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 
[339, 340. G. 
the acqueous and vitreous humors. Then the positions of the pupils 
and the magnification-ratio can be found by the following formulae: 
n 1 n 1 p' — h' 
-=---I~DC,--=--k —--. 
d—hj p — hc p' — h’ p — h n{p — h) 
The distance of the fovea (denoted by 1) being projected from the axis, 
the angle between the line of sight and the optical axis is found by using 
the reduced coefficient of angular projection. As this is equal to the 
reciprocal of the magnification-ratio, that angle is directly proportional 
to ;-, the value of which in the exact schematic eye is 44.67 with 
relaxed accommodation, and 45.25 for maximum accommodation; and 
in the simplified schematic eye 44.7 with relaxed accommodation, and 
45.1 for maximum accommodation. Thus, in accommodation there 
is an increase of the angle between the line of sight and the optical 
axis, and, consequently, for a constant line of sight there must be a 
movement of the eye towards the outside in accommodation. However, 
the amount of this movement might not be sufficient for it to be per¬ 
ceived in the manner mentioned. On the other hand, in the accom¬ 
modative changes of the asymmetry-values along the line of sight, to 
which we shall refer again in the proper chapter, lies the cause of a 
movement of the eye which may be added to that just discussed. 
In case of a strong innervation of accommodation the tension of 
the zonule is diminished, and a décentration of the lens occurs in the 
direction of gravity. Coccius1 had described the oscillations of the 
image in the posterior surface of the lens; and Tscherning2 had noted 
a downward displacement of this image. Neither of them, however, 
understood the real cause of the phenomenon. The oscillations were 
supposed to be due to action of the “Musculus tensor choroideae,” and 
the connection between the displacement and gravity was not dis¬ 
covered. A strictly scientific explanation and definite solution of this 
problem was given first by Hess.3 In the case of a small granular spot 
in his lens, he verified an entoptical parallactic movement of it towards 
the pupil, by exertion of maximum accommodation. A very small 
hole, set up 12 mm in front of the eye, served as the source of illumina¬ 
tion. With vigourous effort of accommodation, towards the end of the 
1 A. Coccius, Über die vollständige Wirkung des Tensor chorioideae. Ber. d. VII. 
intern. Ophth.-Kongr. Heidelberg 1888. S. 197. 
2 Théorie des changements optiques de l’œil pendant P accommodation. Arch, de physiol. 
VII, 1. 1895. p. 181. 
3 C. Hess, Über einige bisher nicht gekannte Ortsveränderungen der menschlichen 
Linse während der Akkommodation. Ber. über die XXV. Vers. d. Ophth. Ges. Heidelberg 
1896. S. 41. Also: Arbeiten aus dem Gebiete der Akkommodationslehre. Arch. f. Ophth. 
XLII, 1. S. 288 and 2. S. 80. XLIII, 3. S. 477.


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