
 
 selves into two. To keep them from doing so, the 
 joint sensations in the brain must all the while be 
 bearing between them the message of continually 
 impending (yet as quickly averted) double vision, 
 by threats of double images, so slight and frequent, 
 that they produce the required effect without our 
 being conscious of their existence. It is difficult to 
 conceive the exquisite mechanism at work when we 
 remember that, if double images are produced 
 artificially, or by disease, it is usually impossible for 
 the mind to tell to which eye each image belongs 
 — whether, therefore, the visual axes are crossed or 
 not, and whether convergence needs to be increased 
 or relaxed to bring the images together. 
 
 I have purposely dwelt at length upon this reflex, 
 because an action so complex must necessarily be 
 more tiring than the mere overflow of one impulse 
 into another. If, therefore, there be an undue pro- 
 portion of reflex convergence, there is a waste of 
 co-ordinating nervous energy. In many cases this 
 waste is of no consequence, but in others it may 
 give rise to the so-called " muscular asthenopia " of 
 V. Graefe, which, however, is really in many instances 
 a central astlienopia, though there may sometimes be 
 a muscular element as well. It is just, I believe, as 
 as in " writer's cramp," and the various " trade 
 pains," where it is not so much the muscles that get 
 tired, as the co-ordinating apparatus. Asthenopia 
 from this cause can be relieved by prisms with their
 
 88 PRISMS. 
 
 edges out, which lessen the convergence necessary 
 for single vision. It is of course desirable to only 
 relieve a sufficient portion of the reflex convergence, 
 and not the whole of it. Take the example of an 
 asthenopic myope, with a latent deviation of io° 
 at reading distance ; this shews that the fusion 
 supplement for each eye is 5 , for since either eye 
 deviates outwards on exclusion, the deviation must 
 be equally divided between them. The normal 
 fusion supplement is nearly 2° for each eye, so that 
 we have to deal with 3 of excess. Should we correct 
 the whole of the excess with prisms ? I think not, 
 for we may assume that a myope has, by long 
 habitude, acquired a toleration for a larger amount 
 of reflex convergence. Prisms to relieve half the 
 excess would probably meet the case. It is taken 
 for granted that the test for deviation is made with 
 the reading lenses on, otherwise the deviation would 
 be greater still. We may of course lessen the 
 deviation by increasing the strength of the reading 
 lenses if these are not full strength, but this throws 
 the strain on accommodation instead, and, in people 
 who are not young, is not always well borne. It is, 
 in any case, too, only practicable within the limits 
 of full correction. 
 
 Endless variations are met with, so that it is 
 better to study the principles of convergence than 
 to make rules of too arbitrary a nature. High latent 
 deviations may occur in other conditions of refrac-
 
 THE STUDY OF CONVERGENCE. 89 
 
 tion than myopia, but in every case in which prisms 
 are ordered to correct divergence in near vision, 
 care should be taken that they are not also used 
 for distant vision, unless indeed the distant diver- 
 gence be great enough to indicate the same prisms 
 for itself. Sometimes, though much more rarely, 
 there is, even in near vision, a tendency to excess 
 of convergence, instead of deficiency. In this case 
 convergence has to be lessened (inhibited ?) in order 
 to see single. Now, therefore, the reflex convergence 
 is negative instead of positive. In some of these 
 cases it is convex lenses that are indicated more 
 than prisms. When the latter are ordered, their 
 edges should be inwards. Latent convergence at 
 reading distance is naturally much rarer than latent 
 convergence in distant vision. Spasm of con- 
 vergence occurs independently of hypermetropia, 
 but its causes, supposed sometimes to be hysterical 
 or reflex, are little understood. The influence of 
 helminthiasis in this direction, however, is un- 
 doubted. 
 
 Initial Convergence. — Of the three elements 
 of convergence this is the first, and is shewn under 
 the name of " tonic . convergence " in Fig. 42. 
 We must first ask " What is the starting point of 
 convergence ? " We do not exactly know what 
 position the eyes would take in the absence of any 
 converging innervation, though the divergence which 
 follows monocular amblyopia seems to shew it
 
 90 PRISMS. 
 
 would be one of considerable divergence. Were all 
 the innervations to cease, the anatomical position 
 of rest of the eyes would undoubtedly be one of 
 considerable divergence, as Hansen Grut ably main- 
 tained in his Bowman* lecture. Le Contef shewed 
 that during sleep, and even, in his case, during 
 drowsiness, the eyes diverge, as they also do in 
 drunkenness, under chloroform, and at death. In 
 ophthalmoplegia externa, divergence also occurs. 
 The ocular muscles no doubt possess a physiological 
 tone, similar to that of the other skeletal muscles, 
 but what influence it has on the position of the eyes 
 it is difficult to decide. In addition to this common 
 muscular tone there is a persistent activity of the 
 converging innervation, which disappears when 
 deeply under chloroform, but which in ordinary 
 conditions prevents the eyes from assuming their 
 position of anatomical divergence. Mr. Berry 
 views it as " the tendency to persistence of a 
 constantly called for state of innervation," and 
 Hansen Grut aptly compares it to the tonic 
 element in the accommodation of a hypermetrope. 
 By this tonic convergence, the visual axes are 
 brought to practical parallelism, so that on viewing 
 a distant object, and occluding one eye, it either 
 remains undeviated, or only aberrates slightly, more 
 
 * Trans. Oph. Soc, Vol. X., p. i. 
 f Le Conte on "Sight," p. 254.
 
 THE STUDY OF CONVERGENCE. 91 
 
 often in the direction of divergence than conver- 
 gence in emmetropia, and more often in the direc- 
 tion of convergence than divergence in ametropia. 
 In the first edition of this book, slight convergence 
 of the visual axes was mentioned as the prevalent 
 latent condition in distant vision, that having been 
 found in the comparatively few cases examined by 
 a difficult and slow method. The conclusions in 
 the text are from an investigation among the 
 students attending Mr. Berry's clinic, by the glass 
 rod test, which enables a large number to be tested 
 with rapidity and accuracy, and they are recorded 
 by Mr. Berry in the " Trans. Oph. Soc," vol. xi., 
 p. 160. If we accept, as I now believe we must, 
 divergence instead of parallelism, to be the anatomi- 
 cal position of the eyes, the diagram in which I 
 once represented three grades of convergence,* 
 must be modified accordingly into the form shewn 
 in Fig. 44. The strong lines (R, R) indicate the 
 supposed position of the visual axes were all nervous 
 impulse abolished. The lines z, i indicate the 
 initial convergence during waking hours, due partly 
 to muscular tone, and partly to involuntary tonic 
 action of the converging innervation. It is this 
 position of the visual axes [i z), to which they are 
 brought by tonic convergence, that is noticed when 
 we use V. Graefe's " distant equilibrium test," or 
 
 * Oph. Rev., Vol. V., p. 345.
 
 92 PRISMS. 
 
 any of its successors, such as the double prism 
 or glass rod. Latent divergence in distant vision 
 indicates a deficiency, and latent convergence 
 
 Fig. 44. — The three grades of convergence. 
 
 an excess, of tonic convergence. In either case the 
 aberration is corrected, when both eyes are in use 
 by reflex convergence, positive or negative, as the 
 case may be. 
 
 Excess of tonic convergence is sometimes apt to 
 occur temporarily after prolonged use of the eyes 
 in near work, also more permanently in a certain 
 proportion of those myopes, who hold their work 
 near their eyes, and yet retain binocular fixation. 
 It occurs, too, in most hypermetropes if uncorrected 
 by lenses, and in a few even when corrected. 
 The so-called spasm of convergence, from reflex 
 and hysterical causes, already referred to, is 
 probably a simple excess of tonic convergence.
 
 THE STUDY OF CONVERGENCE. 93 
 
 If found to be persistent, and suspected to give 
 rise to asthenopia, excess of tonic convergence 
 may be relieved by prisms with their edges in, of 
 a strength that will only partially correct the 
 anomaly. 
 
 Deficiency of Tonic Convergence, evidenced by 
 latent divergence in distant vision, is rather com- 
 mon, and appears to be sometimes due to reflexes 
 through the fifth nerve, especially from carious teeth; 
 also to want of nervous tone in the system generally. 
 It is, however, found besides in many who are free 
 from either of these conditions, and in a class of 
 myopes, especially those who read with one eye. 
 It may, if persistent, and if there be any indication 
 for treatment, be relieved by prisms with their 
 edges out, to correct a portion — say a half — of the 
 defect. I think it would be a useful nomenclature 
 for prisms to designate those with edge in as plies, 
 and those with edge out as minus, just as we speak 
 of plus and minus lenses. Thus — 3°d. would mean 
 a prism, deviating 3 , edge out, and -f 5° P. would 
 mean a prism with physical angle of 5 , edge in. 
 It is so easy to remember that plus conditions of 
 convergence are relieved by plus prisms, and minus 
 conditions of convergence by minus prisms. In 
 normal eyes, plus prisms increase the convergence, 
 and minus prisms lessen it ; this,, too, is easy to 
 remember. 
 
 Accommodative Convergence. — In distant
 
 94 
 
 PRISMS. 
 
 vision, as we have just seen, there are only two grade? 
 of convergence, the tonic and the reflex, shewn in 
 Fig. 45. In near vision there is an intermediate 
 
 9=J^B 
 
 Fig. 45. — The two grades of convergence in distant vision. 
 Tonic C is Ri, and Reflex C is io. 
 
 grade — the accommodative. If one eye be oc- 
 cluded by the hand while vision is directed, 
 first to a distant object, and then to a near 
 one, the occluded eye deviates inwards under 
 the hand from an impulse to convergence, which 
 is due chiefly to sympathy with accommodation, 
 but also to the habit of converging when 
 attention is directed to a near object (Grut's 
 " Nahebewusstein "). The second grade of con- 
 vergence is therefore added on to the first or tonic 
 grade, and its amount depends, of course, on the 
 amount of accommodation in exercise. As a rule,
 
 THE STUDY OF CONVERGENCE. 95 
 
 each dioptre of accommodation is accompanied by 
 about three-quarters of a metre-angle of associated 
 convergence, so that in a typical emmetrope, the 
 4 D of accommodation in exercise for vision at a 
 quarter of a metre, are accompanied by 3 m.a. of 
 convergence, leaving a deficit of 1 m.a. to be made 
 up reflexly, as shewn in Fig. 42. To investigate 
 the accommodative convergence at different 
 distances, I have made scales, similar to that of 
 Fig. 43, for use at im., -5m., -33m., and '25m., but 
 for practical purposes we need only use the last. 
 
 Now we may notice some of the conditions which 
 affect the amount of accommodative convergence. 
 Whatever paralyses the ciliary muscle locally, such 
 as, eg., weak atropine drops, renders the ciliary 
 muscle less responsive to its motor impulses, thereby 
 increasing the effort of accommodation, and with it 
 the associated convergence. If, even without such 
 paralysis, the object fixed be approached to 
 the " punctum proximum " of accommodation, 
 the accommodative effort becomes so much 
 greater than the effect produced in the lens, that 
 the associated convergence exceeds all proportion, 
 and produces a latent convergence. In hyper- 
 metropia, the accommodative convergence, without 
 correction of refraction, is, of course, greater as a 
 rule than in emmetropia. 
 
 What conditions lessen the accommodative con- 
 vergence ? Any which make accommodation easier.
 
 9 6 
 
 PRISMS. 
 
 so that work is done with less effort. Myopia, for 
 instance, renders accommodation unnecessary in 
 vision beyond the far point. Figs. 46 and 47 
 
 Fig. 46. — The conditions in a myope who has latent convergence 
 in distant vision. 
 
 shew how the diminution of accommodative con- 
 vergence (id) in myopia is made up by greater reflex 
 (and perhaps also voluntary) convergence (ao) y the 
 amount of which is influenced by the condition of 
 the tonic convergence (R i) which is excessive in 
 Fig. 46, and deficient in Fig. 47. To observe the 
 effect of eserine, which, in weak solution, renders the 
 ciliary muscle more excitable to stimulation without 
 producing spasm or myopia, I placed gr. 4^00 
 within each lower lid. This allowed me to retain 
 full distant vision, but increased my fusion supple- 
 ment at 10 inches, from one to two metre angles.
 
 THE STUDY OF CONVERGENCE. 
 
 97 
 
 The effect on tonic convergence, as shewn by 
 the distant equilibrium, was practically nil. This 
 experiment shews how truly convergence is affected, 
 not by accommodation, but by accommodative 
 
 f r 
 
 Fig. 47. — The conditions of a myope who has latent divergence 
 in distant vision. 
 
 effort, for accommodation was the same both with 
 and without the eserine, but with it, the effort was 
 less, and the impression on convergence reduced in 
 consequence. 
 
 Reflex Convergence. — This, the third grade 
 of convergence, has already been noticed in part. It 
 is the element most affected by ocular fatigue, as 
 is well seen in cases of " periodic squint," as they 
 are called. On rising in the morning, there is 
 perhaps no squint, but as the day wears on, and 
 the eyes get tired, the squint appears, its mani- 
 
 7
 
 98 
 
 PRISMS. 
 
 festation being partly* due to the diminishing 
 vigour of the visual-reflex, the amplitude of which 
 varies with the nervous vigour of the moment. 
 As soon as the amplitude of the visual reflex 
 becomes less than the squint, the latter is no longer 
 overcome.^ 
 
 Fig. 48 represents a case of true periodic squint 
 
 Fig. 48. — A periodic squint in its latent phase. 
 
 in the early morning. The first two grades of 
 convergence, each excessive if the patient be a 
 
 * I say " partly," because I believe that the converging 
 centre may perhaps become more excitable by the constant 
 stimulus of accommodation in these cases. 
 
 t These cases must not be confused with other groups — 
 such as " accommodative squints," in which the hyperme- 
 tropia may be absolute, or accommodation is partially sur- 
 rendered, except on paying close attention to an object, or 
 cases in which the squint appears only in near vision, because 
 accommodation there reaches the limits in which effort 
 becomes disproportionate to work.
 
 THE STUDY OF CONVERGENCE. 99 
 
 hypermetrope, would bring the visual axes to a & 
 but they are brought back to o by negative reflex 
 convergence (shaded area). As the day wears on 
 the effort is abandoned, though in distant vision the 
 squint may perhaps still be overcome. By cor- 
 recting the hypermetropia we lessen the accommo- 
 dative convergence, and the tonic convergence will 
 thus gradually tend to get less, the excitability of 
 the converging centre being no longer kept up by 
 stimulation from inordinate accommodation. It is 
 thus that squints are sometimes cured by spectacles 
 in the course of years. The effect of tenotomy on 
 the same case is shewn in Fig. 49. By increasing 
 
 ■L ^ I 
 
 Fig, 4 g. — The same case as in Fig. 48, but relieved by tenotomy 
 which displaces the anatomical position outwards. 
 
 the anatomical divergence it allows more room for 
 the excessive tonic and accommodative conver- 
 gences. The amplitude of the visual reflex can 
 often be increased by nerve tonics, such as Fellows'
 
 ioo PRISMS. 
 
 Syrup, rest, and change of air. To measure how 
 great the amplitude of visual-reflex is, we may 
 
 R 7, cc 
 
 Fig. 50. — Higli fusion supplement (ao) from deficient tonic 
 convergence (Ri). 
 
 use the tests described on p. 120. Since the third 
 grade of convergence is complementary to the 
 
 Fig. 51. — Same case as Fig. 50, relieved by prisms. 
 
 other two, its amount can be altered by altering 
 them. In Fig. 50, for instance, the tonic conver-
 
 THE STUDY OF CONVERGENCE. 
 
 :oi 
 
 gence is deficient, the accommodative convergence 
 normal, and the reflex convergence, therefore, 
 excessive. The relief of this by prisms is shewn in 
 Fig. 51, and by tenotomy in Fig. 52. The prisms 
 do not alter the anatomical position of the eyes 
 
 Fig. 52. — Same case as Fig. 51, relieved by tenotomy. 
 
 (R, R), or alter the accommodative convergence, 
 but they alter the " initial position " (z, i) which 
 the eyes assume in consequence of tonic conver- 
 gence. We can alter 
 
 The anatomical position (R, R) by tenotomy \ 
 The initial position (z, z) by prisms, 
 The accommodative convergence by lenses, 
 The reflex convergence by any of the three. 
 Effect of Training. — This is a very important 
 subject, and needs working out more thoroughly. 
 By wearing prisms we can alter the position of 
 equilibrium of the eyes for some little time after-
 
 102 PRISMS. 
 
 wards. Thus, if I wear adducting prisms, amount- 
 ing together to n°d, for ten minutes, the rod 
 test reveals, on their removal, $V of latent con- 
 vergence as the position of equilibrium for 
 distance instead of my usual convergence of only 
 1°. In other words, the tonic convergence 
 has been temporarily increased by 5 , and takes 
 a good many minutes to recover its usual dimen- 
 sions. In near vision, under the same conditions, 
 the accommodative convergence is shewn to have 
 been augmented by 7 . The experiment causes 
 slight headache, not so much during the wearing 
 of the prisms as afterwards, and especially when 
 engaged in near vision, on account of the fact that 
 the customary reflex adduction is replaced by the 
 unwonted requirement of reflex abduction. 
 
 Again, if I wear convex lenses for near vision 
 for a few hours, the latent divergence at reading 
 distance is, after their removal, less than before.* 
 This is because of the training which the converg- 
 ing innervation has undergone in the increased 
 relative demand made upon its energies. It explains 
 why spectacles, causing discomfort at first, become 
 tolerated after a while. There are, however, limits to 
 the effect of training, otherwise prisms would never 
 be needed, except for pareses of ocular muscles. If 
 there were no limits to training, there would never 
 
 * Syme Essay, 18S4.
 
 THE STUDY OF CONVERGENCE. 103 
 
 be a concomitant squint, for the training of the 
 whole life, before the squint appears, is in the 
 direction of overcoming it. The complex process 
 of co-ordination of course requires definite cells 
 and groups of cells (centres) for its seat, but the 
 mutual adaptation and correlation of these, quanti- 
 tatively, seems largely left to be perfected by 
 edtication. As I have said elsewhere, " Circum- 
 stances cannot create a faculty, however much they 
 may develop or retard its exercise, but we can 
 conceive that faculties were created with a view to 
 circumstances, and even capable, within limits, of 
 being modified by them."* The human body is 
 thus made capable, within limits, of adapting itself 
 to its circumstances, and in no part of it is this 
 more beautifully seen than in the relation between 
 convergence and accommodation of the eyes. In 
 neurasthenics the limits of adaptability may be 
 more quickly reached, or adaptation may be only 
 attained at the cost of much discomfort, while even 
 in healthy individuals unusual conditions may make 
 it better to not trust to it altogether, but to meet the 
 case with prisms. Cases which require prisms are 
 generally those in which power of adaptation has 
 already signally failed. 
 
 It is under the heading of " training " that I 
 should mention Dr. Dyer's so-called " invigorant 
 
 * Journ. Anat. and Phys., Vol. XXI., p. 21.
 
 104 PRISMS. 
 
 plan " of treating latent deviations, for it does not, 
 if my belief be correct, invigorate the muscles, but 
 simply trains the efforts of accommodation and 
 convergence to assume broader relations to each 
 other in their work. It consists in giving the 
 patient four squared prisms, of about 2j°, 5 , io° 
 and 1 5 respectively. Twice a day for ten minutes 
 he is to fix a flame, or door knob, at 20 feet, 
 and exercise abduction and adduction, beginning 
 with the weakest prism, and mounting the ladder 
 to the strongest. If these exercises strengthen any- 
 thing, it is the visual reflex, the amplitude of which 
 they increase, and by so doing increase the relative 
 range of convergence. Though I have not yet 
 tried this, I can quite believe a case might now and 
 then be found suitable for its trial. I would, how- 
 ever, believe Dr. Dyer's plan to promise greater 
 success in a modified form, when instead of being 
 used to enlarge the powers of the visual-reflex, it 
 might tend to induce a new relationship between the 
 efforts of convergence and accommodation. If, 
 for instance, in a case of latent divergence, weak 
 plus prisms {i.e. adducting) were worn for half an 
 hour twice a day, say after breakfast and after 
 dinner, or whenever the nervous conditions are 
 strongest, would not the latent squint gradually 
 disappear in some cases? I believe it might, 
 though I cannot speak from experience. Since 
 this plan would be better with vision for all dis-
 
 THE STUDY OF CONVERGENCE. 105 
 
 tances, ordinary occupations could be pursued 
 while the training prisms are worn. 
 
 It cannot be denied that prisms given to relieve a 
 defect tend to stamp permanency upon that defect, 
 therefore they should never be given without ample 
 reason. The great majority of latent deviations 
 call for no treatment at all. Some cause trouble, 
 and should be treated. Constitutional treatment 
 may suffice for some cases. If training is feasible 
 it may be tried. If training cannot be borne without 
 headaches or much discomfort, relieving prisms 
 may be ordered, but such as to under-correct the 
 anomaly. Tenotomy, or advancement, should only 
 be resorted to in a small number of cases, where 
 the deviation causes undoubted trouble, and is 
 too great to be relieved by prisms. It is rarely 
 justifiable, in my opinion, for a latent deviation of 
 less than 6° in distant vision, and often unnecessary 
 even then : all depends on the history and 
 symptoms. It remains to be found out what 
 proportion, and what class of cases can be cured by 
 training. It may be that some cases of hyperphoria 
 which we now relieve by correcting prisms could be 
 "trained away," so to speak, by periodic use of 
 adverse* prisms, but my impression is that many 
 would not tolerate the training process, and it is 
 
 * By adverse prisms, I mean prisms set with the apex in 
 the opposite direction from relieving prisms.
 
 106 PRISMS. 
 
 certainly a great pleasure to afford relief sometimes 
 to the symptoms of years by "relieving prisms," 
 even though we know the defect is not really cured. 
 
 Note. — Strictly speaking, there are four elements of 
 convergence, though the first and third are perhaps 
 closely related. The four are : (i,) Tonic ; (2,) Accom- 
 modative ; (3,) Convergence due to "knowledge of 
 nearness," or in other words, " Voluntary convergence," 
 for we cannot, without special practice, converge the eyes 
 voluntarily, under ordinary conditions, without doing so 
 by thinking of a near object ; (4,) Fusion convergence. 
 Of these four elements I have included the second and 
 third under the one name of " accommodative converg- 
 ence," to simplify practical work. On looking at a near 
 object, the voluntary and accommodative elements of 
 convergence bear very different proportions to each other 
 in different individuals. It is possible that when some 
 persons direct their vision to a near object the voluntary 
 impulse passes chiefly into the channel of convergence, 
 accommodation being more secondary, while in others it 
 passes chiefly into the channel of accommodation, con- 
 vergence being more secondary. In the former class we 
 should expect the latent position of the eyes to be less 
 influenced by changes in accommodation than in the 
 latter class.
 
 ic; 
 
 Chapter XII. 
 
 THE EFFECT ON THE FIXATION LINES 
 
 OF DISPLACED OR DECENTRED 
 
 LENSES. 
 
 THIS study will cause embarrassment if allowed 
 in any way to be confused with those of previous 
 pages. It must be clearly borne in mind that the 
 prismatic equivalent of decentering a lens, and the 
 effect of that decentred lens on convergence, are 
 two distinct things, though at first sight they 
 appear the same. Suppose we decentre a lens, or, 
 what is the same thing, suppose we place a 
 normally centred lens precisely before one eye and 
 associate a prism with it. It has hitherto been 
 supposed that the angle of deviation of this prism 
 would exactly express the effect on convergence. 
 But it is not so. Fig. 53, B, represents a decentred 
 lens, the action of which is precisely similar to a 
 prism and lens, for, as said before, it is as if the 
 lens were split in two, and the prism shewn in 
 dotted outline were inserted between the two 
 halves. Now it will be evident at a glance, that the 
 angle cdf is the deviating angle of the virtual 
 prism, while the greater angle, dee, is that which
 
 ioS PRISMS. 
 
 represents the effect on convergence. It makes no 
 difference to the effect on convergence whether a 
 
 Fig. 53. — A. The right eye is looking at a distant object 
 through a lens displaced inwards, rim and all, by a distance od; 
 d c e is the effect on convergence. B is the same eye looking 
 through a lens of the same focal length, but decentred in its 
 rim by the same distance d. The dotted lines indicate the 
 prism that would be equivalent to the decentering, and the 
 effect on convergence is the same as with A. 
 
 lens is decentred in its frame, as in Fig. B, or dis- 
 placed, frame and all, to the same amount, as in 
 Fig. A. 
 
 There is one exception to the discrepancy 
 between the prismatic equivalent and the effect on 
 convergence, and that is when the lenses are co?ivex 
 and the object of fixation is at their focal length, 
 and immediately in front of the eye. Within that 
 distance the effect on convergence is less, and 
 beyond it more, than the prismatic equivalent. But 
 with concave lenses it is always less. In the first 
 edition I went no further than to point out these
 
 THE EFFECT OF DISPLACED LENSES. 109 
 
 facts, though in a former essay* I had given 
 
 formulae for the effect of decentering on the visual 
 
 axis in distant vision, and a series of simple rules 
 
 for both near and distant vision, which may now be 
 
 reproduced in a slightly altered form. 
 
 If a line (not represented in the figures) be 
 
 dropped from c (the centre of rotation of the eye), 
 
 perpendicularly upon the principal axis ( of) of the 
 
 lens, the length of this perpendicular equals the 
 
 decentration of the lens {0 d). It also cuts off 
 
 from the line of which measures the focal length 
 
 of the lens, a portion equal to dc. 
 
 Therefore - r od 
 
 Tan. ofe = 
 
 of — dc 
 
 But ofe is equal to the angle dee which 
 expresses the effect of the decentred lens on the 
 visual axis, and which we may represent by x. Let 
 d stand for the decentering {od), and f for the 
 focal length of the lens in mm. (fo), and let the 
 distance of the lens from the centre of rotation of 
 the eye be 25 mm. Then, with a convex lens 
 
 d 
 
 Tan. x = 
 
 /-25 
 
 and with a concave lens, 
 Tan. x = 
 
 /+2 5 
 In these formulae,-)- the distance of 25 mm. for 
 
 * Journ. Anat. and Phys., Vol. XXI., p. 36. 
 t Journ. Anat. and Phys., Vol. XXL, p. 35.
 
 no PRISMS. 
 
 the distance of the lens from the centre of the 
 eye was chosen because it allowed some simple 
 rules to be made for forming an approximate 
 estimate of the effect of lenses on the visual axes 
 without the use of tables, or tangents, as follows. 
 They are for distant vision only as they stand, but 
 when modified, as explained further on, they suffice 
 also for near vision. 
 
 I. — To find the effect on the visual axis of combin- 
 ing a lens and a prism, or of decentering a lens. 
 
 (a.) With a + lens. Ride: Divide the deviating 
 angle of the prism (in the case of decentering the 
 virtual prism can be found from Table V.) by the 
 number of indies in the focal length of the lens 
 LESS ONE. This, added to the deviating angle of 
 the prism, gives the effect on the axis of fixation. 
 Example: Given a $° d prism and a + IOD lens, 
 required the effect on the visual axis. A -+- IOD 
 lens has a focal length of four inches. This, less 
 one, is three inches. 
 
 - = i°. Add this to 3 = 4°. 
 3 
 The effect on the visual axis, therefore, is 4 . 
 
 (b.) With a — lens. Rule: Divide the deviating 
 angle of the prism (or of the virtual prism from 
 Table V. in the case of decentering) by the num- 
 ber of inches in the focal length of tlie lens PLUS 
 ONE. This, deducted from the deviating angle of 
 the prism, leaves the effect on the axis of fixation.
 
 THE EFFECT OF DISPLACED LENSES, in 
 
 Example: Given a $° d prism, and a — iod lens, 
 required the effect on the fixation line. The focal 
 length of a — iod lens is four inches, which plus one 
 is five inches. The deviating angle must therefore 
 be divided by 5, thus: 
 
 J = 36' ; 3° - 36' = 2° 24'. 
 
 The effect on the visual axis is, therefore, 2° 24'. 
 
 II. — To find wliat prism we must combine with 
 a lens, in order to produce any required effect on the 
 axis of fixation. 
 
 {a.) With a + lens. Rule: Divide the required 
 effect on tJte fixation line by the number of i?iches in 
 the focal length of the lens. This, deducted from 
 the effect required gives the prism that will produce 
 it. Example: Required with a + iod lens to 
 deflect a fixation line by 4 . What prism is 
 needed? The focal length of the lens is four 
 inches, 4 -=- 4 = I 3 . Deduct this from 4 = 3 . 
 The prism required is 3° d. Or the decentering 
 required is (from Table V.) a trifle more than 5 
 mm., since a lens of iod decentred to that amount 
 has a prismatic equivalent of 3 d. 
 
 (b.) With a — lens. Rule : Divide, as before, 
 the required deflection of the axis by the number oj 
 inches i?i tJie focal length of the lens. This, added 
 to the deflection required, gives the prism that will 
 produce it. Example : Required with a — i.od lens 
 to deflect a visual axis by 4 . What prism is needed?
 
 U2 PRISMS. 
 
 The focal length is four inches. 4 -f- 4 = 1°. Add 
 this to 4 = 5°. The prism required is 5 d. 
 
 From Table V. it is seen that a lens of IOD 
 must be decentred nearly 9 mm. to have the effect 
 of a prism of 5 . 
 
 These rules may prove of value in the correction 
 of hyperphoria, where considerable exactness is 
 required. The examples given illustrate well how 
 much less deflection is imparted to the line of 
 fixation by decentering a concave lens than a 
 convex one. Thus, we have seen that to produce 
 a deflection of 4°, a convex IOD lens needs a 
 decentering of 5 mm., and a corresponding concave 
 lens 9 mm. 
 
 For near vision the rules require a little modifica- 
 tion. Instead of reading the " focal length " of the 
 lens we should read the "conjugate focus." They 
 then apply in near vision with quite sufficient 
 accuracy for practical purposes, for though it is true 
 that they suppose the object of fixation to be in 
 front of each eye, when it is really in the median 
 plane, this only introduces a trifling error, and it 
 must be remembered that no fixed rules or tables 
 are quite accurate clinically, since the interocular 
 distance, and the distance of the lenses from the 
 eyes, vary so greatly in different patients. 
 
 To find the conjugate focus of a lens we subtract 
 from the reciprocal of its focal length, the reciprocal 
 of the distance of the object from the lens. Thus,
 
 THE EFFECT OF DISPLACED LENSES. 113 
 
 with the object at 12 in., a -f 10D lens (whose 
 focal length is therefore 4 inches) has a conjugate 
 focus of (\ — iV = 1) 6 inches. 
 
 Since a concave lens has a virtual focus, it is 
 prefixed by the negative sign, and therefore we 
 add the reciprocals; thus, with a — iod lens under 
 the same conditions as before, the conjugate focus 
 is ( — 4 — t^=— 3)3 inches. 
 
 Some may perhaps find a difficulty in using these 
 rules, and fortunately the subject has recently been 
 followed up by Dr. Percival, who is an able mathe- 
 matician, and has drawn up a series of tables from 
 a formula which assumes reading distance to be 
 \ metre, the distance between the ocular centres 
 to be 64 mm., and the distance of the lenses from 
 the centres of rotation of the eyes to be 27*4751 
 mm. This distance is chosen since it is that at 
 which lenses should theoretically be placed in 
 order that the size of images formed on the retina 
 may be the same as in emmetropia: it is, in short, 
 the distance of the anterior principal focal plane 
 of the eye from the centre of rotation. They are 
 made for distant vision from the formula, similar to 
 my own, 
 
 d 
 f-k 
 
 Where ^ = deflection of visual axis. 
 f = focal length of lens. 
 k = distance of lens from centre of rotation. 
 
 8 
 
 Tan. X =
 
 ii4 PRISMS. 
 
 For near vision I had made no formula, and 
 
 Dr. Percival has supplied the deficiency by the 
 
 following : 
 
 dp-fm 
 Tan. y = 
 
 This is for a convex lens; for a concave one the 
 signs must be reversed, being plus instead of minus, 
 since a negative value must be given to f. 
 
 It will be noticed that in the near vision table 
 the prismatic equivalents differ from those of the 
 distant vision table by a constant quantity, viz., 
 5' for each degree, and io' for each metre angle. 
 I give Dr. Percival's own examples to illustrate 
 their use. 
 
 EXAMPLES ILLUSTRATING THE USE OF 
 THE TABLES. 
 
 TABLE VI. — A hypermetrope of +8D and eso- 
 phoria I ma. at 6 metres will have this convergence 
 defect corrected by decentering the 8d lens 3*1 — 
 mm. outwards, or, what comes to the same thing, by 
 associating it with a prism of i° 26' d (not i° 50'). 
 
 TABLE VII. — A patient requiring +12D glasses 
 for reading, who can only maintain convergence for 
 a distance of \ metre (2 ma.), must have his glasses 
 decentred 4*6 mm. inwards. 
 
 TABLE VIII. — A myope requiring — 6d for read- 
 ing, who can only maintain 2 ma. of convergence, 
 must have his glasses decentred 4 mm. outwards, or
 
 LENSES. 
 
 
 ) D 
 
 12 D 
 
 14 D 
 
 l6 D 
 
 18 D 
 
 20 D 
 
 
 •3 
 iff 
 
 4 54 
 
 5-6 
 
 4V 
 
 4-5 
 
 40' 
 
 3-6 
 
 3*V 
 
 2.9 
 
 3'iS' 
 
 ■- 
 > 
 y. 
 
 z 
 
 •9 
 
 59' 
 
 .6 
 40' 
 
 5-3 
 
 3 41' 
 
 3.6 
 •V 
 
 4-2 
 3°23' 
 
 2.8 
 
 2° 1 5' 
 
 3-3 
 
 35' 
 
 2.2 
 
 23' 
 
 2.7 
 247' 
 
 1.8 
 
 i"5'' 
 
 2.1 
 2°2g' 
 
 I.4 
 
 i°39' 
 
 
 321 
 
 1.787 
 
 11V 
 
 I.4O6 
 
 i c 8' 
 
 1. 121 
 
 .898 
 55' 
 
 .721 
 50' 
 
 
 266 
 
 +3' 
 
 •975 
 
 4 y 
 
 .767 
 37' 
 
 .611 
 33' 
 
 .490 
 30' 
 
 •393 
 27' 
 
 
 225 
 16' 
 
 1-934 
 
 I C 2o' 
 
 I.726 
 
 ^23' 
 
 1-570 
 
 I°26' 
 
 I.449 
 i°3°' 
 
 1-352 
 
 i c 33' 
 
 
 079 
 2. J 
 
 3-546 
 2°26' 
 
 3165 
 
 232' 
 
 2.879 
 
 2^8' 
 
 2.657 
 
 2 44' 
 
 2.479 
 2 c 5«j' 
 
 > 
 
 < 
 
 - 
 
 c 
 
 .1 
 
 40' 
 
 7- 1 
 
 4 52' 
 
 6.3 
 
 5 C 4 
 
 5-7 
 5 = i6' 
 
 5-3 
 
 5=28' 
 
 4-9 
 
 5°36' 
 
 L. 
 
 2.2 
 
 59 
 
 10.6 
 
 7 c i6' 
 
 9-5 
 7 24' 
 
 8.6 
 
 7° 4 2' 
 
 7-9 
 8 = io' 
 
 7-4 
 
 8°27' 
 
 
 5 "3 
 
 '16' 
 
 14.2 
 &°39' 
 
 12.6 
 io c s' 
 
 "•5 
 
 IO"26' 
 
 10.6 
 10" 50' 
 
 9.9 
 11 12' 
 
 
 the 
 
 patient. 
 
 
 
 
 
 valent to that of the decentration of the lenses.
 
 DR. PERCIVAL'S TABLE FOR DISTANT LENSES. 
 
 
 11 
 
 1 
 
 1, 
 
 8 I 
 
 
 ■» 
 
 2„ 
 
 3» 
 
 ♦ » 
 
 5 ■= 
 
 6 D 
 
 7 D 
 
 80 | 9, | ,\n 
 
 
 ■4. 
 
 16 D 
 
 18 D 
 
 20,, 
 
 ' 
 
 4 ma. 7-. 7 - 
 3 ma. 5'29' 
 
 j ma. 3 40 
 1 ma. 1 50' 
 
 124.5 
 933 
 
 31 12 
 16.975 
 
 60.5 
 
 453 
 
 - : 
 [9.6 
 
 '-;■;- 
 
 5 139 
 
 - 
 21 3 
 
 3.884 
 
 3.011 
 
 178 
 S.o 
 
 147 
 3.692 
 
 "J 
 
 9-3 
 6.2 
 
 1.702 
 
 S 
 
 5-3, 
 2.676 
 1.460 
 
 6 
 
 5 3 
 
 '."8- 
 
 •7^7 
 
 4 3 
 
 3 6 
 
 808 
 ,90 
 
 29 
 
 •393 
 
 c 
 
 1 1 
 
 !■ 
 it 
 ii 
 
 1 ma. iV 
 
 3 ma. 5-29' 
 
 4 ma. 7-17' 
 
 17-935 
 
 65.75 
 98.6 
 
 Vi' 5 
 
 9-2°7 
 16.879 
 
 33-7 
 
 'T5 
 
 4.6 2 
 
 , 879 
 17.7 
 
 355 
 
 7.270 
 
 29.1 
 
 8,7' 
 
 3-38? 
 
 6.212 
 
 124 
 
 '?■? 
 24.8 
 
 2973 
 5-,45° 
 
 21 8 
 
 2 661 
 4 ,87,9 
 9 
 
 i.l 6 
 
 8"s> 
 
 4- 135 
 8.8 
 
 ■7 7 
 
 4.079 
 
 « J 
 
 I 934 
 3-54,6 
 
 «V 
 10.6 
 
 M ; 
 
 I 726 
 
 6;3, 
 
 9-5, 
 
 126 
 
 2 ,- 8 j? 
 
 5 ; 7 
 
 8.6 
 1 1 -5. 
 
 ! 1 
 
 5 4 -i«' 
 
 The 
 
 object 
 
 
 
 observ 
 
 The 
 
 figure 
 
 
 n large 
 
 The 
 
 figures 
 
 in 
 
 smaller 
 
 ition is presumed to be at a distance of mc 
 r tvpe indicate the amount of decentration 
 type represent tlie deviating power of the pri 
 
 1 of tllC I. HSCb.
 
 VISION. 
 
 -3 
 
 16.8 
 
 Il°2o' 
 
 I4.8 
 IO4' 
 
 12.8 
 8=43' 
 
 IO.7 
 
 7 = 2l' 
 
 14 D 
 
 13-9 
 
 11V 
 
 12.3 
 
 9°47' 
 
 IO.7 
 B°3i' 
 
 g.I 
 
 7°i5' 
 
 16 D ; 18 D I 20 D 
 
 11. 7 
 
 io°4/ 
 
 IO.4 
 
 9°2 9 ' 
 
 91 
 
 8=17' 
 
 7-8 
 
 7°9' 
 
 IO. O 
 
 IO'2l' 
 
 9.0 
 
 9Il' 
 
 7-9 
 
 8=7' 
 
 6. 9 
 
 7 C 3' 
 
 8.7 
 9°5i' 
 
 6.9 
 
 7°56' 
 
 6.1 
 6°57' 
 
 8.7186 I 7.4731 6.5389 5.8124 5.2312 
 
 5=58' 
 
 6.7 
 
 4°36' 
 
 4.6 
 
 3°I2' 
 
 2.6 
 1=49' 
 
 .61 
 
 5 ; 58' 
 
 5-3 
 
 4°4i' 
 
 4.2 
 3° 2 4' 
 
 2.6 
 27' 
 
 I.02 
 49' 
 
 5°58' 
 
 5°58' 
 
 5-2 4-7 
 
 447' i 4°53' 
 
 3-9 
 
 3°36' 
 
 2.6 
 
 2°25' 
 
 i-3 
 
 3-7 
 
 3 : 4^' 
 
 2.6 
 
 2 45 
 
 I.58 
 
 i°37' 
 
 4-3 
 
 4°59' 
 
 3-5 
 
 4° 
 
 2.6 
 3°i' 
 
 i-77 
 
 2° 2' 
 
 IS 2 2.027O I.6119 I.3CO4 I.O5S2 .8645 
 
 ; i°24' i = i8' 112' i°6' 59' 
 
 Xp7 1 I - I °57 -8792 . 7-°93 -5772 -47* 
 46' 42' 39' 36' 32' 
 
 valent to that of the decentration of the 
 l£es inwards. 
 
 [P.T.O.
 
 DR. PERCIVAL'S TABLES FOR NEAR VISION. 
 
 TABLE VII.— (Convex.) 
 
 
 
 „ 
 
 20 
 
 3D 
 
 40 
 
 5» 
 
 6d 
 
 70 
 
 8d 
 
 9, 
 
 J 
 
 - 
 
 I 4 D 
 
 16 D 
 
 IS 
 
 
 
 4 ma. 7-17' 
 
 35? 
 
 I-y 
 
 # 
 
 3J 
 
 453 
 
 3 ?- 2 
 
 313 
 
 3S 
 
 23.6 
 
 
 16.8 
 
 13.9 
 
 "•7 
 
 35 
 
 8-7 
 
 Sj 3 ma. 5 . 29 . 
 
 206.6 
 
 '"■? 
 
 <7 I 
 
 497 
 
 S? 
 
 32.2 
 
 27-2 
 
 23 5 
 
 20.6 
 
 18.J 
 
 14 s 
 
 12.3 
 
 s? 
 
 90 
 
 Z£ 
 
 q 2 ma. 3-40' 
 
 172.6 
 
 9V 
 
 5. 6 ? 
 
 9>' 
 
 s? 
 
 W 
 
 23.1 
 
 sV 
 
 I ?;. 6 
 
 a*$ 
 
 12.8 
 
 »v 
 
 s?.;- 
 
 7 ;5 
 
 6.9, 
 
 ■ ma. IV 
 
 138.6 
 
 68.8 
 
 4 - 5 i? 
 
 7-« ? 
 
 27.0 
 
 2 . 2 ' 3 
 
 I9.0 
 
 fV 
 
 14.6 
 
 13 3 
 
 10.7 
 
 91 
 
 7-8 
 
 ,". ! 
 
 6.1 
 
 o 
 
 io 4 62 3 r, 
 
 52.3118 
 
 34 K 74i 
 
 26 1 350 
 
 20.9247 
 
 174372 
 
 14.9462 
 
 13.0779 
 
 11.6248 
 
 10.4623 
 
 
 7 1731 
 
 6.5389 
 
 
 5.2312 
 
 
 
 5'SS 
 
 5 58' 
 
 
 5-5* 
 
 
 S*58' 
 
 5-58' 
 
 5'53' 
 
 sV 
 
 s-sa - 
 
 5S- 
 
 .. 38' 
 
 5-- 
 
 5"3S' 
 
 5'58' 
 
 
 I ma. I-5C 
 
 70.6 
 
 35 7 
 
 *' 
 
 *? 
 
 s? 
 
 ♦''i? 
 
 10.8 
 
 9.6 
 4-=3' 
 
 
 7.8 
 
 4 - »3 
 
 6.7 
 4 - 3«' 
 
 5, S , 
 
 5 " 
 
 
 s 
 
 1 
 
 2 ma. 3' 4 0' 
 
 36.6 
 
 19.2 
 
 1.3-4 
 
 =V 
 
 f.7 
 
 7.6 
 
 6.7 
 
 6.1 
 
 ? 6 ' 
 
 5f 
 
 3 
 
 3 4 J 
 
 3-9 
 
 3 7, 
 
 3 ; 5 
 
 O 
 
 3 ma. 5-29 
 
 2.6 
 9' 
 
 * 
 
 2.6 
 
 2.6 
 
 2.6 
 
 2.6 
 
 2_6 
 
 2.6 
 
 2.6 
 
 2.6 
 
 ■V 
 
 : 6 
 
 a 6 
 
 2.6 
 
 2.6 
 
 4 6 
 
 
 4 ma. 7-17' 
 
 — 3I.3 
 
 — J3;9 
 
 (■V) 
 
 — 5- 2 
 
 toi 4 
 
 73" 
 
 13> 4 
 
 -.84 
 
 —.36 
 
 03 
 
 '3 
 
 ^ 
 
 H 
 
 r ;5 8 
 
 y7 
 
 Di 
 
 ference for 1 ma. 
 
 33905 
 
 16.558 
 
 10.743 
 
 7-839 
 
 60957 
 
 4 ,3 3 
 
 ««■ 
 
 " 1 :■■'' 
 
 29957 
 
 2.6082 
 
 ■33° 
 
 '£« 
 
 
 ,0582 
 
 .SO,, 
 
 Difference for i° 
 
 18.54 
 
 903; 
 
 5.861 
 
 4.276 
 
 3.325 
 
 2.691 
 
 2.2 f 
 
 1 8983 
 
 ,634: 
 
 ,4227 
 
 
 .8792 
 
 7.093 
 
 -5772 
 
 II' 1 
 
 The object of observation is presumed to be J metre from the centre of rotation of the globe. 
 The figures in larger type give the amount of decentration in millimetres. 
 — ve sign indicates decentration outwards; +" sign decentration inwards. 
 
 The figures in smaller type represent the deviating power of the prisms whose action is equivalent to that of 1 
 lenses. When enclosed in brackets the prisms are adducting in function, and should be placed edges inwards.
 
 DR. PERCIVAL'S TABLES FOR NEAR VISION. 
 
 
 
 
 
 
 
 TABLE VIII 
 
 —(Concave.) 
 
 
 
 
 
 
 
 
 
 4 ma. 7 - i7' 
 
 -,d 
 
 -2 
 
 -30 
 
 -40 
 
 - 5 D 
 
 — 6D 
 
 -70 
 
 _., 
 
 -9D 
 
 ,00 
 
 -.20 
 
 -40 
 
 — 16 D 
 
 -.8 
 
 — 
 
 
 —247.6 
 
 —I25.6 
 
 —84.9 
 
 T 4 - 4 s' 5 
 
 -5.y 
 
 IS? 
 
 ~ 3 v 4 
 
 ■iV 
 
 7& e 
 
 —27.9 
 ■s'36' 
 
 7 2 ?? 
 
 ~TJ 
 
 — 1S.8 
 
 — 17.1 
 
 ^ 
 
 I 
 
 3 ma. 529' 
 
 —211. 9 
 
 -\v 
 
 -g$ 
 
 —54-9 
 
 —445 
 
 7 3 # 
 
 -3 2 9 .5 
 
 — 28.8 
 
 ~3 ? 7 ? 
 
 T 3 -.V 
 
 ■JW 
 
 S& 
 
 SP 
 
 —-4 3 
 
 — I3.I 
 
 5 
 
 2 ma. 3 V 
 
 -176.1 
 
 —889 
 
 —59? 
 
 —45-3 
 
 io-i;' 
 
 —36.6 
 
 —30.8 
 
 ~°V 
 
 IS? 
 
 ■jsg 
 
 —19.2 
 
 -16.3 
 
 T.-.V 
 
 7" 7 6 
 
 — 1».4 
 
 T-y 
 
 
 
 ^ 4 S 4 
 
 —70.6 
 
 8V 
 
 "S? 4 
 
 —357 
 
 — 28 ; 8 
 
 "ft 1 
 
 7>v 8 
 
 -*• 
 
 — ;6.,4 
 
 S-.6' 
 
 "»> 
 
 —10.8 
 
 8- 3 8' 
 
 —9.6 
 
 8"«' 
 
 7s! ;6 
 
 7// 
 
 
 o 
 
 -104.6236 
 
 
 
 -26.155.3 
 
 -209247-17.4372 
 
 -14 c^r,2 
 
 -13 n 77 , 
 
 -11 6248 
 
 -IO.4623 
 
 -8.7186l-7.4731 
 
 -6 Si-. 
 
 -5.8124 
 
 -5 23" 
 
 
 
 s'58' 
 
 5 - 58' 
 
 
 s'sf 
 
 5V 
 
 j"a* 
 
 
 S-S8' 
 
 5*58 
 
 S-J8' 
 
 5 - S»' 
 
 5-58' 
 
 5 - 5B' 
 
 S - 58' 
 
 s'ss' 
 
 
 1 ma. I> 
 
 -»• 
 
 ? s r 
 
 7v 4 
 
 7# 5 
 
 Iv 1 
 
 ~ IO ;7 
 
 IF 
 
 T?; 8 
 
 -6.g 
 
 —6.1 
 
 —4-9 
 
 7. 4 / 
 
 ~ 3 ,5 
 
 —3,0 
 
 —2.6 
 
 I 
 
 2 ma. 3-4- 
 
 ~, 3 ?' 
 
 —157 
 
 —98 
 
 — 6.g 
 
 ,•36' 
 
 T 5 . 2 
 
 73° 
 
 —3; 2 
 
 —2.6 
 
 ~3 ?I 
 
 — 1-7 
 
 "7™ 
 
 "Is 73 
 
 —.42 
 
 — 18 
 
 To" 
 
 \ 
 
 3 ma. jW 
 
 w 
 
 26 
 
 <.E) 
 
 2.6 
 (.7') 
 
 4-2.6 
 (3«'l 
 
 2-6 
 
 (45") 
 
 2.6 
 
 m 
 
 2,6 
 (...) 
 
 2.6 
 
 <■•*■') 
 
 (>3.) 
 
 2.6 
 
 2.6 
 
 2.6 
 WW 
 
 26 
 
 26 
 (3 .) 
 
 
 4 ma. 7-17' 
 
 3S.4. 
 
 20.9 
 
 H i. 
 
 '-Y' 
 
 '^ 
 
 (3 - "') 
 
 8-5 
 
 (aV) 
 
 7-9 
 
 7.4 
 
 7-0 
 
 U") 
 
 6 -« 4 ' 
 
 6.0 
 
 (4%8'J 
 
 &> 
 
 5-4 
 (i'36') 
 
 5 <*-> 
 
 Difference for i ma. 
 
 35754 
 
 'Va' 6 1 I2 =' 5 ° 4 
 
 Vij 8 
 
 7 3 - 8 , 5 ' 4 
 
 6.6916 
 
 5 ;:- 
 
 52385 
 .•14' 
 
 ♦j/; 1 
 
 *& 
 
 3 '' S | 4 
 
 3 37^2 
 
 3-OS88 
 
 2 8167 
 
 2.622, 
 
 Difference for i g 
 
 ic 502 
 
 10.088 
 
 1 
 
 5 £¥ 
 
 4.284 . 3.65O 
 
 3.1971 
 
 2-8574 
 
 2.5932 
 
 8.3819 
 
 2.0648 1 1.8383 j 1.6685 
 
 I.5364 1 I4307 
 
 The object of observation is presumed to be 1 metre from the centre of rotation of the globe. 
 The figures in larger type give the amount of decentration in millimetres. 
 — "sign indicates decentration outwards; + v * sign decentration inwards. 
 
 The figures in smaller type represent the deviating power of the prisms whose action is equivale 
 lenses. When enclosed in brackets the prisms are abducting in function, and should be placed edge
 
 EAR VISION. 
 
 - 9 D 
 
 10 D 
 
 — 12 D 
 
 — 14 D 
 
 16 D 
 
 —18 D 
 
 20 D 
 
 -30.6 
 1525' 
 
 —27.9 
 
 i5°36' 
 
 -23.8 
 I 5°59' 
 
 20.9 
 
 l6°2l' 
 
 —18.8 
 i6°43' 
 
 — 17.I 
 i7 c 5' 
 
 —15-7 
 
 1727' 
 
 -259 
 13 V 
 
 —235 
 
 I3°i6' 
 
 — 20.I 
 i/33' 
 
 — 17.6 
 *3°5°' 
 
 —15-7 
 14V 
 
 —14-3 
 14*24' 
 
 —13- } 
 
 I4°4l' 
 
 -21. 1 
 
 io°46' 
 
 — 19.2 
 
 IO°52' 
 
 -16.3 
 
 11 v 
 
 —14.2 
 Il0 i5' 
 
 12.6 
 
 II°27' 
 
 — II.4 
 «°39' 
 
 — IO.5 
 
 n°5o' 
 
 -16.4 
 
 8°23' 
 
 —14.8 
 
 8°26' 
 
 —12.5 
 
 8°32' 
 
 —I0.8 
 
 8° 3 8' 
 
 —9.6 
 8° 44 ' 
 
 —8.6 
 
 8°5o' 
 
 -7.8 
 8°56' 
 
 I.6248 
 
 --IO.4623 
 
 --8. 7186 
 
 -7-4731 
 
 "6.539 
 
 -5.8124 
 
 -5.2312 
 
 5°58 
 
 -6.9 
 3*V 
 
 2.6 
 
 (l°2l') 
 
 7-4 
 
 (3 D 48') 
 
 5-58' 
 
 5°58' 
 
 —6.1 
 
 3°29' 
 
 —4.9 
 
 3°23' 
 
 — 1.7 
 
 — I.I 
 
 59' 
 
 47 
 
 2.6 
 (131') 
 
 2.6 
 (i°49') 
 
 7.0 
 (4°) 
 
 6.4 
 (4°24') 
 
 5 C 58' 
 
 —4.I 
 3° 1 7' 
 
 -3-5 
 
 3 u 
 
 -•73 
 
 2.0 
 
 (2°7') 
 
 6.0 
 
 ( 4 ° 4 8' 
 
 .42 
 
 2.6 
 
 (2°2 5 ') 
 
 5-7 
 
 (5°i2') 
 
 5°58' 
 
 -3;0 
 3 3 
 
 18 
 
 ',.6 
 
 5°58' 
 
 -2.6 
 :9' 
 
 -.OI 
 
 d') 
 
 2.6 
 
 (2°43') j (3°0 
 
 5-4 ' 5-2 
 
 (5 C 36') ; ( °) 
 
 f-754i 
 
 2°2j' 
 
 43667 
 2°3o' 
 
 37854 
 
 2° 3 6' 
 
 3-3702 
 
 2,2' 
 
 3.O588 
 
 2°48' 
 
 2.8l67 
 
 2°54 
 
 2.6229 
 3° 
 
 J-5932 
 
 I°2o' 
 
 2.3819 
 
 I°22' 
 
 2.0648 
 
 I°2 5 ' 
 
 1.8383 
 
 I°28' 
 
 I.6685 
 
 I° 3 2' 
 
 I-5364 
 i°35' 
 
 I 4307 
 i'oS' 
 
 the globe. 
 
 on is equivalent to that of the decentration of the 
 3 placed edges inwards.
 
 THE EFFECT OF DISPLACED LEXSES. 115 
 
 combined with a prism of i° 24'^, which is prac- 
 tically the same thing. Table VII. and Table VIII. 
 are useful also in estimating the relative range of 
 convergence for reading distance. A myope using 
 — 5D for reading can obtain binocular vision with 
 a 3 prism held edge inwards before each eye, as 
 well as with a \2 32' prism held edge outwards. 
 His relative range is not, however, represented by 
 1 5 32', but by 12' 46', or 7 ma.
 
 n6 
 
 Chapter XIII. 
 
 THE CLINICAL APPLICATIONS OF 
 PRISMS IN DIAGNOSIS. 
 
 i. — To measure the functional * minimum of con- 
 vergence (r c ). This is generally a negative quantity, 
 so that the minimum of convergence of the visual 
 axes is synonymous with their maximum of diverg- 
 ence. It is, in other words, the maximum binocular 
 abduction of the visual axes in distant vision. Its 
 measure is therefore taken by finding the strongest 
 prisms with their edge outwards compatible with 
 single vision of some distant object, as shewn in 
 Fig. 54. The deviating angle of each prism ex- 
 
 Fig. 54. — The functional minimum of convergence. 
 presses the " functional minimum of convergence " 
 
 * The word " functional " is used in contrast with the 
 " absolute " minimum, which is the anatomical position of 
 the eyes.
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 117 
 
 for each eye. The figure also makes clear that the 
 visual axes meet behind the head during the 
 experiment, and their point of intersection is " the 
 far point of convergence." If a single prism be 
 used, since its effect is distributed between the two 
 eyes, its angle of deviation must be mentally halved 
 for each. Remoteness of the point of fixation 
 during the experiment is an important considera- 
 tion if it is desired to reach the real minimum, for 
 the knowledge of the object being at a great 
 distance favours the relaxation of convergence. 
 In ametropia, if lenses of sufficient strength are 
 placed in a trial-frame, the experiment can be made 
 by separating them if concave, or approximating 
 them if convex, till double vision occurs, and then 
 the prismatic effect can be calculated from rule I, 
 p. 1 10, or the Tables by Dr. Percival. 
 
 Thus, if the distance between the optical centres 
 of lenses of — 4D be increased till it is 16 mm. 
 greater than the distance between the centres of 
 motion of the eyes, we divide the 16 mm. between 
 the two eyes, for clearly each lens is displaced 8 
 mm., and therefore there is, for each eye, i° 40' 
 of divergence. It is expressed by saying that the 
 functional minimum of convergence is — 1° 40'. 
 Dr. Risley's Rotary Prism, p. 48, or the apparatus 
 in Fig. 25, affords the easiest and best means of 
 making this test. 
 
 With vision for six metres, the normal power of
 
 n8 PRISMS. 
 
 abduction is 2° for each eye, and is therefore 
 measured by a single prism of 8°. The average 
 abduction is greater in myopia and less in emme- 
 tropia, according to Schuurman. In testing the 
 power of abduction with M., refraction should first 
 be corrected, and the effect of the lenses on the 
 direction of the visual lines be allowed for. In 
 H., the test should be made both with and without 
 lenses. 
 
 2. — To measure the absolute maximum of conver- 
 gence (fl c ). Find the strongest adducting prisms, 
 as in Fig. 55, compatible with single vision of a 
 
 Fig. 55- — The absolute maximum of convergence. 
 
 test type or printed page held as close to the eyes 
 as accommodation will permit. A strong prism 
 can be placed in a trial frame before one eye, and 
 Dr. Risley's Rotary Prism before the other, or the 
 " prismatic trial frame" of Fig. 25 can be used, which 
 possesses the advantage of dividing equally between 
 the eyes the prismatic astigmatism and chromatic 
 aberration. 
 
 This test, though described for completeness, is 
 not easily enough made with ordinary prisms to
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 119 
 
 be much used, or to replace in practice the old 
 established custom of advancing a ringer towards 
 the root of the nose till one eye deviates outwards, 
 or the use of Dr. Landolt's Dynamometer in which 
 the finger is replaced by a line of light. The two 
 last tests, however, it may be suggested, do not 
 give the "absolute maximum of convergence," for 
 as soon as the point of fixation passes within the 
 binocular near point of accommodation, diffusion 
 circles appear on the retinas, and increase rapidly 
 in size with every approach till the eyes resign 
 the impossible task of accommodation — then 
 the ciliary muscle relaxes, and with it the con- 
 vergence. 
 
 These tests depend largely, I believe, on the point 
 of the resignation of accommodative effort. Even 
 were the accommodative efforts to persist, it is 
 scarcely to be expected that two pictures on their 
 respective retinae, each composed of a mass of 
 diffusion circles, should excite the desire for fusion 
 in its full strength, as clearly defined pictures 
 would. At first sight the highest ad ducting prisms 
 compatible with single vision of a test type held 
 at the absolute near point of accommodation would 
 seem to give the true " absolute maximum " of 
 convergence; but here there is a new difficulty, for 
 the chromatic dispersion of the prisms spoils the 
 definition of the pictures on the retinae, though truly 
 it might be avoided by using a monochromatic
 
 120 
 
 PRISMS. 
 
 light* By adding the maximum convergence to the 
 already ascertained " minimum convergence," we 
 get the "absolute range (amplitude) of conver- 
 gence" (V), of which, according to Dr. Landolt, 
 not more than one third or one fourth can be 
 continuously in exercise for comfortable vision. I 
 have never, however, worked by this rule, as Dr. 
 Landolt does. 
 
 3. — To measure the "relative range of conver- 
 gence" (af). For this, perhaps more valuable 
 
 Fig. 5C. — The relative range of convergence. 
 
 experiment, we find the strongest pair of abducting 
 prisms, as shewn in dotted outline in Fig. 56, and 
 
 * Such light may be obtained of a pure yellow by placing 
 common salt, or of a pure red by placing some salt of 
 strontium upon the wick of a spirit lamp, of which the 
 flame is kept steady by incombustible gauze, but the 
 illumination is far too feeble to be of any use, and I do 
 not in practice recommend the test at all.
 
 CLIXICAL APPLICAT10XS IX DIAGNOSIS. 121 
 
 then the strongest pair of adducting prisms, as 
 shewn in continuous outline, compatible with single 
 distinct vision of an object or type at some chosen 
 distance. The distance most suitable is that at 
 which the patient's daily work is done (occupation 
 distance), and for which spectacles are most 
 required. 
 
 The abducting prisms measure the negative part 
 of the range (rj), and the adducting prisms its 
 positive part (p\). This test, though beset with 
 practical difficulties in its application, would be the 
 most scientific of any, if the best ratio between the 
 negative and positive parts were well worked out 
 for different distances of vision. 
 
 The following table shews the relative conver- 
 gence in a man of 32, with conditions otherwise 
 
 TABLE IX. 
 
 
 A. Single Prism. 
 
 D. Deflection of each 
 axis. 
 
 R. Relative 
 Range. 
 
 6 m. 
 
 + \6°: - 3 
 
 + 4^r° 
 
 _ 3 ° 
 
 $r 
 
 1 m. 
 
 + 1S : - 8° 
 
 + 5° 
 
 - 2° 
 
 7° 
 
 *m. 
 
 r20°: - 12° 
 
 + 5 1 ? 
 
 - 3.1° 
 
 £"0 
 
 °47 
 
 £m. 
 
 + 24 : - 16 
 
 + er 
 
 - 4^° 
 
 "1° 
 
 1 m. 
 
 + 30 : - 18" 
 
 + 9° 
 
 .0 
 5 
 
 14° 
 
 normal. The first column A gives the refracting 
 angle of the highest + and — prism he can overcome 
 at the various distances. The second column D 
 shews the deviation of each eye produced by the
 
 122 PRISMS. 
 
 aforesaid prisms ; it is found by calculating the 
 deviating angle of each prism, and dividing it 
 between the two eyes. Thus the deviating angle 
 of a prism of i6° is g°d, and half this is 4J , so that 
 at 6 m. each eye can converge 4J without losing 
 the distinctness of an object. The third column R 
 gives the relative range for each eye, calculated 
 from the figures in column D. 
 
 It will be noticed that both the positive and 
 negative parts of the range increase as vision 
 becomes nearer; also that the positive part exceeds 
 the negative, though less so as vision becomes 
 nearer. The case cannot be taken as expressing 
 the normal amounts, but the features just men- 
 tioned will, I think, be found to prevail. The 
 table agrees more closely with Nagel's chart than 
 with Donders'. The results obtained vary not only 
 according to the peculiarities of the individual, but 
 according to the method pursued. Thus, if we test 
 the negative side of the range first, the positive 
 side will be smaller than if we began with it first. 
 As a rule, the limit of the negative part shews 
 itself by the appearance of diplopia, and of the 
 positive part by indistinctness from commencing 
 excess of accommodation. The impairment of 
 distinctness by strong prisms is apt to be con- 
 founded with this latter, so it is not easy to get 
 exact results. On the whole, though I once 
 attached considerable importance to the relative
 
 CLIXICAL APPLICATIONS IN DIAGNOSIS. 123 
 
 range, and, indeed, it is theoretically important, I 
 do not now commend it in practice except for a 
 few rare cases requiring more careful investigation 
 than we are generally able to give. The best 
 apparatus for testing would be that of Fig. 25. 
 4. — To dissociate convergence and accommo- 
 dation. Yon Graefe was the first to suggest 
 the use of prisms for this purpose. By placing a 
 vertical prism before one eye, strong enough to 
 create vertical diplopia, the reflex stimulus to 
 fusion is suppressed, and the eyes assume 
 what V. Graefe called their "position of equi- 
 librium." In distant vision this position is, in the 
 case of an emmetrope, that of the tonic convergence, 
 but in near vision there is the accommodative con- 
 vergence as well. A prism of four degrees (2°d) is 
 generally strong enough to create vertical diplopia 
 which cannot be overcome in distant vision, but 
 for near vision a stronger prism must be used (cf. 
 p. 69). V. Graefe used one of 15 . The distant 
 object which he employed was a candle flame, 
 the false image of which lay in the same vertical 
 line when the equilibrium was perfect, while 
 homonymous or heteronymous diplopia indicated 
 respectively relative convergence or divergence. 
 His object for near vision was a dot on a piece of 
 card with a vertical line through it, so that the 
 prism reduplicated the dot, but only lengthened the 
 line. The disadvantage of this device was that
 
 i2 4 PRISMS. 
 
 the overlapping portions of the line were sufficient 
 to maintain the exercise of fusion, and thus mask 
 any tendency to latent deviation that might exist. 
 It was only considerable insufficiencies that mani- 
 fested themselves by this test. The degree of 
 deviation was measured by finding what additional 
 horizontal prism was required to bring the candle 
 flames of the distant test into one vertical line, and 
 to unite the dots and lines of the near test; or, 
 without using a second prism, the first prism may 
 be rotated till the images are vertical, and then 
 from the strength of the prism, and the amount 
 of rotation, a calculation can be made of the 
 deviation of the eyes.* 
 
 Since V. Graefe's near and distant tests both 
 require a simple vertical prism, they give a false 
 result unless the prism is held exactly vertical, and 
 the head held perfectly steady. The slightest obliq- 
 uity of the prism introduces a lateral displacement 
 of the false image, which we may easily mistake for a 
 
 * The formula is as follows, where d is the deviating 
 angle of the prism, r its angle of rotation, and H the angle 
 by which the eye deviates, and by which, therefore, the false 
 image is misplaced, 
 
 Tan. H = Tan. d Sin. r. 
 In words, the tangent of the horizontal angle we wish to 
 measure, through which the false image is misplaced, is the 
 multiple of the sine of the angle through which the prism 
 has been rotated, and the tangent of the angle by which it 
 deflects rays of light.
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 125. 
 
 latent deviation where none such exists. To 
 remedy this I made use, several years ago, of a 
 double prism, which is shewn in Fig. 57. It is com- 
 posed of two prisms, each of 2° or 3 united by their 
 
 Fig. 57. — A double prism. 
 
 bases. The patient, shutting the left eye, holds 
 this prism before the right one and looks through 
 it at a flame, two images of which are seen, one above 
 and one below the real position of the flame. 
 Nothing is easier than to place the prism so that 
 the two images appear vertical. On opening the 
 left eye the flame is seen mid-way between its two 
 images, and in the same vertical line if there be no 
 latent deviation * The double prism makes the 
 test more delicate than a single one, but it is now 
 replaced by the still better plan of a glass rod, 
 suggested by a faint streak of light seen uniting the 
 
 * When I devised the double prism, I was not aware 
 that a similar one, called a bi-prism, had been used by 
 Fresnel to demonstrate the phenomena of " interference."
 
 126 
 
 PRISMS. 
 
 two false images, clue to the fact, proved by Mr. 
 Berry, that the edge of the obtuse prism is not a 
 mathematical line, but from imperfect manufacture, 
 a rounded ridge. It was easy to deduce from 
 this that a glass rod would produce a better streak 
 of light, by acting as a strong cylindrical lens.* 
 
 The first form of this little instrument was that 
 shewn in Fig. 58, consistin 
 
 g of a short glass rod, 
 
 Fig. 5S. — The first form of the glass rod test. 
 
 mounted in a metal disc. A convenient modifi- 
 cation consists of a series of glass rods, placed 
 parallel and in apposition, and united at their endsf 
 by sealing wax. This form anyone can make for 
 himself by breaking up a thin glass rod into several 
 pieces an inch long, laying them together on a 
 
 *"Oph. Review," May, 1890. 
 
 + For a figure of this form, suggested by Mr. Berry's 
 proposal to use corrugated glass, the reader is referred to 
 Mr. Berry's " Diseases of the Eye," second edition, Fig. 
 166 B.
 
 CLINICAL AP PLICA TIONS IN DIA GNOSIS. 1 2 7 
 
 smooth level surface, and sealing their ends together. 
 On looking at a distant flame with this before one 
 eye, it appears converted into a long streak of 
 light, which there is no desire to regard as a false 
 image of the flame, from its dissimilarity, especially 
 if red glass be used. If the streak pass through 
 the flame, equilibrium is perfect, but if otherwise, 
 its distance indicates the amount of latent deviation. 
 The prism that is able to bring the line and the 
 flame together is the measure of it. A very con- 
 venient way, in the absence of a tangent scale 
 {Fig. 59), is to place the rod test in one side of a 
 trial frame, and Risley's " rotary prism " in the 
 other, and turn the latter till the line crosses the 
 flame. Scales graduated in degrees, as in Fig. 59, 
 
 6-M 
 
 1 m 1 
 
 7S54s32l 1234-5 
 
 l2H0987S5g32 
 
 2 3) 10 
 
 ■56789K3I2I4-- 16/ (40-4£ 
 
 Fig. 59. — Tangent scale for use with the glass rod test. 
 
 afford the best means, however, since the patient 
 can read at any moment the figure crossed by the 
 line of light, and thus variations can be followed. 
 The full extent of a latent deviation does not 
 occur at once, but the line gradually moves farther
 
 128 PRISMS. 
 
 from the flame. Such a scale, graduated for use 
 at 5 metres, and with directions for use, can be 
 obtained from Messrs. Curry and Paxton : it is also 
 furnished with smaller figures for the objective 
 measurement of squint, but that does not belong 
 to the subject before us. 
 
 For near vision, a tangent scale is published, 
 graduated in degrees and metre-angles, for % metre, 
 with a vertical arrow running up from zero, such 
 that when reduplicated, as in Fig. 43, by a square 
 vertical prism held before one eye, the lower arrow 
 points to that figure on the upper scale which 
 measures the deviation. It is best to use a prism 
 of 12° (6° d), permanently mounted in an ordinary 
 strong cataract frame, which can be placed on the 
 patient in a moment, and needs no hand to hold it. 
 A thread, }£ metre long, should be permanently 
 fixed to the card to adjust its distance from the 
 patient correctly. This scale can also be obtained 
 from Messrs. Curry and Paxton, provided with a 
 printed sentence, as well as the figures, to ensure 
 full accommodation — an improvement suggested by 
 Mr. Berry. The rod test can be used instead of a 
 prism if the arrow be replaced by a small polished 
 metal button to reflect the light from a window or 
 a flame. The illumination, however, is rather too 
 feeble to be of much use clinically. The best device 
 for economising the light, by admitting the maxi- 
 mum amount into the pupil, is a convex cylindrical
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 129 
 
 lens, with a radius of curvature of about 20 mm. 
 By holding the scale vertically, instead of horizon- 
 tally, we can, by this method, measure latent vertical 
 deviations, for the estimation of which, in near 
 vision, we possess no other very satisfactory 
 method. 
 
 Tangent scales can be made for any intermediate 
 distance, but though I have used them for physio- 
 logical investigation, they are not necessary in 
 practice. If graduated in degrees or metre angles, 
 a different scale is of course needed for each dis- 
 tance ; while if marked in centimetres, and provided 
 with an arrow capable of being lengthened or 
 shortened, one is sufficient, but then a calculation 
 is necessary. 
 
 What is the due significance to attach to the 
 near vision test ? It clearly does not decide the 
 strength of one rectus, for convergence is a 
 single function affecting both eyes equally. It 
 is true that each rectus is a link in the chain of 
 convergence, and may be the weak link, but that 
 would shew itself best in testing the lateral move- 
 ments of the eyes. Neither does it afford a pure 
 test of the strength of convergence, for the ampli- 
 tude of convergence may be quite normal, and yet 
 an " insufficiency " (as it used to be called) appears 
 in the test for latent equilibrium, from one of its 
 stimuli being wanting, as in myopia, where accom- 
 modation is slight, or absent. The section on 
 
 9
 
 130 PRISMS. 
 
 " The study of convergence," contains an account of 
 the conditions that need consideration. 
 
 5. — To detect vertical latent deviations (hyper- 
 phoria). These are of two kinds, paretic and con- 
 comitant. The name " simple hyperphoria " should 
 be confined to the latter. If the deviation be of 
 the same amount on looking upwards or down- 
 wards, it is concomitant ; if otherwise, paretic. 
 
 The old way of disclosing such deviations was 
 by placing before one eye a prism, with its edge 
 outwards, and slightly stronger than can be over- 
 come — say one of 6° d. In this test especially, 
 precision in the setting of the prism is essential, 
 since imperfect setting, or an inclination of the 
 patient's head, cause apparent hyperphoria, when 
 such does not exist, as shewn in Fig. 19. Slight 
 vertical deviations are less frequent and more im- 
 portant than slight horizontal ones, since in all 
 normal individuals the vertical equilibrium is per- 
 fect. The glass rod is a delicate test for it, free 
 from the sources of error referred to in the use of 
 a prism, since slight rotations of the rod, or of the 
 head, do not appreciably affect the distance of the 
 line of light from the flame. The object should be 
 a gas-jet turned down to about a quarter of an inch 
 irr height, at the distance of 5 or 6 metres, while a 
 piece of blue glass held before the other eye greatly 
 improves the test, by subduing the illumination of 
 the flame, which otherwise is apt to eclipse the line
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 13] 
 
 by its superior brightness. Care should be taken 
 that direct light from no other source, such as a 
 window or a fire, falls on the glass rod, and this 
 can be obtained by standing so as to place it in 
 one's own shadow : a dark room is not necessary. 
 The measure of the hyperphoria can be taken by 
 finding what prism brings the flame and line 
 together, or how much rotation must be given to 
 Risley's " rotary prism." A scale of degrees, as 
 shewn in Fig. 60, is, however, what I have generally 
 used. 
 
 Fig. 60.— A tangent scale to measure hyperphoria with 
 a glass rod. 
 
 For near vision it is not so easy to measure 
 hyperphoria, nor is it often required. The plan 
 mentioned on page 1 29 can be used, or a stereoscope, 
 marked before one eye with a vertical line gradu- 
 ated in degrees up and down from a central zero
 
 1 3 2 PRISMS. 
 
 point, and before the other eye with a horizontal 
 line exactly level with the zero point just men- 
 tioned. On looking into the instrument, the hori- 
 zontal line appears to be across the zero of the 
 vertical one if equilibrium is perfect, but if not, 
 the figure crossed by the horizontal line measures 
 the hyperphoria. Stevens* suggests the desirability 
 of finding the highest prism, edge up, and the 
 highest, edge down, compatible with single vision. 
 Instances of hyperphoria are not so rare as they are 
 thought to be. It is well, when opportunity offers, 
 to test them again after a considerable interval to 
 see if the amount is stationary : often their per- 
 sistency is remarkable, and the same case will show 
 year after year, exactly the same measurement 
 Even slight hyperphorias sometimes cause great 
 inconvenience, and even headache and asthenopia. 
 On the other hand, hyperphoria may be very con- 
 siderable without causing a single symptom, or 
 seeming to be of any consequence. I have recorded 
 elsewheref the case of a young man, 1 8 years of age, 
 who had right hyperphoria of nearly io°, without 
 any headache or discomfort from it. His right eye 
 was noticed by his mother to occasionally " roll 
 up," and since his grandmother was said to exhibit 
 the same phenomenon, it is more than likely that 
 
 * "Archives d' Ophthalmologic " XVI. ; 6 ; p. 544. 
 t "Ophth. Review," Vol. XII., p. 44-
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 133 
 
 there was hereditary transmission of the defect, and 
 its toleration would thus be accounted for. This 
 case called for no treatment, since the anomaly 
 caused no discomfort ; tenotomy of the right 
 superior rectus, or advancement of the left inferior, 
 would have been indicated had distressing symp- 
 toms been present. 
 
 In true hyperphoria one eye turns up when it is 
 covered, as much as the other turns down when it 
 is covered. Mr. Berry has noticed some rare 
 aberrant forms of hyperphoria, in which one eye 
 turns up without the other turning down, or 
 in which either eye turns up when covered. 
 In paretic hyperphoria the latent deviation is 
 greater in some directions than in others, and by 
 using the rod test, with the patient's head in 
 different positions, it is easy to discover which eye 
 is at fault, and which muscle is affected.* For the 
 correction of hyperphoria, see page 140. 
 
 6. — Prisms are sometimes used to measure stra- 
 bismus, or the degree of any existing diplopia, by 
 finding what prism is able to unite the two images, 
 but this plan is fallacious since prisms of different 
 strengths will be found equally to succeed. The 
 weakest prism which enables the two images to be 
 united, though it does not measure the diplopia, 
 yet gives us the useful information of how much 
 
 * " Ophthalmic Review," Vol. IX., p. 287.
 
 134 PRISMS. 
 
 the diplopia needs to be lessened in order to allow 
 the remainder to be corrected by the desire for 
 single vision. The deviating angle of the prism 
 tells us the proportion of diplopia which is beyond 
 the control of fusion. It is sometimes recommended 
 to prescribe prisms of this kind, so as to exercise 
 the neuro-motor mechanism till the strength is 
 regained. 
 
 Since homonymous diplopia is due to excessive 
 convergence, we use plus prisms {i.e. edge in), and 
 since heteronymous diplopia is due to excessive 
 divergence, we use for it minus prisms {i.e. edge 
 out). In simpler language, " place the apex of the 
 prism in the same direction as the eye deviates " 
 (Juler). 
 
 7. — To decide the presence or absence of binocular 
 vision. 
 
 The fact that a prism before an eye deflects the 
 line of fixation was turned to account by Von 
 Graefe, in cases of suspected malingering, to see 
 whether an eye has such a thing 2^ a line of fixation, 
 or in other words whether it is a seeing eye. The 
 following is perhaps the fullest plan. After fixing 
 the patient's attention, we may first place a strong 
 prism, say of 30° (edge in or out), before the sound 
 eye. If, while doing this, the other betray no 
 associated movement, vision is almost certainly 
 binocular, for nothing but fixation could preserve 
 it from accompanying the deflection of its fellow,
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 135 
 
 except in paralytic cases. Should it move, how- 
 ever, nothing is proved beyond the fact that its 
 fixation power is less perfect than that of the 
 other. 
 
 The same prism is now similarly placed before 
 the doubtful eye ; if while doing so the other dis- 
 play an associated movement, vision is not only 
 binocular, but the impugned eye is the better of the 
 two, at least for the distance of vision employed at 
 the time : but if there be no associated movement 
 nothing is proved. 
 
 Lastly, on placing a plus prism of about io c 
 before the doubtful eye, and quickly withdrawing 
 the prism, we closely watch the eye from which it 
 is taken ; for a corrective movement, if detected, at 
 once tells us that its line of fixation has been 
 deflected by the prism, and that it has therefore a 
 line of fixation and is a seeing eye. 
 
 The subjective test, in which the patient's state- 
 ments have to be relied on, is, for obvious reasons, 
 often unsatisfactory, though it possesses the pecu- 
 liar advantage of convincing a by-stander from the 
 patient's own mouth, and of thus relieving the 
 surgeon from the sole responsibility. It consists 
 in placing a prism first before the unsound eye, 
 and asking whether any object, preferably a flame, 
 appears double. The reply is almost certainly 
 negative. The prism is next placed before the 
 sound eye, and the question repeated, " Do you
 
 136 PRISMS. 
 
 now?" If incautious, the patient may admit that 
 though he sees nothing with the bad eye, he sees 
 double when the prism is held before the good one. 
 To confuse the patient in a case suspected to be 
 one of simulated unilateral blindness, Alfred Graefe 
 suggested to show him, first of all, that diplopia is 
 obtainable with one eye. This is best done by 
 making him look at a distant flame with the im- 
 pugned eye covered, while a square prism, the base 
 of which is held uppermost and has sharp angles, is 
 moved upwards till it reaches almost to the lower 
 margin of the pupil. Double images of the flame 
 are thus produced. On repeating the experiment, 
 but this time without covering the impugned eye, 
 the prism is held higher up so as to cover the whole 
 pupil. If, under these conditions, diplopia results, 
 it must be because both eyes see. It is much 
 more difficult to produce monocular diplopia by 
 placing the apex of a prism opposite the pupil, 
 than by placing the base opposite its lower margin. 
 Mr. Adams Frost has pointed out a possible source 
 of fallacy in making this test, namely, that the 
 image by double internal reflection, explained on 
 page 51, may be noticed by the patient, who may 
 thus say that he sees double, though the other 
 eye be blind. The image spoken of is extremely 
 faint, but though with a strong prism it is too far 
 removed from the true image to attract attention, 
 it micrht be noticed with a weak one.
 
 CLINICAL APPLICATIONS IN DIAGNOSIS. 137 
 
 8. — To elicit diplopia in cases of suppression of the 
 false image. After a squint has lasted a sufficient 
 length of time, the mind has so learned to ignore 
 the false image that it is impossible to produce 
 diplopia by looking at a flame. The false image 
 is then said to be " mentally suppressed." If the 
 suppression be not deep, attention can be called 
 to the false image by placing a piece of green or 
 red glass in front of the fixing eye, or, if this fail, 
 by placing a vertical prism before either eye to 
 throw the picture of the flame on to a different 
 part of the retina. There are cases of even alter- 
 nating squint in which the false image is suppressed, 
 whichever eye fixes. The suppression is sometimes 
 so deep, in long-standing cases, that nothing can 
 overcome it. In a few cases the glass rod has 
 elicited diplopia when prisms have failed to do so : 
 it should be combined with a coloured glass before 
 the other eye.
 
 i 3 8 
 
 Chapter XIV. 
 
 THE USE OF PRISMS IN TREATMENT. 
 
 Prisms may be used, — 
 I. — To relieve excess of tonic convergence. We 
 need first to exclude causes which can be relieved 
 by constitutional treatment — reflex, hysterical, 
 cerebral, etc. Hypermetropia needs correction. 
 If the latent convergence does not exist for all 
 distances of vision, care must be taken that the 
 prisms ordered should only be worn for distant 
 vision. If there be excess of convergence in near 
 vision also, they can be worn for all purposes. In 
 myopia it is not uncommon to find considerable 
 latent convergence in distant vision giving rise to 
 occasional diplopia, which can be remedied by 
 displacing the lenses nearer together till the excess 
 of convergence, shewn by the rod-test, is reduced 
 almost to nil. It is well not to correct more 
 than two-thirds of the latent deviation.* Slight 
 excesses can be left alone. 
 
 * Noyes recommends its full correction, on his supposition 
 that it is due to insufficiency of the externi. This is not 
 a supposition I feel able to endorse.
 
 USE IN TREATMENT. 139 
 
 2. — To relieve deficiency of tonic convergence. 
 This is a much commoner condition than the last, 
 and can generally be left alone. It occasionally, 
 however, gives rise to diplopia, or to asthenopia 
 and headache. It may then be relieved by prisms 
 which annul half the latent condition. Convex 
 lenses can be displaced inwards, and concave 
 lenses outwards. Latent divergence in distant 
 vision is nearly always accompanied by still greater 
 latent divergence in near vision, so that the same 
 prisms can be worn for near work as for distant. 
 In some neurasthenic individuals great variability 
 occurs in the equilibrium of the eyes. These are 
 not the cases for prisms. 
 
 3. — To relieve excess of accommodative conver- 
 gence. It is extremely rarely that this occurs in 
 other than hypermetropes, where correction of the 
 refraction is all that is indicated. I have not met 
 with an emmetropic case. 
 
 4. — To relieve deficient accommodative convergence. 
 In myopia, since accommodation is less than in 
 emmetropia, the accommodative convergence is 
 less. This is rectified by wearing the full cor- 
 rection for the myopia, but sometimes the full 
 correction cannot be borne, and it is advisable to 
 prescribe weaker lenses either displaced or decen- 
 tred outwards, or combined with prisms, edge out. 
 What frequently happens is that both the tonic and 
 accommodative convergences are deficient, and
 
 RV = A : LV = 
 
 5%. 
 
 tangent scale, 
 
 
 
 5 m. 
 
 
 In 
 
 140 PIUS MS. 
 
 then the correction of the former generally suffices 
 if the same spectacles are used for all purposes. A 
 high amount of latent divergence at reading 
 distance is often tolerated without discomfort. It 
 occurs too in cases other than myopic. 
 
 Illustrative case. — Mrs. L., 38 years of age, has 
 had extensive corneal nebulas from childhood. 
 Equilibrium by rod test, and 
 
 -12° 
 
 She is obliged to hold her sewing, or small print, 
 near her eyes, to obtain sufficient visual acuity, yet 
 this causes headache and asthenopia. As shewn 
 above, she has slight latent divergence for distance, 
 namely, i°, which is V for each eye, and can be 
 neglected. At J metre she has 12° of latent diver- 
 gence, which is 6° for each eye. She was ordered, 
 for fine work, spectacles of +3*5D, with prisms of 
 6 V, base in. With these she can hold her work 
 near, and get good acuity without discomfort; the 
 nebulae making her less observant of the prismatic 
 aberrations. She could not tolerate them at the 
 first trial, but in a day or two said, " I would not be 
 without them," and writes after a few months : 
 11 spectacles very useful to me in reading." 
 
 5. — To relieve hyperphoria. This is one of the most 
 useful of the services rendered by prisms. Well 
 marked cases of persistent hyperphoria, with dis-
 
 USE IN TREATMENT. 141 
 
 comfort from threatened diplopia, and eye strain, 
 are immensely relieved by prisms, which should 
 correct about two-thirds of the defect I think. It 
 will be remembered that prisms set vertically have 
 less effect over hyperphoria in near than in distant 
 vision, p. 69, so that full correction for distance is 
 under-correction for near. The prisms should be 
 equally divided between the two eyes, the edge of 
 each being in the same direction as the axis of the 
 eye, that is edge up before the higher eye, and edge 
 down before the lower. 
 
 Illustrative case. — Miss Mary T , age about 
 
 45, with # 5D of hypermetropia in each eye and V 
 = f§, complains that she has had a tendency to 
 double vision for the last two years, and that when 
 she does see double the objects appear superposed; 
 thus she thought she saw two rows of cows, one above 
 the other, discovering afterwards there was only one 
 row. A similar difficulty, encountered in reading, 
 she had learned to overcome by tilting her reading 
 spectacles to make one lens higher than the other 
 (an unconscious use of prisms). The rod test 
 shews at 5 m. right hyperphoria {i.e. the right eye 
 highest) of i°. She also complains of headaches 
 and asthenopia, such that, though highly intellec- 
 tual, she has almost ceased to read or use her eyes 
 for close work for the last year or two. She 
 remembers that, when a child, she could not see 
 properly through a stereoscope from the two images
 
 142 PRISMS. 
 
 appearing superposed. Treatment. — Prisms of f ° 
 before each eye, edge up before right, edge down 
 before left, with lenses of +o*5D. Similar prisms to 
 be combined with her reading spectacles. Result. — 
 The headaches greatly relieved; asthenopia gone; 
 says glasses have taken her back several years in the 
 use of her eyes, so that she can sew and read again 
 as of old, but if she takes them off for a moment 
 the diplopia is more troublesome than before. 
 This last fact illustrates a great disadvantage in the 
 use of prisms prescribed for relief rather than cure. 
 The prisms, being less than the hyperphoria, 
 cannot really have created an increase, but have 
 probably allowed more of what was latent to 
 become manifest. This, however, is more than 
 compensated for by the relief they have given. 
 
 6. — To correct diplopia from oculo-motor paresis. 
 In recent cases we, of course, wait for cure of the 
 condition, but if it seems to come to a standstill, 
 we may afford relief by ordering prisms such that 
 the images can be united in at least the most 
 useful direction of vision. At first, the diplopia 
 occurs only in a certain area of the field of fixation, 
 but after a while through what is called " contrac- 
 ture of the antagonist " there is often latent diplopia 
 over the whole field. This latent element should 
 be corrected, and a little of the manifest as well. 
 Prisms should have their edges placed in the direc- 
 tion in which the axis of the affected eye deviates,
 
 USE IN TREATMENT. 143 
 
 remembering, if we wish to divide the prism between 
 the two eyes, that the one before the sound eye 
 should have its apex in exactly the opposite 
 direction. If for instance the right eye deviate 
 down and out, its prism should be apex "down and 
 out," and the prism for the left eye be apex " up 
 and out" In old paralysis of the superior oblique, 
 prisms are very valuable, since on looking down 
 at the work the diplopia is troublesome. The most 
 thorough way to examine a case is to combine the 
 vertical and horizontal scales of Figs. 59 and 60 
 with a flame at their centre, and then test the 
 equilibrium of the eyes with the glass rod in each 
 of the nine positions of the field of fixation ; this 
 is done by placing the patient's head in different 
 positions. From a chart thus made, it is easy to 
 reason out what prisms it is best to order. But a 
 quicker way is just to place the patient's head so 
 that on looking at the flame his axes of fixation 
 are in the position mostly required at his work; 
 the vertical and horizontal deviations can then be 
 measured, and prisms be prescribed to correct a 
 certain proportion of each. Thus, if the right eye 
 deviate upwards 5 we may order a prism of 2°d, 
 edge up, before the right eye, and the same, edge 
 down, before the left. If the same eye also con- 
 verges 3 , we may combine with each of the above 
 a plus prism of i°d, on the principle of "resultant 
 prisms." A man with paralysis of the right
 
 144 PRISMS. 
 
 superior oblique, who could only look down at his 
 work comfortably by shutting one eye to avoid 
 diplopia, greatly valued resultant prisms of 3 
 (iJV) each which were ordered him. 
 
 7. — To assist in the cure of paralytic diplopia 
 (diphtheritic, rheumatic, etc.). Donders wrote, "We 
 may further, in paresis of a muscle, so far meet 
 the disease by means of a prism, that in order to 
 make the double images which have been brought 
 near one another run together, the muscles will 
 become powerfully tense, which, for the alleviation 
 of the paresis, appears to be no matter of in- 
 difference."* In recent cases, without secondary 
 contraction of the antagonist, this plan is not very 
 feasible. In older cases, where the defect is slight, 
 it might possibly serve a purpose, but I doubt if 
 it would really have a curative effect since the good 
 it is supposed to do in one part of the field would 
 be undone in another part, unless the field of 
 diplopia were very extensive. 
 
 8. — To disguise a squint in an amblyopic eye. The 
 cosmetic use of prisms was brought to my notice by 
 a case in the practice of Mr. Berry, who suc- 
 ceeded in concealing, to a considerable degree, a 
 vertical squint in a young woman, by prescribing 
 a vertical prism to be worn before it, in conjunction 
 with a lens equal to that needed before the seeing 
 eye. Since prisms cause apparent displacement of 
 
 * Anomalies, &c., p. 134.
 
 USE JN TREATMENT. 145 
 
 objects towards their edges, the edge of a cosmetic 
 prism should be in the opposite direction to the 
 squint. Thus if the eye squint up, the edge of 
 the prism should be down ; if the eye squint out, 
 the edge should be in. This procedure is chiefly 
 applicable to slight vertical squints, which are more 
 disfiguring than slight horizontal ones. 
 
 10
 
 146 
 
 Chapter XV. 
 
 ANALYSIS OF SPECTACLES. 
 
 HITHERTO we have dealt with the synthetical part 
 of our subject, how to prescribe prisms and com- 
 bine them with lenses. The analytical part needs 
 but brief consideration. When a patient comes to 
 us with a pair of spectacles already in use, but 
 which cause discomfort, in spite of having the 
 correct focal length, how are we to investigate their 
 prismatic effect, and find how the glasses are 
 centred ? Clinically, nothing is easier than to test 
 the positions of equilibrium by the glass rod, etc., 
 with and without the spectacles. We then see 
 what effect they have on the visual axes, and by 
 what distance lenses of similar focus, when placed 
 in a trial-frame, need to be separated to produce a 
 desirable equilibrium. 
 
 We can reach the same result in another 
 way, by measuring the distance between the 
 centres of the eyes and between the optical 
 centres of the lenses. If these two distances are 
 equal, and the spectacles be for distant vision, they 
 have practically no effect on convergence. If, 
 with reading spectacles, the distance between the
 
 ANALYSIS OF SPECTACLES. 
 
 ^47 
 
 optical centres be 5 or 6 mm. less than the inter- 
 ocular distance, the effect on convergence is also 
 practically nil. In Fig. 61 is represented a rough 
 
 so 
 
 Ji 
 
 iTTiTf 
 
 . HiUontcrcs 
 
 Fig. 61.— A simple way of telling the distance between the 
 optical centres of a pair of spectacles. 
 
 but ready method of telling the distance between 
 the optical centres. The spectacles are held hori- 
 zontally, and some inches above a card marked to 
 one side with a vertical line jr, and towards the 
 other side with parallel lines y t at different mea- 
 sured distances from the single one. The observer, 
 holding his left eye about a foot above, and as 
 nearly vertically over the left lens as he can judge, 
 closes the right eye, and moves the spectacle frame 
 from side to side till the line x appears unbroken 
 by the left lens. Now, without moving the head, 
 the right eye is opened and the left closed, and 
 that line which appears to be least displaced by 
 the right lens is the line nearest its optical centre, so 
 that the number above it furnishes a rough estimate 
 of the required distance between the two optical 
 centres. 
 
 To ascertain whether each optical centre is
 
 148 PRISMS. 
 
 midway between the upper and lower border of 
 its rim, each lens must be held lengthwise over the 
 left hand line till it appears to run continuously. 
 If we wish to measure the distance of each optical 
 centre from the middle of the bridge, it is easily 
 done by marking each lens with an ink dot where 
 a single line (x in Fig. 61) appears unbroken, 
 so as to measure the distance of each dot from 
 the centre of the bridge. If the optical centre lie 
 outside the lens altogether, then the " analyser " in 
 Fig. 63, which was described in the first edition of 
 this work, can be used, though it has since been made 
 unnecessary by the introduction of the " prism 
 measure " of the Geneva Optical Company. The 
 analyser, however, though more difficult to use, 
 possessed the advantage of giving a dioptric mea- 
 surement true for media of any index of refraction, 
 while the " prism measure " only gives the phy- 
 sical inclination of the surfaces. The latter instru- 
 ment, shown in Fig. 62, is very simple in its use. 
 If a lens be placed within it, and be moved about 
 in the horizontal plane till the index points to zero, 
 the tooth in the centre of the foot of the index 
 points to the optical centre. If, on the other hand, 
 the geometrical centre be placed just below this 
 tooth, the index points to the number which mea- 
 sures the physical angle of the virtual prism with 
 which the lens is combined. This does not in 
 itself, however, give us much information about the
 
 ANALYSIS OF SPECTACLES. 
 
 149 
 
 effect of the spectacles on the visual axes, for the 
 geometrical centre may not be directly in front of 
 the eye. If we measure from the centre of the 
 bridge a distance equal to the distance of the 
 centre of the eye from the median plane, and 
 
 .f 
 
 Fig. 62. — The " prism measure," used to discover the optical 
 centre of a lens. 
 
 mark this distance by an ink dot on the glass, 
 then we can place the said ink dot under the tooth 
 and read off what prism is virtually combined with 
 the lens at this point, directly in front of the eye. 
 In this way we discover the prismatic effect of the
 
 ISO 
 
 PRISMS. 
 
 spectacles without any calculation. This appli- 
 cation of the instrument, though not mentioned by 
 its inventor, makes it as useful to the surgeon as 
 it is to the optician, and renders any description 
 of the analyser almost unnecessary, except for a 
 few who may have had it constructed, or who wish 
 great exactness with pebble lenses, as well as with 
 glass ones. 
 
 The "analyser," which is shown in Fig. 63, ha? a 
 plate of glass, c d, which is movable from side to side. 
 The letters a b indicate a narrower plate of glass, also 
 
 k, 
 
 \f 
 
 Fig. G3. — The Analyser. 
 
 movable, marked exactly across the middle with a 
 transverse line x. On either side of the slides is
 
 ANALYSIS OF SPECTACLES. 151 
 
 a millimetre scale with the zero in the centre. The 
 broad slide has a long line w right across it opposite 
 the zero of its scale. The card r s has only one line 
 upon it, exactly beneath the central lines of the glass 
 strips, and it can be placed either in the bottom of the 
 apparatus, as in the figure, or in the grooves higher up, 
 for lenses whose focal length is shorter than the height 
 of the glass plates above the lowest grooves. The card 
 is generally used in its lowest position, because distance 
 of the line upon it from the lenses, as we have already 
 seen with prisms, magnifies the phenomenon, and makes 
 the experiment more delicate. The height of the upper 
 surface of the glass plates from the card in the lowest 
 grooves is about 4^ inches. 
 
 To analyse a pair of spectacles, lay the centre of the 
 bridge on the line w, and place the observing eye so 
 that the lines x and n p appear to coincide. Now move 
 the broad slide bearing the spectacles till the line n p 
 appears undeviating through one lens ; then w points to 
 the distance between the optical centre of that lens and 
 the centre of the bridge. Repeat in the same way for 
 the other lens. 
 
 Lastly, by laying the geometrical centre of a lens 
 opposite the zero of the scale k <?, the line n p will, if it 
 be a decentred lens, appear displaced through it. How 
 great is the apparent displacement ? By answering this 
 we tell the prismatic equivalent of the decentering with- 
 out recourse to any table. We must use another sight* 
 fixed to the narrow slide perpendicularly beneath its line 
 x, then by holding the eye so as to keep them both in 
 
 * Another way is to use a plane mirror instead of the card 
 r s and keep the line x in line with its reflection — a little 
 difficult sometimes.
 
 152 PRISMS. 
 
 apparent coincidence (thus ensuring a vertical line of 
 vision) and moving them till they appear exactly abreast 
 of the apparent displacement of the line n p as seen 
 through the lens, the prismatic equivalent of the de" 
 centering is indicated by the degree on the scale ef to 
 which x points. The special applicability of this mode 
 is when the optical centre lies outside the lens. When 
 the lenses under test are of shorter focal distance than the 
 height of the analyser, the card must be placed in one 
 of the other two pairs of grooves : then, though the use 
 of the scale k e is unchanged, it must be remembered 
 that when the card is in the grooves half way up, each 
 figure in the scale ef must be multiplied by two, and 
 when the card is in the highest grooves, as for cataract 
 lenses, each must be multiplied by four. The scale ef 
 can be marked either in millimetres or in degrees ; if 
 the latter, then the height of the lenses above the card 
 must be 53*3 mm. or some multiple of that number, for 
 the degrees to be one millimetre from each other, or 
 some multiple of a millimetre. But if marked in milli- 
 metres the height of the lenses above the card should be 
 100 mm., so that by a table of tangents affixed to the 
 analyser the degree can be found. This is the most 
 exact method, especially for strongly prismatic lenses
 
 153 
 
 Chapter XVI. 
 
 LOCALISING THE EYES. 
 
 It is often desirable to measure the distance of 
 the centre of each eye from the bridge of the nose, 
 to estimate correctly any apparent want of sym- 
 metry, and to know at what distance from the 
 middle line to place the geometrical or optical 
 centre of a lens. Many tests exist for the mutual 
 distance between the two eyes, of which, perhaps, 
 the best is Snellen's frame, but they estimate the 
 distance between the two pupils, whereas what we 
 need for the exact study of prisms is the distance 
 of the centre of rotation of each eye from the 
 median plane which bisects the nose. 
 
 For a test to be true in principle, not only must 
 the visual lines of the observing and observed eye 
 coincide, but the line so composed must be exactly 
 at right angles to the line uniting the centres of the 
 two eyes, or, at least, if one eye be examined with 
 any angle of inclination, the inclination must be the 
 same in the examination of the other.* It need 
 
 * On the principle of the parallelogram.
 
 154 PRISMS. 
 
 hardly be said that this cannot be ensured when 
 only a single point is used for a bearing. To over- 
 come this difficulty a little device, Fig. 64, may 
 
 Fig. 64. — The Localiser. 
 
 be used with two sights so disposed as to always 
 be in a line at right angles to any trial-frame 
 in which it is placed. One pupil is localised at a 
 time, all that is necessary being to increase or 
 diminish the breadth of the frame till the two 
 sights and the centre of the pupil are in line, as in 
 Fig. 65 ; the patient meanwhile is bidden to be 
 
 Fig. 65. — The Localiser in use. 
 
 looking at the pupil of the surgeon's observing eye,, 
 by doing which the two visual lines (i.e., that of the 
 observing and that of the observed eye) come to* 
 practically coincide. If the patient is a child it is 
 quite easy to excite its interest in its own miniature
 
 LOCALISING THE EYES. 155 
 
 reflection in the surgeon's pupil while taking the 
 observation, adeptness in which needs a few trials 
 to become familiar with the parallactic motion. 
 The instrument is then placed in the other rim of 
 the frame, and the observation repeated for the 
 other eye. 
 
 By this method we comply with the two afore- 
 named conditions of accuracy ; the visual lines of 
 the observing and observed eyes coincide, and of 
 necessity they are both at right angles to the trial- 
 frame. The frame must, of course, be one movable 
 by a screw, and marked in millimetres, so that the 
 record can be read off after localising each pupil. 
 The distance of the centre of each eye from the 
 middle line is in each case half what is registered 
 by the frame. It is true that the present methods 
 may be considered sufficiently exact for practical 
 purposes, but there is, nevertheless, a pleasure in 
 working as truly as possible, and the frequent and 
 careful use of this instrument will shew how many 
 an unsuspected difference exists in the position of 
 the two eyes. When ordinary spectacles are pre- 
 scribed for eyes placed unsymmetrically, the 
 prismatic effect is greater for one than the other, 
 which, however, is only of importance with very 
 strong lenses, being counteracted by involuntary 
 inclination of the head; another consequence is 
 that the fields of fixation for each eye are 
 unsymmetrical.
 
 i 5 6 
 
 PRISMS. 
 
 TRIAL-FRAME FOR TEMPORARY FRISMS. 
 In the first edition of this work it was said that 
 prisms should not be prescribed without wearing 
 a temporary pair for a few evenings first, to learn 
 how they suit, but I now think this rarely needful, 
 for if the conditions of convergence be carefully 
 studied we need hardly ever prescribe prisms without 
 feeling pretty sure beforehand of their effects, even 
 though, as is often equally the case with cylinders, 
 they do not seem well borne just at first. Still, 
 there are occasions where temporary prisms are of 
 service, and the diagram of the frame to hold them 
 may be reproduced, Fig. 66. It is made to hold 
 
 Fig. 66. — Rectangular prisms in a frame as suggested in the text. 
 This frame may be obtained from Messrs. Curry & Paxton. 
 
 rectangular* prisms, the shape of which permits 
 them to be adjusted at once, and removes any 
 possibility of their displacement. Each prism has 
 a longitudinal groove in its upper and lower sur- 
 face, so that it need only be pushed in between the 
 wires till caught by the elbow. So light a frame as 
 this could be worn together with an ordinary pair 
 
 * Dr. Percival has proposed a slight modification, namely, 
 that the prisms should be square instead of oblong.
 
 LOCALISING THE EYES. 157 
 
 of spectacles when it is desired to try for a few 
 evenings the joint effect of prismatic and spherical 
 glasses.* 
 
 I would recommend, in prescribing prisms, 
 the following simple maxims : 
 
 1. — Never order strong prisms unless the indica- 
 tions for their use are unmistakable. 
 
 2. — Rarely order them stronger than 4 (2°d) 
 unless there be amblyopia, as from corneal nebulae, 
 etc. 
 
 3. — Never give them on account of a mere 
 anomaly in the behaviour of the eyes under the 
 various tests, if it causes no fatigue or discomfort. 
 
 4. — Do not judge by the rod test alone, but also 
 try the "finger test" of p. 119, and the "card test" 
 of p. 128, and, if specially indicated, the "relative 
 convergence test," p. 120. 
 
 5. — Remember that latent deviation in distant 
 vision is more important than in near vision, though 
 the latter is not to be ignored; and that moderate 
 divergence in near vision is physiological. 
 
 6. — Always, more or less, under-correct. 
 
 * It may be obtained from Messrs. Curry & Paxton.
 
 . 5 8 
 
 APPENDIX. 
 
 I. — Resultant Prisms. For those who dislike 
 calculations, the following method of combining a 
 vertical with a horizontal prism may be of service. 
 Draw a horizontal line as many inches long as there 
 are degrees in the deviating angle of the horizontal 
 prism. From one end of this line draw another 
 vertical line as many inches long as there are 
 degrees in the deviating angle of the vertical prism. 
 Then the number of inches between the free ends 
 of these two lines equals (approximately) the 
 number of degrees in the required resultant prism ; 
 and the inclination of the base-apex line of the 
 resultant prism to the horizontal is given by the 
 angle between the horizontal line and the hypothe- 
 nuse, or resultant line, which unites the free ends 
 already spoken of. 
 
 2. — Sines, Arcs, and Tangents. Figure 67, to 
 shew the relation between the arc, sine, and tan- 
 gent, is introduced for the sake of any reader who 
 may not be acquainted with trigonometrical ratios. 
 Let any angle be included between the two radii 
 of a circle, then the portion of the circumference 
 included between the radii, as aR in the figure, is
 
 APPENDIX. 
 
 '59 
 
 the arc of the angle, and, if the radius be taken as 
 unity, a perpendicular (RS) dropped from the 
 extremity of one radius perpendicularly upon the 
 
 Fig. 67. — To illustrate the cine, arc, and tangent of an angle. 
 
 other radius is the sine, and a line drawn perpen- 
 dicularly from the extremity of one radius to meet 
 the other, as R t in the figure, is the tangent of the 
 angle. It will be seen at once that the sine is 
 always less, and the tatzgent always greater, than 
 
 Fig. 68. — To illustrate a tangent scale, 
 the arc, and the greater the angle, the greater is 
 the disproportion between the three quantities. 
 Fig. 68 shews how when angles are projected on to
 
 i6o 
 
 APPENDIX. 
 
 a straight line, as in the tangent scales represented 
 in Figs. 59 and 60, the graduations increase in 
 magnitude with each departure from zero. The 
 following table (Table X.) of natural sines and 
 tangents is inserted only for convenience, to save 
 reference to a book of mathematical tables which 
 may not always be at hand. The column of sines 
 may be used for resultant prisms, and the column 
 of tangents for making a tangent scale. For 
 accurate working out of formulae a fuller table must 
 of course be used. 
 
 3. — Formula for refraction through prisms. In 
 Fig. 69, a ray of light (ef) is seen traversing a 
 
 Fig. 69. 
 
 prism in the plane of a principal section. Then, 
 whatever be the angle of incidence (/), the total 
 deviation (d) is the sum of the deviations at the two 
 surfaces, so that 
 
 (1) d = w + v.
 
 APPEXD1X. 161 
 
 TABLE X. (SIXES AXD TAXGEXTS.) 
 
 Degrees. 
 
 Sines. 
 
 Tangents. 
 
 Degrees. 
 
 Sines. 
 
 Tangents. 
 
 1° 
 
 •01745 
 
 •OI745 
 
 23 d 
 
 3907 
 
 •4245 
 
 2° 
 
 "0349 
 
 •03492 
 
 24° 
 
 4067 
 
 •4452 
 
 J 
 
 •05233 
 
 •0524 
 
 25° 
 
 4226 
 
 •4663 
 
 4° 
 
 •06975 
 
 •0699 
 
 26° 
 
 4384 
 
 •4877 
 
 5° 
 
 •0S715 
 
 •0874 
 
 2 7 > 
 
 4540 
 
 •5095 
 
 6° 
 
 •10452 
 
 •IO5I 
 
 28 3 
 
 4695 
 
 •5317 
 
 7° 
 
 12187 
 
 •1228 
 
 2 9 
 
 4848 
 
 •5543 
 
 8° 
 
 •13917 
 
 •I405 
 
 3° : 
 
 5 
 
 •5773 
 
 9° 
 
 •15643 
 
 •I584 
 
 3i° 
 
 5150 
 
 "6009 
 
 IO° 
 
 •17364 
 
 •I763 
 
 32° 
 
 5299 
 
 •6249 
 
 ii° 
 
 •19081 
 
 •1944 
 
 33' 
 
 5446 
 
 •6494 
 
 12° 
 
 •2079 
 
 •2125 
 
 34° 
 
 5592 
 
 '6745 
 
 13° 
 
 •2249 
 
 •2309 
 
 35 J 
 
 5736 
 
 7002 
 
 14° 
 
 •2419 
 
 •2493 
 
 3& 
 
 5878 
 
 7265 
 
 T -° 
 
 •25S8 
 
 •2679 
 
 37° 
 
 6018 
 
 7535 
 
 1 6° 
 
 •2756 
 
 •2867 
 
 3S> 
 
 6157 
 
 7S13 
 
 i 7 ° 
 
 •2924 
 
 •3057 
 
 39° 
 
 6293 
 
 •8098 
 
 1 8° 
 
 •3090 
 
 •3249 
 
 40° 
 
 642S 
 
 •8390 
 
 19° 
 
 •3256 
 
 •3443 
 
 4i° 
 
 6560 
 
 •8693 
 
 20° 
 
 •3420 
 
 •3640 
 
 42 ° 
 
 6691 
 
 •9OO4 
 
 21° 
 
 •3534 
 
 •3339 
 
 43° 
 
 6820 
 
 •9325 
 
 22° 
 
 •3746 
 
 •404O 
 
 44° 
 
 6946 
 
 •9657 
 
 1 1
 
 1 62 APPENDIX. 
 
 [Moreover, since 11 and n' are normals to the 
 refracting surfaces, 
 
 (2) A = r + i\ 
 
 But w = i — r. 
 
 and v = r — 1. 
 
 so that by substitution, 
 
 (3) d=i+r' -A. 
 
 If the ray pass in the direction of minimum 
 deviation , so that i = r, then from (3) 
 
 (4) d= 2i - A. 
 
 A t*S ■ d + A - 
 
 and (5) 1 = 
 
 2 
 
 This last formula tells us that if we wish to pass 
 a ray through a prism in the direction of minimum 
 deviation, we must allow an angle of incidence 
 equal to half the sum of the deviating and refract- 
 ing angles. 
 
 Moreover, under the same conditions, 
 
 _. d 
 
 2 
 
 and since, by the law of sines, if we let /x stand 
 for the index of refraction, 
 
 sin. i = p sin. r. 
 
 (6) i = sin. -1 ( 11 sin. — — A. 
 
 \ 2 / 
 
 Substituting this value for i in formula 4 we get 
 
 (7) d = 2 sin. ~ T fx sin. — j — A. 
 
 This formula enables us to find the deviating
 
 APPENDIX. 163 
 
 angle of any prism, given its refracting angle (A) 
 and its index of refraction (/x). 
 
 If we treat angles and their sines as equivalents, 
 which we may do without serious error in the case 
 of very weak prisms, then 
 
 (8) d = A (p - 1 ). 
 
 This useful formula has been utilised on p. 19. 
 
 Lastly, if we wish to find the index of refraction 
 •of any transparent material, we can do so as 
 follows. 
 
 By the law of sines, 
 
 
 - / n sin - * 
 
 (9) P — . ' 
 
 sin. r 
 
 And since 
 
 . . d+A 
 
 y s) t= - . 
 
 and r = —> 
 
 2 
 
 sin. 
 
 (10) fM= 
 
 A 
 
 Sill — 
 
 2 
 
 From this formula, after finding the refracting 
 angle {A) of any prismatic piece of glass, and the 
 deviating angle (d) by the methods described on 
 pp. 3 and 30, we can readily discover the index 
 of refraction.
 
 1 64 
 
 INDEX. 
 
 Aberrant Hyperphoria, 133 
 Aberration, Chromatic, 27 
 
 — Prismatic, 40 
 Abducting Prisms, 64, 81, 88 
 Abduction, Maximum Binoc- 
 ular, 116, 118 
 
 Accommodative Convergence, 
 
 93 
 
 Excess of, 139 
 
 Adaptability, the faculty of, 
 103 
 
 Adducting Prisms, 64 
 
 Adjustment of Prisms in Trial- 
 frame, 61 
 
 — by viewing straight lines, 61 
 double internal reflection, 
 
 53 
 
 Advancement for Latent Devi- 
 ation, 105 
 
 Adverse Prisms, 104 
 
 iEther, 11 
 
 Analyser, 150 
 
 Analysis of Spectacles, 146 
 
 Anatomical Position of the 
 Eyes, 90 
 
 Angle, Deviating, 163 
 
 — of Deviation, 17 
 
 Measurement of, 29 
 
 with variations of in- 
 cidence, 25, 26 
 
 False Projection, 59 
 
 Refraction, 2 
 
 Measurement of, 3 
 
 — Visual, Effect of Prism -on, 
 
 43 
 Antagonist, Contracture of, 
 
 142 
 Apex of a Prism, 7 
 
 Testing for, 36 
 
 Apparent Curvature of a 
 
 straight line seen through 
 
 a Prism, 43 
 
 Apparent Displacement of 
 objects by Prisms, 8, 56 
 Lines by Prisms, 57 
 
 — Hyperphoria, 130 
 Deficiency of, 139 
 
 — Size of objects through a 
 
 Prism, 43 
 Associated Convergence, 95 
 Asthenopia, Muscular, 87 
 
 — Central, 87 
 
 Asymmetry of the Eyes, 155 
 Atropine, effect on Conver- 
 gence, 95 
 
 Axis of a Prism, 24 
 
 Bar of Prisms, 6 
 Base, 4 
 
 — of a Rectangular Prism, 3 
 
 — of a Circular Prism, 7 
 Base-apex Line, 7 
 
 Berry, Mr., 90, 91, 126, 133, 
 
 144 
 Binocular Distortion by 
 
 Prisms, 45 
 Wadsworth's Ex- 
 planation of, 45 
 
 — Vision, 86 
 Bi-Prism, 125 
 
 Bowman Lecture, Hansen 
 Grut's, 90 
 
 Card Test, 85, 128 
 Centrads, 34 
 Central Asthenopia, 87 
 Centre (Geometrical) of a Lens, 
 
 73 
 
 — (Optical) of a Lens, 71, 73 
 Centres, Optical, mode of test- 
 ing distance between, 147 
 
 Chloroform, Divergence of 
 
 Eyes under, 90 
 Chromatic Aberration, 27
 
 INDEX. 
 
 165 
 
 Ciliary Muscle, Paresis of, 95 
 Circular Prism, base of, 7 
 
 Relation to a rectangular 
 
 one, 7 
 
 — Prisms, 5, 6 
 
 Clinical Properties of Prisms.56 
 
 — Strength of Prisms, 69 
 Coloured Glass in using rod 
 
 test, 130 
 
 to elicit Diplopia, 137 
 
 Concomitancy in Hyperphoria, ' 
 
 130 
 Conjugate Innervations, 83 
 Construction for Deviation, 26 
 
 Resultant Prisms, 158 
 
 Contracture of Antagonist, 142 
 Convergence, 138 
 
 — Accommodative, 93, 139 
 
 — and Accommodation, 85 
 Dissociation of, 123 
 
 — Associated, 95 
 
 — Effect of Lenses on, 81 
 Prisms on, 69, 81 
 
 — Far Point of, 117 
 
 — Finger tests for, 119 
 
 — Functional, minimum of, 
 
 116 
 
 — Graefe's tests for, 123 
 
 — in Myopia, 96, 138, 139 
 
 — Innervation of, 83 
 
 — Initial, 89 
 
 — Insufficiency of, 129 
 
 — Landolt's rule for, 120 
 
 — Latent, in near vision, 89 
 
 — Maximum of, 118 
 
 — Near Point of, 119 
 Vision test for, 128 
 
 — Reflex, 86, 97 
 
 — Relative Range of, 120 
 
 — Spasm of, 89, 92 
 
 — Starting Point of, 89 
 
 — Study of, 83 
 
 — Three Grades of, 84, 91 
 
 — Tonic, 89, 92 
 
 — Voluntary Element in, 106 
 Co-ordinating Centres, Educa- 
 tion of, 103 
 
 — Energy. 87 
 Cosmetic' Prisms, 144 
 
 Cramp, Writers', S7 
 Cretes' Prism, 47 
 Crown Glass, 10 
 
 Dispersive power of, 28 
 
 Refractive Index of, 19, 
 
 20 
 Curry & Paxton, Messrs., 128 
 Cylindrical Lens for testing 
 deviations, 128 
 
 Dark, Behaviour of an Eye in 
 
 the, 85 
 Decentred Lens, Manufacture 
 
 of and Prescriptions for, 78 
 Decentering, Rule for, 82 
 
 — of Lenses, 71, 74 
 Degrees, as Units of Prismetry, 
 
 33 
 
 Dennett's Unit for Prisms, 34 
 Density of Media, 10 
 Deviating Angle, 163 
 Deviation, Angle of, 17 
 with variations of in- 
 cidence, 25, 26 
 
 — Construction for, 19, 26 
 
 — Minimum, 162 
 
 — of Light by Prisms, 16 
 Ray refracted at one 
 
 surface only of a 
 Prism, 27 
 
 — Protractor, 22, 23 
 Deviations, Latent, 86 
 — ■ — Vertical, 130 
 Diagnosis, Use of Prisms in, 
 
 116 
 Diplopia, Eliciting by Prisms, 
 
 137 
 
 — Prisms for, 142 
 
 — Produced by Prisms, 62 
 Dispersion, 27 
 Displacement (Apparent) of 
 
 Objects by Prisms, 8, 56, 57 
 
 — of Lenses, 72, 77 
 
 the Visual Axis by 
 
 Prisms, 60 
 Dissociation of Convergence 
 
 and Accommodation, 123 
 Distortion (Binocular) by 
 
 Prisms, 45
 
 1 66 
 
 INDEX. 
 
 Divergence, Latent, 88 
 
 — under Chloroform, 90 
 Donders, 122, 144 
 Double Prism, 125 
 Dyer's, Dr., Exercises, 103 
 Dynamometer, Landolt's, 119 
 
 Edge of a Prism, 8 
 Education of co-ordinating 
 
 centres, 103 
 Effect of Prismatic Lenses on 
 
 Fixation Lines, 107 
 Formula 
 
 for, 109, 113 
 Rules for, 
 
 no 
 Eliciting Diplopia by Prisms, 
 
 137 
 Emergence of Light, 16 
 Equilibrium in near vision, j 
 
 author's tangent scale for, 
 
 85, 108 
 
 — Position of, 123 
 
 — Test, Graefe's, ne'.r, 85, 123 
 
 distant, 91, 123 
 
 Eserine, effect on Convergence, 
 
 95 
 Externi, insufficiency of, 138 
 Eye, Behaviour of in the dark, 
 
 85 
 Eyes, asymmetry of, 155 
 
 — Localising, 153 
 
 False Image, 61 
 
 Suppression of, 137 
 
 — Projection, Angle of, 59 
 Far Point of Convergence, 117 
 Finger Test for Convergence, 
 
 119 
 
 First Method of Prismetry, 30 
 
 Fixation Lines, Effect of Pris- 
 matic Lenses on, 107 
 
 Flint Glass, 28 
 
 Focal Plane, Anterior princi- 
 pal, 113 
 
 Formula for Rotation of Prism, 
 124 
 
 Formulae for Refraction 
 through Prisms, 160 
 
 Formulae for Resultant Prisms. 
 68 
 
 Fresnel, 125 
 
 Frost, Mr. Adams, 136 
 
 Functional Convergence, Mini- 
 mum of, 116 
 
 Fusion, 87 
 
 — Supplement, 86 
 
 Division of between two- 
 eyes, 88 
 
 Geneva Optical Company, 148 
 Geometrical Centre of a Lens, 
 
 73 
 
 — — — Best position 
 
 for, 81 
 
 — Properties of Prisms, 1 
 Glass Rod Test, 126, 130 
 Goniometry, 29 
 
 Graefe, Alfred, 136 
 Graefe's Near Equilibrium 
 Test, 85, 123 
 
 — Distant Equilibrium Test, 
 
 91, 123 
 
 — Prism Tests for Malinger- 
 
 ing, 134 
 
 — Tests for Convergence, 123 
 Grinding a Prism, 3 
 
 Hansen Grut, 90 
 
 " Nahebewusstein," 94 
 
 Helminthiasis, 89 
 Heredity of Hyperphoria, 133 
 Hering's Theory, 64, 83 
 Herschell's Prisms, 47 
 Homocentric Light, 40 
 Homogeneous Media, 10 
 Horizontal Prisms, 67 
 Huygens, law of, 12 
 Hyperphoria, 130 
 
 — Different effect of Prisms 
 
 on in near and distant 
 vision, 69 
 
 Rule for find 
 
 ing, 70 
 
 — Measurement of, 131, 132 
 
 — Prisms for, 140 
 
 — Test for in Near Vision, 119
 
 IXDEX. 
 
 167 
 
 Illusion by Prisms, 56 
 Images by Internal Reflection, 
 
 5 1 
 
 ■ Formula for, 54 
 
 Inaccuracy in the Apex of a 
 
 Prism, 36 
 Incidence of Light, 16 
 Index of Refraction, 163 
 Initial Convergence, 89 
 
 — Position of the Eyes, 101 
 Innervations, Conjugate, 83 
 Insufficiency, Muscular, 85 
 
 — of Convergence, 129 
 Externi, 13S 
 
 Internal Reflection by Prisms, 
 
 Isotropic Media, 10 
 
 Jackson's Proposition, 20 
 Juler, Mr., 134 
 
 Landolt's Dynamometer, 119 
 
 — Prism, 47 
 
 — Rule for Convergence, 120 
 Latent Convergence in Near 
 
 Vision, 89 
 
 — Deviation, advancement for, 
 
 105 
 
 — Deviations, 86 
 
 Harmlessness of most, 
 
 104 
 
 Treatment of, 104 
 
 Tenotomy for, 105 
 
 — Divergence, 88 
 
 — Vertical Deviations, 130 
 Law of Sines, 162 
 
 Le Conte, 90 
 
 Lens Measure of Geneva 
 Optical Company, 80 
 
 — Rotation of, 58 
 
 Lenses, Decentering of, 71, 74 
 
 — Displacement of, 72, 77 
 
 — Effect on Convergence of, 81 
 Light, Deviation of by Prisms, 
 
 16 
 
 — Emergence of, 16 
 
 — Homocentric, 40 
 
 — Incidence of, 16 
 
 — Monochromatic, 120 
 
 ! Light, Oblique Incidence of, 13 
 
 — Perpendicular Incidence of, 
 
 13 
 
 — Refraction of, illustrated, 14 
 I — Undulatory, theory of, 11 
 
 — Velocity of in different 
 
 media, 10, 13 
 
 — Wave front of, 1 1 
 
 — Waves, and water, 11 
 Lines viewed through a Prism, 
 
 Localiser, The Author's, 154 
 Localising the Eyes, 153 
 
 Malingering, Graefe's Prism 
 
 Test for, 134 
 Manufacture of Decentred 
 
 Lens, 78 
 Maxims for prescribing Prisms, 
 
 T-57 
 Maximum of Convergence, 118 
 Measurement of Angle of Devi- 
 ation, 29 
 
 Refraction, 3 
 
 Hyperphoria, 131 
 
 Prisms bv reflection, 53 
 
 Table for, 55 
 
 Prisms, unit of, 33 
 
 Media, homogeneous, 10 
 
 Metre-angle, 36 
 
 Minimum Deviation, 24, 162 
 
 — of Convergence, Functional, 
 
 116 
 
 Minus Prisms, 93 
 
 Monochromatic Light, 120 
 
 Motion of Light, 11 
 
 Geometrical demon- 
 stration of, 26 
 
 Physical demonstra- 
 tion of, 24 
 
 Mounted Prism, 128 
 
 Muscular Asthenopia, 87 
 
 — Insufficiency, 85 
 Myopia, Convergence in, 96, 
 
 138, 139 
 
 — Density of, 10 
 
 — Isotropic, 10 
 
 — Velocity of light indifferent, 
 
 10, 13
 
 1 68 
 
 INDEX. 
 
 NAGEL, 122 
 
 "Nahebewusstein," Hansen 
 
 Grut's, 94 
 Near Point of Convergence, 
 
 119 
 
 — Vision, Latent Convergence 
 
 in, 89 
 
 Test for Convergence, 
 
 128 
 
 Significance of, 129 
 
 Neurasthenic Variability, 139 
 Normals, 16 
 Noyes, 138 
 
 Noyes' Series of Prisms, 6 
 Numeration of Prisms by devi- 
 ating angles, 20 
 
 Duane's objection to, 
 
 23 
 
 Oblique Incidence of Light, 
 
 13 
 
 — Paralysis of the Superior, 
 
 143 
 
 — Vision, effect of Prisms on 
 
 Convergence in, 69 
 Ocular Paralysis, Prisms to 
 
 aid cure, 144 
 Ophthalmoplegia Externa, 90 
 Optical Centres, Mode of test- 
 ing distance between, 147 
 of a Lens, 71, 73 
 
 — Properties (simplest) of 
 
 Prisms, 10 
 Orthoscopic Spectacles, 81 
 Overcoming of Prisms, 61, 63 
 
 Paresis of Ciliary Muscle, 95 
 Paretic Hyperphoria, 130, 133 
 Percival, Dr., 79 
 Percival's, Dr., Formula, 114 
 
 Tables, 115 
 
 Periodic Squint, 97 
 Perpendicular Incidence of 
 
 Light, 13 
 Persistency of Hyperphoria, 
 
 132 
 Plus Prisms, 93 
 Position of Rest of the Eyes, 90 
 
 Prentice's Unit for Prisms, 34 
 
 — Prismometer, 35 
 Prescribing Prisms, Maxims 
 
 for, 157 
 Prescription for Decentred 
 
 Lens, 78 
 Principal Section, 4 
 Prismatic Aberration, 40 
 
 Variation in, on tilting a 
 
 Prism, 42 
 Diagram of, 41 
 
 — Equivalent of decentering, 
 
 75 
 Table for, 76 
 
 — Lenses, 72, 78, 79 
 
 Effect on fixation lines, 
 
 107 
 
 — Trial Frame, Rotary, 49 
 Prism-dioptres, 34 
 Prismeters, 30, 32 
 Prismetry, 29 
 
 — First method of, 30 
 
 — Second ,, ,, 32 
 
 — Unit of, 33 
 Prism, Grinding, 3 
 
 — Measure, 148 
 
 of Geneva Optical Com- 
 pany, 3, 79 
 Prismometer, Prentice's, 27, 35 
 Prismosphere, 79 
 Prisms, effect of Convergence 
 
 on, 81 
 Projection, Line of, 61, 63 
 Proportion between Refracting 
 
 and Deviating Angles, 18 
 
 Calculation 
 
 for, 21 
 Protractor for Deviation, 22 
 
 23 
 
 Radian, 34 
 
 Rectangular Prism, base of, 5 
 Rectangular Prisms, 4, 156 
 Reflex Convergence, 86, 97 
 Refracting and Deviating An- 
 gles, Diagram of, 18 
 
 Protractor for, 22 
 
 Table of, 20 
 
 Refracting Surfaces 1
 
 1XDEX. 
 
 169 
 
 Refraction, Angle of, 1 
 
 — Index of, 163 
 
 — Measurement of Angle of, 3 
 
 — by Prisms, 10 
 
 — of light, 1 
 Illustrated, 14 
 
 — through Prisms, Formulae 
 
 for, 160 
 Refractive Index of Crown 
 
 Glass, 19, 20 
 Relation between Convergence 
 
 and Accommodation, 85 
 
 — of a Circular to a Rectan- 
 
 gular Prism, 7 
 Relative Range of Convergence, 
 
 120 
 
 Table for, 121 
 
 .Rest of the Eyes, position of, 
 
 90 
 Resultant Prisms, 67, 143, 158 
 
 Construction for, 158 
 
 Formulas for, 68 
 
 Risley's Rotary Prism, 48 
 Rock Crystal, 10 
 Rod Test, 126, 130 
 
 Coloured glass in using, 
 
 130 
 .Rotary Prismatic Trial-frame, 
 
 49 
 — Prism, Risley's, 48 
 Rotating a Prism, Effect of, 
 
 49 
 
 — Prisms, 47 
 
 Table for, 50 
 
 Rotation of a Lens, 58 
 Prism, 57, 124 
 
 Formula for, 124 
 
 Scale, Author's Tangent, for 
 Equilibrium in Near 
 Vision, 85, 128 
 
 — for Hyperphoria, 131 
 
 — for Measuring strength of 
 
 Prisms, 31 
 
 Scales for Associated Conver- 
 gence, 95 
 
 Schemer, Dr., 81 
 
 Second Method of Prismetry , 32 
 
 Series of Prisms (Xoyes'), 6 
 
 Setting a Prism, by reflected 
 
 images, 53 
 Shape of a Prism, 5 
 
 Objects seen through 
 
 Prisms, 42 
 Simple Hyperphoria, 130 
 Simplest Optical Properties of 
 
 Prisms, 10 
 Sines, 159 
 
 — Law of, 162 
 
 — Table of, 161 
 Snellen's Frame, 153 
 Solar Spectrum, 27 
 
 Spasm of Convergence, 89, 92 
 Spectacles, acquired toleration 
 of, 102 
 
 — Analysis of, 146 
 
 — a cause of Squints, 99 
 
 — Orthoscopic, 81 
 Square Prisms, 5 
 Squint, Periodic, 97 
 Squints cured by Spectacles, 99 
 Starting Point of Convergence, 
 
 89 
 Stereoscope for measuring 
 
 Hyperphoria, 131 
 Stevens, 132 
 Strabismus, Prisms to measure, 
 
 133 
 
 Strength of Prisms in Spec- 
 tacles, 28 
 
 Scale for Measure- 
 ment, 31 
 
 Superior Oblique, Paralysis of, 
 
 143 
 Suppression of False Image, 
 
 137 
 Symmetrical passage of light 
 
 through a Prism, 24 
 Symptoms of Hyperphoria, 132 
 
 Table for measuring strength 
 of Prisms, 32 
 
 — of Deviation, 20 
 Tangent Scale, the principle of, 
 
 159 
 
 tor Hyperphoria, 131 
 
 for Near Vision, 128 
 
 — Scales for all distances, 129
 
 170 
 
 INDEX. 
 
 Tangent Scales for Rod Test, 
 
 127, 131 
 Tangents, 159 
 
 — Table of, 161 
 
 Teeth, Effect of on Conver- 
 gence, 93 
 
 Temporary Prisms, 156 
 
 Tenotomy, 99, 101-105 
 
 Test for Hyperphoria in near 
 vision, 119 
 
 Vertical Deviations in 
 
 near vision, 119 
 
 Testing the Apex of Prisms, 36 
 
 Toleration of Spectacles ac- 
 quired, 102 
 
 Tone, Physiological, 90 
 
 Tonic Convergence, 89, 92 
 
 Deficiency of, 93, 139 
 
 Excess of, 92, 138 
 
 Trade Pains, 87 
 
 Training by Prisms and Lenses, 
 101, 102 
 
 Treatment, use of Prisms in, 
 138 
 
 Trial-frame, Adjustment in, 61 
 
 — for Prisms, 156 
 
 Under-correction by Prisms, 
 
 157 
 
 Undulatory Theory of Light, 11 
 
 I Unit of Measurement for 
 
 Prisms, 33 
 j Use of Prisms in Diagnosis, 1 16- 
 in Treatment, 138 
 
 , Velocity of Light in different 
 media, 10, 13 
 Vertical Deviations, Test for 
 in Near Vision, 119 
 
 — Latent Deviations, 130 
 
 — Prisms, 67, 124 
 Virtual Prisms, 75 
 Vision, Binocular, 86 
 
 Visual Angle, effect of a Prism 
 on, 43 
 
 — Axis, Displacement by 
 
 Prisms, 60 
 Visual-reflex, 86 
 
 — Scales for, 95 
 Voluntary Element in Conver- 
 gence, 106 
 
 Ward Holden's Rule for De- 
 centering, 82 
 I Wave-front of Light, 11 
 Waves of Light and Water, 1 1 
 Writer's Cramp, 87 
 Wrongly set Prisms, effect 0L. 
 
 37 
 Formula for, 37 
 
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