ON THE BINOCULAR METAMORPHOPSIA 
PRODUCED BY CORRECTING 
GLASSES 
BY 
J. A. LIPPINCOTT, M.D , Pittsburg, Pa. 
Reprinted from the Archives of Ophthalmology, Vol. xyiii., No. i, 1889. ON THE BINOCULAR METAMORPHOPSIA PRO- 
DUCED BY CORRECTING GLASSES. 
By J. A. LIPPINCOTT, M.D., Pittsburg, Pa. 
IN a recent number 1 of the Journal of the American 
Medical Association appeared an article (by Dr. H. Cul- 
bertson) which had been read before the Ophthalmological 
Section of the Association in May of last year, describing 
certain apparent changes in the forms of objects observed 
by some persons after the correction of astigmatism of one 
or both eyes. 
These changes were, in the article referred to, stated to 
be seen in regarding comparatively near objects, and only 
in binocular vision. A rectangular board, at the distance 
of a metre, appeared to be wider at one end than the other, 
and the floor seemed to slope to the right or left. With 
either eye singly, the phenomenon was not noticed. On 
rotating the cylinders a few degrees, the objects again ap- 
peared normal, and the radiating test lines of equal dis- 
tinctness. These apparent changes were attributed by the 
author of the article to a want of muscular balance, owing 
to which, in using both eyes, one eye (or both) rotates 
more or less on its antero-posterior axis, thus necessitating 
a corresponding rotation in the correcting cylinders; and 
this change in the eyes he denominates " binocular astigma- 
tism." 
Now the phenomena noticed began to attract my atten- 
tion, and what I conceive to be the true mode of their 
production occurred to me a number of years ago ; but the 
1 Nov. 3, 1888. 
Reprinted from the Archives of Ophthalmolq^A^ xvfiCT?^J. 1889. 19 
Binocular Metamorphopsia. 
matter did not seem to be of such engrossing importance 
as to develop an attack of cacoethes scribendi. The publica- 
tion of the above-mentioned article, however, illustrating, 
as I believe it does, the fact that an unscientific hypothesis 
is apt to be followed by improper treatment, prompts me to 
commit my reflections on the subject to paper. 
The literature of the subject is, so far as my opportuni- 
ties for investigation have gone, conspicuous by its absence. 
Donders, Stellwag, and other systematic writers speak of 
the effect of glasses in changing the form of retinal images, 
and Knapp,1 in pointing out the features of irregular astig- 
matism, mentions inter alia metamorphopsy-straight lines 
appearing curved, etc. But it is evident that monocular 
phenomena are referred to, and I can find no allusion to an 
apparent change in the forms of objects produced by correct- 
ing refractive aberrations, this change necessitating, as an 
essential condition, the existence of binocular vision. How 
necessary the latter is will, I think, appear in the course of 
this paper. 
The hypothesis of a change in the position of the meridi- 
ans of the astigmatic eye, either from rotation of the globe 
incident to muscular incoordination, or from a modification 
of the lenticular curvature incident to the act of accommo- 
dation, is, in my judgment, not satisfactory for the following 
reasons: (i) In the rather rare cases of actual paralysis or 
paresis in which there is an abnormal rotation of the globe, 
the abnormity evidences itself, and the relations of the 
objects are changed spontaneously; and no correction of an 
existing refractive error is required to bring out the defect. 
(2) The cases in which the astigmatic meridians occupy one 
position in distant and another in near vision, however the 
change may be brought about, are exceedingly rare; and, 
moreover, in such cases binocular vision plays no necessary 
role. (3) A fairly normal appearance of the radiating test lines 
after rotating the correcting cylinders in order to obviate 
a supposed rotation of the globe, by no means demonstrates 
a real correction of the astigmatic defect, because each eye 
supplements the other, and the deficiencies of each are thus 
1 Quoted by Power, Lond., 1868, p. 614. y. A. Lippincott. 
20 
neutralized or veiled. (4) The phenomena with which we 
are concerned are not rare, not even comparatively rare. 
On the contrary, they are to be seen in all cases of anisom- 
etropia with binocular single vision, with exceptions to 
some of which allusion will be made. The existence of an 
astigmatic defect is not a sine qua non, although the phe- 
nomena are especially noticeable in cases of astigmatism of 
one or both eyes, in which the chief meridians are oblique. 
When both eyes require cylinders of the same degree, 
the axes must be unparallel. When the glasses correspond 
in strength, and the axes in position (actual isometropia), 
any obliquity of the latter is compensated for by turning 
the head, and the observed objects are thus prevented from 
assuming an unnatural appearance. 
For the production of the phenomena described in this 
paper binocular single vision is necessary, because a means 
or standard of comparison is essential, and, as is well known, 
the field of accurate binocular fusion is quite limited, the 
mind receiving information from each eye, separately, in 
regard to its own side of all but very small objects. 
Before generalizing further on the subject of binocular 
metamorphopsy, it will be proper to illustrate some of 
its manifestations. These manifestations may, for sake of 
simplicity, be divided into two groups : (1) Those charac- 
terized chiefly by an alteration in the relative dimensions 
of the top and bottom of the object-unparallelism of the 
sides. (2) Those characterized chiefly by an alteration in 
the relative dimensions of the two sides-unparallelism of 
the top and bottom. 
Group I.- Top wider or narrower than bottom. (1) Sup- 
pose A., who rejoices in binocular single vision, requires, 
and is furnished with, R E-j- 1 D, L E 1.25 c, axis 60 °. 
On looking at a perfectly rectangular book, held upright, at 
ordinary reading distance, the right side of the book looks 
natural and perpendicular, whereas the left side appears to 
slope upwards and to the right, so that the top of the book 
seems to him narrower than the bottom. (2) Suppose R E 
fitted with 1 D and L E with -J- 1.25 c, axis 105 0, the 
right side of the book is normal, while the left side slopes 21 
Binocular Met amorphopsia. 
upward and to the left, making the top look wider than the 
bottom. (3) R E fitted with - 1 D, L E with - 1.25 c, 
axis 60 0 ; while the right side of the book remains natural, 
the left side slopes upward and to the left, and the book is 
wider at the top. (4) R E - 1 D, and L E - 1.25 c, 105 0 ; 
the left side now slopes upward and to the right, and the 
book is narrower at the top than at the bottom. (5) If A. 
be fitted with R E-f. 1.25 c, 100 °, L E 1.25 c, 60 °, the left 
side of the book will appear to slope upward and to the 
right, while the right side will slope upward and to the left, 
though not so much as the left side. Hence the book will 
appear narrower at the top than at the bottom, the loss in 
width being sustained mainly by the left side. (6) With 
R E fitted with 1.25 c, 80 °, and L E with 4- 1.25 c, 115 °, 
the book will seem wider at the top than at the bottom, the 
accession in width pertaining chiefly to the left side. To 
avoid repetition, the conditions of the last two cases will be 
reversed by substituting concave for convex cylinders. 
Finally, the form-changes described in the foregoing hypo- 
thetical cases can be observed by emmetropes before whose 
eyes cylinders are placed under the conditions stated above. 
The explanation of the above-mentioned phenomena will 
be obvious from a consideration of the annexed diagrams : 
PAOX may be taken to represent a convex cylinder with 
its edge turned toward the observer and with its axis, AX, 
oblique. It is scarcely necessary to add that each half AOX 
and APX may be regarded as a prism with its base at AX. 
KLNM is a surface parallel to the plane of the lens. It is 
clear that a ray of light, starting from the head of the verti- 
cal arrow, H, will fall to the distal (from the observer) side 
of the axis, and will thus be deflected by the prism APX J. A. Lippincott. 
22 
towards the proximal side, KL, of the surface KLNM, to 
the point H.1 Similarly a ray starting from F will come 
within the influence of the prism AOX, and will be deflected 
towards the distal side, MN, to the point F.1 Again, if in 
fig. 2 PAOX be a simple concave cylinder, thus consisting 
virtually of two prisms whose bases lie towards P and O, it 
is plain that the ray HH1 will be deflected by passing 
through the prism APX towards the distal side MN, while 
the ray FF1 will be refracted towards KL. Hence the 
image on the surface KLNM is inclined instead of vertical. 
It may be added that the deflection of the rays will be 
greater in proportion as the cylinder is stronger, and in 
proportion as the axis approximates the position midway 
between vertical and horizontal. 
Let us suppose KLNM, in fig. 2, to represent the retina 
of an emmetropic left eye before which is placed the - cyl. 
PAOX. In the retinal image the arrow-head will point 
downwards and to the left, and, by the well-known law, the 
mental image will be projected in the opposite direction, so 
that the arrow will appear to be inclined upwards and to the 
right. 
Now, we may, for our present purpose, consider an eye 
affected with simple HAS as equivalent to an emme- 
tropic eye with a concave cylinder, such as PAOX (fig. 2), 
placed in front of it. In like manner we may regard an eye 
affected with MAS as equivalent to an emmetropic eye with 
a convex cylinder, such as PAOX (fig. 1), in front of it. 
Hence, in a case of astigmatism, axis oblique, the image of 
a vertical line occupies not a vertical but an oblique posi- 
tion on the retina; and hence, in such a case, there ought 
to be an apparent inclination of one or both sides, as the 23 
Binocular Metamorphopsia. 
case may be, of a square. To this part of the subject we 
shall return. 
Group II.-Characterized mainly by a change in the rela- 
tive heights of the two sides. This group may, for sake of 
convenience, be divided into two sub-classes: Sub-class {a). 
Anisometropia without astigmatism. Examples : 
R E piano, L E i D. The left side appears wider. Or, to 
quote from my records, R E - .75, S = L E emmetropic, 
S = R E reads best with a piano, L E with -|- .75 ; left side 
appears wider. To quote another case : R E + .25, S = 47; 
L E + 2.5, S = ; RE reads best with + 1.75 ; L E with 
-|- 4 D. Left side appears much wider. 
As in Group I, experiments with emmetropes confirm the 
results of clinical observation, and show that if spherical 
glasses of differing degrees be placed before the eyes, the 
side of the object corresponding to the higher refractive 
index appears to be wider ; and, furthermore, that the differ- 
ence in width is proportionate to the difference in the 
indices of the lenses. Sub-class (b\ Unilateral or bilateral 
astigmatism, but having a different modus agendi from 
astigmatism, as illustrated in Group I. It may be here re- 
marked, that several years ago, when my attention was in 
the first place drawn to this subject, only the phenomena 
represented by Group I presented themselves clearly to me, 
the explanation, which then suggested itself, being amply 
corroborated by my record books. The matter was then 
gradually allowed to drop, and it was not until recently that 
the subject was again taken up, with the results illustrated 
by Group II. For this reason, although such cases as those 
given in sub-class (a) of Group II are numerous enough, 
typical clinical material coming under sub-class (b) is not, 
so far, abundant. From the cases which I have had the 
opportunity of examining during the past few weeks, I 
select the following: 
(1) Miss McC. aet. twenty-two, R E .5 c. vert., S = ; LE 
piano, S = ~ ; right side wider. (2) S. P. B., R E emm., S = 
L E 4- .5 c. vert., S = "°; left side wider. (3) Miss M, 
W., aet. fifteen, R E + 1.25 Sp, S = ; L E + 1.5 c., 103 °. y. A. Lippincott. 
24 
S = ; left side appears wider than right. (4) Mrs. W., set. 
forty-seven, R E -[ 1. Sp. - 4. c., axis hor., S = ; L E + .5 
-3. c.( 24°, S = R E reads best with 4- 4 c. vert., L E with 
+ -75 + 3- c-> 114°. Thus right side appears somewhat wider. 
(5) H. J. K., set thirty, RE - .5, S = ^-; LE - .5 - 1.75 c. 
vert., S = ; RE reads best with a piano, L E with - 1.5 c. 
vert. Thus the right side appears much wider than the left. 
From the above-cited cases it may be observed that if a 
4- cylinder, ax. vert., be placed on one eye, and a piano 
[cases (1) and (2)], or a comparatively weak spherical [case 
(3)] on the other, the side corresponding to the cylinder 
appears wider. Case (5) shows that, on the other hand, a 
- cylinder with axis vertical has the effect of diminishing 
the width of its side. 
The effect of convex and concave cylinders, with axes 
vertical, horizontal, and oblique, on the relative heights of 
the right and left sides of a square, was investigated in a 
considerable number of experiments with emmetropic eyes, 
and, while the results hinted at above were confirmed, the 
facts elicited were in some respects so unexpected, and, 
moreover, so suggestive, that it may be proper to briefly 
state them : (a) A 4- cyl. vertical, or a - cyl. horizontal, 
before either eye, widens the corresponding side of a 
square. (/?) A - cyl. vert., or a 4- cyl. hor., narrows the 
corresponding side, (y) If the cyl. (4- or -) is placed verti- 
cal, its effect is much greater than when placed horizontal. 
The magnifying effect of a 4- cyl. progressively dimin- 
ishes as the axis is turned away from the vert., until a point 
is reached midway between the vertical and horizontal (45° 
or 1350), at which point it is nil. If the movement of the 
axis be continued, a minifying effect is instituted, which 
progressively increases till the horizontal is reached. Pre- 
cisely the converse takes place in employing a minus cyl- 
inder. (d) The narrowing or widening increases with the 
strength of the cylinder (4- or -), until the latter is so 
strong that the image is blurred sufficiently to be sup- 
pressed mentally, and monocular vision in this way practi- 
cally established, (f) Lastly, while the effect of a given 
cylinder in the same position is not absolutely uniform in 25 
Binocular Metamorphopsia. 
different persons, nor even absolutely constant in the same 
person, the following table, which represents the results of 
a number of experiments, will probably be generally found 
very nearly exact. It is scarcely necessary to explain that 
on one side of the equation is placed the cylinder, and, on 
the other, the spherical glass which restores equality in 
height to the two vertical sides of the square. 
(a) L E + 1 De, vertical = R E -k 2.25 
(b) " - 1 D c, " = " - T.75 
(c) " +iDc, horizontal = " - .75 
(d) " -iDc, " = " +1.25 
From the above it will be seen [(a) and (d)] that a 4- cyl. 
vert, magnifies about twice as much as a - cyl. hor.; and 
that a - cyl. vert, diminishes about twice as much as 4- cyl. 
hor. If, then, one or both of the eyes be fitted with vert, 
or hor. cylinders, and if the two lenses bear to each other 
the relation given in the above table, there will be no 
metamorphopsy, notwithstanding the anisometropia. As 
already intimated, the effect of a 4- cyl. progressively de- 
creases as it is turned from vertical to45° or 1350, as shown 
in the following table : 
+ i, vertical LE = 4- 2.2c RE 
" i°5 ° " = + 165 " 
" I2O° " =+ ,75 " 
" 135 ° " = o " 
Thus if L E be fitted with -f- I c. vert., and R E with 
2 c, 115 °, the top and bottom of the square may be 
parallel, but meta-morphopsy will result, as illustrated by 
the cases in Group I. 
An explanation of the cases coming under sub-class (a) of 
Group II is scarcely required. Donders (Syd. Soc. Ed., p. 
152) shows that a convex glass placed before the eye, by 
moving the nodal point forward, enlarges the retinal image, 
while a concave glass, by moving the nodal point backward, 
diminishes the retinal image. But to explain the phenomena 
illustrated by the cases in sub-class (b) is a rather more diffi- 
cult task, e. g., a 4- 1 cyl., axis vert., held before the left eye, 
the right being covered, while it increases the width, cer- y. A. Lippincott. 
26 
tainly does not increase, rather seems to diminish, the height 
of a square. Nevertheless, if the right eye be uncovered, 
the left side at once appears markedly higher. 
In like manner a - I cyl., ax. vert., before L E, R E being 
covered, appears to increase, rather than diminish, the 
height of a square ; but, on uncovering the right eye, the 
left side seems markedly lower. So also, a priori, a «/-cyl., 
axis horizontal, ought to increase, instead of diminishing, 
the height of its side, while a - cyl., axis horizontal, ought 
to act in a contrary manner. 
There are some reasons for supposing the explanation to 
be connected in some way with accommodation. Bonders 
(p. 155) has shown that if the accommodative tension is re- 
laxed, objects appear larger, because the mind conceives them 
to be at a greater distance. Besides, experiments do not 
give entirely uniform results in the same person. Indeed, 
at times the effect of the cylinder is not always obvious at 
the first glance, depending somewhat perhaps on the per- 
sonal equation ; and it changes from moment to moment as 
we look. Furthermore, the effect is most manifest at the 
reading distance-the point where accommodation is most 
exercised. On the other hand, it would seem that the 
mechanical change in the dioptric apparatus, known as the 
accommodative act, is not an essential factor, because in a 
number of thoroughly atropinized eyes precisely the same 
results, both in kind and degree, followed the use of cylin- 
ders, as are stated above to have been observed in non- 
atropinized eyes, whether astigmatic or emmetropic. It is 
possible, however, that the explanation of the phenomena 
lies in a change, produced by cylindrical lenses, in the 
dynamical or mental element of accommodation-in the 
accommodative impulse. 
If this view be correct, we must, in order to account for 
the facts, assume that the accommodative impulse is. 
affected in the cases under consideration unequally on the 
two sides ; and, furthermore, that the degree to which, and 
the manner in which, it is affected vary according to the 
position of the axis. E.g., a + cyl., vert., must markedly re- 
lax, while - cyl., vert., must markedly stimulate, the accom- 27 
Binocular Metamorphopsia. 
modative impulse of the eye before which it is placed, as 
compared with its effect on the other eye. Conversely, 
a + cyl., hor., must exert a stimulating, while a - cyl., hor., 
exerts a relaxing influence. 
When the axis of the cylinder is vertical, and therefore 
the transmission of rays lying in a vertical plane uninter- 
fered with, the full extent of this relaxation or stimulation 
is shown ; but when the axis of the cylinder is horizontal, 
the influence on the accommodative impulse is partially 
neutralized by the action of the glass itself. E. g., a -|- i 
cyl., hor., before left eye diminishes the height of the left 
side of a square less than the same cylinder, vert., increases 
it, because a -j- cyl., hor., before one eye (the other being 
closed) increases the height of objects, a'nd to that degree 
lessens its binocular diminishing effect. Similarly a - I c.( 
hor., L E, increases the height of the left side less than a 
- i c., vert., decreases it, because such a cylinder, monocu- 
larly used, diminishes the height, and so partially neutralizes 
its binocular magnifying effect. 
The appearances under discussion might possibly be 
explained, though, to my mind, not so satisfactorily as in 
the manner above indicated, in the following way. The 
estimation of the height of each side is relegated to the eye 
on that side, whereas horizontal measurement is a common 
ground for the action of the two eyes. Now a -|- cyl., vert., 
L E, increases the horizontal dimensions on the left side; 
and the relation established by the right eye between verti- 
cal and horizontal measurements, being transferred to the 
left side, makes it appear magnified vertically, because it is 
magnified horizontally. 
In what mode soever the phenomena of metamorphopsy 
are produced, they are very rarely consciously observed 
spontaneoiisly. Hence, doubtless, the lack of attention de- 
voted to the subject. With very few exceptions, the only 
persons, in my experience, who, after correction of their 
anisometropia, have complained of irregularity in the forms 
of objects, have been artists. This is a curious illustra- 
tion of the extreme rarity of accurate observation. But, 
seldom as the patient speaks of the matter of his own y. A. Lippincott. 
28 
accord, if his attention is drawn to the subject, it is gen- 
erally easy, by indirect suggestion, to make the apparent 
form-changes visible to him. E. g., when the conditions 
required are present, the patient may be asked if he ob- 
serves any peculiarity about the book. Sometimes he re- 
sponds at once: "Oh, yes, it is wider at the top." More 
frequently, however, he replies: "I see nothing peculiar 
but the clearness of the type." He may then be asked 
(e. g., in a case in which the left side of the square ought 
to look wider than the right): "Don't you think the 
right side of the page looks wider? " The patient, after a 
moment's consideration, will reply: " No, it is narrower" ; 
and he is surprised that he did not notice it before. On 
the other hand, I have seen persons who were made dizzy, 
even to faintness, by the tipsy appearance of doors and 
windows; and it is not unreasonable to attribute, in part 
at least, to this distortion of retinal images, the discomfort 
which many persons experience, without being able to 
explain why, on being furnished with glasses which we feel 
sure are correct in every respect. 
It has already been stated that, in a case of astigmatism, 
with axis oblique, there ought to be an apparent inclination 
of one or both sides, as the case may be, of a square ; that 
objects, therefore, and their retinal images do not corre- 
spond in form. Experience, however, derived especially 
through the sense of touch, enables the mind to correct 
the erroneous information furnished by the sense of sight. 
In other words, inaccurate retinal images are translated into 
more or less accurate mental impressions. In adjusting 
his relations to external objects, in finding the haven of 
correct knowledge with so untrustworthy a compass to 
guide his search, what rocks and shoals the anisometropic 
child runs into, what falls and bruises he encounters from 
sloping floors, distorted furniture, and erratic stairways, 
none can know, since the educational process he is doomed 
to go through is an unconscious one. But a field of obser- 
vation is here opened up which might repay investigation. 
For example, in children who are constantly stumbling and 
falling, it might be well to endeavor to discover whether 
the conditions of metamorphopsy are not realized. 29 
Binocular Metamorphopsia. 
Once the habit of correction is formed, and approxi- 
mately accurate notions of form, notwithstanding the imper- 
fection of the retinal images, are obtained, if the refractive 
defect be corrected, the mind, under the influence of habit, 
over-corrects, and the result is that, whereas an oblique 
retinal image gave the mental impression of a rectangular 
object, the corrected and rectangular retinal image gives 
the mental impression of a non-rectangular object. In this 
way the sides of the book appear to slope, and the top 
appears wider than the bottom, etc. 
In regard to the more practical aspects of the subject 
of this paper, it may be remarked that as metamorphic 
vision depends on the formation of a mental habit, so 
its remedy consists in breaking up this habit; and it is 
probable that this end can be attained, at least fully 
enough to prevent serious annoyance, within a few months 
by the persistent use of the correcting glasses. The follow- 
ing case is interesting, as showing what can be done in this 
direction : 
Miss S. K., get. twenty-four, artist, examined under atropine 
September io, 1886. R E -1-.75 c., vert., S=^ ; L E -1, 
S = ^R. E reads best +.75 c., hor., L E +.75. Franklin glasses 
were ordered as follows : Above, full correction ; below, R E 
+.75 c., hor., prism 2, inwards ; L E +.75, prism 2, inwards. De- 
cember 5, 1888 : Has worn the glasses constantly, and has painted 
almost incessantly without inconvenience. With the glasses on, a 
square card looks perfectly natural. On removing the glasses, the 
right side appears decidedly wider. 
This patient has thus been restored by the use of correct- 
ing glasses to a veritable "state of nature,"-to the condi- 
tion in which she found herself when she first began to use 
her eyes, and before the educational process spoken of above 
was commenced. On the other hand, when the glasses are 
worn only for near vision, it is doubtful whether the meta- 
morphopsy ever entirely disappears, although it may be 
somewhat lessened in degree. 
W. C., aet. thirty-two, examined October 17, 1887. R E 
+-25+-5 c-> vert., S=-^; L E +.25, S=-^. Reads best R E J. A. Lippincott. 
30 
+-75+-5 c-» vert.; L E +.75. These glasses were prescribed. 
December 21, 1888, comes to have the prescription duplicated. 
With the glasses the right side is wider, but the sides are made 
equal by adding +-75 to the left side, instead of +1.5, which 
would be the average addition required. 
Other cases which I have recently examined show very 
little, if any, diminution of the metamorphopsy after the 
use of reading glasses for two or three years. 
According to my experience, the phenomena coming 
under Group I, unparallelism of the sides, are more disturb- 
ing than those illustrated by Group II. In such cases when 
the correcting cylinder is strong-above 2 D,-it is desira- 
ble to compromise with a weaker lens; but the correct 
glass ought to be given just as soon as the patient will 
tolerate it. Changing the position of the axis of the cylin- 
der is as unnecessary as it is unphilosophical. 
In conclusion, I scarcely deem it necessary to prolong this 
article by further citation of cases illustrative of the fore- 
going remarks. To report all of the material bearing on 
this subject which has come under my notice, would be to 
fill a good-sized volume. 
Besides, I am satisfied that the every-day experience of 
my colleagues will furnish them with all the cases of bin- 
ocular metamorphopsy which they can possibly desire to 
investigate. g. p. putnam's sons, printers 
NEW YORK