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 
[362, 363. G. 
planes, not simply because the mechanical relations for the ciliary 
processes are different from those for their interstices, but also because 
these relations must be modified by the way the fibres of the zonule 
cross each other in proceeding to the anterior and posterior sides of the 
capsule of the lens. It is true, the number of these maxima and minima 
is much greater than the number of rays in the star-pattern. But since 
the tension for the various maxima cannot be mathematically and 
precisely the same, the lines of force will have to merge together towards 
the centre. The star-figure illustrates the same thing. With a larger 
pupil, the rays of the star are often seen to separate from each other 
at a certain distance from the bright nucleus. As the lens is composed 
of fibres, the peculiar form of the iso-indicial surfaces ought to be mani¬ 
fested by a corresponding characteristic arrangement of these elements. 
Now it is even probable that with steady growth of the lens the ana¬ 
tomical arrangement of the fibres is affected by the tensions that occur, 
and thus the stellar appearance seen on the anterior surface of the lens 
by oblique illumination may represent this structure as acquired under 
the influence of the tension of the zonule. The best way to observe 
this starry form is with dilated pupil, by the same sort of experiment 
as was used for inspecting the reflex image in the anterior surface of 
the lens, where the light was concentrated on this surface by a convex 
lens. This figure indicates real discontinuities in the variation of the 
index; but without a very complicated mathematical study, it can 
hardly be regarded as conclusive on this point, inasmuch as the 
“creases” in the iso-indicial surfaces certainly seem to be qualified to 
produce the reflex phenomenon in question. 
Owing to the property of the wave surface of the bundle of rays 
refracted in the eye which has just been proved, it is a mathematical 
impossibility for any cross section to cut the caustic surface in a 
smooth curve in the form of a circle concentric with the pupil. On the 
contrary, this section must be serrated everywhere or must consist of 
separate isolated points. Accordingly, the serrated curve described 
above is a section of the caustic surface, and the concentration of light 
at the centre that is seen at the beginning of the stigmatoscopic in¬ 
vestigation is the vertex or cusp of the same surface. Now this means 
that the aberration along the axis is positive, because the cusp points 
in the direction in which the light goes. Pursuing farther the stig¬ 
matoscopic investigation with dilated pupil, by steadily increasing the 
hypermetropia of the reinforced eye, we find that in the last section 
of the bundle of rays where the line of intersection of the caustic sur¬ 
face can still be seen, it does not coincide with the boundary line. The 
inference is that a meridian section of the caustic surfacehas three cusps, 
like the curve drawn in Fig. 120, where the serrations that are the last


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