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
Dioptrics of the Eye 
[284, 285. G. 
latest value of 6.5 mm for the radius of the posterior surface, would 
perhaps seem to indicate their adequacy also. However, owing to the 
discrepancy that exists between too small a schematic value of the 
corneal refraction and the results of anatomical measurements of the 
length of the eyeball—a matter to be considered presently in detail— 
further investigations were deemed desirable. The writer therefore 
has measured four other eyes of different individuals by an approxi¬ 
mate method, assuming the line of centres to be a line inclined to the 
line of sight ( Visierlinie) at an angle of 6°, and using in the calculation 
the value of the angle as obtained for the case when the thickness of 
the cornea was found to be 0.46 mm. Now a discussion of the formulae 
proves that for a given value of e the ratio — will be greater in pro- 
P 2 
portion as the cornea is thicker; therefore the value of the radius of 
the posterior surface found by this approximate method cannot be too 
small. In this way the following values of — were found: 1.1864, 
P 2 
1.1734, 1.1486, and 1.1427. For the schematic value 7.8 mm for the 
radius of the anterior surface, these numbers give values of the radius 
of the posterior surface between 6.57 and 6.83 mm. Hence, the Ophthal¬ 
mometrie mean value of the radius of the posterior surface of the optical 
zone of the cornea can hardly be greater than 6.7 mm, which is the value 
that is hereafter assumed by the writer. 
However, the Ophthalmometrie mean values of the radii of curva¬ 
ture of the optical zone cannot be used without further consideration 
for calculating the ray procedure by means of the imagery laws of the 
first order. In a calculation of this kind the curvatures that are in¬ 
volved are those at places where the line of sight ( Visierlinie) is incident 
on the temporal side of the Ophthalmometrie axial point. The radius 
of the anterior surface must needs be somewhat less at such a point 
than the ophthalmometric mean value for the whole zone—all the 
more so because the latter value was found by measurements in which 
the one point of the cornea used for reflection is at the edge of the 
optical zone and therefore has probably turned out rather too large. 
On the other hand, on account of the greater flattening of the anterior 
surface in the vertical section, the ratio ^ may be here somewhat 
P 2 
larger than in the horizontal section ; and, besides, it must prove to be 
greater in case the measurement was not made exactly along the 
line of centres. Therefore, in calculating the ray procedure a radius 
of the anterior surface should be used that is somewhat smaller, and a 
radius of the posterior surface that is somewhat larger, than the


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