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THE LIBRARY

THE UNIVERSITY
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KAUFMANN'S

Pathology

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(OVER)

PRISMS

THEIR USE AND EQUIVALENTS

JAMES THOR1NGTON, A. M., M. D.

AUTHOR OF "REFRACTION AND HOW TO REFRACT"; "THE OPHTHALMOSCOPE AND HOW
TO USE IT"; "RETINOSCOPY". PROFESSOR OF DISEASES OP THE EYE IN THE
PHILADELPHIA POLYCLINIC AND COLLEGE FOR GRADUATES IN MEDI-
CINE; FELLOW OF THE COLLEGE OF PHYSICIANS OF PHILADEL-
PHIA; MEMBER OP THE AMERICAN OPHTHALMOLOGICAL
SOCIETY; OPHTHALMIC SURGEON TO THE PRES-
BYTERIAN HOSPITAL, ETC

118 ILLUSTRATIONS
OF WHICH 18 ARE COLORED

PHILADELPHIA

P. BLAKISTON'S SON & CO

1012 WALNUT STREET
1913

THE. MAPLE' PRESS- YOBK. PA

35V

PREFACE

The preparation of this book on "Prisms, their use and
equivalents," has been prompted by the request of many
students and correspondents, though it is written pri-
marily for those who may desire a more extended
knowledge on this branch of refraction than is con-
tained in works on Ophthalmology.

In fact, this volume is in part a compilation of the
writer's lectures on prisms delivered during the winter
course at the Philadelphia Polyclinic.

The author's double prism, a new and delicate
test, for the detection of errors of muscular imbalance
whether of small or great amount, is incorporated in the
text.

To make the subject-matter more entertaining, the
writer has not limited himself to the consideration of
prisms in ophthalmic practice alone, and by omitting
mathematic formulas and inserting many illustrations,
the text is made easy of comprehension.

CONTENTS

CHAPTER I.

PAGE

GENERAL DESCRIPTION i

CHAPTER II.
REFRACTION OF LIGHT AND REFRACTION OF LIGHT BY PRISMS . . 10

CHAPTER III.

OPTICAL EFFECT OF A PRISM 23

CHAPTER IV.
PRISM NOMENCLATURE; DENNETT'S METHOD; PRENTICE'S METHOD;

AND NEUTRALIZING PRISMS 40

CHAPTER V.

COMBINED PRISMS 54

CHAPTER VI.

COMBINING A PRISM WITH A SPHERE, CYLINDER OR SPHERO-
CYLINDER 61

CHAPTER VII.

USES OF PRISMS IN OPHTHALMOLOGY 78

CHAPTER VIII.

PRISM TREATMENT FOR HETEROPHORIA AND HETEROTROPIA . . .113

CHAPTER IX.

GENERAL REMARKS ON PRISMS AND THE PRISMATIC EFFECT OF
LENSES ' 134

INDEX 141

PRISMS

CHAPTER I
GENERAL DESCRIPTION

A Prism is a wedge-shaped portion of a refracting
medium (usually of glass) contained between two plane
polished surfaces (Figs, i, 2, 3 and 5), or a prism is a
transparent homogeneous medium with two plane sur-
faces which are not parallel to each other. Prisms
used in the practice of ophthalmology are seldom very

FIG i.— Prism on base. PX = Edge or Apex. BASE = Base. PBAX
and PESX = Faces or Surfaces. BPE and AXS = Angle.

strong and therefore have their surfaces placed at a
very acute angle.

The sides of a prism are the inclined surfaces, also
spoken of as refracting surfaces or faces (PBAX and
PE SX in Figs, i, 2 and 3).

PRISMS

The edge (also frequently spoken of as the apex of a
prism) is that part of the prism where the two plane sur-
faces meet (P X in Figs, i, 2 and 3).

FIG. 2.— Prism on edge. PX = Edge or Apex. BASE = Base. PBAX
and PESX = Faces or Surfaces. BPE and AXS = Angle.

FIG. 3.— Prism on side. PX = Edge or Apex. BASE = Base. PBAX
and PESX = Faces or Surfaces. BPE and AXS = Angle.

The base of a prism is the thick part of the prism
and is opposite to the edge or apex (BASE in Figs, i,
2 and 3). The base of the prism is occasionally referred
to as the third surface.

GENERAL DESCRIPTION

The refracting angle is a physical feature of the
prism and is the angle at which the two sides or refract-
ing surfaces come together; it is this angle together with
the index of refraction of the glass (or medium) which

Base
FIG. 4.— Principal section of a prism.

determines the strength of the prism (B P E and A X S
in Figs, i, 2 and 3).

Section of a Prism. — Dividing or cutting through a
prism at right angles to its refracting surfaces or faces

B A

FIG. 5. — Rectangular prism.

makes a principal section; this is shown in Fig. 4, and

will assist in explaining what has just been described.

Shape or Form of a Prism. — By this is meant the

outline or contour of the prism and not the section, this

PRISMS

FIG. 6. — Dr.
Noyes' prism bar
or battery.

latter being wedge-shaped (Fig. 4).
Figs, i, 2 and 3 illustrate square
prisms. Fig. 5, a rectangular prism
and Figs. 7, 8 and 9, round prisms.
Rectangular prisms are not ordinarily
used in ophthalmology. Square
prisms, while easily handled cannot
be placed in the ordinary trial-frame.

The late Dr. Noyes recommended
a battery of prisms which was a series
of small square prisms of increasing
strength, numbered in degrees, 1/2,
i, 2, 3, 4, and 6, mounted in a frame
as shown in Fig. 6. The operator or
patient held this vertically in front
of the eye and moved it up or down
when it was desired to get a stronger
or weaker prism before the eye. Two
of these batteries or "bars" were re-
quired, one with the bases of the
prisms placed laterally and the other
with the bases placed vertically.
These batteries of prisms are not now
in general use.

Round or Circular Prisms (Figs.
7, 8 and 9). — These are found in the
trial case and as their diameters (set
in cells) are the same as the spheres
and cylinders they fit easily into the
trial-frame. Unfortunately the base
of the prism being quite thick in

GENERAL DESCRIPTION 5

some instances (Fig. 10) takes up considerable space
in the trial-frame and therefore when in the frame it has
to be placed in the outer opening, so as to leave room
for the sphere and cylinder back of it. If placed in
the back opening of the frame it is liable to rub against
the eye lashes or the eye lid.

Recognition of the Edge or Apex and Base of the
Prism. — When a prism is square (Fig. i) in contour its
long edge or apex is immediately and easily detected

^.^ i "

FIG. 7. — Spuare prism marked foe cutting out the round or circular prism.

and likewise its base (Fig. 7), but when round or circular
(Figs. 8 and 9) in contour, its thinnest part will then be
recognized as a point in the apex or edge of the
original square prism (Fig. 7). The thickest part or
base of the round or circular prism is diametrically
opposite to the edge or apex and it too corresponds to a
point or line in the base of the original square prism
(Fig. 7). These two points indicating the edge (or
apex) and base of a round or circular prism are marked
with a broad diamond scratch on the glass (Fig. 8) the
same as seen on cylinder lenses, to indicate the axis of
the cylinder. Likewise the number of the prism is also

6 PRISMS

scratched upon the glass. The position of the base of a
circular prism is occasionally marked with a white or
black line connecting the two plane (circular) surfaces or
faces at their greatest separated points (Fig. 7). This
method of marking the position of the prism edge, base
and number, does not meet with the writer's approval, as
they are not sufficiently distinct and he therefore has the
prisms in his own trial case marked as shown in Fig. 9.
These prisms have very wide black metal frames without

FIG. 8. — Prism in wire frame. Diamond scratches on glass to indicate base
and apex line, also number of prism.

handles, the wide frame or cell acting as a handle. The
direction of the edge and number of the prism are
marked in white on this black metal frame as shown in
the figures referred to and the base is indicated by an
arrow head, also marked in white.

Base-apex Line. — This is an imaginary straight
line connecting the edge (apex) with the center of the
base (A B in Fig. n). This base-apex line is of as
great importance to a knowledge and use of prisms as
the axis line of a cylinder lens. In Chapter II it will be
shown that an object viewed through a prism always

GENERAL DESCRIPTION 7

appears displaced in the direction of the edge of the
prism and exactly parallel to the base-apex line (Fig. 31).

The Axis of a Prism. — This is an imaginary straight
line midway between the edge and the base and at right
angles to the base-apex line, therefore parallel to the
edge (X S in Fig. n).

The Plane of a Prism. — This is midway between the
two plane surfaces, bisecting the angle of the prism
(Fig. n).

FIG. 9. — Prism with wide frame showing markings of base and apex and
number on frame or cell.

Position of a Prism. — When a prism is placed in
front of an eye its position is indicated or described by
the direction of the base-apex line and this direction of
the base must always be carefully specified in the pre-
scription. Base down means that the thickest part of
the prism is toward the cheek, this may be written in the
prescription, Base down axis 90°. Base up means that
the base-apex line is still vertical but the base is directed
upward or toward the brow and this may be written in
the prescription, Base up axis 90°. Base in means that
the base-apex line is horizontal and the base of the

8 PRISMS

prism toward the nose, this may be written in the pre-
scription, Base in axis 180°. Base out means that the
base-apex line is horizontal and the base of the prism
is toward the temple, this may be written in the pre-
scription, Base out axis 180°.

The base of the prism may be placed in any desired
direction or meridian but the prescriber must specify
definitely in his prescription — (i) the strength of the
prism, (2) which eye the prism is for, and (3) whether

FIG. 10. — Profile view of Fig. 9.

the base is up, down, in or out; or up and in, or up and
out, or down and in, or down and out ; for instance, the
following :

Right Eye, 2 Prism, base down axis 75°; 2 Prism base
up axis 75°; 2 Prism base down axis 45° or 2 Prism base
down and out axis 45°; 2 Prism base up axis 135° or 2
Prism base up and out axis 135°, etc. The reader may
obtain a clearer idea on this point by referring to the
arrow marking on the cell of the prism pictured in Fig. 9,
and if he will place a prism in a trial-frame and study it

GENERAL DESCRIPTION 9

in the positions just described he will obtain a definite
knowledge of the position of prisms before the eye.

The prisms in the trial case are made of crown glass
which is practically isotropic and therefore has but
little dispersive power, whereas prisms made of flint
glass or rock crystal are not found in the trial case as
such prisms are highly dispersive (anisotropic) and are
principally used for the production of the spectrum
(Fig. 43).

FIG. ii. — BA = Base-apex line. XS = Axis.

Achromatic Prisms. — These are seldom if ever
prescribed, because they are heavy, cumbersome and
expensive. Such prisms can be made by joining or
cementing together two prisms of different strength and
of different index of refraction, one of flint and the other
of crown glass, with the base of one to the edge of the
other.

CHAPTER II

REFRACTION OF LIGHT AND REFRACTION OF
LIGHT BY PRISMS

For a proper understanding of the action of prisms
upon light it is necessary to briefly review some facts on
the subject of refraction in general.

Refraction. — From the Latin "refrangere," meaning
to bend back, i.e., to deviate from a straight course.

FIG. 12. — Illustrating refraction through a piece of plate glass with parallel

surfaces.

Refraction may therefore be denned as the deviation

which takes place in the direction of rays of light as they

pass from one medium into another of different density.

Two laws govern the refraction of rays of light :

i. A ray of light passing from a rare into a dense

REFRACTION OF LIGHT II

medium is deviated toward the perpendicular (A in
Fig. 12).

2. A ray of light passing from a dense into a rare
medium is deviated from the perpendicular (R in Fig.
12). Aside from these laws, there are other facts in re-
gard to rays of light which should have consideration.
A ray of light will continue its straight course through
any one or any number of different transparent media,
no matter what their densities, so long as it forms right
angles with the surface or surfaces (P P in Fig. 13).

^ Ice

£ Flint Glass

Crown Glass

^ Plate Glass

FIG. 13. — Illustrating the passage of a perpendicular ray through transparent
media of different density with parallel surfaces.

Such a ray is spoken of as the perpendicular or normal.
Such surfaces are plane, the surfaces and perpendicular
forming right angles.

In the study of refraction the incident and refracted
ray may be reversed, that is to say, the refracted ray
may be called the incident ray, and the incident ray may
be called the refracted ray; for instance, in Fig. 12, the
incident ray A becomes the refracted ray R; now if R
is considered the incident ray, it would become the
refracted ray at A.

12 PRISMS

Figure 12 shows the ray P P perpendicular to a piece
of plate glass with plane surfaces. The thick ray A in
air is incident at O on the surface S F and is bent in the
glass toward the perpendicular (P P), fulfilling the first
law of refraction. The dotted line indicates the original
direction of the incident ray A and the direction it would
have pursued if it had not been refracted. As the ray
A in the glass comes to its second surface at R it under-
goes the second law of refraction and passing into the

FIG. 14. — Illustrating the critical angle.

rarer medium (air) it is bent from the perpendicular (P
P). The ray now continues its original direction paral-
lel with the dotted line, but it has been deviated from
its original course, it has undergone lateral displace-
ment. Attention must be directed to the thickness of
the incident ray A as it falls upon the surface S F, as
only part of it is refracted, and part of it is reflected,
the reflected portion is marked D. This accounts for
the thinness of the ray A in the glass. A substance that
could transmit or absorb all the rays of light coming to
it (if such a substance existed) would be invisible. Re-
flection therefore always accompanies refraction. Fi-

REFRACTION OF LIGHT 13

nally if the refracted ray A' in Fig. 12 is, for illustration,
considered the incident ray at R, it would be deviated
toward P' P' in the glass and make its exit at O and be
the refracted ray at A. This demonstrates the path of
the incident ray to become the refracted, or the re-
fracted to become the incident ray, i.e., the path of
the ray is reversible.

Critical Angle. Limiting Angle of Refraction. —
This is the angle of incidence which just permits a ray
of light in a dense medium to pass into a rare medium.
The size of the critical angle depends upon the index of
refraction of different substances. The critical angle
for crown glass is 40° 49'.

Figure 14 shows an electric light suspended in water.
The ray from this light which forms an angle of 48° 35'
with the surface of the water will be refracted and pass
out of the water, grazing its surface; but those rays
which form an angle greater than 48° 35' will not pass
out of the water, but will be reflected back into it. The
surface separating the two media beyond this point of
48° 35' becomes a reflecting surface and acts as a plane
mirror.

Index of Refraction. — By this is meant the relative
density of a substance (not its specific gravity) or the
comparative length of time required for a ray of light
to travel a definite distance in different substances. The
absolute index of refraction is the density of any substance
as compared with a vacuum. According to the first law
of refraction, a ray of light passing from a rare into a
dense substance is refracted toward the perpendicular;
in other words the angle of refraction is smaller under

PRISMS

these circumstances than the angle of incidence. In
the study of the comparative density of any substance
it will be seen that the angle of refraction is usually
smaller the more dense the substance; this is well
illustrated in Figs. 15 and 16. The greater the density,
the slower the velocity, or the more effort apparently

FIG. 15. FIG. 16.

FIG. 15. — Angle of deviation in glass.

FIG. 16. — Angle of deviation in diamond.

for the wave or ray to pass through the substance. A
ray passes through a vacuum without resistance, but
in its course through air it is slightly impeded, so that
air has an index of refraction compared with a vacuum
of 1.00029+, but this is so very slight that air and a
vacuum are considered as one for all purposes in ophthal-

Vacuum

AA/XAA/XA. \AAAAAAA /UUUWUUl Ir

Air

Glass

-'' Diamond

FIG. 17. — Illustrating the comparative density of different substances.

mology (Fig. 17). To find the index of refraction of any
substance as compared with a vacuum it is only neces-
sary to divide the sine of the angle of incidence by the
sine of the angle of refraction and the quotient will be
the index. In Fig. 18 the angle of incidence I C P is the
angle formed by the incident ray I with the perpendicu-

REFRACTION OF LIGHT

lar P P. Drawing the circle P H P O around the point
of incidence C and then drawing the sines X D and F B
perpendiculars to the perpendicular P P, divide the sine
X D of the angle of incidence by the sine F B of the angle
of refraction, in this instance water compared with air,
X D equalling 4 and F B equalling 3, then 4 divided by

FIG. 18. — Illustrating the comparative index of refraction.

3 equals 4/3 or 1.33+, the index of refraction of water
compared with air. To find the index of refraction of
a rare compared with a dense substance, divide the sine
of the angle of refraction by the sine of the angle of inci-
dence, i.e., air as compared with water, would be 3/4
or 0.75.

THE REFRACTIVE INDEXES OF SOME ORDINARY MEDIA

Vacuum i

Air i .000,294

Pure water i . 3336

Sea water i .343

Alcohol i .365

Diamond 2 .487

Canada balsam i . 530

Crown glass i . 540

Rock salt i . 545

Rock crystal i . 548

Flint glass i .635

PRISMS

Besides a knowledge of refraction preliminary to
understanding the action which prisms have upon light,
the reader should also understand or know what is
meant by the following terms in trigonometry.

F ~ " E
FIG. 19.— AB, BC, CD, DE, EF, FG, GH and HA = Arcs of the circle.

FIG. 20.— SE = Sine of the Arc AC.

Arc and Arc of an Angle. — This is the portion of
the circumference of a circle included between two radii
(Fig. 19 and A C in Fig. 20).

REFRACTION OF LIGHT 17

Sine of an Arc. — A perpendicular line extending from
one end of an arc to the diameter drawn through the
other end of the arc (S E in Fig. 20 is the sine of the
arc A C).

Tangent (Latin "tangere"— "to touch").— The
touching or meeting of a curve or surface at a point. A
tangent is a straight line which touches the circum-
ference but does not intersect it (Fig. 21).

FIG. 21.— TTTTT = Tangents.

The tangent of the angle is a line drawn perpen-
dicularly from the extremity of one radius to meet the
other radius prolonged (T S in Fig. 22). A reference to
Figs. 19, 20, 21 and 22 will show that the arc is less
than the tangent and greater than the sine, in fact these
quantities are always controlled by the magnitude of the
angle.

PRISMS

Radian. — A radian is an angle subtended at the
center of any circle by an arc equal in length to the
radius of the circle (Fig. 23).

C T

FIG. 22.— SAC = Acute Angle. SE = Sine. SC = Arc. TS = Tangent.

FIG. 23. — Illustrating the radian.

Prismatic Action. — Rays of light in a prism con-
tinue in straight lines and are not perceptibly broken up
into different wave lengths (colors) so long as the glass
composing the prism is isotropic. The surfaces of a

REFRACTION OF LIGHT 19

prism alone deviate the rays and not the glass between
the surfaces, hence the reason for speaking of the faces
of a prism as refracting surfaces. Rays of light which
pass through a prism are always refracted away from
the edge and toward the base of the prism.

Maximum Deviation or Refraction. — By this is
meant the greatest deviating power of the prism and it
is obtained when all the refraction is done at one surface,
namely, (i) if an incident ray is perpendicular to the

FIG. 24. — Illustrating maximum refraction or deviation. FS and FX
= Surfaces. AR and BP = Incident Rays. PD and RC = Refracted
Rays.

first surface of a prism, then it will pass to the second
surface before it is deviated or refracted and all the
refraction in this instance is done at this one surface,
namely, as the ray emerges from the prism (B P,Fig. 24),
(2) or if the entering (incident) ray is so bent or re-
fracted on its entrance into the prism (A R in Fig. 24)
that it becomes a perpendicular (R C) at the second
surface, it will pass out of this second surface without
any further deviation ; all the refraction taking place at
the first surface.

20 PRISMS

Minimum Deviation. — By this is meant the least
effect or the smallest amount of deviating power of the
prism; this takes place when the ray in the prism is
parallel with the base in an equilateral prism or when
it is equidistant from the edge at each surface or is de-
viated in an equal amount at each surface, or when the
angle of incidence (I R N) is equal to the angle of emer-
gence (V Y N') (Fig. 25). The position of the prism

FIG. 25. — Illustrating position of minimum refraction or deviation. AB
and AC = Surfaces. I = Incident ray directed toward D. RY= Course
of ray in the prism and parallel to the Base (BC). V = Refracted Ray as
if it came from I'. N and N' = Perpendiculars or normals to surfaces
AB and AC.

when this occurs is spoken of as the position of minimum
deviation. Fig. 25 shows the prism BAG. The ray
I incident on the surface A B at R is refracted to Y and
emerging at Y is again refracted toward V. The ray
R Y in the prism is parallel with the base (B C) ; R and
Y are equidistant from the edge A.

Angle of Deviation (Fig. 25). — This angle is formed
by the light and is situated between the directions of
the incident ray carried forward (I to D) and the emer-
gent ray (V to I') carried backward, it measures the de-
viation (V E D). In all prisms of ten degrees or less the

REFRACTION OF LIGHT 21

angle of deviation is slightly more than half the angle
of the prism, but in prisms of more than ten degrees the
angle of deviation is much larger.

Summary. — The deviation of a ray of light passing
through a prism is influenced chiefly by two factors, i.e. :

FIG. 26. — A and B, parallel rays entering the prism, are parallel as they
leave the prism.

1 i ) The obliquity of the refracting surfaces : The more
acute the edge angle, the less the deviation ; the greater
the edge angle, the greater the deviation.

(2) The index of refraction of the prism : The less the
index of refraction, the less the angle of deviation; the

FIG. 27. — A and B are divergent as they enter and leave the prism.

greater the index of refraction, the greater the angle of
deviation.

Prisms do not cause rays of light to converge or di-
verge : Rays of light that are parallel before refraction are

PRISMS

parallel after refraction (Fig. 26). Rays of light that
diverge (A B, Fig. 27) as they enter a prism will di-
verge as they leave it. Rays of light that converge

FIG. 28. — A and B are convergent as they enter and leave the prism, these
rays cross at C.

(A B, Fig. 28) as they enter a prism will converge when
they leave it. Prisms do not form images. Prisms
have no foci. A prism and a plane mirror act similarly
upon rays of light, namely, if the rays of light are par-

123 123

L D C

FIG. 2Q. — PM = Plane Mirror. L = Parallel rays 1,2,3, reflected parallel.
D = Divergent rays reflected divergently. C = Convergent rays i 2, 3,
reflected convergently.

allel, divergent or convergent as they fall upon a plane
mirror they will be reflected in like manner. See
Fig. 29.

CHAPTER III
OPTICAL EFFECT OF A PRISM

The purpose, or use, or effect of a prism is to make an
object looked at through the prism appear in a different
place from that which it really occupies, the prism
actually producing an optical illusion. In producing
this effect the object always appears displaced and in a
direction always opposite to the position of the base of
the prism, namely, in the direction of the edge of the

FIG. 30. — Optical effect of a prism. X appears in the position of X'.

prism. For instance, in Fig. 30, rays of light from the
object X strike the prism at C, undergo minimum re-
fraction and falling upon the retina of the eye are pro-
jected outward in the direction from which they came
to the eye, and the position of X is apparently changed
to X', away from the base and toward the edge of the
prism.

Before proceeding further, the mind of the reader must
be impressed with the fact that the word edge and apex

24 PRISMS

as applied to a prism are synonymous terms, because
only too frequently the student confuses these terms with
a difference. This confusion has arisen apparently
from the markings on the circular or round prisms, but
by observing Fig. 7 the reader will see, as already stated
in Chapter I, that the apex mark of a circular or round
prism corresponds to a point in the edge of the original
square prism. If the reader will also bear in mind that

FIG. 31. — H appears displaced toward the edge of the prism and parallel to
the base-apex line.

the base-apex line as marked on the prism is only a
guide and that there are as many imaginary base-apex
lines in the prism as there are imaginary lines parallel
to the one base-apex line indicated on the prism, he will
fully appreciate the statement that every point in an
object seen through a prism is displaced toward the
edge of the prism and on a line parallel with the base-
apex line. It is a very erroneous idea to get the im-
pression in mind that because the prism is round, the

OPTICAL EFFECT OF A PRISM 25

object looked at through the prism is displaced in all
its parts toward the apex marking on the prism, as if it
was to be crowded toward the apex of an angle. In
Fig. 31 the letter H is seen through the prism to the right
of the prism markings for the apex and base and this H
is displaced immediately upward on an imaginary line
exactly parallel to the base-apex line and not toward the
apex marking of the prism.

A straight line, at a long distance viewed through
a strong prism, held base-apex at right angles to the

FIG. 32. — The straight line looked at through the prism appears curved, the
concavity being toward the edge of the prism.

line, appears to be curved and with the concavity
toward the edge of the prism (Fig. 32). This same
straight line viewed through the prism held with the
base-apex line in the same meridian as the line, does
not at first appear displaced, although it is dis-
placed, the displaced portion simply overlying the
original line and toward the edge of the prism (Fig. 33),
making the line appear a trifle darker and heavier. Any
prism held before the eye and revolved on its plane
gives an object looked at through the prism the appear-

PRISMS

ance of moving in a circle about its real position. In a
right-angled triangle prism (a principal section of which
is a right-angled isosceles triangle) the hypotenuse may

FIG. 33. — The straight line seen through the prism on its base-apex line does
not appear displaced.

123

FIG. 34. — The hypotenuse HY acting as a plane mirror, producing total

reflection.

act similar to a plane mirror (Fig. 34). Rays of light
entering such a prism at H B as normals (1,2 and 3)
fall upon the hypotenuse (H Y) at an angle of incidence
of 45 degrees and as this angle is greater than the critical

OPTICAL EFFECT OF A PRISM

angle (40° 49') for crown glass, the rays are totally
reflected. At the same time these rays are deviated

FIG. 35. — Hypotenuse acting as a plane mirror.

FIG. 36. — Showing how light rays are bent by means of prism angles.

through an angle of 90 degrees, consequently they
emerge at B Y as normals from the other surface of

PRISMS

the prism. See also Fig. 35. This fact is taken ad-
vantage of in a mechanical way by the use of these
and other prisms for purposes of illumination or for
deviating rays of light into dark basements, stair-

FlG. 37. — Illustrating Fresnel's lighthouse apparatus.

ways, etc. (Fig 36). Likewise prismatic action is
employed in the construction of the lenses sur-
rounding the light in a lighthouse (Figs. 37 and 38).
"At the center of such an apparatus is a piano-

OPTICAL EFFECT OF A PRISM

convex lens, one foot in diameter, the focus of
which corresponds with those of the concentric
lenticular rings of glass which surround it. The
rings are ground and polished with great accuracy and
resemble in shape an ordinary quoit and in their refrac-
tion are equivalent to a plano-convex lens with its center
removed. Such lenses are so powerful that the light
in a clear atmosphere may be seen at a distance of fifty
or sixty miles. The apparatus is octagon in shape and

FIG. 38. — Lantern of a first-class lighthouse.

provided with reflecting mirrors at those parts above and
below the light which are out of the range of the lenses.
The oil flame, as the radiant, is so placed that when its
rays pass through the lens and prism and are reflected
by the mirrors, they are deviated so as to follow the
horizon very closely and do not go promiscuously sky-
ward or immediately downward."1

Corneal microscopes, marine glasses, and loupes are
now most ingeniously constructed with prism combina-

1 "Wonders of Optics," C. Scribner & Co.

30 PRISMS

tions whereby the object is greatly enlarged and given
a flat surface.

Prism Aberration or Prismatic Astigmatism. — A
divergent pencil of light passing through a prism and
received into the normal 31/2 millimeter round pupil
of an eye is naturally projected toward the edge of the
prism as just described, but it is not seen as a distinct
radiant point ; it appears as a point, however, with those
edges blurred or indistinct which coincide with the base-
apex line of the prism, while the rays of light which were
refracted in the meridian corresponding to the axis of
the prism are distinct ; in other words, the rays which fall
upon the prism in the vertical meridian appear a trifle
further off than the rays which fall upon the prism
parallel to its edge. A circle viewed through a prism
appears very slightly oval on this account and with the
upper and lower edges faintly blurred. This effect of a
prism is spoken of as prism aberration or prismatic
astigmatism and the interval between the two focal
planes is known as Sturm's interval. Very weak prisms
(less than 2 centrads) have such a minute amount of
aberration or astigmatism that it is really infinitesimal
and often non-appreciable. It takes a strong prism
(10 or more centrads) to demonstrate abberration and
as strong prisms are seldom prescribed this astigmatic
effect need not have further consideration at this time.

Metamorphopsia. — Rotating a prism on its axis or on
its base-apex line as the observer looks through it at an
object, the object becomes distorted and this distortion
is spoken of as metamorphopsia ; for instance, holding a
strong prism base downward axis 90° before the eye and

OPTICAL EFFECT OF A PRISM

PRISMS

OPTICAL EFFECT OF A PRISM

looking at an object (window A in Fig. 39) it naturally
appears displaced upward (B in Fig. 39) then tilting
the edge forward toward the object (dotted prism, same
figure), thus bringing the base toward the observer's eye,
gives B the appearance of being displaced still further
upward (C in Fig. 39) and at the same time the object
(window) is very much elongated (magnified) vertically,
the horizontal width remaining unchanged.

Holding a strong prism base downward axis 90° be-
fore the eye and tilting the base toward the object (bring-
ing the edge toward the observer's eye) (Fig. 40) gives
the displaced object (B) the appearance of being still

FIG. 41.

FIG. 42.

further displaced from B to C and very much reduced
in size (minified) in the vertical meridian and the
horizontal width of the object remains unchanged.
Rotating a prism to the right on its base-apex line as it is
held base downward axis 90° before the eye, and the eye
views a square through the prism, the right side of the
square appears to move upward (Fig. 41) and if the
prism is rotated to the left, the left side appears to move
upward (Fig. 42). In each instance the square object
has a distortion resembling a rhombus.

Dispersion of Light. — When a beam of solar light
(B in Fig. 43) is made to pass through a prism of rock
crystal or flint glass it is broken up or divided into its

PRISMS

constituent parts and this phenomenon is spoken of as
dispersion. This beam of light directed toward E, if
intercepted by a screen will be seen as a colored image,
known as the solar spectrum at C. This image is
rounded at the ends and the colors seen are red, orange,
yellow, green, blue, indigo and violet in the order named
-^violet being the most refrangible and red the least.

FIG. 43. — Dispersion or the production of a spectrum by a flint glass or rock

crystal prism.

These colors do not have sharp lines of demarcation,
but blend into each other. Dispersion plays but an
infinitesimal part in ophthalmology for the reason that
strong prisms are not prescribed and furthermore the
prisms in the trial case are of crown glass.

COMPARING THE ACTION OF A PRISM, A SPHERE AND
A CYLINDER

A Prism. — Looking at a straight line through a prism
held in its position of minimum deviation and its base-

OPTICAL EFFECT OF A PRISM

apex line exactly at right angles to a line, the line appears
displaced in the direction of the edge of the prism (Fig.
32) and this exact amount of displacement never changes
so long as the prism and line are kept at a definite dis-
tance apart, no matter how far to the right or to the
left the prism may be moved. As already stated, when
the prism is held so that the base-apex line coincides
with the straight line a displacement of the line exists
but is not always apparent, because in this position the
displaced portion is superimposed on the original line
(Fig- 33)-

FIG. 44.

The Optic Center of a Convex Lens. — Looking at a
vertical straight line and passing a convex lens before the
eye from left to right has the effect of displacing toward
the right edge of the lens that portion of the line seen
through the lens (Fig. 44) and as the lens is slowly
moved still further to the right, the displaced portion of
the line will finally coincide with the original straight

36 PRISMS

line making one continuous line through the lens (Fig.
45). Marking this straight line on the surface of the
lens, and then turning the lens to the opposite meridian

FIG. 45.

and repeating the examination, and marking the lens as
before, the optic center will be in the lens beneath the
point of intersection of the two lines (Fig. 46).

FIG. 46.

A Convex Sphere. — Objects viewed through a con-
vex lens as it is moved before the eye, from left to right
and right to left or up and down, appear to move in an

OPTICAL EFFECT OF A PRISM

opposite direction to that in which the lens is moved.
The weaker the lens, the slower the object appears to
move; and the stronger the lens, the faster the apparent
movement of the object. A convex lens being a magni-
fier, has the effect of making objects appear larger and
closer when it is moved away from the observer's eye;
or if brought toward the eye, objects already enlarged
appear smaller and more distant.

A Concave Sphere. — When a concave sphere is
moved before the eye from left to right and right to left

FIG. 47.

or up and down, objects appear to move in the same
direction as that in which the lens is moved. A concave
lens being a minifier, makes objects appear smaller and
more distant as the glass is moved away from the eye,
and if brought closer to the eye, it makes objects appa-
rently small appear somewhat larger and nearer. Look-
ing at a straight edge or line through a concave sphere,
and passing the lens from left to right, the portion of the
line seen through the lens appears displaced toward the

38 PRISMS

center of the lens (Fig. 47), and as the lens is still further
moved to the right, the displaced portion of the line
finally coincides with the original straight edge, as in

Fig. 45-

The optic center of a concave lens is found in the same
way as finding the center of a convex lens.

A Convex Cylinder. — When a convex cylinder is
moved in front of the eye in the direction of its axis,
objects looked at do not change their positions; but
when the lens is moved in the direction opposite to its
axis, the movement of the object is the same as that of a

FIG. 48.

convex sphere. Looking at a straight edge through a
convex cylinder, and rotating it, has the effect of dis-
placing away from its axis that portion of the straight
edge seen through the lens (Fig. 48).

A Concave Cylinder. — When a concave cylinder is
moved in front of the eye in the direction of its axis,
objects looked at do not change their positions; but
when the lens is moved in the direction opposite to its
axis, the movement of the object is the same as that of a
concave sphere. Looking at a straight line through a

OPTICAL EFFECT OF A PRISM 39

concave cylinder, and rotating it, has the effect of dis-
placing toward its axis that portion of the straight line
seen through the lens (Fig. 49). A circle viewed

FIG. 49.

through a strong concave cylinder appears as an oval
with its long diameter corresponding to its axis (Fig. 50).

FIG. 50.

A circle viewed through a strong convex cylinder ap-
pears as an oval with its long diameter opposite to its
axis.

CHAPTER IV

PRISM NOMENCLATURE. DENNETT'S METHOD.

PRENTICE'S METHOD AND NEUTRALIZING

PRISMS

Numbering of Prisms.— Formerly prisms were
numbered by their refracting angles or the edge angle
formed between the two refracting surfaces. Such
prisms were known as one degree (i°), two degrees (2°),
three degrees (3°), etc. Early trial cases had these
prisms numbered in this way, sometimes as high as num-
ber twenty-four. They were often spoken of as num-
ber one, number two, number three, etc. The unit
(number one) or any degree numbered prism does not,
unfortunately, signify or designate definitely the amount
of deviation a ray of light will undergo in passing
through such a numbered prism; the degree simply
designates the inclination or angle formed by the sides
of the prism. It will be noted later that this method of
numbering prisms was most unsatisfactory because it
did not indicate the angle of deviation which the ray of
light would make when it passed through the prism.
Or to state it in another way, the degree notation of
prisms did not inform the surgeon just how much such

PRISM NOMENCLATURE 41

a prism would deviate a ray of light when in its position
of minimum deviation (Chapter II, also Fig. 25).

When referring to the strength of a prism it is always
better to mention its deviating power; for instance, a
number 4 prism does not convey the proper meaning
except that the surfaces of such a prism have an apical
angle of four degrees, and therefore if we wish to say
that a 4 prism will deviate a ray of light four degrees,
we must insert the letter "d" after the 4, which would be
"4 d prism." A change from this " degree" nomen-
clature of prisms was urged by Dr. Edward Jackson
(now of Denver, Colorado) before the Ninth Inter-
national Medical Congress and he very wisely and prop-
erly recommended that prisms be numbered or marked
according to their power of deviating rays of light and
the edge angle to be ignored.

An instrument for measuring the edge angle of the
prism is made by the Geneva Optical Company and
called a "prism measure," but it is of no use to the
oculist as it does not register the deviating power of the
prism. It is an instrument, however, which the optician
can use to advantage.

Since Dr. Jackson's recommendation for a new or
exact prism nomenclature, two methods have come into
use, namely, Dennett's Method and Prentice's Method.

The size of the angle of deviation produced by a ray
of light passing through a prism measures the strength
or the effect of the prism and it is this angle which has
given us the new nomenclatures now to be described.

Dr. Dennett's Method. — TheCentrad. Abbreviated
by an inverted Greek letter D (Delta) V. The unit of

42 PRISMS

this method (one centrad) is a prism which will deviate
a ray of light the one-hundredth part of the arc of the
radian. (See Radian, Chapter II.) This is an arc
measurement and the arc of the radian always equals a
little more than fifty-seven degrees (57-295+°). In
Fig. 51 R A and R C are radii of curvature, A C is the
arc of the radian and is equal in length to either R A
or R C. This arc is now divided into 100 equal parts.

R A

FIG. 51. — Illustrating Dennett's method of numbering prisms.

A prism base up axis 90° at the center of curvature (R)
which will deviate a ray of light just one-hundredth
part of this arc is a unit prism of one centrad (iv)
and in its deviating power equals therefore the one-
hundredth part of 57.295 degrees, or 0.57295 of a
degree. This unit power tells at once the deviating
power of any number of centrads by simply multiplying
this unit power (0.57295) by the number of centrads in

PRISM NOMENCLATURE

the prism; for instance, a five centrad prism (5V) will
deviate a ray of light 5X0.57295 which equals 2.8647°,
and a ten centrad prism (iov) will deviate a ray of
light 10X0.57295 which equals 5.7295° etc.

Mr. Charles F. Prentice's Method. — Prism-diopter
or prism-dioptry. Abbreviated by the Greek letter D
(Delta) A- The unit of this method (one prism-diop-

FIG. 52. — Illustrating Prentice's method of numbering prisms.

ter) is a prism which will deviate a ray of light just one
centimeter for each meter of distance that it travels.
The prism-diopter is strictly a tangent measurement
(Fig. 52). As the deviation of a prism-diopter is
always one centimeter for each meter of distance
then one prism-diopter will deviate a ray of light two
centimeters for two meters of distance, three centi-

PRISMS

I I I I

H .

PRISM NOMENCLATURE

meters for three meters of distance, four centimeters
for four meters, etc. (Fig. 53).

The comparative values of centrads and prism diop-
ters is quite uniform up to 20, but above 20 the centrad
becomes the stronger (Fig. 54). As the every-day use

50°

FIG. 54. — Comparing Dennett's and Prentice's methods of numbering
prisms.

of prisms seldom calls for a prism stronger than 20
(centrad or prism-diopter) the surgeon need not be
annoyed with any distinction between the two nomen-
clatures until he passes to a prism stronger than 20.
The following table is self explanatory.

PRISMS

TABLE SHOWING THE EQUIVALENCE OF CENTRADS IN PRISM-DIOPTERS AND
IN DEGREES OF THE REFRACTING ANGLE (INDEX OF REFRACTION 1.54)

Centrads

Prism-diopters

Refracting angle

i .

i°.oo

2 .OOOI

2°. 12

3.0013

3°-i8

4.0028

4°-23

5-0045 „'.

5°. 28

6.0063

6°. 32

7.0115

7° -35

8.0172

8°. 38

9.0244

9° -39

10.

10.033

10°. 39

ii .044

"°-37

12.

12.057

12°. 34

*3-

J3-074

13°. 29

14.

14.092

14° -23

IS-

15.114

15°. 16

16.

16.138

i6°.o8

i7-

17.164

i6°.98

18.

18-196

17°. 85

19.

19.230

i8°.68

20.

20.270

19° -45

25-

25-55

23° -43

30-

30-934

26°. 81

35-

36-50

29°. 72

40.

42.28

32°. 18

45-

48.30

34°. 20

So-

54-5J4

35° -94

60.

68.43

38°. 31

70.

84.22

39° -73

80.

IO2 .96

40°. 29

90.

I26.OI

40°. 49

IOO.

155-75

39° -i4

"The actual difference between corresponding num-
bers of the two scales is the difference between the

PRISM NOMENCLATURE 47

tangent and the arc of the same number of hundredth-
radians. The practical difference within the limits of
actual use is hard to see."1

"In 1891 the Ophthalmic Section of the American
Medical Association passed a resolution recommending
the adoption of the centrad unit and scale and equally
with that up to 20, the prism-diopter."1

Neutralization of Prisms. — The word neutraliza-
tion as used in opththalmology means to counteract
or render inert or it may be described as antagonizing
or as an opposite effect. For instance, if a ray of
light passing through a prism is deviated two centi-
meters at one meter of distance, then to neutralize this
effect or antagonize this deviation it will be necessary
to find a prism of equal strength and place it with its
base to the apex of the other prism, or to be able to neu-
tralize a prism all that is necessary is to find its numeric
strength. To do this, the prism to be tested must be
held in its position of minimum deviation with base-
apex line at right angles and over a series of numbered
parallel straight lines separated by an interval of one
centimeter (or multiple or fraction thereof) and note
the amount of displacement that results when the prism
is held at a distance in meters (or multiple or fraction
of a meter) according to the interval between the lines.
Fig. 55 shows a series of vertical, parallel straight lines
one-half centimeter apart and numbered from o to 9.
An X is placed at the foot of the zero line. All the
parallel lines are at right angles to the black line B L.

1 William S. Dennett, M. D.: "System of Diseases of the Eye," Norris
and Oliver, Vol. II, page 150.

PRISMS

9876543210

FIG. 55. — Author's method of estimating the strength of a prism.

PRISM NOMENCLATURE

Holding a prism base to the right, axis 180°, at a dis-
tance of 50 centimeters (half a meter) from the lines
(as the lines are one-half centimeter apart) and look-
ing through the prism at X on the zero line and also
at the line B L, it will be seen that the X line has been
displaced to the line to the left corresponding to the

9876543210

FIG. 56.

number of centrads or prism-diopters in the prism
which is being tested — in this instance, three. The
displaced portion of the B L line is carried forward
and superimposed upon itself, otherwise it would
appear out of alignment, if the prism was not held with
the base-apex line corresponding to the B L line, as
shown in Fig. 56. If the zero line (X) had been dis-

50 PRISMS

placed between the lines marked 2 and 3 then the
number of the prism would have been more than two
or less than three centrads or prism-diopters. If it
has been displaced to the line marked 5 then it would
have been a 5 prism, etc. It might be just as well
to remind the reader that it makes no difference at
what distance his eye may be from the prism while
making this test, but it is of the utmost importance to

987654 3 2101234567S9

-i

- fi

9876543210123456789
FIG 57. — Prismometric scale of Charles F. Prentice.1

hold the prism in the manner mentioned and at the
exact distance in meters or fraction of a meter, corre-
sponding to the centimeter interval between the lines.
To find the strength of a prism. Mr. Prentice, who pro-
posed the prism-diopter, recommends using a graduated
card having lines upon it separated by an interval of
six centimeters and this of course must be placed at a
distance of six meters and used as in the former test.
This scale is exact and called by its author a "prismo-

1 Copyright, see footnote page 98.

PRISM NOMENCLATURE 51

metric scale" (Fig. 57). This scale may also be used
for muscle testing and is described in Chapter VII.

A prism may be neutralized by placing another
numbered prism from the trial case in opposition to it,
the base of one to the edge of the other (Fig. 58), so
that in looking through the two prisms at a straight
line, no matter at what distance, the straight line will
continue to make a straight line. The strength of the
neutralizing prism will correspond to the number of
the prism being neutralized. As the prisms in the

FIG. 58. — Neutralization of prisms.

trial case occasionally get loose in their individual
frames or cells, it will be well for the surgeon to test
the 'prism in the manner described in Fig. 55 to make
sure that they are properly placed. The base-apex
line should coincide with the B L line and with the
makings on the frame. Dr. Ziegler's prism scale (Fig.
59) is an excellent one. The directions for its use are
as follows:

This prism scale is to be used at a distance of a
quarter meter, but a larger one for use at two meters
is preferable as the possibility of error is much less.
To use the scale close one eye, and with the other look
at the scale both through the prism and over it. A

PRISMS

20 18 16 14 12 10 8 6 4 2

-10

FIG. 59. — Prism scale of Dr. Lewis S. Ziegler.

PRISM NOMENCLATURE 53

comparison of these two views gives the required regis-
tration. Each field must contain either the indicator
singly or the numbered gradations singly; the fields
being in conjunction at the margin of the lens.

Rotate the prism until the base line seen through the
prism is continuous with the base line of the scale.
Always keep the plane of the prism parallel with that
of the scale, and on a level with it. The index line will
be displaced along the scale until the indicator stands
opposite the proper numbered gradation. By moving
the prism up and down along this gradation, it can
be seen whether the index line accurately coincides or
not.

CHAPTER V
COMBINED PRISMS

Combined Prisms. — Any two prisms of the same
strength with the base of each against the edge of the
other will neutralize each other and the effect will be
negative. See neutralization of prisms, Chapter IV,

Fig. 58-

Any two prisms of the same or different strength
with the base of one to the base of the other will equal
the effect of a single prism of the combined strength

FIG. 60. — Two prisms in apposition. Base and edge of one to the base and
edge of the other.

of the two (Fig. 60). Any two prisms, each less than
5V , of the same strength held in apposition and with
their base-apex lines at right angles to each other (Fig.
61) will equal or be equivalent to a single prism one or
two units stronger than one of the prisms, with its
base midway of the two bases. For instance, 5 prism-

COMBINED PRISMS 55

diopters base down axis 45 combined with a 5 prism-
diopter base down axis 135 will equal a 7 prism-diopter
base down axis 90°. This is a very close equivalent
in effect and applies to pairs of prisms as high as
5 centrads or 5 prism-diopters, but when pairs of
prisms as strong as 15 are used the effect is much greater
and with i5v the effect will approximate a single 21
prism-diopter.

That the reader may fully appreciate these statements,
he should make these tests for himself and in this way

Prism

FIG. 61. — Two prisms of the same strength superimposed. One base down
axis 45 and the other base down axis 135.

become familiar with the prism effects or equivalents.
The following description will also be of assistance:

Fig. 62 shows a single 8 prism-diopter held about
10 inches away from and directly over the word
"Prism." (Both eyes of the observer must be kept
open to make this test.) The base-apex line is at
axis 45° and base downward. The word "Prism"
now seen through the prism appears displaced upward
to the right on the base-apex line, on axis 45°. Likewise

PRISMS

Fig. 63 shows another prism of same strength held in
the same manner over another word "Prism" and the
base of the prism downward on axis 135°. It pro-

Prism

FIG. 62.

duces a similar amount of displacement of the word
"Prism," upward and to the left on axis 135°. If
these two prisms are now superimposed in their re-

Prism

FIG. 63.

spective positions (45° and 135°) as shown in Fig. 61,
and the word "Prism" as also shown in Fig. 61, is now
looked at through this combination, the word "Prism"

COMBINED PRISMS 57

will appear displaced upward on axis 90° and the effect
thus produced is equivalent to a single 11 prism base
down axis 90°, Fig. 64.

As just stated and illustrated (Fig. 58), any two prisms
of the same strength with the base of each to the apex of
the other, neutralize each other and the effect is negative,
but if these two prisms still held in opposition are now
revolved in opposite directions at an equal rate of
speed, the effect produced is that of a prism gradually

Prism
FIG. 64.

growing stronger and stronger in its effect until the
bases of the two prisms become superimposed and the
resulting effect will be the combined strength of the
two prisms (Fig. 60)

At first thought the student will naturally imagine
that such a mechanism (Fig. 61) must produce two
images (diplopia) of any object looked at, but the error
of this supposition will be dispelled by reference to
Fig. 6 1 and by making the tests for himself. Sir John
Herschel was the first to show the effect of combining
two'prisms and by rotating them in opposite directions to

PRISMS

obtain the effect of a single prism of increasing strength
up to the combined value of the two.

Crete of Paris was the first to bring forth an instru-
ment which gave practical use to two superimposed

FIG. 65. — Front view of tne revolving prisms as arranged by Crete.

prisms. It is called "Crete's Prism" or the "Prisme
mobile." See Fig. 65. These two prisms are mounted
in a circular cell with a straight handle. This handle
contains a slot through which travels a movable button

COMBINED PRISMS 59

adjusted to the prisms so that on pushing the button
upward or downward the prisms are made to revolve
in opposite directions at an equal rate of speed. The
figures on the handle opposite the gauge record the
strength of the prism thus produced.

The handle of the "Crete prism and also the posi-
tion of its degree markings interfere with its usefulness
and make it cumbersome for every-day practice ;ns.
fact the instrument is rather obsolete for these reaso in
The most adaptable form of Crete's prism which does
away with the handle is that of Dr. S. D. Risley, known

FIG. 66.

as the "Rotary prism," Fig. 66. This apparatus which
may be used in the trial-frame is composed of two super-
imposed prisms of 15 prism-diopters or 15 centrads
each, and mounted in a cell of the size of the trial lens.
By means of a milled edged screw these prisms are
made to revolve so that in the position of zero they
neutralize each other, and when revolved over each
other the prism strength gradually increases until the
bases of the two prisms superimpose, equalling (15 + 15)
30 centrads, The prism strength is indicated by a

PRISMS

pointer directed to the scale on the periphery of the
cell. "Rotary prisms" are made in two strengths,
one contains two 10 prisms and the other, as just de-
scribed, two 1 5 prisms. See Chapter on Muscle Testing.

FIG. 67. — Jackson's triple prism.

Jackson's triple prism (Fig. 67) is very similar
to the Cre"te or Risley prism. It contains three prisms,
as its name implies; one of these is stationery and the
other two revolve.

CHAPTER VI

COMBINING A PRISM WITH A SPHERE, CYLINDER OR
SPHERO -CYLINDER

Before taking up the consideration of these combina-
tions, the reader must be acquainted with the following:

The geometric center of a lens is a point midway
of the diameters of the surface; therefore there is a
geometric center for each surface and these are super-
imposed. As the geometric center is always con-

FJG. 68. — The dot in G at the point of crossing of BB with AA indicates the
optic and geometric centers superimposed.

trolled by the midpoint of the diameters, it is easily
located. Fig. 68 shows a circle which may be considered
as the outline or contour of a lens. A A and BB are di-
ameters. The dot in the G is the midpoint of these
diameters and is therefore the geometric center. As

PRISMS

another illustration, see Fig. 69. This is the outline of
a spectacle lens; AA and BB represent the two chief
diameters and the dot in the G is the midpoint of these
diameters and hence is the geometric center. Also
see dot on surfaces of lens pictured in Fig. 70.

FIG. 6g. — Dot in G = geometric center.

Axial Ray <-

FIG. 70. — Dot in O = Optic center. Dots = Geometric centers.

Optic Center. — This term is used synonymously
with nodal point, but it is not and must not be confused
with the geometric center. The optic center is the
point where secondary rays cross the axial ray (dot

COMBINING A PRISM WITH A SPHERE 63

in the O, Fig. 70). Rays of light crossing the optic
center in thin lenses are not considered as undergoing
refraction (S A in Fig. 70). The optic center is always
a fixed point and may be located at any part of the lens
or at an imaginary point beyond its edge. In Fig.
70 the optic and geometric centers coincide, but in
Fig. 71 they do not coincide. To summarize, the optic
center is always at the thickest part of a convex lens
and the thinnest part of a concave lens.

FIG. 71.

True Center of a Lens. — A lens is said to be cen-
tered when the optic and geometric centers coincide
or are both on the visual axis (Figs. 70 and 72).

When the optic and geometric centers do not coincide
then such a lens has a prism effect or combination,
hence (Fig. 71)

(1) The nearer the optic and geometric centers coin-
cide with or approximate the axial ray the less the pris-
matic effect.

(2) The further apart the optic and geometric cen-
ters the greater the prismatic effect (Fig. 71).

(3) In weak lenses or lenses with long radii of curva-

PRISMS

ture, a slight lateral displacement of the optic center
produces but little prismatic effect.

(4) In strong lenses or those with short radii of cur-
vature, a slight lateral displacement of the optic center
from the geometric center will produce considerable
prismatic effect.

Or 3 and 4 may be restated briefly ',i.e., a strong lens
requires less lateral displacement of the optic center
from the geometric center than a weak lens to obtain
the same amount of prismatic effect in each.

-V-A:

FIG. 72.

Unless otherwise prescribed, every lens placed
before the patient's eye is supposed to have the optic
and geometric centers coincide with the visual axis of
the eye (Fig. 72), then there will not be any prismatic
effect. If there is any departure from this correct
position for the lens and the eye together, then a pris-
matic effect is produced and its amount is in proportion
to the displacement or separation and the strength of
the lens in use (Fig. 71).

Decentering (Decentring) a Lens. — This may be
described as having the optic center of a lens laterally
displaced from the geometric center, so that the eye

COMBINING A PRISM WITH A SPHERE 65

looking through such a lens sees through the geometric
center but not the optic center (Fig. 71). In other
words the geometric center is on the visual axis but the
optic center is to one side (Fig. 71).

A decentered lens may therefore be described as one
whose optic and geometric centers do not coincide
(Figs. 71, 75, 76, 77 and 78).

When ordering a prism in combination with a lens
the prescriber may write his prescription out in full

FIG. 73. — Dots at GG = Geometric centers. Dot in O = Optic center of
this combination.

or he may specify that the lens is to be decentered.
For instance +4 sphere O 4A base down axis 90°.
This is equivalent to a piano +2 sphere1 on each
surface of the 4 prism (Fig. 73).

The optician would, however, take a + 4 sphere (in
the rough2 as he calls it) and grind or polish the
other surface at an angle as indicated by the straight
dotted line. See Fig. 74. The angle at which he

1 It might be well to mention that the optician carries spheric lenses in
stock that are round or circular in contour and cylinders that are square.

2 In "the rough" means that one surface is not polished or finished.

PRISMS

grinds the second surface must be in keeping with the
prismatic effect which the prescription calls for.

In place of the above formula the prescriber could
have ordered +4 sphere decentered 10 millimeters
downward axis 90°. For this prescription the optician
would take the +4 sphere and mark with a dot the
true center (dot i in Fig. 75) and also mark the shape
of the lens he is to cut out and in place of cutting it as

FIG. 74. — Plano-convex sphere in the rough. Straight dotted line for a
plano-sphero-prism. Curved dotted line for meniscus sphero-prism.

indicated by the dotted line, follows the continuous
line and in this way leaves the optic center 10 milli-
meters downward or below the geometric center at 2.
In profile (Fig. 76) this +4 spheric lens shows the
prism thus manufactured by decentering.

The rule for decentering lenses to obtain a certain
amount of prismatic effect is as follows:

"For every centimeter (10 millimeters) of decentering
there will be produced as many centrads or prism-

COMBINING A PRISM WITH A SPHERE

diopters as there are diopters in the meridian which is
decentered." In the example just given (+4 sphere
O 4A base downward axis 90°) it must first of all be
remembered that this is a 4 diopter lens and secondly
if the optic center is placed 10 millimeters away from
the geometric center the effect will be a +4 sphere O
4 prisms; in other words, as previously mentioned, it

» . c

FIG. 75. FTG. 76.

FIG. 75 — CIRCLE = plano-convex lens in the rough. I = optic and
geometric centers superimposed. At 2 the geometric center is above.

FIG. 76. — Profile of Fig. 75 showing geometric center at 2 and optic
center at i.

will be +4 sphere decentered 10 millimeters downward
axis 90° (Figs. 75 and 76). According to the same rule if
the +4 sphere had been decentered 5 millimeters the
effect would have been 2 prisms, if it had been decen-
tered 21/2 millimeters the effect would have been i
prism, if it had been decentered 15 millimeters the

68 PRISMS

effect would have been 6 prisms. Likewise if the
denominator of the sphere had been a minus in place
of a plus, the effect would have been the same, also
if a plus or minus i, 2, 3, 5, 6, 7, 8, etc., was decentered
10 millimeters, the prismatic effect would be i, 2, 3, 5,
6, 7, 8, etc., centrads or prism-diopters respectively.
If the sphere is plus or minus 0.25, 0.50 or 0.75 and is
decentered 10 millimeters the prismatic effect is 1/4,
1/2, and 3/4 of a centrad or prism-diopter respectively.
Another rule for decentering is to multiply the number
of prisms in the prescription by 10 and divide the
amount by the number of diopters in the meridian
which is to be decentered and the quotient will be the
number of millimeters for decentering. In the above
example, +4 sphere O 4A base downward axis 90°,
the number of prisms is 4 and multiplying 4 by 10
equals 40, dividing this amount by 4 (the number of
the diopters in the meridian of 90°) and the quotient
is 10 millimeters, namely +4 sphere decentered 10
millimeters downward axis 90°.

Combining a prism with a cylinder (plus or minus)
requires extra consideration, as it depends in which
meridian the base-apex line of the prism is to be placed
and which meridian is to be decentered. The reader
must remember that a cylinder does not refract rays
of light in the meridian corresponding to its axis. Fig.
77 shows a +4 cylinder axis 90°. Opposite to axis
90° (that is in the 180 meridian), the strength of
the cylinder is +4, but on axis 90° there is no curve
to the glass, and there is therefore no refraction in the
90° meridian. Outlining the spectacle lens on the

COMBINING A PRISM WITH A SPHERE 69

surface of the cylinder as indicated by the figure i
in Fig. 77, there would not be any prismatic effect
produced if this lens was thus cut out of the cylinder,
but if the lens outlined below was cut out, then the
prismatic effect would be 4 centrads or prism-diopters
because the geometric center would then be 10 milli-

^-180° =+4

FIG. 77.

meters to one side of the axis. Namely, +4 cyl.
axis 90 o 4A base in axis 180° is equal to a +4 cyl.
axis 90° decentered 10 millimeters in, on axis 180°.

From the above statements, the following may be
deducted:

(i) A cylinder per se cannot be decentered on its
axis.

70 PRISMS

(2) Decentering a cylinder one centimeter in the
meridian at right angles to its axis will produce the
effect of as many prism-diopters or centrads as there
are diopters in the cylinder. Plus or minus i, 2, 3, 4, 5,
or 6 cylinder axis 90°, decentered 10 millimeters on
the meridian of 180° will give the effect of i, 2, 3, 4, 5,
and 6 prism-diopters or centrads respectively. The

FIG. 78. — Cylinder in the rough marked with dotted lines ready to be ground
to get the prism combination.

same rule applies to 0.25, 0.50 and 0.75 cylinder axis
90°. The equivalent of +4 cyl. axis 180 o 4A base
down is a 4A base down axis 90° with a +4 cyl. axis
1 80 superimposed or as in Fig. 78 the optician will
take a +4 cyl. axis 180° in the rough and grind the
other surface plane (see dotted line same Fig) and at
an angle which would produce the desired prismatic
effect — in this instance 4.

COMBINING A PRISM WITH A SPHERE 71

COMBINING A PRISM WITH A PLUS OR MINUS CYLINDER
WHICH HAS ITS AXIS OBLIQUELY PLACED
TO THE BASE-APEX LINE OF THE
PRISM

For instance, +4 cylinder axis 45 o 2A base in,
axis 1 80. This is equivalent to a 2A base in and a
+4 cylinder axis 45 superimposed or the optician
takes the +4 cylinder in the rough and grinds the

135

FIG. 79. — Cylinder in the rough marked with dotted line and an X ready
to be cut thus producing a decentered cylinder.

opposite surface plane and at an angle to give the
desired prismatic effect. In this formula for the pur-
pose of decentering it is necessary to know the dioptric
strength of the +4 cylinder in the 180 meridian when

72 PRISMS

the axis of the cylinder is at 45°. Fig. 79 shows such
a cylinder with its axis at 45°. The meridians of 90°,
1 80° and 135° are also shown. If the spectacle lens
indicated by the continuous line was cut out of
the cylinder there would not be any prismatic effect
produced as the geometric center and cylinder axis
coincide and it would simply be a + 4 cyl. axis
45°. But if the spectacle lens was cut out as indi-

FIG. 80. — Geneva lens measure.

cated by the dotted line then there would be a 2A
base in axis 180 in combination with the cylinder.
This cylinder was decentered 10 millimeters*. The
method of finding out the strength of any cylinder in
any meridian is to apply the Geneva Lens measure
(Fig. 80) to the meridian to be decentered.

In other words, a +4 cyl. axis 45° has the strength

COMBINING A PRISM WITH A SPHERE 73

of 2 diopters in the 180 meridian and decentering a 2
diopter lens 10 millimeters gives the effect of 2 prisms.

COMBINING A PRISM WITH A SPHERO-CYLINDER OF
SAME SIGN

In the following example +1.00 o +3.00 cyl.
axis 90 o i A base out, axis 180°. This is equivalent
to a + 1 .00 sphere on one surface of the i prism base
out axis 180 and a +3.00 cyl. axis 90° on the other
surface. Or if decentered all that is necessary to re-
member is that in the 180 meridian where the decen-
tering is to be done, there are 4 diopters, i for the
sphere and 3 for the cylinder, and to get the effect of
a i prism in 4 diopters the sphere-cylinder must be
decentered 21/2 millimeters; namely, + i.oo sphere

0 +3.00 cyl. axis 90° decentered 2 1/2 millimeters
outward, axis 180°.

If this sphere-cylinder had been decentered in the
same meridian 5, 7 1/2 or 10 millimeters, the prismatic
effect would have been 2, 3 and 4 prisms respectively.
This applies of course to the 180 meridian, but if the
decentering had been done in the vertical meridian
then the calculations would be entirely different, for it
will be observed that in the meridian of 90° there is only

1 diopter. If the sphero-cylinder to be decentered
contains a plus sphere with a minus cylinder, the pre-
scriber must remember that one neutralizes the other
to a certain extent and he must calculate accordingly,
for example, in — i, sphere O +3.00 cyl. Axis 90°
O 2V base out, axis 180°, this sphero-cylinder would

74 PRISMS

have to be decentered 10 millimeters as follows: — i
sphere O + 3- cyl. axis 90° decentered 10 millimeters
outward axis 180°. Finally a decentered lens differs in
no respect optically from a lens which contains a
prism.

If for any reason, there is a desire to order prisms
which will give rays of light a deviation of i degree,
then it will be necessary to decenter the lens 17 1/2
millimeters (11/16 of one inch) for each degree.

A very important fact to remember in the ordering
of lenses to be decentered is that many lenses are not
of sufficient width or strength to permit of decentering,
especially if the lens is weak and the prism is strong.
For instance the following: +0.50 sph. O 4V base up.
This should be made by taking a +0.50 sphere in the
rough and cutting off the second surface at the angle
which would produce the 4V base up (Fig. 74). If
the prescriber wrote this formula for decentering as
follows: +0.50 sph. decentered 80 millimeters (8 centi-
meters) upward axis 90 he would find that such a
prescription would display great ignorance and invite
suspicious criticism of the prescriber's knowledge.
Weak lenses do not come large enough for any such
purpose.

The following tables by Dr. Jackson and Dr. Wallace
are self-explanatory:

COMBINING A PRISM WITH A SPHERE

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To detect malingerers who profess monocular
blindness, so as to obtain damages for supposed injuries,
or who wish to escape war service, or those cases of
hysteric blindness wishing to create sympathy. This
test or use of a prism is known as the diplopia test,
and is practised as follows: A seven P. D., base up
or down, and a blank are placed in the trial-frame
corresponding to the "blind" eye; nothing is placed
in front of the seeing eye; the trial-frame, thus armed
(without the patient seeing what is being done), is
placed on the patient's face and he is instructed to
read the card of test-letters on the wall across the room.
While he is thus busy reading, and purposely contra-
dicted by the surgeon, so as to get his mind from his
condition, the surgeon suddenly removes the blank
from the "blind" eye. The patient exclaiming that
he sees two cards and two of all the letters proves the
deception. Another way to detect "deceivers" is to
place the trial-frame on the patient's face with a blank
on the "blind" eye, nothing is placed in front of the
seeing eye; the examiner then slowly passes a square
prism of 10 or 12 centrads base down, axis 90° before
the seeing eye as the patient observes the card of test
letters across the room. As the prism base bisects
the patient's pupil horizontally the eye immediately

USES OF PRISMS IN OPHTHALMOLOGY

sees two test cards, etc.; then the examiner suddenly
and gracefully removes the blank from the "blind"
eye with his other hand and at the same time passes
the prism over the entire pupil of the good eye. The
patient, still admitting diplopia, proves his conspicuous
inexactness for veracity. This latter test does not
merit the writer's consideration as much as the former
test, although it is wrell to bear in mind both of these

FIG. 81. — Phorometer. This apparatus contains two eye-pieces for trial
lenses; two rotary prisms; a Stevens phorometer; twoMaddox multiple rods
(one for each eye, one at axis 90, and the other at axis 180) ; also a spirit
level, etc.

prism tests in case the patient has been previously
examined by either one of them.

To ascertain the power of Adduction (Prism
convergence) .

Abduction (Prism divergence) and Sursumduc-
tion.

In making these tests the patient should be comfort-
ably seated facing a point of steady white light on a
plane dark surface situated at a distance of 6 meters ;
this light should be on a level with the eyes or slightly

80 PRISMS

below the level. A suitable trial-frame should rest
easily on the patient's nose and ears, although a pho-
ro meter (Fig. 81) is recommended in place of the trial-
frame.

Adduction. — To test adduction, prisms with their
bases inward are placed before one or both eyes (pref-
erably before one eye).1 Begin with a weak prism and
gradually increase the strength of the prism until the
patient states that he sees two distinct lights. For ex-
ample, if with 19 centrads, base out before the left eye,
two lights are seen in the horizontal plane and with 18
centrads only one light, then 18 centrads represents the
maximum prism convergence for these eyes.

Abduction. — This test is pursued as in testing for
adduction, but the prism is placed base inward,
beginning with a weak prism and gradually increasing
the strength until the patient states that he sees two
distinct lights. For example, if with 7 centrads, base in,
before the left eye two lights are seen in the horizontal
plane, and with 6 centrads only one light, then 6 cen-
trads represents the maximum prism divergence.

Sursumduction. — This is the power of uniting or
fusing the image of the light of one eye with the image
of the same light seen by the other eye through a prism
base up or down axis 90°. For example, if a 3 1/2
centrad prism is placed base up axis 90° before either
eye1 and diplopia results and persists, and then a 3
centrad is substituted and there is no diplopia, then
the maximum amount of sursumduction is said to be
3 centrads.

1 The writer is in the habit of placing the prism before the left eye in
making these estimates.

USES OF PRISMS IN OPHTHALMOLOGY 8 1

The writer strongly recommends the use of the
rotary prism, which will greatly facilitate making the
above tests, and those referred to later.

The following nomenclature of muscular anomalies
suggested by Dr. George T. Stevens of New York is
in popular use :

Orthophoria is perfect binocular fixation, also spoken
of as equipoise, binocular equilibrium or parallelism.
With a thorough understanding of the three conditions
just described and which most authorities consider as
standard (adduction being three times as great as ab-
duction, and sursumduction equalling 2 1/2 or 3 cen-
trads), the reader may now appreciate any departure
from these standard conditions.

Heterophoria, imperfect binocular balance, or
imperfect binocular equilibrium.

Heterotropia, a squint or decided deviation or
turning from parallelism.

Hyperphoria, a tendency of one eye to deviate
upward.

Hypertropia, a deviation of one eye upward.

Esophoria, a tendency of the visual axis to deviate
inward.

Esotropia, a deviation of the visual axis inward.

Exophoria, a tendency of the visual axis to deviate
outward.

Exotropia, a deviation of the visual axis outward.

Hyperesophoria, a tendency of the visual axis of
one eye to deviate upward and inward.

Hyperesotropia, a deviation of the visual axis of
one eye upward and inward.

82 PRISMS

Hyperexophoria, a tendency of the visual axis
of one eye upward and outward.

Hyperexotropia, a deviation of the visual axis of
one eye upward and outward.

As the title of this work does not call for any extended
discussion on the subject of the extra-ocular muscles,
the writer therefore limits himself to the consideration
of prisms as applied to making tests for muscular
anomalies or for their treatment. For a full considera-
tion of the extra-ocular muscles the reader is referred to
the author's work on " Refraction and How to Refract."

Tests for Heterophoria and Heterotropia. —
There are many of these tests and each has more or
less value. Like the many tests for astigmatism they
should be understood and then the reader may decide
for himself to use one or more of them as they appeal
to his judgment.

Von Graefe Equilibrium Test.— Fig. 82, A. This
test is a black dot one inch in diameter at the middle of
a straight line 1 2 inches long passing through it, drawn
on a white card and hung on the wall 6 meters from the
patient's eyes, the dot being on a level with the eyes.
This card should be hung in a bright light or illuminated
by reflected light. As the patient gazes at this dot and
line a 7 centrad prism is placed base down axis 90°
before the left eye. This produces an image of the line
and dot upward which belongs to the left eye (B in Fig.
82), the lower image belongs to the right eye. If the
upper dot is directly above the lower dot and the black
lines are superimposed, running through both dots then
there is no lateral deviation (Fig. 82, B).

USES OF PRISMS IN OPHTHALMOLOGY 83

Esophoria. — If, however, the upper dot and line
appear to the left (Fig. 82, C) then there is esophoria
and the amount of the esophoria is represented by
the strength of prism placed base outward before the

FIG. 82. — Von Graefe line and dot test. A = Line and dot. B = No
lateral deviation. C = Esophoria. D = Exophoria. E = No vertirle
deviation. F = Left hyperphoria. G = Right hyperphoria. L = Image
of left eye. R = Image of right eye.

right eye (or the left) which will put the upper dot
directly above the lower one as Fig. 82, B.

Exophoria. — If the upper dot and line appear to
the right (Fig. 82, D) then there is exophoria and the
amount of the exophoria is represented by the strength

84 PRISMS

of prism placed base inward before the right eye1
(or the left) which will put the upper dot directly
above the lower one.

Hyperphoria. — Place a 10 centrad prism base in
axis 1 80° before the left eye, and have the line and dot
placed horizontally. If the eyes see two dots on one
line (Fig. 82, E) then there is no vertical deviation. If
the right dot and line appear higher than the left line
and dot then there is left hyperphoria (Fig. 82, F). If
the right dot and line appear lower than the left line and
dot then there is right hyperphoria (Fig. 82, G).

Prism Tests. — Place a 7 centrad prism in the trial-
frame or phorometer base down axis 90° before the
left eye as the two eyes look at the point of light as
described under Adduction. This prism produces ver-
tical diplopia. The upper light naturally belongs to
the left eye under these conditions, and if it is directly
above the other, then there is no lateral deviation.

Esophoria. — If the upper light is to the left of
the lower, then the condition is one of esophoria and
its amount is equal to the strength of the prism placed
base outward before the right eye which will bring one
light directly above the other.

Exophoria. — If the upper light is to the right of

1 The reader's careful attention is called to the writer's method of making
the foregoing test as it is similar to the tests which are to be described ; namely,
that the right eye is free or unencumbered to fix the object or white light; and
the right eye is thus reserved for the use of the correcting prism. Furthermore,
the amount of the esophoria is estimated by the prism base out; exophoria by
the prism base in; left hyperphoria by the prism base up before the right eye
and right hyperphoria by the prism base down before the right eye. Finally,
in place of any lengthy description of esophoria, exophoria and hyperphoria
as each test is described, the reader is referred to the respective illustrations.

USES OF PRISMS IN OPHTHALMOLOGY 85

the lower, then the condition is one of exophoria and
its amount is equal to the strength of the prism placed
base in before the right eye which will bring one light
directly above the other.

Hyperphoria. — Place a 10 centrad prism base
in axis 180° before the left eye, then the left light
belongs to the left eye. If the two lights then appear
in the horizontal meridian there is no vertical de-
viation. If the left light is lower than the right then
there is left hyperphoria. If the left light is higher
than the right then there is right hyperphoria.

The amount of the left hyperphoria is represented
by the strength of the prism placed base up axis 90°
before the right eye which will bring these two lights
exactly horizontal. The amount of the right hyperpho-
ria is represented by the strength of the prism placed
base down axis 90 before the right eye, which will
bring these two lights exactly horizontal.

Use of Ruby Red Glass also Cobalt Blue Glass.
-To avoid confusion on the part of the examiner and
patient in making these tests for esophoria, exophoria
and hyperphoria, as is the case when both lights are
white, it is decidedly better to use a plane piece of ruby
red glass .or cobalt blue glass with the prism over the
left eye and in this way the lights seen by the two eyes
are quickly differentiated.

In making the above tests, the writer uses a 7 centrad
prism, made either of cobalt blue glass or ruby red
glass.

Maddox Double Prism (Fig. 83). — (Obtuse-angled
prism.) This is two prisms of 6 centrads each with

86 PRISMS

their bases united. Placed before the left eye so that
the bases bisect the pupil horizontally, the left eye
will see two images, one higher and one lower than the
true light seen by the right (fixing) eye.

Maddox double prism with a piece of ruby red
glass or a Maddox Double Prism made of ruby red
glass. This is far more attractive and avoids the con-
fusion incident to having the lights all of one color seen
by both eyes (Figs. 84 and 85).

FlG. 83. — Maddox double prism.

Cobalt Blue Glass with the Maddox double prism

or the Maddox Double Prism made of Cobalt Blue
Glass (Figs. 86 and 87) gives the test as shown in Fig. 88.

The writer has been unable to demonstrate with his
own eyes, as some authorities have done, that there is
any definite streak of light connecting the two lights
produced by the Maddox Double Prism of colored or
colorless glass.

Cone or Quadrant or Quadrilateral Prism (Fig.
90). — This is equivalent to a pair of Maddox Double
Prisms superimposed, one at axis 90 and the other at

USES OF PRISMS IN OPHTHALMOLOGY

WL
C

FIG. 84. — Maddox double prism of ruby red glass. A = Two images
produced by double prism. B = No lateral deviation. C = Esophoria.
D = Exophoria.

PRISMS

FIG. 85. — E = No verticle deviation. F = Left hyperphoria. G = Right
hyperphoria. L = Image of left eye. R = Image of right eye.

^^^-

FIG. 86.

FIG. 87.

FIG.

Maddox double prism made of cobalt blue glass. FIG. 86 is profile of
Fig. 87. FIG. 88 is double image produced by Maddox double prism of
cobalt blue glass.

USES OF PRISMS IN OPHTHALMOLOGY

FIG. 89. — Quadrilateral prism or cone in red producing four red images
connected by red streaks.1 E = True light seen by right eye. When E is
equidistant from ABCD there is no displacement, hence = Orthophoria.
When E is in the direction of i = Left Hyperphoria; in the direction of 2 =
Esophoria; in the direction of 3 = Exophoria; in the direction of 4 = Right
Hyperphoria; in the direction of 5 = Left Hyperexophoria; in the direction
of 6 = Left Hyperesophoria.

1 See footnote page 84.

go PRISMS

axis 1 80. Four images of the light are produced (Fig.
89), forming the corners to a square which are connected
by a streak of light of the color of the glass. As this is
made in colorless glass, it will be of great advantage to
combine with it the plane ruby red glass or have the
quadrant prism made of ruby red glass.

The Author's Double Prism, Truncated1 (Figs.
91, 92 and 93). — The difficulty experienced by the

FIG. 90. — Cone or quadrant prism.

writer in the use of the obtuse-angled prism in testing
for hyperphoria of small amount has been to have
patients describe whether the central light seen by the
right eye approached the upper or lower images as seen
by the left eye. To overcome this difficulty of decision
on the part of the patient, the author had the edge or
top of the double prism cut off evenly leaving a flattened
top 3 millimeters wide, see Fig. 91, making what he has

1 Shown and described to the Section of Ophthalmology of the College
of Physicians of Philadelphia, October 17, 1912.

FIG. 91.

FIG. 92.

FIG. 93.

Author's double prism of cobalt blue glass. Fig. 91 is profile of Fig. 92.
Fig. 93 is triple images connected by a streak as seen through this double
prism.

Qfir)

IL R

FIG. 94. — Triple images and streak produced by author's double prism in
cobalt blue glass. B = No lateral deviation. C = Esophoria. D =
Exophoria. E = Left Hyperexophoria.

IWB

FIG. 95. — F = No verticle deviation. G = Left Hyperphoria. H
Right Hyperphoria. L = Image of left eye. R = Image of right eye.

USES OF PRISMS IN OPHTHALMOLOGY

FIG. 96. — Author's double prism of ruby red. A
nected by streak. B = No lateral deviation. C
Exophoria. E = Left Hyperexophoria.

Three images con-
Esophoria. D -»

PRISMS

FIG. 97. — F = No verticle deviation. G = Left Hyperphoria. H
Right Hyperphoria.

USES OF PRISMS IN OPHTHALMOLOGY

chosen to call a truncated prism.1 This is made either
of ruby red glass, cobalt blue glass or colorless glass.
With this form of double prism placed before the eye the
observer immediately sees a central true light, and an
image above and an image below, equidistant from it,
if the truncated prism has been accurately ground.
These three lights are seen to be connected by a band
of light, Fig. 93, and the whole is distinctive from the
single white light of the right eye. For the illustrative
description of the tests see Figs. 94, and 95, also 96
and 97.

FIG. 98. — Maddox rod.

FIG. 99.

Maddox Rod.— This is a single glass rod or a series
of glass rods of red or colorless glass (Figs. 98 and 99)
placed in a metal cell of the trial case, and the eye
looking through it at the light, will see the image of the
light distorted into a streak of broken light. A strong
+ cylinder from the trial case may be used for the same
purpose. As the rod refracts rays of light opposite to
its axis, the eye will see a streak of light in the reverse

1 " A cone or pyramid whose vertex is cut off parallel to the base by a
plane."

PRISMS

FIG. too. — A = Image of Maddox single rod in red. B = No lateral
deviation. C = Esophoria. D = Exophoria. E = Left Hyperexophoria.
R = Image of right eye. L = Image of left eye.

USES OF PRISMS IN OPHTHALMOLOGY

•

©R

FIG. ioi. — F*= No verticle deviation. G = Left Hyperphoria. H = Righ
Hyperphoria, L = Image of left eye. R = Image of right eye.

PRISMS

FIG. 102. — A = Double images produced by Maddox double prism in red
with Maddox rod. B = No lateral deviation. C = Esophoria. D =
Exophoria.

USES OF PRISMS IN OPHTHALMOLOGY

FIG. 103.— E = No verticle deviation. F = Left Hyperphoria G
Right Hyperphoria. R = Image of right eye.

98 PRISMS

meridian to that in which the axis is placed. See Figs.
98 and 99, also Figs. 100 and 101.

Maddox Double Prism and Rod Combined. — This
produces two streaks of light (Fig. 102, A) white or red
as the operator may choose. See illustrations in Figs.
101, 102 and 103. This combination like the double
prism by itself is not as satisfactory a test for esophoria
or exophoria as it is for hyperphoria. In the former
condition the right eye will frequently fuse its image
with one of the light streaks of the left eye, i.e., with
the right one in esophoria and the left one in exophoria
(Fig. 102, C and D).

Convex Spherical. — Using a +15 diopter sphere
before the left eye a very much blurred image is seen
by this eye, and the position of the image of the right
eye relative to this blurred image gives the diagnosis
of the muscular inbalance. If the image of the right
eye centers on the blurred image then the condition
is one of orthophoria ; if to the right or left or above or
below the blurred image, then it will be esophoria,
exophoria, right hyperphoria or left hyperphoria re-
spectively. However, the writer is not partial to this
test, as it is most difficult for the average patient to
maintain exact fixation with his left eye.

Tangent Scale and Maddox Rod. — This tangent
scale1 of Prentice (Fig. 57) with a central light as a
fixing object and a Maddox rod before the left eye
furnishes an ideal test as the record of the amount
of the deviation can be stated by the patient.
Each line of displacement of the streak is equivalent

1 Archives of Ophthalmology, Vol. XIX, No. i, pages 64 and 68.

USES OF PRISMS IN OPHTHALMOLOGY 99

to one centrad or prism-diopter. For example, if the
patient states that the streak is situated vertically on
the zero line there is no lateral deviation, if the streak
is situated horizontally on the zero line there is no
vertical deviation ; if the streak is to the left or right or
above or below the zero line then esophoria, exophoria,
and right or left hyperphoria are present and to the
amount as indicated by the position of the streak whether
on line numbered i, 2, 3, etc. If the streak is between
two lines then there is also a fraction of a centrad or
prism-diopter of deviation.

Another way to use the tangent squares (Fig. 57)
is to place a 7 centrad prism base down axis 90° before
the left eye and in this way produce an upper image
of the chart. If the upper image is displaced directly
upward with the vertically numbered lines coinciding
then there is no lateral deviation. If the upper image
appears to the left the amount of the esophoria is
quickly diagnosed and likewise the amount of exophoria
if the upper image is to the right. A 10 centrad prism
base in axis 180 before the left eye would diagnose
the presence of left or right hyperphoria and also the
amount of each.

Cyclophoria. — (Insufficiency of the oblique mus-
cles.) This test is usually made at thirteen or eighteen
inches from the patient's eyes. A narrow straight black
line is placed horizontally on a white card, as the fixing
object at the distance indicated. A Maddox Double
Prism is placed before the left eye so that the bases bisect
the pupil horizontally and this eye then sees two parallel
horizontal lines if its oblique muscles are in a standard

IOO

PRISMS

condition. The right eye sees but one line between
the two lines seen by the left eye. The right eye is the
one being tested and the position of the middle line
furnishes the diagnosis. If the left eye is to be tested
then the Maddox Double Prism must be placed before
the right eye (Fig. 104).

FIG. 104. — Tests for insufficiency of the oblique muscles, i = Ortho-
phoria or equilibrium of the obliques. 2 = Insufficiency of left superior
oblique. 3 = Insufficiency of right superior oblique. 4 = Insufficiency of
the left inferior oblique. 5 = Insufficiency of the right inferior oblique.

Cyclophoria and its varieties may also be diagnosed
by using two Maddox rods ; one at axis 90° before one
eye and the other at axis 180° before the other eye and
a point of light as the fixing object at 6 meters. If
orthophoria is present the two streaks produced by the
two rods will naturally form a cross; but if cyclophoria
is present, then one of the streaks will show a tilting
or inclination from an otherwise true position of being

USES OF PRISMS IN OPHTHALMOLOGY IOI

horizontal or vertical; indicating at once therefore
which eye is at fault or has the oblique insufficiency.
Whenever the writer is suspicious of the existence of
cyclophoria, he is partial to the use of a colorless rod
before one eye and a red rod before the other eye, but
each must be placed with its axis exactly horizontal.
If the two streaks appear parallel or are superimposed,
there is no oblique insufficiency, but if one streak dips,
so to speak, then cyclophoria is present and corresponds
to the eye having the corresponding rod; the inclina-
tion or dip furnishing a prompt diagnosis of the muscle
at fault. In making either of these tests extreme care
must be exercised to see that the phorometer or trial-
frame and patient's eyes are true to the horizontal
meridian. Hyperesophoria and Hyperexophoria
may be diagnosed by any of these tests and are
easily recognized as shown in the tests figured in 89
and 94.

While the foregoing tests are used for heterophoria or
latent squint, yet they are also used for testing hetero-
tropia or manifest squint. It is not necessary there-
fore to describe the tests for heterotropia except to
say that when heterotropia is of very high degree and
one eye has defective sight, it may be necessary to
begin the test with a red glass and strong prism before
the poor seeing eye so as to engage its attention.

Other tests for heterophoria and heterotropia are
made with the use of apparatus and the following
have been selected from several as most worthy of
consideration.

Steven's Phorometer (see Fig. 81). — This is

102 PRISMS

composed of two 5 centrad prisms each mounted in
a separate large cell with cogged edges; one prism is
mounted before each eye and these are connected by
a small cogged wheel. A convenient handle on the
right cell when pushed to either side makes both prisms
revolve at the same rate of speed. The marking on
the cell to which the prism pointer is directed indi-
cates the degree and variety of heterophoria. The
reader will appreciate the fact that this apparatus is
ideal, but its usefulness is limited to errors of 10 cen-
trads. If the operator wishes to use the Steven's
phorometer to test errors higher than 10 centrads he
must place an additional prism from the trial-case next
to one of the patient's eyes. To avoid confusion it
might be well to state that these two prisms of the
Steven's phorometer never occupy the same position at
the same time. They may both be base in or both base
out, or one base up while the other is base down. They
never reach a point where one is base in and the other
base out, or both bases down or both bases up at the
same time.

The apparatus is used as both eyes are looking at the
point of light.

Dr. E. A. Prince's Phorometer (Fig. 105).— This
instrument with its convenient handle is for the patient
to hold before either eye as directed. A 4 centrad
prism and a maddox rod are enclosed in a metal case.
A milled head screw on one side permits the patient
or operator to revolve the prism. The patient is told
to fix with both eyes on a point of light at 6 meters.
If the streak is vertical and to one side of the light, the

USES OF PRISMS IN OPHTHALMOLOGY 103

prism is revolved until the streak and light appear to
unite. The scale records the amount and character
of the lateral deviation. To test hyperphoria, the
apparatus must be taken off of the handle and replaced
with the rod vertical so as to produce a horizontal
streak and then revolve the prism until the streak and

FIG. 105.

light appear to unite. Unfortunately this apparatus
is limited in its usefulness to 4 centrads. The Prince
phorometer is admirable, however, for testing the in-
sufficiency of some private patients away from the
office.

TheMeister Phorometer (Fig. 106). — This appara-
tus, with its folding handle, spirit level and adjustable
pair of 15 centrad prisms and adjustable Maddox
multiple red rod is a veritable "Multum inParvo".
The writer takes great pleasure in giving it his cordial
endorsement, for with its strong prisms it will do as
much and more than the Stevens and Prince Phoro-
meters combined.

104

PRISMS

FIG. 106. — Meister's Phorometer.

FIG. 107. — Savage's cyclophorometer.

USES OF PRISMS IN OPHTHALMOLOGY 105

Savage's Cyclophorometer (Fig. 107). — This in-
strument is used for detecting and measuring cyclo-
phoria — a tendency of the vertical axes of the eyes to
lose parallelism with the median plane of the head.

The instrument consists of the equivalent of a two-
cell trial-frame, with revolving cells mounted so the
pupillary distance may be varied by a set screw at the
end of the supporting bar. The arm carrying the cells
is provided with a leveling attachment and a spirit
level.

In examining for cyclophoria a multiple Maddox rod
is placed in each of the revolving cells and a 5 -degree
prism, base up, behind one of them. The patient sees
two horizontal lines of light, which should be parallel
and the ends even. The latter can be regulated by
varying the pupillary distance. If the lines are not
parallel they may be made so by rotating either Maddox
rod, the kind (plus and minus) and degree of the error
being shown on the scale.

Cyclo-duction, the intrinsic power of each oblique
muscle or of both superior or of both inferior obliques
may also be measured.

Savage's Monocular Phorometer (Fig. 108).—
This instrument is designed for the determination and
measurement of insufficiencies of the various ocular
muscles and is based on the principle that the image in
one eye throughout every test shall be undisturbed.

It consists principally of a rotary variable prism
correctly marked in degrees and lettered to show the
various conditions of muscular imbalance, such as
exophoria, esophoria, hyperphoria, etc. On each side

106 PRISMS

of the rotary prism are cells, in one of which, toward the
patient's face, is to be placed the displacing prism for
causing diplopia. These prisms are carefully mounted
in square cells for securing accurate position at either
90 degrees or 180 degrees. The instrument is supplied
with a spirit-level and a leveling-screw.

FIG. 108. — Savage's monocular phorometer.

The prism is reversible for either eye.

While most of the apparatus and descriptions just
mentioned are for testing the muscular conditions at
6 meters, it is necessary to test muscular anomalies at a
close range, i.e., at 13 inches (33 centimeters) as this is

USES OF PRISMS IN OPHTHALMOLOGY

107

the average reading and working distance with the eyes
at close occupations.

Convergence. — Con, "together," and vergere, "to
turn"; literally turning together. Standard eyes, when
looking at an object at a distance of six meters or more,
are not supposed to converge, the visual lines are spoken
of as parallel and the power of convergence in a state
of repose. The angle which the visual line makes in
turning from infinity ( oo.) or six meters to a near point
is called the angle of convergence, and the angle which

FIG. 109.

is formed at one meter distance by the visual axis with
the median line is called the meter angle, or the unit of
the angle of convergence. (See I in Fig. 109.)

If the visual line meets the median plane at 1/2 meter,
it has then two meter angles of convergence; at 1/4
meter, four meter angles of convergence, etc., or five
meter angles means that the eye is converging to a point
1/5 meter distant. The size of the meter angle varies;
it is not the same in all individuals; in fact, the meter
angle is smaller in children than in adults, as a rule, on
account of the shorter interpupillary distance. In chil-

108 PRISMS

dren this distance is about 50 mm., whereas in adults
it is, on the average, 60 or 64 mm.

If the average distance between pupils in the adult is
64 millimeters, then one meter angle equals a deviation
for one eye of 32 millimeters. As the eyes converge
closer than one meter, the meter angle increases corre-
spondingly, the number of meter angles is, therefore,
the inverse of the distance expressed in meters. As one
meter angle equals a deviation of 32 millimeters, this
equals or is equivalent to 3.2 centrads. One centrad
deviates a ray of light .57295° and 3.2 centrads would
therefore equal a deviation of i° 50'. Knowing the
prismatic effect or equivalent of converging to a point
at i meter, then at 3 meter angles the effect would be
three times as great or 9.6 centrads or 5° 30'.

The reverse of this is equivalent therefore to placing
a 9.6 centrads base in axis 180° before each eye and the
eyes would see an object at 33 centimeters as if it were
located at infinity. In other words when a pair of
standard eyes with standard muscles turn from looking
at a distance of 6 meters to fix on an object at 33 cen-
timeters, these eyes have developed a power of conver-
gence equivalent to 19 or 20 centrads.

Any departure from this standard unit of convergence
produces muscular inbalance of the varieties already
described. /

Tests for Muscular Inbalance at 33 Centimeters.
—Have the patient look at a small black dot with a fine
black line 2 or 3 inches long running perpendicularly
through it, at a distance of about 13 inches. This is
known as the line-and-dot test of von Graefe for near

USES OF PRISMS IN OPHTHALMOLOGY IOQ

testing, and on a larger scale is described in the previous
tests at 6 meters. A prism of seven or eight centrads
is placed, with its base down, in front of the left eye.
If the patient sees two dots exactly one above the other
on one line there is not supposed to be any lateral in-
sufficiency. If, however, there are two lines and two
dots, and the upper dot and line is on the left then there
is esophoria for near. The amount of the esophoria
is represented by the strength of the prism, placed base
outward before the right eye, which will bring the two
dots exactly on one line. If the upper dot and line are
to the right, then there is exophoria for near, and the
amount of the exophoria is represented by the strength
of the prism placed base inward over the right eye
which will bring the twro dots, one above the other, on
one line.

Another method for testing lateral insufficiency at
the reading distance of 13 inches is to have a card about
6 inches square, and on this card to draw a heavy black
line about 3 inches long; this line to be placed exactly
horizontal. At the middle of the horizontal line draw
a heavy black line, 1/2 inch long, extending vertically
from the horizontal line; this short vertical line to be
capped with an arrow point. The horizontal line is
divided off into equal spaces, each 31/3 millimeters
apart and numbered from i to 15 each side of the arrow;
those to the left of the arrow are marked " esophoria,"
and those to the right of the arrow are marked " exo-
phoria" (Fig. no).

To use this method, a prism of 8 centrads is placed
base down before the left eye; this doubles the scale

PRISMS

vertically; the upper scale belongs to the left eye. The
number and the word in the upper scale to which the
arrow in the lower scale points, is the approximation in
centrads of the amount of the esophoria or exophoria.
For instance, if the lower arrow points to figure 9 in
the upper scale to the right of the upper arrow, that is to
the word "exophoria," then there will be approximately
9 centrads of "exophoria" at this distance of 13 inches,
the distance at which this scale is intended to be used.

Esophoria

15 14 13 12 H 10 9 8 76 54 32 1

Exophoria

1 2 3 4 5 0 7 8 9 10 11 12 13 14 15

FIG. no. — Scale for testing lateral insufficiency at 13 inches.

To Test for Hyperphoria at 33 Centimeters.—

Place a 10 centrad prism base in before the left eye as
the right eye fixes the line and dot of von Graefe as in
the former test, except that the line is placed horizon-
tally. If there are two dots on the horizontal line, then
there is no vertical deviation, but if there are two dots
and two lines one above the other then there is a vertical
deviation. If a prism base down before the right eye
brings the two lines together, then there is right hyper-
phoria; if the prism base up before the right eye brings
the two lines together, then there is left hyperphoria.

The large black square and small white millimeter
square in its center as suggested by Dr. Jackson makes
an excellent test for muscular imbalance at 33 centimeters
(Fig. in). The small white square is made to appear
double with a 10 centrad prism base down before the
left eye.

USES OF PRISMS IN OPHTHALMOLOGY III

The small Greek cross (Fig. 112) suggested by Dr.
S. L. Ziegler answers the same purpose as the Jackson

FIG. in. — Dr. E. Jackson's test for muscular insufficiencies at 33 centimeters.

FIG. 112. — Dr. S. L. Ziegler's Greek cross as a near test object.

squares. Other authorities are parital to a printed
word like DIOPTER, for instance; this is made to

112

PRISMS

appear double with a 10 centrad prism base down before
the left eye. If the letteis appear directly above each
other, D over D, I over I, etc., then there is no lateral
deviation, etc.

FIG. 113. — Place a 10 centrad prism base down before left eye, if upper
cross appears to the left, the condition is esophoria; if to the right, the con-
dition is exophoria. Next place a 10 or 12 centrad base in over left eye, if
the left cross is below, then there is left hyperphoria, if above, then there
is right hyperphoria.

The writer, however, is partial to the Maddox Scale
shown in Fig. no. The Narrow Lined Cross with
central dot is also popular and is not without merit
(Fig- 113)-

CHAPTER VIII

PRISM TREATMENT FOR HETEROPHORIA AND
HETEROTROPIA1

As ametropia is the most common cause of insuffi-
ciency (and of squint), the first consideration must be to
select the proper correcting glasses. After this has been
accomplished, if the insufficiency still persists and the
patient is not comfortable, then the muscular imbalance
should receive careful attention, and the condition of
insufficiency be studied from every point of view.

The prescribing of prisms, as a fixed rule, for per-
manent use, which neutralize an insufficiency, except
in vertical errors, or for old people (see Exophoria) is
often a serious mistake, as in most instances prisms
often do more harm than good by increasing instead of
diminishing the insufficiency.

Remarks. — Patients with heterophoria cannot all be
prescribed for alike with the expectation of equally
good results in every instance and the writer from per-
sonal experience divides these cases into two classes :

Class i embraces those who are not presbyopic and
can use one pair of glasses for all purposes of distant and
near vision.

1 As the treatment of the extra-ocular muscles other than by prisms has
been fully explained in the Author's work, "Refraction and How to Re-
fract," the reader is referred to that volume.
8 II

PRISMS

Class 2 embraces those who are presbyopic or those
who require two corrections, one for distant vision and
another for near work, or bifocals.

Exophoria. — (Fig. 114). Because the tests for
heterophoria at 6 meters show an ability on the part of
the patient to maintain equilibrium, it must not be
supposed that there may not be a latent insufficiency.

FIG. 114. — Tendency of visual axes outward.

The normal ratio of adduction to abduction (three to
one) should be taken into consideration in every instance
before coming to any definite conclusion.

After the proper correcting glasses have been pre-
scribed and the patient's general health looked after,
attention if necessary, should be directed to strengthen-
ing the weak innervation and to do this a certain amount
of systematic exercise known as ocular gymnastics

HETEROPHORIA AND HETEROTROPIA 11$

must be employed. That success may result from
ocular gymnastics means perseverance on the part of the
patient and the exercises systematically executed.
There are two methods of procedure to strengthen
innervation in cases of exophoria :

Adduction Exercise. — i. Have the patient "fix"
with both eyes the point of a pencil, or the end of his
finger held at arm's length and slowly draw it to a
point 5 or 3 inches from the bridge of his nose. If
diplopia results while doing this, the exercise should
cease, and be repeated at once from the original dis-
tance. This is a very convenient exercise and should be
practised for five or ten minutes after meals; never be-
fore a meal, as some patients become nauseated if the
stomach is empty. This mode of exercise to developed
adduction, while equivalent to the use of prisms, is
much better in every way than by prism exercises ; in
fact, the writer has long since abandoned exercises with
prisms for cases of exophoria.

Prism Exercise. — 2. The patient is placed, standing,
about a foot or two from a point of steady light, on a
level or slightly below the level of the eyes, and told to
look at it and at nothing else. In this position a pair of
weak prisms (2 or 3 centrads), bases out, in the trial-
frame are placed in front of his eyes.

Then he is told to walk slowly backward^across the
room, as he keeps his eyes fixed on the point of light.
Should diplopia develop at any distance short of 20 feet,
then he is to raise the prisms, go back to his original
position, and start over again. Repeating this a num-
ber of times in the surgeon's office, it will be found in

Il6 PRISMS

most instances, that at this first practice a pair of 5 or
10 centrads can be overcome at a distance of 20 feet.
When the distance of 20 feet from the light is reached
without developing diplopia, the patient is instructed
to slowly count 20 or 30 (keeping the light single during
this time by careful fixation), then raise the prisms
(gazing at the light), and slowly count 20 or 30 again.
This exercise is repeated three times a day after meals
and a number of times at each practice. A prescrip-
tion is then given for such a pair of square prisms
with a convenient frame to wear over the patient's
glasses, and with these the patient continues the exer-
cises at home. These exercises should, as a rule, be
conducted with the patient wearing his correction.
Instead of the prism-frame the patient may hold the
square prisms with his hands ; but these are tiresome to
hold, and for general use the prism-frame, if not too
heavy, is preferable. After a few days practice at
home, the patient returns, and stronger prisms which
will permit the patient to maintain single vision are
again ordered. This practice with stronger and
stronger prisms is renewed weekly or bimonthly
until the patient is able to overcome prisms greatly
in excess of the normal ratio of adduction to abduction.
It is often well to develop the innervation power of
adduction to three or four times the strength of abduc-
tion; for when the exercises are stopped, some of the
adduction power will rapidly disappear.

It has been incidentally mentioned that prisms should
not be prescribed in combination with the ametropic
correction for the treatment of insufficiency, and yet

HETEROPHORIA AND HETEROTROPIA 117

there is an occasional exception to this statement for
patients who must have prompt, though temporary,
relief. When ordering prisms as a temporary expe-
dient, it is best to prescribe them in the form of " hook
fronts," so that they may be thrown aside at any time.
What has just been stated in regard to treatment exer-
cises applies particularly to patients in Class i.

Treatment of Class 2. — Patients in this class, as
just stated, are usually presbyopic and therefore re-
quire two corrections. Presbyopes with exophoria have
reached a stage in life when it is difficult or almost im-
possible to put new life into old structures, and it does
seem as if the extra-ocular muscles like the ciliary
muscle were no exception to this statement; and this
fact becomes more and more evident as the patient passes
beyond fifty years of age. Developing adducting power
by practising fixation at 33 centimeters may accomplish
a great deal of good in some young presbyopes, but
taking a presbyope of fifty or fifty-five or sixty years of
age and trying to develop adduction with fixation or
prism exercise is, in almost every instance and with few
exceptions, a waste of time and patience. Presbyopes
do not take kindly to such treatment and, in the writer's
experience, patients so treated soon seek assistance
elsewhere.

In hyperphoria the full prismatic correction (except
in cases of presbyopia) is seldom ordered, only about
two-thirds or three-fourths of the amount is pre-
scribed and, if of high degree, this amount is usually
divided between the two eyes, base down before one,
and base up before the other.

Il8 PRISMS

Testing the muscular condition at 33 centimeters
with the presbyopic near correction before the patient's
eyes, there should be about ten1 centrads of exophoria
normally at this distance, but if there happens to be
12, 14 or 1 6 centrads of exophoria then the presbyope
is uncomfortable and complains correspondingly when
using the eyes at near work for any length of time. The
prism treatment for exophoria at the working distance
in presbyopes is to add or prescribe prisms bases in
to be made in the near correction. The amount of the
prism to be so ordered is usually divided between the
two eyes. As 10 centrads of exophoria is considered
normal for this distance of 33 centimeters as just men-
tioned, then the amount of prism prescribed will be
practically the amount shown in excess of the normal 10
centrads. For example, a patient at fifty years of age
selects for each eye plus one sphere periscopic and has a
vision of yj in each eye with this correction and does not
reveal any insufficiency at six meters, but with the near
correction added (plus 2 sphere is added for near), then
at 33 centimeters there is found to be 16 centrads of
exophoria. After using these glasses for a few days at
home the patient returns complaining that at close
work the eyes pain, feel sore to the touch, and there
develops occipital headache, smarting of the lids, and
blurred vision. The exophoria in this instance at 33
centimeters is 6 centrads in excess of the normal amount.
Ordering this amount (six centrads) divided between

1 Some authorities say five.

HETEROPHORIA AND HETEROTROPIA 1 19

the two eyes, the patient will receive one of the following
prescriptions :

I£. O. D. +1.00. S. D. Periscopic.
O. S. +1.00. S. D. Periscopic.
SIG. — For distance.

Also,

]$. O. D. +3.00. S. D. O 3 centrads. Base in, axis 180°.
O. S. +3.00. S. D. o 3 centrads. Base in, axis 180°.
SIG. — For near only.

Or,

R. O. D. +3.00. S. D. decentered in 10 mm.
O. S. +3.00. S. D. decentered in 10 mm.
SIG. — For near only.

Or,

1$. O. D. +1.00. S. D. Periscopic.
O. S. +1.00. S. D. Periscopic.
SIG. — For distance.

Cement on to lower part of the above for near.

]$ O.D. +2.00. S. D. O 3 centrads. Base in, axis 180°.
O. S. +2.00. S. D. o 3 centrads. Base in, axis 180°.
SIG. — Make bifocals.

If another patient had two or three centrads of
exophoria at 6 meters with the same correction (i.oo
S. D. Periscopic in each eye) it would not be wise to
give any distance correction, but allow him to use his
relative hyperopia and at the same time to prescribe
the fixation exercises if he becomes uncomfortable hi
the use of his eyes at a distance.

Esophoria (Fig. 115). — As esophoria is a tendency of
the visual axes to deviate inward, it will be found that
some patients with this form of insufficiency, when of two
or three or four centrads, suffer very little, as a rule, when
using the eyes at near work; their chief discomfort

120

PRISMS

arises from using the eyes for distant vision. The
" shopping headache," the " opera headache," the
"train headache," may be due to this form of insuffi-
ciency, as well as in some cases of exophoria, but it is not
so apt to cause discomfort if the full ametropic correction
is worn constantly. In other words, if a hyperope with
esophoria does not wear his distance correction and

FIG. 115. — Tendency of visual axes inward.

accommodates at the same time that he endeavors to
maintain equipoise (relative hyperopia), he may at times
suffer severely. If the symptoms of muscular asthenopia
persist after prescribing the full ametropic correction,
then prisms, bases out, may be prescribed as hook fronts
to be worn over the constant correction when using the
eyes for distance. Prism exercises (prisms, base in) for
esophoria do not always benefit, and are occasionally a

HETEROPHORIA AND HETEROTROPIA 121

waste of time; yet they should be tried thoroughly if
the case appears to demand it.

When the patient has several centrads of esophoria for
distance he must use his full distance correction and this
usually corrects any former discomfort in the use of his
eyes for distance ; but he may continue to have discom-
fort at any near work, such discomfort as ocular pains,
occipital headache, pains running into the neck and
sometimes felt in the shoulders. Such patients do not
have any comfort from their eyes when reading or writ-
ing or at any close work which requires the eyes to move
instead of remaining fixed. For instance, a sewing
woman will come with the story that she can sew with
comfort with her glasses on, but that she cannot read
with comfort and she cannot understand why. A
stenographer who runs the typewriter during the day
suffers from the symptoms just described, yet she can sit
and sew in the evening and not get a headache. The
trouble lies in weak abducting power. The question
of treatment in such cases is not to weaken adduction
but to strengthen abduction. The writer's method of
treatment, which he believes to be original, is to practise
abduction or turning outward of each eye while its
fellow is covered. This is illustrated in Fig. 116. The
patient is told to fix his head in one position and not to
turn if while practising, as follows: to cover the eye
with a card as shown in the illustration and in such
manner that the covered eye cannot see what the other
eye is doing; then, holding the index-finger point on a
level with the eye, the finger is gradually made to de-
scribe a quarter circle or more to the same side as the

122

PRISMS

eye being exercised; the eye fixes the point of the finger
to the limit of external rotation. First one eye and then
the other eye is exercised in this way for five or ten min-
utes after each meal. Marked improvement will follow
this treatment in a few days, and the writer can testify
to some remarkable results by this very simple method

FIG. 116.

of strengthening abduction. Occasionally this practice
alone will not suffice and the patient will also have to
use prism exercises (prisms, bases in).

Hyperphoria. — Having prescribed the ametropic
correction, an attempt should be made to develop the
innervation of the weak muscles by prism exercises;
prism base down before one eye, and base up before the
other eye. While this does not often give satisfactory

HETEROPHORIA AND HETEROTROPIA 123

results, yet it should be tried in each instance. If prism
exercises do not correct the difficulty, then prisms which
overcome most of the insufficiency should be prescribed
with the ametropic correction for constant use. See
Presbyopia.

Hyperesophoria and Hyperexophoria. — The hy-
perphoria as previously stated and directed is to
be corrected by the necessary prism which is to be
combined with the ametropic correction and the re-
maining esophoria or exophoria to have any required
treatment as described under these headings.

Heterotropia ("Cross-eye," strabismus, squint or
manifest squint). — This is a condition of the eyes in
which the amount of turning of the eye is so great
that it cannot (always) be overcome by the effort
of the patient; and, in fact, inspection often shows the
manifest condition. Or heterotropia may be defined
as the condition in which the visual axis of one eye is
positively deviated from the point of fixation. The eye
which has the image of the object on its fovea is spoken
of as the fixing eye, while the other eye is termed the
squinting or deviating eye. The squinting eye does
not always have normal visual acuity; and, in fact,
correcting lenses will not always produce such a
result.

As ametropia is the chief factor in the cause of squint,
this cause must be promptly removed by the use of cor-
recting glasses.

The correction of the ametropia means four essentials :

i. In young subjects the eyes must be put at rest, and
kept at rest for two, three, or four weeks, with a reliable

124 PRISMS

cycloplegic and dark glasses. Preference is given to
atropin in each instance, the writer considering it folly
to use homatropin in such cases.

2. During the use of the cycloplegic, the lenses which
correct the ametropia are selected with care and the
greatest precision, by every known means to this end;
and just here is the place of all places to use the retino-
scope, as most cases of strabismus appear in children,
and, too, the squinting eye often being amblyopic, can-
not assist in the selection of the glass.

3. The correcting glasses are ordered in the form of
spectacles, and are to be worn from the time of rising
until going to bed. The strength of the glasses should
be as near the full correction as it is possible to give.

4. The "drops" are continued for a day or two after
the glasses have been obtained, and in this way, while
the drops are still in the eyes, and as their effect slowly
wears away, the eyes gradually become accustomed to
the new or natural order of accommodation and con-
vergence. After the cycloplegic has entirely disap-
peared, the patient should be carefully restricted in the
use of the eyes for near-work for several days or
weeks.

As hyperopia and astigmatism in combination are
generally congenital conditions, it therefore follows that
convergent squint appears quite early in life, as soon as
the child begins to concentrate its vision on near objects.
The squint, at first periodic or intermittent, finally
becomes constant. Such eyes should be refracted at
once, and before amblyopia exanopsiacan be established,
prisms should not be ordered. It is interesting to note

HETEROPHORIA AND HETEROTROPIA 125

that the eyes in many young children begin to fix or lose
their squint as soon as cycloplegia is established. The
prognosis is favorable for good vision with glasses
when this occurs. It will also be observed in other
subjects that while the drops are in the eyes and glasses
worn constantly, the squint disappears entirely; but as
soon as the cycloplegia passes away and near vision is
attempted, the squint returns, and vision falls back in
the squinting eye to almost the same point that it had
before the cycloplegia. This occurs in cases in which the
amblyopia is becoming established, or when there is a
strong muscle deviating the eye. If the squint is due to

FIG. 117.

amblyopia exanopsia, then the vision may be improved
in one of two ways. One way is to use drops in the
fixing eye, and thus compel the squinting eye to do the
seeing; or the other way is to cover the fixing eye with a
blank over the glass (see Fig. 117), and have the patient
practise in this way for one or two hours each day, using
the squinting eye alone.

Worth's Amblyoscope or "Fusion Tubes." — To
cultivate or develop binocular vision Worth has given
us an instrument which he calls an amblyoscope. (See
Fig. 1 1 8.) This instrument consists of two halves
joined by a hinge. Each half consists of a short tube

126 PRISMS

joined to a longer. one at an angle of 120°; at the
junction of the tubes is an oval mirror. A translucent
glass object slide is placed at the distal end of each tube.
At the hinged ends are lenses whose focal length equals
the distance of the reflected image of the object slide;
in front of these lenses are grooves into which additional
lenses of the trial case may be placed to correct the
refractive error of the patient. The two halves of the
instrument are united by an arc, having a long slot at
one end and an adjusting screw at the other. The object
slides can be brought together to suit a convergence of

FIG. 118. — Worth's Amblyoscope. (Reduced size.)

60°, or a divergence of the visual axes of 30°. When
the adjusting screw is used an additional movement of
10° is obtained.

At the far end of each tube there is also a square slot
into each of which may be placed half a pictured object;
for instance, a picture of the right side of a man, showing
his arm and leg extended, may be placed in the left tube,
and in the right tube is placed a picture of the same size,
of the left side of the man with his leg and arm similarly
extended. When the patient looks into the tubes, the

HETEROPHORIA AND HETEROTROPIA 127

surgeon (or the patient) may adjust the tubes until the
two half pictures unite and form one complete picture.
Or the picture in one tube may be a picture frame, and
in the other tube is a picture of an animal or an object,
the idea being to have the patient so fuse the two pictures
that the object is placed in the frame. There are many
different pictures accompanying the instrument so as
to give variety to the daily exercises and thus maintain
the patient's interest. This instrument is certainly a
valuable one and in many instances (in patients under
seven years of age) accomplishes its purpose.

Cases that are cured by correcting the ametropia
must wear their glasses constantly. Glasses in such
cases can seldom be abandoned. In young children the
squint returns almost at the instant the glasses are
removed. The earliest age at which glasses can be
prescribed is three years or thereabouts, as it would
be unreasonable in most cases to expect a child to
appreciate the glasses as anything but a toy before
this age.

The younger the patient when glasses are prescribed,
the more favorable the prognosis and less likelihood of
a tenotomy. The older the patient when glasses are
ordered, the less the likelihood that glasses will cure the
squint and the greater probability of a tenotomy being
necessary. This is explained from the fact that the
squint having persisted for a long time, the muscle
which held the eye in the deviated position has grown
strong and the opposing muscle weak.

The correction of squint by glasses applies particu-
larly to cases of the concomitant (convergent or diver-

128 PRISMS

gent) form. Vertical squint is seldom cured by cor-
recting glasses alone. Prisms should not be prescribed
for the correction of heterotropia.

Monocular and alternating squint are greatly relieved
by the correction of the ametropia, and may or may not
be cured with glasses alone.

Periodic or intermittent squint, if due to permanent
opacities in the media, cannot, as a rule, be cured by
any form of treatment, but may be benefited by the
prescribing of a prism to be referred to later.

It may be stated as a good rule to follow that no case
of squint should ever be operated upon until the glasses
which correct the ametropia have been worn constantly for
several weeks after all apparent improvement has ceased.
If cases for operation can be selected, the best age is
about puberty, when the muscles have reached a fair
state of development. If the squint is due to an ana-
tomically short muscle, then there need not be any
great delay in operating after glasses have been ordered.

Whenever a tenotomy has been performed, the eyes
should again be carefully refracted, as it is a well-
established fact that tenotomy often relieves a tension
that will materially change the radius of corneal curva-
ture ; and hence the amount of the astigmatism and the
cylinder axis will be altered.

Final Summary. — From the descriptions just de-
tailed it will be observed that prisms are seldom pre-
scribed and the careful refractionist will not order
prisms with freedom or impunity. There are five con-
ditions, however, which warrant the prescribing of
prisms as follows:

HETEROPHORIA AND HETEROTROPIA I2Q

Hyperphoria. — As previously stated, the patient with
hyperphoria will usually accept and wear a prism which
corrects about three-fourths of the amount of the hyper-
phoria, and this amount may be divided between the
two eyes depending, of course, upon the strength of the
prism and also upon the strength of the correcting lenses.
If the amount is one or two centrads which is to be pre-
scribed, this may all be placed before one eye if the
lens for the other eye is a strong or compound one, for
instance, if the prescription is as follows:

O. D. +2.ooO + i.oo cyl. axis 60°
O. S. +1.00

and the prism is a 2 base down before the right eye, it
would be well to place the prism base up before the left
eye making it + i.ooO2vbase up axis 90° and in this
way equalize somewhat the weight and thickness of the
lenses for the two eyes. In this instance it would have
made a very expensive, cumbersome and heavy lens
for the right eye, if the prism had been added to it,
namely,

O. D. + 2.ooO + i.oo cyl. axis 6oO2A. Base down
axis 90°.

In other words the prescriber must use some judgment
in the matter as to which eye is to receive the prism
or whether to put the entire prism before one eye or
divide it between the two.

Ordering a Prism after a Tenotomy. — When a
tenotomy has been performed for the relief of an insuf-
ciency or manifest squint, and there still remains an

130 PRISMS

annoying imbalance, a prism that assists the weak
innervation may be prescribed for constant use made
up in the lens which corrects the refractive error. For
instance, if the tendon of the left internal rectus has been
divided on account of a squint and after the tenotomy
there remains possibly 3, 4 or 5 centrads of esophoria;
the patient may have a 3, 4 or 5 centrad prism ordered
with the ametropic correction, the base of the prism to
be placed base out axis 180° over the left external rectus.
It might be well to remember when prescribing prisms
after a tenotomy that the base of the prism is to be
placed over the weak muscle.

Ordering Prisms in Presbyopia. — This has already
been explained in great part on page 119. However, the
prescriber should be on his guard and never prescribe
too strong a prism in the reading or near glasses, a prism
in other words that would produce annoying metam-
orphopsia. The way to guard against this is to place
the prisms (bases in) over the near correction and let
the patient read the paper or look at a plane or flat sur-
face, such as the top of a table or a desk and note whether
the paper or table or desk appears conspicuously con-
vex, i.e., raised in the middle. If slightly so, then the ap-
pearance of convexity will gradually disappear after
wearing the glasses, but if this condition is extreme, then
the strength of the prisms must be reduced. Prisms,
bases in, at close work may produce the convex effect
just described and prisms, bases out, for esophoria may
produce the opposite or concave effect.

Prisms for Cosmetic Purposes. — When an eye
squints or is turned by reason of injury or disease

HETEROPHORIA AND HETEROTROPIA 131

(corneal opacities), or very poor vision or a palsy, and
is not a suitable one for surgical intervention, the wear-
ing of a prism over such an eye may give it a more
sightly appearance, thus making it appear nearer the
normal position than it actually is.

Prisms for Cyclophoria. — Cyclophoria is not a com-
mon condition. It is the least common of the hetero-
phorias and yet it does exist and when present it should
be prescribed for in full with a correcting prism, using
either one of the three tests for Cyclophoria already
described in Chapter VII.

It is hoped that the reader will not confuse hyper-
esophoria and hyperexophoria with cyclophoria. The
descriptions under these headings should guard him
against any such error in diagnosis.

A prism at an oblique axis while it may temporarily
neutralize an hyperesophoria or hyperexophoria does
not necessarily signify that cyclophoria exists. Hyper-
esophoria and hyperexophoria are to receive the neces-
sary prism for the hyperphoria only, i.e., prism base
up or down, axis 90. (See Hyperesophoria.) The
writer does not advocate prisms at oblique axes except
in cyclophoria and cyclotropia.

When the diagnosis is made then the amount of the
cyclophoria is estimated by the strength of the prism
which is necessary to make the lines parallel as shown
in Fig. 104. The base of this prism may be up or down
and at an "off axis," and before the eye which has the
cyclophoria. The prism is to be combined with the
prescription glasses for constant use.

Cyclotropia is to be prescribed for in the same way

132 PRISMS

as cyclophoria. Cyclotropia is a very rare condition.
The writer never saw but one such patient and he re-
quired the following:

O. D. +2. 750+0.50 cyl. axis 15°

O. S.+2.75O 2A. Base down axis 30°.

These glasses the patient is wearing with great comfort
and satisfaction:

Summary : — Cases of hyperopia with 2 or 3 centrads
of esophoria for distance and near vision are usually
made comfortable for all purposes with a full correction
of the refractive error. By 'full correction' is meant
the cycloplegic correction less 0.25 sphere.

Cases of hyperopia with orthophoria for infinity and
possibly 2 or 3 centrads of exophoria for near should
receive 0.50 or 0.75 less than the full cycloplegic cor-
rection to be worn constantly.

Cases of hyperopia with exophoria of 3 or 4 centrads
for distance should receive a partial correction of the
hyperopia and be instructed in convergent exercises.
When the exophoria disappears and orthophoria or
esophoria is present the hyperopia should receive further
correction. The writer's experience while it may differ
from others, docs not warrant him in advising a prism
in these cases.

Cases of myopia with exophoria should receive the
full static correction if the eyes are apparently free
from fundus changes.

Cases of myopia with esophoria should receive an
under correction, or be prescribed for as if they were

HETEROPHORIA AND HETEROTROPIA 133

presbyopes, i.e., one correction for distance and another
for near.

Hyperphoria associated with any of the above men-
tioned cases should receive the necessary prismatic cor-
rection, see page 129.

CHAPTER IX

GENERAL REMARKS ON PRISMS AND THE
PRISMATIC EFFECT OF LENSES

That muscle over which the base of a prism is placed
is put at rest to the extent of the power of the prism so
used ; or the prism may be said to act as a sedative to the
muscle over which its base is situated. That muscle
over which the edge of a prism is placed is put into
action to the extent of the power of the prism so used,
the prism may be said to act as a stimulant to the
muscle over which its edge is situated.

Prisms with their bases in or bases out could be worn
if the eyes would remain fixed, but on account of
accommodation and convergence prisms for the relief
of esophoria and exophoria in young patients cannot be
tolerated. A prism with its base up or down for the cor-
rection of hyperphoria is tolerated and accepted because
in these positions the accommodation and convergence
do not alter the prism effect in the vertical meridian.

There are several reasons why prisms bases in or out
stronger than a unit cannot be worn constantly and with
comfort, but the chief reason is the resulting metamor-
phopsia or distortion which appears when the patient's
eyes are turned laterally from the center of the lenses.

Illustrations which give some idea of distortion may
be seen in Figs. 39, 40, 41 and 42.

Another reason why prisms which correct esophoria

134

GENERAL REMARKS ON PRISMS 135

and exophoria cannot be worn constantly, is that by
stimulation they soon increase the amount of the
esophoria or exophoria and it is therefore very bad
treatment to prescribe prisms in these cases, except in
the instances mentioned in the text.

It seems hardly necessary to explain to the reader that
(i) a convex sphere is equivalent to prisms with their
bases at the center of the sphere; (2) that a concave
sphere is equivalent to prisms with their edges at the
center of the sphere ; (3) that a convex cylinder is equiva-
lent to prisms with their bases at the axis of the cylinder
and (4) a concave cylinder is equivalent to prisms with
their edges at the axis of the cylinder; i.e., (a) on the
axis of a cylinder there is no prismatic effect and (b) at
the true center of a sphere there is no prismatic effect.

Strong convex spheres worn before both eyes, by an
adult for the first time (as he looks through the true cen-
ters of these lenses), produce the effect of making a flat
surface appear convex or raised in the middle and as the
eyes look downward through the lenses (below the true
centers) at the floor, it appears as if it were further away
than it actually is or further away than it did without the
lenses; giving the patient the sensation of having sud-
denly grown taller, i.e., the sense of "distance" with
these lenses, has been more or less disturbed. If the
convex spheres are each + 3 and the patient glances
through them 10 millimeters below the centers, he has
the effect of seeing through a pair of 3 prisms bases
upward. If he looks through these same lenses 10
millimeters above the centers an object appears shorter
than it actually is, or if the patient tips his head far

136 PRISMS

enough over and looks through the lenses above the
centers at the floor, the floor seems closer than it is
normally and the patient has the sensation of having
grown shorter in stature.

Such complaints are not uncommon and are due
entirely to the prismatic effect of the lenses.

Strong concave spheres worn before both eyes, by
an adult for the first time, produce the opposite effect
to that of convex spheres. The pavement or flat surface
appears "dished" or hollowed out. If the spheres are
—3 and the patient looks downward through them 10
millimeters from the centers, he has the equivalent of
seeing through a pair of 3 prisms bases down; the floor
or pavement appears raised or closer than without the
lenses, the patient feels as if he had suddenly grown
shorter and the sense of distance is correspondingly dis-
turbed. If he looks through these lenses 10 millimeters
above the centers, he has the sensation of feeling taller,
for now the prismatic effect is equivalent to prisms bases
up and distant objects appear elongated vertically
(Figs. 39 and 40).

These optic illusions are also conspicuous with some
patients as they turn their eyes from right to left or
left to right. Some patients cannot explain exactly
what the sensation may be except to say that they feel
more comfortable without glasses and would rather
endure poor vision than wear them. It is not always a
case of "vanity."

Prismatic effect is more evident with certain varieties
of spheres. Some patients cannot wear toric lenses (or
menisci) for this very reason, they cannot get accustomed

GENERAL REMARKS OX PRISMS 137

to toric lenses but still they can wear plano-convex
lenses. The writer has seen patients who could not
even wear periscopic lenses on account of the distortion,
and wonder how others wear them and they cannot.

Nearly all of these patients will admit that they can
wear their spheres with pleasure and comfort, it they
do not walk around with them on or turn their eyes
from side to side and look through the edges of their
lenses. In other words these patients have no trouble
as long as they keep their visual axes on the line of the
true centers of their lenses, but when they turn the visual
axes from the true centers, then discomfort comes on
and persists until the glasses are removed. Of course,
and fortunately all patients are not alike in this re-
spect, in fact, it is the very few who are thus disturbed.
Finally some of the prismatic effect may be the result
of poorly fitting lenses, and naturally this fact must
have first consideration. However, it must be ad-
mitted, that there are different nervous sensibilities in
different patients. Any observer along these lines has
many opportunities of seeing individuals wearing strong
lenses that are so out of adjustment that one would
imagine the resulting metamorphopsia would be suffi-
cient to produce migraine, but the truth is, very likely
the individual is only seeing with one eye at a time or
possibly has "nerves of steel."

A Strong Convex or Concave Sphere before One
Eye and a Weak Lens of Any Variety before the
Other Eye. — Adults whose eyes require such lenses
also occasionally suffer from metamorphopsia before
they get accustomed to their glasses, but the distortion

138 PRISMS

complained of is more of the tilting variety, that is to
say, in looking at a plane surface, one side seems to slope
upward or downward. The pavement or floor seems
raised or lowered to the right or left as the case may
be. Yet again the wearers of such lenses usually have
comfort as long as they do not turn their visual axes
from the true centers of the lenses.

A Strong Convex or Concave Cylinder before
One Eye and a Weak Lens of Any Variety before
the Other Eye. — Such a pair of lenses may with some
adults produce metamorphopsia similar to that experi-
enced by patients who require a strong sphere before
one eye, but if the cylinder axis is oblique, then these
patients have a metamorphopsia similar to the picture
shown in Figs. 41 or 42. These patients do not see
picture frames as square-cornered but rather of the
appearance of a rhombus.

Remarks. — Young patients (children) if required to
wear correcting glasses such as first mentioned, seldom
refer to any distortion but seem to adapt their vision to
the glasses without difficulty.

Many patients who suffer from metamorphopsia also
temporarily may have muscular imbalance, esophoria,
exophoria or cyclophoria, etc., that they never knew or
complained of before getting glasses, and possibly the
metamorphopsia is due as much to the temporary
cyclophoria as to the prismatic effect of the lenses;
however, it is for the patient to persevere and wear the
lenses and train his innervation, otherwise there must be
a compromise in his lenses by reducing their strength and
from time to time give stronger lenses up to the strength

GENERAL REMARKS ON PRISMS 139

of the necessary lens to correct the ametropia. Prisms
are not to be prescribed for such cases of cyclophoria
or temporary hyperphoria.

With all these cases of anisometropia and hetero-
metropia, the wise prescriber will have such patients
test their vision by looking at picture frames, the door,
the floor, etc., in his office before ordering the glasses
and in this way make sure just how much distortion does
exist and let the patient know what to expect.

Prismatic Effect in Bifocal Segments. — At the true
center of a lens there is no prismatic effect, but from
this center to the edge of the lens, the prismatic effect
gradually increases and the stronger the lens, the
greater this prismatic effect, no matter whether the lens
is convex or concave. With this understanding the
prescriber must bear in mind when he orders segments
(scales or wafers), placed on the distant correction to
make bifocals, that it is the duty of the optician to
place enough prism in each segment to counteract
sufficiently the prismatic effect at the edge of the lens
used for distant vision so as to give the segment a
mid-center of its own.

If the strength of both distance lenses is the same
then the prism in each segment must be the same, but
if the strength of the distance lenses is not the same,
then the strength of the prism in each segment must be
different.

The prescriber must be on his guard for this con-
dition of things and the prismatic element at the edge in
the distance glasses must be eliminated in part by each
segment separately.

140 PRISMS

The reader can readily understand for himself that
if the patient's distance glass was —9.00 sphere in the
right eye, and —6.00 sphere in the left eye, and +3
segments are to be added, the optician must add more
prism base up to the right segment than to the left seg-
ment, otherwise such a patient would be getting a false
hyperphoria when using the segments.

It is not uncommon to hear patients complain that
they have tried bifocals and could not wear them;
possibly the segments were not centered.

Prismatic combinations in bifocals were described
under class 2, presbyopes, page 119.

In conclusion and that the reader may not become
confused as to the effect of prisms, the writer takes
great pleasure in quoting his friend Dr. G. C. Savage
who says that "when a prism base in or base out is
placed before one eye, only one nerve center is excited
and only one muscle is brought into a state of contrac-
tion." "When the base is placed up or down, it must
excite two centers, one to elevate or depress the eye,
the other to prevent torsion."

INDEX

Abduction, 79, 80
Aberration, prismatic, 30

astigmatic, 30

chromatic, 30
Accommodation, 134
Achromatic prism, 9
Adduction, 79, 80
Air, 14, 15

American Medical Association, 47
Ametropia, 113

Amblyoscope, Worth's, 125, 126
Angle, apical 21

critical, 12, 13

deviation, 20, 21

meter, 107, 108

refracting, 3

of incidence, 13

of refraction, 3

tangent of, 17, 1 8
Anisotropic medium, 9
Apex, i, 2, 6, 7
Arc, 16, 17

of angle, 16

of radian, 17

Arrow-scale of Moddox, 109, no
Astigmatism, prismatic, 30
Author's prism scale, 48, 49

truncated prism, 90, 91, 92,93
Axis of cylinder, 6

of prism, 7, 8, 9

visual, 63, 64

Bar of prisms, 4
Base-apex line, 67

of prisms, i, 2, 3, 4, 5
Battery of prisms, 4
Bifocal segments, 139, 140

Center, geometric, 61,62

optic, 62, 63

true, 63

Centimeter scale, 50
Centrad, 41, 42
Circle, 16, 17

Circular prism, 4, 5, 6, 7, 8
Cobalt-blue glass, 85
Cone, 86

Convergence, 107, 108
Cosmetic purposes, 130, 131
Cret6, 58
Crown glass, 15
Critical angle, 12, 13
Cyclophoria, 99, 100, 101, 131
Cyclophorometer, 103, 104
Cyclotropia, 131
Cylinder, 68, 69, 70, 138

Decentered lenses, 65, 66, 67, 68,

69, 70, 71, 72, 73, 74
Decentering, 64, 65

tables for, 75, 76, 77
Deflection, 10, n, 19
Degree prisms, 40, 41
Dennett, Dr., 41, 42, 44, 45, 47
Density, 10, n, 15
Deviation, 10, n, 19

angle of, 18, 19, 20, 40

maximum, 19

minimum, 20
Diamond, 14
Diplopia, 57
Dispersion, 33, 34
Displacement, 23
Distortion, 33
Divergence, 78

141

142

INDEX

Dot and line test, 82

Double prism, 85, 86, 90, 91, 92, 93

Edge, i, 2, s, 6, 7
Equilibrium, 81
Equipoise, 81
Esophoria, 83, 119, 120, 121

at distance, 119, 120, 121

at near, 119, 120, 121

exercises for, 119, 120, 121
Exercising prisms, 115, 120
Exophoria, 83, 84, 119, 120

at distance, 119, 120

at near, n

exercises for, 115, 116
Eyes, 107, 108

equilibrium test, 82
Eyelashes, 5
Eyelids, 5

Faces, i, 2

Fixing eye, 123

Flint glass, 15

Fresnel's lighthouse apparatus, 28

Fusion tubes, 125, 126, 127, 128

Geneva lens measure, 72
Geometric center, 61, 62
Glass, cobalt blue, 85

crown, 15, 1 6

flint, 15, 16

rod, 93, 94

ruby red, 85
Graefe, von, 82
Greek cross of Ziegler, 1 1 1

Herschel, 57
Heterophoria, 82
Heterotropia, 82, 123, 124, 125
Homogeneous, i
Hyperesophoria, 101, 123
Hyperexophoria, 101, 123
Hyperphoria, 84, 85, 122, 123, 129
Hypotenuse, 26, 27

Ice, 15

Illusion, 23

Images, 23

Incident, angle of, 12, 113

ray, 12

Inclined surfaces, i
Index, absolute, 13

of refraction, 13, 14, 15, 16
Inter-ocular distance, 108
Isoceles triangle, 26
Isotropic medium, 9

Jackson, Dr. Edward, 41, 60

Light, 28

Lighthouse, 28, 29
Lenses, 35, 36, 37, 38, 39

cylinder, 68, 69, 70, 138

decentered, 65, 66, 67, 68, 69,
70, 71, 72, 73, 74

prismatic, 64, 65, 66, 67, 68,
69, 70, 71, 72, 73, 74

spheric, 98, 135, 136, 137
Line cross, 112
Lines, 6, 7

Maddox, 85, 86, 87, 88, 89
Malingerer, 78, 79
Maximum deviation, 19
Media, anisotropic, 9

homogeneous, i, 9

isotropic, 9
Meter angle, 107, 108
Metamorphopsia 30, 31, 32, 33,
Minimum deviation, 20
Mirror plane, 21, 22
Monocular phorometer, 106

Noyes, Dr., 4
Neutralization of prism, 47,

5°, 51, 52, 53
Number of prism, 6, 40, 41

Ophthalmic Section, 47
Ophthalmology, i

48, 49

INDEX

Optic axis, 64

center, 35, 36

illusion, 23
Orthophoria, 81

Phorometer, 79, 101, 102

Crete's, 58

cyclo-, 104, 105

Jackson's, 60

Meister's, 103, 104

monocular, 105, 106

Prince's, 102, 103

Risley's, 59

Savage's, 104, 105, 106, 107

Steven's, 79, 101, 102
Position of prism, 7, 8
Prentice,Charles F. , 41 , 43 , 44, 45, 50

scale, 50
Presbyopia, 130
Prince, Dr., 102, 103
Principal section, 3
Prism, i, 2, 3, 4, 5, 6, 7, 8, 9

achromatic, 9

angle of, i, 2

axis, 7, 9

bar, 4, 5

base of, i, 2

cobalt-blue, 85

cone, 86, 87

circular, 4, 5, 6, 7, 8

combined, 54, 55, 56, 57, 58,
S9,6o

convergence, 79

definition of, i

divergence, 78

double, 85, 86, 90

effect of, 23

exercising, 115

face of, i, 2

general properties, Chapter III

neutralization, 47, 48, 49, 50

S1, 52, S3

nomenclature, 6, 40, 41
obtuse-angled, 85, 86

Prism, plane, 17

position, 7, 8

quadrilateral, 86, 87, 89, 90

rectangular, 3

ruby red, 85

rotary, 59

round, 4, 5, 6, 7, 8

section of, 3

shape of, 3

side of, i, 2

square, i, 2, 4, 5

surface of, i, 2

testing, 84

treatment, 115, 116, 117

Thorington, 90, 91, 92, 93
Prismatic aberration, 30

action, 18,19

astigmatism, 30

metamorphopsia, 30

scale, 30
Prism-diopter, 43, 44, 45

markings, 5, 6

measure, 41

sedative, 134
Prisme mobile, 58
Prismometric scale, 50
Projection of image, 23

Radian, 18
Radiants, 17
Rays, 13, 14

convergent, 22

divergent, 21, 22

parallel, 21, 22

reflected, 10, n, 22

refracted, 10, n
Rectangular prism, 3
Reflection, 27

total, 26, 27
Refracting angle, 3

surface, 2, 3
Refraction, Chapter II

index of, 13, 14, 15

laws of, 10, ii

144

INDEX

Refraction through prism, 17, 18, Strabismus, 123, 124

19, 20

Refractionist, 128
Risley, 59
Rock crystal, 15
Rod test, 93, 94, 95, 96, 97
Rotating prism, 50
Rotation of prisms, 55
Ruby red glass, 85

Savage, 104, 105, 106, 107, 140

Secondary rays, 62

Sine, 16, 17

Spectrum, 34

Sphere, spherical, 98, 135, 136,

137

Spirit level, 79
Square prism, i, 2, 3, 4, 5
Squint, 123, 124
Stevens, 79, 8 1

Sturm's interval, 30

Tangent, 17

scale, 98, 99
Tangents, 17
Tenotomy, 129, 130
Total reflection, 26, 27
Trial-frame, 5
True center, 63
Truncated prism, 90, 91, 92, 93

Unit prism, 41, 42, 43, 44, 45

Vacuum, 14

Visual axis, 107, 108

Von Graefe, 82

Worth, 125

Ziegler, Dr. L. S., 51, 52, in

UNIVERSITY OF CALIFORNIA LIBRARY

Los Angeles

This book is DUE on the last date stamped below.

Form L9-Series 4939

A 000386991 4

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