A CRITICAL STUDY OF THE MAIN DEFECTS 
OF JAVAL’S OPHTHALMOMETER. 
BY 
CARL WEILAND, M.D., 
ASSISTANT IN THR EYE DEPARTMENT OF JEFFERSON MEDICAL 
COLLEGE HOSPITAL, OF PHILADELPHIA. 
FROM 
THE MEDICAL NEWS, 
June 4, 1892. [Reprinted from The Medical NEWS, June 4, 1892.] 
A CRITICAL STUDY OF THE MAIN DEFECTS OF 
JAVAL’S OPHTHALMOMETER. 
By CARL WEILAND^.D., 
ASSISTANT IN THE EYE DEPARTMENT OF JEFFERSON MEDICAL 
COLLEGE HOSPITAL, OF PHILADELPHIA. 
Javal’s ophthalmometer was first brought before 
the profession about a decade ago with the claim 
that it enabled the ophthalmologist to determine 
corneal astigmatism objectively to within a quarter 
of a diopter. This claim seems now to be conceded 
by many members of the profession; but I think 
it will be clear after the following exposition that 
such a claim is untenable, especially according to 
Javal’s own mathematic method, and that it is only 
by accident (sit venia verbo !') that this claim has 
been partially substantiated in practice. 
To understand this seemingly paradoxic state- 
ment I must ask my readers to glance at a few 
mathematic formulae. First, however, let us recall 
the method of finding the radius of curvature of a 
convex mirror, such as the anterior part of the 
cornea is. 
If A B (Fig. i) be the object, at a right angle to 
the optic axis ED; if M N be the surface of the 
convex mirror, the center of which lies at D, and 2 
WEI LAND, 
Fig. i. 
if E C = d and the distance of the image A' B' from 
M N = b, then we have 
(I) (if r=CD), 
do r 
and further, 
AB d + r Size of object 0 
A' B' r — b Size of image I 
If we express r in equation (II) in terms of d and b 
of (I), we get — — or expressing here b in terms 
I b 
of d and r by equation (I) we have --= ~h r (III) 
I r 
Now, here lies the first inaccuracy of Javal, for he 
makes — — —, which is right only if the object lies 
I r 
so far from the mirror that its image falls at the 
focus of the mirror, which is at — . Really, Helm- 
2 javal’s ophthalmometer. 
3 
holtz did use the formula — — 2-~ because he placed 
I r 
his object at 2000 mm. from the cornea, while Javal 
makes d — only 280 mm. To prove the inaccuracy 
we have only to remember that Javal’s instrument 
is so constructed that the image, I, always = 3 mm. 
as soon as the two reflectors have been moved so 
that their two inner images touch. Therefore, 
O 2 d, O k6o ,. 
—=— becomes — = J—, as r, the average radius 
I r 3 7-8 
of curvature of the cornea, equals 7.8 mm. Then 
0 = 216, while by using — = 2 Jrr we get Q 
I r 
219 mm., which is a difference of about 1.5 per 
cent. 
Another inaccuracy of Javal's instrument arises 
from the fact that his reflectors slide on an arc, for 
this sliding changes d continually, as will be easily 
seen by the following diagram (Fig. 2). Here 
A B C is the arc on which the reflectors are moved. 
Suppose, now, that the one slider has to be moved 
from B to C to get contact of their images, then d 
will change also. It will become R cos a -J- L 
if R = A D, or the distance of the arc from the cor- 
nea, and <x the primary angle ADS, and e the 
angle between B D and C D. Javal, however, 
makes d = R cos ex a constant quantity all through 
his calculation. One may object to this criticism 
as being very trivial, and, indeed, numerically it 
does not amount to much; but it must be mentioned 
here, because it can be so easily remedied that it is 
astonishing that it escaped Javal’s mind. 4 
W El LA N D, 
Fig. 2. 
The main error of Javal, however, lies in the fol- 
lowing : In his own description of his instrument 
he states that f the focal distance of the cornea, 
— ———, if r is the radius of the cornea and n 
n — i 
the index of refraction of the cornea and aqueous 
humor. Now, as we want to find the refractive 
power of the cornea for rays coming from the outer 
world, it is undoubtedly true that f can only = 
r n , for this alone tells us how far back from the 
n — i 
anterior surface of the cornea parallel rays from dis- 
tant objects would meet. Or, if we express it in 
diopters, then we must say, the refractive power of 
the cornea D - = ± '. This is the 
f r n 
right formula, and not Javal's, whose expression for javal’s ophthalmometer. 
5 
D is D — 1000 (n j). The following table will 
r 
illustrate the difference: 
43.1 D of Javal ought to be 32.3 D for r= 7.8 mm. 
40.5 D “ “ “ 30.3 D for r= 8.3 mm. 
37.1 D “ “ “ 27.7 D for r— 8.8 mm. 
30 D “ “ “ 22.5 D for r— 11.2 mm., etc. 
Now, it may be said that the question is not so 
much as to the absolute refractive power of the 
cornea, but the difference between those powers in 
the different meridians, or the amount of astigma- 
tism. But it must be replied that the amount of 
astigmatism is affected also, as is shown by the fol- 
lowing examples: 
6 D astig. of Javal only = 4.6 D astig. of cornea. 
3.4 D “ “ “ =2.6 D “ “ 
2.6 D “ “ “ =2 D “ 
1 D “ “ “ =o.74D “ “ 
In short, all the values of Javal for the amount of 
refractive power of the cornea and the amount of 
corneal astigmatism are 11 times too large, if 71 = 
index of refraction = 1.337. 
“But how is that?” the impatient reader will 
ask. “ Does not clinical experience show that 
Javal’s instrument does often give very good re- 
sults?” I answer, Yes, often, but not always; and 
must add that this result is not obtained by the 
right calculation, but results very strangely from 
accidental causes, as follows: It is well known that 
the value of a lens changes with regard to its optic 
effect on the eye according to the position the lens 
occupies. Now, if Javal were right in his calcula- 6 
WEILAND, 
tion, so that his instrument showed the real astigma- 
tism of the cornea, then quite a different glass would 
have to be used at 15 mm. from the cornea, the 
anterior focal point of the eye, where our lenses 
ought to be placed. Still we use Javal’s numbers 
even at that distance from the eye, which shows 
plainly that his calculations for the integral corneal 
astigmatism must be wrong. To make this more clear 
let us look at the following figure (Fig. 3) : Let A B 
be the vertical and C D the horizontal meridians of 
the cornea, which are of differing curvatures, so 
that F is the focus of the rays through the vertical 
and E the focus of those through the horizontal 
meridian. If the refractive power of the cornea 
in the horizontal meridian = D diopters, and that 
of the vertical — D' diopters, if D' is supposed to 
be greater than D, what lens have we to place at 
the anterior focal point of the eye at the distance 
of <p mm. from the cornea, or, more correctly, from javal’s ophthalmometer. 
7 
the first principal point of the eye, in order to 
make the combined refractive power of a cylin- 
drical lens and the cornea in the horizontal me- 
ridian equal to that same power in the vertical 
meridian? To simplify the problem, however, let 
us put the cylinder, not at <j>, but at the anterior focal 
point of the cornea, which is = ——— = • = 23 
n— 1 0.437 
mm., while <p would be about 15 mm. from the cor- 
nea. Now, it is well known that if a lens is placed 
at the anterior focal point of an optic system, the 
second principal point, and with it the second prin- 
cipal focus, of the combined system is obtained by 
moving these points of the given system in the same 
direction through the same definite extent. In our 
example the second principal point lies, together 
with the first principal point, at the apex of the 
cornea, and it is moved through ~y- mm. away from 
the cornea, if V' and are the anterior and posterior 
foci of the cornea and / the focal distance of lens 
or cylinder. As we want the rays through C D also 
to come to a focus at F, we have to choose our lens 
so that 
F E =t*L= t x loc°, because D = 
/ fp r 
This we may write 
F E = , if we mean by DL = 1 the refrac- 
tive power of the cylinder in that meridian. Further, 
it is clear that F E, the focal interval, = - — IOO°, 
’ ’ D D' 8 
WEI LAN D, 
asOE=:1000 and O F = Therefore, we 
D D' 
, 1000 1000 ip Dr 1000 (D' — D) 
D D' D D D' 
a j , r j t-> 1000 (n—i) 
And as ip — and D == A we can 
n — i rn 
write for — the value 1000, so that we have 
D D2 n 
1000 (D' — D)_ioooDl D'—D DL 
DD' nU2 ’ °r D7 1Tb' 
Therefore, DL = n 51, if D' — D = the 
amount of real corneal astigmatism = d. The value 
of our lens, therefore, which, at the anterior focal 
point of the cornea = 23 mm., corrects the corneal 
astigmatism, is DL = d = 5__—5) d. This 
we may write DL = n n d • and as we know 
n D 
from former considerations that the real values of 
astigmatism and corneal diopters have to be multi- 
plied by n to get those of Javal, and if the respec- 
tive values of Javal are called A, A'? and <1, we have 
Dl — ti = ———5 6 — 6 —Now, usually 
—-— is not much different from 1, and so we get 
A + 6 & 
approximately DL = 6, if d = Javal’s astigmatism. 
Suppose, for example, that there was a real corneal 
astigmatism of 3 D, then Javal’s instrument would 
indicate an astigmatism of 4 A, while the real cor- 
rection at 23 mm. would be a cylinder of 3.6 D. 
So 1 real D would be 1.337 of Javal = 1.19 at 23 javal’s ophthalmometer. 
9 
mm. if the meridian of lowest curvature was 37.1 A. 
These values would change a little if the lens were 
placed at 15 mm. away from the cornea—e. g., 3.6 D 
at 23 mm. would be 3.7 D at 15 mm. In the higher 
forms of astigmatism, however, the difference is very 
considerable; for, suppose that Javal’s instrument 
showed 8 A astigmatism, then this would equal 6.5 D 
at 23 mm. from the eye and 6.8 D at 15 mm. away 
from the eye, so that between Javal’s glass and the 
true cylinder there would be a difference of about 
1.25 D, certainly a very considerable amount. In the 
same way, Javal’s 6 would be equal to a 5 cylinder. 
Another inaccuracy must be mentioned still, with 
reference to the graded reflector, where each step is 
supposed to indicate one diopter. To get the size of 
those steps Javal uses the formula A — IQ°° 
2 d 1 
where d is the distance of the object O from the 
cornea, while the right formula would be 
£ 1000 (n — 1) (O — I) 
2 dn I 
Now, Javal makes d about 281 mm. in his latest 
model (it changes continually, as already proved), 
and 1 = 3 mm.; and as n — 1.337 we get 
A = 337 X O and , 337X (>._(> 
281 X 6 281 X 6 5 
from which it follows that 0=5 mm. for each di- 
opter, while from the true formula 
j-j xooo (n— 1) (O — I) 
2 d n I 
it follows that the object O ought to increase 6.7 mm. 
for each diopter. But while Javal is right in making 
2 10 
javal’s ophthalmometer. 
the steps of his reflector — 5 mm. each for his own 
diopters, he is wrong in making those reflectors 
curved, because each step has then less value than 
5 mm. as measured in the line of union of the two 
reflectors. 
So far, all the objections raised have nothing to do 
with the principle of the instrument, but only with 
the special form given to it by Javal. For it must 
not be forgotten that the instrument is almost the 
same as that described by Rochon in the Journal de 
Phys., vol. liii, in 1801, and that it has a good place 
in science under the name of Rochon’s micrometer. 
Javal only gave the bi-refracting prism a definite place 
in the telescope and then made the calculation for 
the refractive power of the cornea, adding an arc and 
two reflectors. Now, the calculation and the arc, 
as well as the two reflectors, are not quite correct, 
but the error might be easily rectified, and so a more 
perfect ophthalmometer on Rochon’s principle be 
constructed. But it seems to me that there is a seri- 
ous defect in the very principle of the instrument, 
because the bi-refracting quartz-prism is not achro- 
matic, so that the margins of the images are not 
sharply defined, which makes it impossible to get 
the accurate contact so necessary for an accurate 
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