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 
[331, 332. G. 
high bending of the unaccommodated lens does not produce any more 
asymmetry in the arrangement of the iso-indicial surfaces than is shown 
in Fig. 133. Again, as to the connection between the optical mechanism 
and the dynamics of accommodation, this will be discussed more at 
length presently; but here attention is directed simply to the fact that, 
if, in accordance with Besio’s researches, the peripheral parts of the 
anterior surface of the lens are flatter than those of the posterior sur¬ 
face, the result might be an asymmetry of the external form of the lens 
without any asymmetry of the core lens. 
A comparison of the distribution of the iso-indicial surfaces in the 
passive and in the accommodating lens shows at once that the shifting 
of the individual parts in the direction of the axis during increase of 
thickness of the lens is greatest in the equatorial plane, and that here 
the parts lying nearer the axis of the lens are shifted more than those 
nearer the equator. The mathematical investigation shows that this 
latter condition is an expression of the alteration of the total index 
with the change of shape of the lens. As this might have been postulated 
a ;priori from the anatomical structure of the lens, the conclusion is 
that the change of the total index accompanying accommodation is 
necessarily connected with the anatomical structure. 
In order to understand this relationship, it is simply necessary to 
remember that the lens fibres are attached both anteriorly and pos¬ 
teriorly, describing in their course arcs which are convex toward the 
equator. When the points of attachment of the fibres are separated 
from one another by the increase of thickness of the lens, the arches 
must be spread, involving the greatest amount of dislocation of 
particles in the parts of the fibres farthest from the points of attach¬ 
ment. If the lens were always symmetrical, a centripetal shifting would 
have to occur at the equator. If the point of maximum centripetal 
shifting on each lens fibre were determined, and a surface passed 
through all these points, this surface of maximum accommodative 
shifting would coincide with the equatorial plane. But since the 
passive lens is asymmetrical, and the change of shape is particularly 
marked on the anterior surface, the surface of maximum accom¬ 
modative shifting must be concave towards the front. This con¬ 
clusion, drawn entirely from the anatomical structure of the lens 
with respect to its asymmetrical accommodative change of shape, 
may also be deduced directly from the figures given above, as a result 
of mathematical analysis. The slight change of form of the posterior 
surface of the lens demonstrates that the points of attachment of 
the lens fibres adjacent to this surface must, on the average, be less 
separated from one another during accommodation than those of the 
fibres lying on the anterior surface. Since, on the whole, the fibres of


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