160
Dioptries of the Eye
[135, 136.
the choroid so that the retinal image can be seen through the posterior part of
the sclerotica. As a matter of fact, however, the image cannot be seen through
the sclerotica well enough defined to observe the slight differences that are
involved in accommodation. Ritter,1 Haldat,2 and Adda3 corroborated
Magendie. Haldat and Engel4 maintained that it is true for the crystalline
lens alone. When the crystalline lens is separated from the humors of the eye
and examined in the air, its focal length is extraordinarily short, and, by
ordinary optical laws, the distance of an image in it is not markedly different
whether the object is at infinity or just 7 inches away. This explains the
results obtained by Engel.5
On the contrary, Hueck,6 Volkmann,7 Gerling,8 Mayer5 and Cramer,9
by more accurate experiments, verified the fact that the eyes of human beings
and other animals had different focuses for objects at different distances,
although theoretically the matter was beyond doubt. Treviranus10 believed
that he could give a theoretical explanation of the supposed fact that the
position of the image is independent of the position of the object by assuming
for this purpose a special law for the increase in thickness of the lens. His
mathematical discussion was refuted by Kohlrausch.11
Sturm12 believed he could utilize the fact that the refracting surfaces of the
eye are not strictly accurate surfaces of revolution, to explain accommodation
for different distances. To begin with, he studied the behaviour of a homo¬
centric bundle of rays refracted at a curved surface which is not a surface of
revolution, and found that the rays, instead of being united in a single focal
point, have two focal planes. In each of these planes the rays meet in a focal
line, the directions of the two focal lines being perpendicular to each other.
Thus, if the cross section of the bundle of rays in one focal plane is a short
horizontal straight line, it will change through an ellipse with its major axis
horizontal into a circle as we proceed towards the other focal plane and then
through an ellipse with its major axis vertical into a vertical straight line
when the second focal plane is reached. Sturm’s idea was that between the
two focal planes the cross section of the bundle of rays in the eye contracted
enough to give clear images. If the luminous point is close to the eye, the
two focal planes are at some distance beyond the lens, but as long as the
retina lies between them, the images are perhaps distinct enough for vision.
Aberrations of the kind that Sturm supposes actually do seem to occur in
most human eyes, and the phenomena dependent on them will be described in
§14; where, however, it will be shown that the interval between the two focal
planes is by no means so important as Sturm thinks and that, instead of
promoting the clearness of vision, this defect in the eye tends rather to
impair it.
1 Graefe und Walthers Journal. 1832. Bd. VIII. S. 347.
2 Comptes rendus. 1842.
3 Ann. d. Ch. et de Phys. Sér. 3. Tom. XII. p. 94.
4 J. Engel, Prager Vierteljahrsschr. 1850. Bd. I. S. 167.
6 See refutation of above by Mayer, ibid. 1850. Bd. IV. Ausserord. Beilage.
6 Diss. de mutationibus oculi internis. Dorpati 1826. p. 17. — Die Bewegung der
Kristallinse. Leipzig 1841.
7 Neue Beiträge zur Physiol, d. Gesichtssinnes. 1836. S. 109.
8 Poggendorffs Ann. XLVI. 243.
9 Het Accommodatievermogen. Haarlem 1853. S. 9.
10 Beiträge zur Anat. u. Physiol, der Sinneswerkzeuge. 1828. Heft I.
!1 Über Treviranus Ansichten vom deutlichen Sehen in der Nähe und Ferne. Rinteln 1836.
12 Comptes rendus. XX. 554,761 and 1238. See refutations by Crahay, Bull, de Bruxelles.
XII. 2. 311. Brücke, Berl. Berichte. I. 207.