Spectacles and Eyeglasses/Chapter 2

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4637103Spectacles and Eyeglasses — Chapter 2

II.	The Principles of Spectacle Fitting, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		49
		Centering and Decentering, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	49
		Prismatic Effect of Decentering, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	51
		Normal Lateral Centering, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	55
		Normal Vertical Centering, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	56
		Distance of the Glasses from the Eyes, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	57
		Perpendicularity of the Plane of the Lenses to the Visual Axes, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	58
		Periscopic Glasses, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	62

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II. The Principles of Spectacle Fitting

We have now to consider the essential principles of placing glasses before the eyes. The usefulness of spectacles depends almost as much upon the fidelity with which these principles are carried out as it does upon a careful correction of the errors of refraction.

Centering and Decentering.—By the visual axis, or, in English, the line of sight, is meant a line from the yellow spot of the retina through the nodal point of the eye to the object sighted.

By the principal axis of a lens we mean a line passing through the optical center of the lens (the thickest part, if the lens is convex; the thinnest if concave) at right angles to its surfaces.

The geometrical center of a spectacle glass may be shortly said to be that point on its surface which is equally distant from the extremities of the figure to which it is cut. The principal axis of the lens may or may not pass through this latter center.

We habitually regard as the normal position for glasses one in which, when the eyes are looking at a distant object, the visual axes correspond exactly in position with the principal axes of the lenses, and together they pass through the geometrical centers of the spectacles. In other words, the geometrical center of the spectacle eye and the optical center of the spectacle lens coincide, and the center of the pupil for each eye lies directly behind them. Regarding decentering, some confusion is apt to arise because the word is used in two different connections. If the visual axis pass to the temporal side of the optical center of a glass held before an eye, then, with respect to that eye, the glass is said to be "decentered in." If the visual axis pass to the nasal side of the optical center of the glass, the latter is "decentered out." Similarly a glass may be decentered in any other direction. When speaking of spectacles, however, without reference to the eyes of the wearer, they are said to be "decentered in" when their optical centers lie to the inner side of their geometrical centers; "decentered out" when the optical centers are to the external side of the geometrical centers, etc. A glance at Fig. 14, which represents a pair of spectacles decentered in, will make clear what is meant.

Fig. 14.Spectacles with Lenses Decentered in.

G G show the position of the geometrical centers; O O, that of the optical centers.

From the above it will readily be seen that when it is desired that a patient wear decentered lenses, the effect may be obtained in either of the two ways: first, by decentering the lenses in their frame; second, by displacing them, together with their frames, from what I have described as the normal position. The first method has the disadvantage of increasing the weight of the glass while the second limits the field of binocular vision. In practice, the second method should be employed to the greatest extent possible without unduly interfering with binocular vision for the distance at which the spectacles will be used, and, should still farther decentering be required, the method first mentioned should be brought into service. For instance, suppose we wish to order glasses with each lens decentered in 8 mm. This would mean that the optical centers are to be 16 mm. nearer together than the patient's pupils. Let us suppose that by a careful consideration of the distance for which the glasses are prescribed, of the distance at which they must be placed in front of the eyes, and of the size of the spectacle eye used, we find that the frame can only be made 10 mm. narrower than normal without the outer rims of the "eyes" becoming annoying. This leaves 6 mm. to be obtained by decentering the glasses in their eye-wires. If the distance between the patient's pupils were 60 mm., we would order the distance between the geometrical centers of the spectacle eyes to be 50mm., and each eye to be decentered in 3 mm.

Prismatic Effect of Decentering.—It is to obtain a prismatic effect from spherical lenses that decentering is generally ordered, since a decentered lens is identical with a lens of the same strength combined with a prism. This is graphically shown by Figs. 15 and 16, the latter of which represents a section of a decentered lens, which will readily be seen to be precisely the same as the result would be if the normally centered lens shown in Fig. 15 were split into halves and the prism b a c introduced between them.

The size of the glass disc from which spectacle lenses are ground will not allow of more than about 2 mm. of lateral decentering for a No. 1 "eye;" 3 mm. for Nos. 2 and 3; and 4 mm. for No. 4. Vertically, they may be decentered much more. When ordered to decenter laterally more than this, or to furnish a prismatic effect greater than can be obtained by this much decentering, the optician first manufactures a prism of the requisite strength, and then grinds spherical surfaces upon its two faces. It is, therefore, of not much importance whether, in ordering a sphero prismatic combination, we express the prismatic element in degrees of the refracting angle, or in millimeters of decentration of the lens: the optician produces the glass by whichever method is most convenient.

Fig. 15.

Fig. 16.

Showing the Prismatic Effect of Decentering.

The optical center, O, in Fig. 15 coincides with the geometrical center, G, in Fig. 16, which represents a decentered lens of the same spherical curvature; O has been removed toward the base of the virtual prism b a c. (After Maddox.)

The stronger the lens, the less decentering it requires to produce a given prismatic effect, and where the combination desired is that of a strong lens with a weak prism, the more accurate practice probably is to order the lens decentered the requisite number of millimeters. For this purpose a table of equivalents, such as is given below, is necessary. To use it, we find in the first column the strength of the lens used, and on a level with this, in the column at whose head stands the strength of the prism required, is given in millimeters the amount of decentration necessary.

TABLE III.^[1]—DECENTERING EQUIVALENT TO A GIVEN REFRACTING ANGLE (INDEX OF REFRACTION, 1.54).
Lens	1°	2°	3°	4°	5°	6°	8°	10°
1 D,	9.4	18.8	28.3	37.7	47.2	56.5	75.8	95.2
2	4.7	9.4	14.1	18.8	23.6	28.2	37.9	47.6
3	3.1	6.3	9.4	12.6	15.7	18.8	25.3	31.7
4	2.3	4.7	7.1	9.4	11.8	14.1	18.9	23.8
5	1.9	3.8	5.7	7.5	9.4	11.3	15.2	19.
6	1.6	3.1	4.7	6.3	7.9	9.4	12.6	15.9
7	1.3	2.7	4.	5.4	6.7	8.1	10.8	13.5
8	1.2	2.3	3.5	4.7	5.9	7.1	9.5	11.9
9	1.	2.1	3.1	4.2	5.2	6.3	8.4	10.5
10	.9	1.9	2.8	3.8	4.7	5.6	7.6	9.5
11	.9	1.7	2.6	3.5	4.3	5.1	6.9	8.7
12	.8	1.6	2.4	3.1	3.9	4.7	6.3	7.9
13	.7	1.4	2.2	2.9	3.6	4.3	5.8	7.3
14	.7	1.3	2.	2.7	3.4	4.	5.4	6.8
15	.6	1.3	1.9	2.5	3.1	3.8	5.1	6.3
16	.6	1.2	1.8	2.4	3.	3.5	4.7	6.
17	.6	1.1	1.7	2.2	2.8	3.4	4.5	5.6
18	.5	1.	1.6	2.1	2.6	3.1	4.2	5.3
19	.5	1.	1.5	2.	2.5	3.	4.	5.
20	.5	.9	1.4	1.9	2.4	2.8	3.8	4.8

It is one of the beauties of the reformed numbering of prisms (see page 85), that by a simple calculation one can tell in a moment the amount of decentration required to produce any required number of centrads, by means of any given lens.

Divide the number of centrads required by the strength of the lens, in diopters. The quotient is the necessary decentration, in centimeters. For example: to produce a prismatic effect of 3. Cr. by means of a lens of 5. D., it is necessary to decenter as many centimeters as 5 is contained times in 3, which is .8 centimeters.

Table IV is constructed by applying this rule. In it, however, the distances which the lenses must be decentered have been reduced to millimeters by moving the decimal point one place to the right, in order to make it practically more convenient, and render it homologous to Table III, like which it is used.

TABLE IV.—DECENTERING EQUIVALENT TO A GIVEN NUMBER OF CENTRADS.
Lens	1 Cr.	2 Cr.	3 Cr.	4 Cr.	5 Cr.	6 Cr.	8 Cr.	10 Cr.
1 D,	10.	20.	30.	40.	50.	60.	80.	100.
2	5.	10.	15.	20.	25.	30.	40.	50.
3	3.3	6.6	10.	13.3	16.6	20.	26.6	33.3
4	2.5	5.	7.5	10.	12.2	15.	20.	25.
5	2.	4.	6.	8.	10.	12.	16.	20.
6	1.6	3.3	5.	6.6	8.3	10.	13.3	16.6
7	1.4	2.8	4.2	5.7	7.1	8.2	11.4	14.2
8	1.2	2.5	3.7	5.	6.2	7.5	10.	12.5
9	1.1	2.2	3.3	4.4	5.5	6.6	8.8	11.1
10	1.	2.	3.	4.	5.	6.	8.	10.
11	.9	1.9	2.8	3.7	4.6	5.5	7.3	9.
12	.8	1.8	2.5	3.3	4.1	5.	6.6	8.3
13	.7	1.5	2.3	3.	3.8	4.6	6.1	7.6
14	.7	1.4	2.1	2.8	3.5	4.2	5.7	7.1
15	.6	1.3	2.	2.6	3.3	4.	5.3	6.6
16	.6	1.2	1.8	2.3	3.1	3.7	5.	6.2
17	.5	1.1	1.7	2.3	2.9	3.5	4.7	5.8
18	.5	1.1	1.6	2.2	2.7	3.3	4.4	5.5
19	.5	1.	1.5	2.1	2.6	3.1	4.2	5.2
20	.5	1.	1.5	2.	2.5	3.	4.	5.

A cylindrical lens, or the cylindrical clement of a sphero-cylindrical lens, when decentered in a direction vertical to its axis, acts as a spherical lens of the same strength. Thus, a + 2. Sph. ( ) + 1. Cyl. axis vertical, decentered horizontally, would have the same prismatic effect as a + 3. Sph. treated in the same way. As the axis is inclined toward the direction of decentration, the prismatic effect of the cylinder diminishes, and disappears when they coincide. Thus, a + 2. Sph. ( ) + 1. Cyl. axis horizontal, decentered horizontally, would have merely the prismatic effect of a +2. Sph. so treated.

Normal Lateral Centering.—In proportion as the prismatic effect of decentered lenses is a valuable property where this effect is desired, it has to be guarded against in those cases which do not require it, to which number belong, of course, the great majority of the cases we are called upon to treat. If the objects looked at through spectacles were always situated in the same direction and at the same distance, fixing the position proper for the centers would be a simple matter; but, in the movements of the eyes, each pupil roves over a territory some 18 mm. (³⁄₄ in.) long by 15 mm. broad. When the eyes are directed toward a distant object the centers of the pupils are about 60 mm. apart, and on convergence only 56 mm., so that the proper adjustment of spectacles is a series of compromises between that proper for the position of the eyes in which the glasses will be most used and other positions in which they will be less used. Of course, the position in which they will be most used must receive the greatest consideration.

The proper position for the centers of "distance" glasses has already been stated. When glasses are to be used for near work only, they should be decentered "in" two or three millimeters on each side from this "normal" position, as such glasses, being never used in that position, but only when the visual axes are converged, would otherwise never be rightly centered. What amounts to the same thing, and is more often done, is to make the front of the near spectacles four or six millimeters narrower than if they were intended for distant vision: four millimeters narrower for a working point of 15 inches; six millimeters narrower for one of 10 inches. Concerning the centering of glasses which are worn constantly, no rule for all cases can be laid down, since accurately centering for any one distance is decentering for every other. Fortunately, as a glance at Table III will show, it is only with lenses of high power that a considerable amount of prismatic effect is developed by slight decentering. Where such glasses must be worn constantly by a person who spends several hours daily at near work, they should certainly be slightly decentered inward.

The distance between the geometrical centers is regulated by the size of the spectacle eyes and the width of the space between them occupied by the bridge. Where the interpupillary distance is short, as in children, opticians are apt to make the eyes of the spectacles so small as to interfere seriously with the field of vision through them. With the saddle-bridge there is no difficulty in diminishing the space between the spectacle eyes without interfering with the form of that part of the bridge which is applied to the nose, and the required adjustment should be made in this way, leaving the spectacle eyes of good size.

Normal Vertical Centering.—The glasses require, further, to be so placed that the points where the wearer's visual axes penetrate them shall neither be above nor below the centers. This adjustment is readily seen to depend upon the relative height of the bridge of the spectacles and the bridge of the nose at the point where the spectacles rest. The higher the spectacle bridge, the lower will the glasses stand upon the patient's face, and vice versa.

On the bridge of nearly every nose there may be felt a point at which the narrow, upper portion of the nasal bones gives place rather suddenly to the broader lower portion. Just here, in what has been called the "natural" position (A, Fig. 17), the bridge of the spectacles tends to rest, and the attempt to make it remain at any other point will not be very successful. In distance spectacles, then, the bridge should be made of such height that when resting at this natural position, the centers of the spectacle eyes arc at the same height as the centers of the pupils when the patient looks straight forward. When the glasses are to be used for near work only, their bridge should be made about 2mm., or ¹⁄₈ inch, higher than otherwise, allowing the centers to drop that much lower, as the wearer's eyes will nearly always be directed to objects below their own level.

Fig. 17.

Distance of the Glasses from the Eyes.—As a rule, the glasses should be placed just far enough from the eyes to escape the lashes in the act of winking. If the lashes touch the glass the latter quickly becomes soiled, and to the spectacles is, moreover, attributed any falling out of the lashes which may occur. Some persons, however, with myopia of high degree, prefer the glasses to be placed as close to the eyes as possible, regardless of the lashes, because of the larger clear images which they thus obtain. This adjustment of the glasses depends upon the relation of the top of the spectacle bridge to the plane of the glasses. Where the eyes are deep set, or the nose of the aquiline type, the top of the spectacle bridge must be in front of the plane of the glasses, or, as it is shortly called, "out" (Fig. 18). When the bridge of the nose is low and the eyes relatively prominent, as in the negro, Chinese, and children, the top of the bridge must be back of the plane of the glasses, or “in,” as represented in Fig. 19.

Fig. 18.

Fig. 19.

Perpendicularity of the Plane of the Lenses to the Visual Axis.—A very important requirement, and one not sufficiently regarded in the fitting of frames, is that the plane of the correcting lens when in use shall be as nearly as possible perpendicular to the visual axis. The stronger the lens the more important is this detail, whose warrant lies in the fact that the refractive value of a given lens placed obliquely to the visual axis is no longer that indicated by its number, but is that of some other, stronger lens. A cylindrical lens so placed acts simply as a stronger cylindrical lens; a spherical lens, however, as a stronger spherical lens combined with a cylindrical lens with its axis at right angles to that about which the lens is rotated.

The results of the investigations of himself and others, of the effect of the obliquity of a lens to an incident pencil of rays, was summarized by Dr. Edward Jackson in a paper read before the American Medical Association in 1877, and their practical application to this part of our subject pointed out. From that communication the following table is extracted. It gives in the first column the degrees of obliquity at intervals of 5° up to 45°. In the second column is shown the refractive value of a 1. D. cylindrical, in the third that of a 1. D. spherical lens so inclined.

TABLE V.
Obliquity of the Lens.	Refractive Power of a 1 D. Cylindrical Lens so Placed.	Sphero-Cylindrical Equivalent of a 1 D. Spherical Lens so Placed.
0°	1. D. cyl	1. D. spherical.
5°	1.01 „	1.00 sph. () 0.01 cyl.
10°	1.04 „	1.01 sph. () 0.03 cyl.
15°	1.10 „	1.02 sph. () 0.08 cyl.
20°	1.17 „	1.04 sph. () 0.13 cyl.
25°	1.30 „	1.06 spb. () 0.24 cyl.
30°	1.44 „	1.09 sph. () 0.36 cyl.
35°	1.69 „	1.12 sph. () 0.56 cyl.
40°	2.01 „	1.16 sph. () 0.83 cyl.
45°	2.46 „	1.22 sph. () 1.24 cyl.

To fulfil this requirement of perpendicularity to the visual axis, the lenses of spectacles used only for distance should lie in a vertical plane; that is, they should face directly forward, as shown in Fig. 20. Since the visual axes are directed downward and forward when near work is done below the level of the eyes, glasses for near must face downward and forward, as in Fig. 21, in order that the plane in which they lie shall be perpendicular to those axes. Furthermore, in viewing near objects the visual axes are directed inward and toward each other. This will

Fig. 20.

Fig. 21.

require the glasses to face inward also, as represented in Fig. 22, so that they come to lie in different planes, instead of in the same plane, as formerly.

When “constant” glasses are prescribed, the lenses should be placed midway between the proper facing for near and that for distance glasses. Then, though the lens is not exactly properly inclined either for distant vision or near work, the result of such slight obliquity to the visual axis is unimportant, since, as a reference to Table V will show, it is only in the higher degrees of obliquity that the increase in power, and especially the development of cylindrical effect from spherical lenses, is rapid. Moreover, by slightly bending the neck a moderate degree of obliquity of the glasses to the visual axes may be removed without discomfort to the wearer.

Fig. 22.

The position of bifocal glasses should also be between that proper for near and for distance glasses, but nearer that of the stronger glass. This will generally be the near glass, as convex bifocals are much more frequently prescribed than concaves, and such glasses should face only a little less downward than glasses intended entirely for near work. When concave bifocals are worn, however, they should face more forward and much less downward.

The angle which the plane of the glasses makes with the plane of the wearer's face depends entirely upon the angle formed by the plane of the glasses and the temples of their containing frames. Thus, when the temples are perpendicular to the plane of the glasses, as in Fig. 20, the latter will face forward and not at all downward. They may be made to face downward to any required degree by simply turning down the temples at the points where they are hinged to the end pieces. These must be equally turned down, however, as where only one is turned down, or one more so than its fellow, the result is not to make the glasses face downward, but to make the glass on the side of the lower temple ride higher on the face than its fellow.

Periscopic Glasses.—In the effort to further apply the law requiring that the plane of the lenses shall be perpendicular to the visual axes, we are met with the fact that with biconvex and biconcave lenses this relation is only strictly possible within a comparatively limited arc surrounding the optical center of the lens. When the wearer looks through the periphery of his glasses the visual axes will pierce the lenses obliquely, and the refractive value of the latter will, of course, be governed by all the laws of tilted lenses. For instance, when the wearer of an ordinary convex lens looks through it near the edge, the optical effect of the glass before his eye is that of a stronger convex lens combined with a cylindrical lens; the axis of the latter depending on the part of the periphery pierced by the line of sight. In weak lenses, the slight inaccuracy of vision produced in this way is of small moment, but where the strength of the lens used is greater than about 2 D. the patient's field of accurate vision is greatly reduced in size, and in viewing objects not directly in front of him he is obliged to perform wide motions of the head in order to be able to see them through the central portion of his glasses. This is especially true of cases of aphakia, where, of course, very strong lenses are generally necessary. To escape or lessen these disadvantages, strong spherical lenses should be, and generally are, made in the form of a meniscus, which when placed with its convex surface from the eye constitutes a periscopic glass. The ideal of this form of lens may be defined as a glass in which the center of curvature of one surface coincides with the center of rotation of the eye, and that of the other surface approaches it as closely as the required strength of the glass will permit. In such a glass the visual axis will always be perpendicular to the first surface, and nearly so to the second, at whatever point it pierces the glass, and in whatever direction the eye may be turned.

When a cylindrical or sphero-cylindrical lens is required, the best form of glass is the toric lens described on page 37. These lenses have, however, never been manufactured extensively, and the process of their manufacture, as well as the lens itself, being patented in this country, their cost is considerable. By transposing the usual formula, however, there may be obtained from any optician a sphero-cylindrical lens which approaches the periscopic form, and is certainly superior to one ground after the usual method. For illustration, if one desires to order + 2. D. Sph. () +.75 D. Cyl. Ax. 90°, the formula may be transposed and the order written for + 2.75 D. Sph. () —.75 D. Cyl. Ax. 180°. This glass, though optically of the same strength as the first, would have an approach to the periscopic form if placed with the cylindrical surface next the eye. The field of accurate vision would gain in all directions, especially in the vertical one, in which diameter, however, its enlargement is not of so much consequence as it is laterally. Aphakic eyes offer the best field of usefulness for this practice, as in them we have generally to deal with a high hyperopia, and often with hyperopic astigmatism requiring for its correction a convex cylinder with its axis horizontal. Let us suppose that after a cataract extraction we wished to order + 10. D. Sph. () + 6. D. Cyl. Ax. 180°. With this lens, accurate vision would be limited to a vertical oval field situated directly in front of the patient, beyond the confines of which all objects would appear distorted by various cylindrical effects. We would, therefore, transpose the formula into + 16. D. Sph. () —6. D. Cyl. Ax. 90°, and this glass will be likely to give the patient much more satisfaction than the other would have done, as with it he obtains a very good lateral field.

↑ Jackson: “Transactions of the American Ophthalmological Society," 1889.

[1] Jackson: “Transactions of the American Ophthalmological Society," 1889.

[1]