Bauhaus-Universität Weimar

Helmholtz's treatise on physiological optics. Volume 1. Edited by James P. C. Southall. Translated from the 3rd German edition
Helmholtz, Hermann von
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.


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