THE MODE OF ACTION OF FACETTED EYES. 
343 
of vision which, may he assumed for various insect-eves from 
their anatomical structure. As two neighbouring facets include 
between their axes very different angles in different animals, it 
is to he expected that this circumstance will correspond to an 
unequal sharpness of vision, and of course that the sharpness is 
greater, the smaller the angles. Further, however, I do not 
think we can go with him in his conclusions, especially as we do 
not know in how many of the individual facets some sensation 
is produced by light issuing from the same point. Notthaft 
gives figures, although with some reserve, which are intended 
to show the sharpness of the retinal picture of a given object. 
These have been constructed, however, upon the supposition 
that rays from one point only excite one retinal element of 
a facetted eye, a supposition as to which at present we know 
nothing. 
I will here pass over much interesting detail that this 
Memoir contains, and pass at once to the kernel of it. This re- 
lates to the physiological interpretation of the facetted eye, and 
consists in the belief that by means of this eye the animal is able 
to estimate directly the distance of objects, just as is possible to 
the vertebrate eye. 
Thus the picture of an object is supposed to diminish in 
brightness as the object is removed, and indeed the brightness 
is supposed to be in inverse proportion to the square of the 
distance. The proposition is expressed for the case of a definite 
hypothesis, which runs as follows : — ‘ TJpon every retinula there 
falls a cylindrical fascicle or line of light precisely in the direc- 
tion of the optical axis of the element of the eye. The individual 
rays of light composing this fascicle maintain strictly the same 
direction. The portion of the object from which they issue 
and which occupies a single elementary field of vision, is conse- 
quently exactly of the same size for all distances, however dif- 
ferent they may be ; in fact it is exactly equal to the transverse 
section of the posterior, pointed, non-pigmented end of the 
crystalline cone, or to that of the retinula/ 
Valuable as such a new point of view may appear for the 
understanding of the facetted eye, I cannot help protesting 
against it. Thus I regard the hypothesis which I have quoted 
above as perfectly unjustified. In the first place, it is not true 
that under the supposed circumstances the intensity of an illu- 
mination striking the retinula diminishes in the proportion of 
the square of the distance. It rather remains the same at all 
distances. This at once becomes clear if we go back upon the 
basis of the theory that light diffuses itself in all directions in 
rectilinear rays. The idea that lies at the foundation of this 
theory is, that the individual: ray retains the same intensity 
in its whole course ; the weakening of the illumination in 
