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 (PI. XL., Figs, i 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 Phronimidse (Claus and Oscar 



