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
95, 96.] 
§10. Optical System of the Eye 
and visual axis, and also because the definition of nodal points and principal 
points are valid only for much smaller angles of incidence than he used in 
these experiments. Burow1 found, moreover, in repeating Volkmann’s 
experiments with the eyes of white rabbits, that for very wide angles of inci¬ 
dence the retinal image falls nearer the optical axis than it should if all the 
direction lines intersected in a point. Both of these influences would have the 
effect of making the distance from cornea to nodal point, as determined by 
Volkmann’s method, somewhat too large. 
We shall now explain how the centering of the eye and the positions of 
the optical axis and the visual axis may be determined. The method utilizes 
the reflex images formed by the cornea and lens surfaces of a bright source 
of light placed in front of the eye. 
Concerning the appearance of these reflex images and the best methods of 
observing them, the reader is referred to §12. In Fig. 51, cd represents the 
axis of an accurately centered eye; the eye of the observer is at a and the 
source of light at b. Suppose ab is per¬ 
pendicular to cd, and ac = cb. With this 
arrangement, everything being sym¬ 
metrical, it is clear that the light from 
b, falling upon the three reflecting sur¬ 
faces at their vertices, where they 
intersect the axis cd, will in each case be 
reflected to a. If the observer and the 
source of light are interchanged, the 
same thing will occur again, and the 
three reflected points will appear in the 
same perspective, on account of the 
bilateral symmetry of the whole appa¬ 
ratus. Since the anterior surface of the 
lens is about half-way between the 
cornea and the posterior surface of the 
lens, the image in the anterior surface 
of the lens should, for either position 
of the light and observer, appear about 
halfway between the other two images. 
The following method may now be employed to ascertain the adjustment 
of any given eye. Let a horizontal graduated scale be placed along the line 
ab, suitable openings being provided at a and b for the observer and the 
source of light. The eye under examination is brought into some convenient 
position d, on the perpendicular bisector cd, and its owner is directed to look 
fixedly at some adjustable object, g, which is then moved up or down and to 
right or left until the observer can see the reflex from the anterior surface of the 
lens lying between those from the cornea and the posterior surface of the lens. 
The observer then changes place with the light and notes whether, with the 
fixation mark unchanged, the three images remain in the same relative posi¬ 
tions as before. If the eye under examination were correctly centered, it 
would be possible to find a position for the object g such that this would be 
the case. 
The writer has never examined a human eye that quite fulfilled this condi¬ 
tion. If the three reflexes are in the right positions when viewed from one 
side, they are not so when viewed from the other, and in order to adjust them 
in the right positions again, the point of fixation (g) has to be shifted more or 
less. For each of the three eyes on which this method was tried, it was found 
necessary to place the fixation point g somewhat above the plane abd. The 
visual axis was invariably found to lie on the nasal side of the line cd, its 
1 Beiträge zur Physiologie d. menschl. Auges. S. 56-60. 
Fig. 51.


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