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 
[173, 174. 
with the axis of the cylinder parallel to the line that is in focus at the 
distance P, or concave with the axis of the cylinder perpendicular to 
that line. The other surface of the lens may be ground spherical 
(spherocylindrical lens) so as to correct at the same time any ame¬ 
tropia that may need correction. 
The best way of ascertaining easily whether there is any astigmat¬ 
ism, the amount of it, and the meridians of greatest and least re¬ 
fraction, is by means of a set of cylindrical lenses. Stokes has 
proposed the use of an astigmatic lens of variable degree of astigmatism 
composed of two equal cylindrical lenses in contact. Placed with their 
cylindrical axes at right angles, the combination is not astigmatic 
but equivalent to an ordinary spherical lens; but by rotating one of 
the lenses relatively to the other, the cylindrical axes can be inclined 
to each other at various angles, so as to increase the amount of 
astigmatism to its maximum value when the cylindrical axes are par¬ 
E. Javal has devised a convenient apparatus, made by Messrs. 
Nachet of Paris, for quick measurement of astigmatism. Two charts 
each consisting of 24 radial lines are observed through a pair of con¬ 
vex lenses with their optical axes parallel. The charts are adjusted 
at such a distance that at first only one of the lines can be seen dis¬ 
tinctly; and then cylindrical lenses, either single or combined in pairs, 
and set in circular mountings capable of being rotated, are inserted 
and adjusted until all the lines in both figures stand out clearly. 
The cylinders can be rotated around the optical axis so as to bring the 
cylindrical axes in the right azimuths for most distinct vision for each 
Corneal measurements of astigmatic eyes made by Donders 
and Knapp show that almost invariably regular astigmatism is a 
case of corneal astigmatism, and that the higher degrees of corneal 
astigmatism are frequently masked to a slight extent by an opposite 
astigmatism of the crystalline lens. 
The azimuth in which the distance of distinct vision is greatest 
is, as a rule, nearer the vertical meridian than the horizontal, as, 
for example, in the cases of both A. Fick and the writer, as above 
stated; but the contrary condition is also not uncommon, as illus¬ 
trated by Young’s vision in this respect. 
1852. A. Müller, Über das Beschauen der Landschaften mit normaler und abgeänderter 
Augenstellung. (Supposedly due to astigmatism.) Poggendorffs Ann. LXXXVI. 
147-152. Cosmos. I. 336. 
1852. A. Beer, Über den optischen Versuch des Herrn Libri. Poggendorffs Ann. 
LXXXVII. 115-120. 
— J. Hippesley, Phenomena of light. Athen. 1852. p. 1069-1070; 1368.


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