THE THEORY OF ARTHROPOD VISION. 563 
be by a second lens, and such a second lens exists in the Blow- 
fly in the rhabdome. The diagrams (Pl. XL., Figs. 1 and 2) 
will show how images which are not inverted are capable of 
being formed in both cases. 
In the majority of insects, in which a crystalline cone 
exists, both the rhabdome and the convex surface of the cone 
probably act as a single refractive system, the function of which 
is to bring each divergent pencil of rays from the subcorneal 
image to a second focus on the retinal plane, and by a second 
inversion to produce an erect image. 
As soon as such a second refraction and the formation of an 
erect image of external objects on a retinal plane is admitted, 
all the optical difficulties inherent in the theory of mosaic 
vision vanish—we have no longer the extremely minute axial 
pencil of parallel rays. 
The difficulty arising from the variable number of facets in 
different insects has always been admitted as one of great 
moment. When only a dozen, or even thirty or forty, 
ommatea exist it is impossible that any visual picture of any 
value could arise under the ‘mosaic’ theory, but under the 
dioptric theory, as each element of the picture is itself a 
picture, we have only to assume that the receptive elements 
beneath each ommateum are more numerous in eyes with 
fewer than in those with more numerous ommatea. 
Unfortunately I have not examined the eyes of Insects with 
very few facets with a view to elucidating this question, as my 
attention has only recently been directed to its import, so that 
I can only speak generally on the subject. In Tipula, where 
the ommatea are comparatively few, the retinal end organs are 
more numerous in each retinula than in the Blow-fly where the 
ommatea are numerous, and it is well known that in the 
simple eyes of Arthropods the retinal elements are very 
numerous. Therefore it is probable that there is an inverse 
ratio between the number of ommatea and the number of 
receptive elements in each ommateum. 
The Theory of Total Reflection —In the compound eye of some 
Crustacea, especially in the Phronimide (Claus and Oscar 
