NOTES AND MEMORANDA. 
227 
were found. These curves approach more or less closely to an 
epicycloid. 
It is easy with such curves and the size of the corneal facets to 
determine the angles made by adjacent facets. The angles vary 
inversely as the radius of curvature, and, therefore, the acuity of 
vision varies directly as the radius of curvature when the diameter 
of the facets remains the same, and inversely as the diameter of the 
facets when these vary in size. In many insects, as Tahanus, the 
peripheral facets of the cornea are twice or three times the diameter 
of those in the centre, and the radius of curvature is very short at the 
extreme periphery. 
In most insects the acuity of vision determined in this manner 
diminishes very rapidly at the periphery of the field. In the centre 
of the field it enables them to perceive, as distinct, objects which 
subtend one degree. In ^schna grandis the sharpness of vision is 
much greater, as the adjacent facets make an angle of only eight 
minutes with each other. This was the least angle measured in any 
insect ; but there is no doubt, from the nature of the curve forming 
the meridians of the eye in the great dragon-flies, that a small part of 
the centre of the field has a much greater acuity of vision than this ; 
in the wasp the angle subtended by the smallest visual perceptions is 
twice as great as in j3Esclina ; and in the bee it is half a degree. 
The size of the corneal facets varies in different insects from 
2 oV^ to -Yzo diameter. Their size, except in a few 
insects, is dependent on the size of the insect, the largest insects 
having the largest, and the smallest the smallest corneal facets. From 
this it follows that the vision of large insects is more perfect than 
that of small ones, except where the curvature of the cornea is very 
flat. This corresponds with the manner in which the insects fly, the 
small Diptera flying round in small circles, whilst the larger species 
take long flights when disturbed or in search of food. The experi- 
ments of Muller and others have shown that the direction and length 
of flight of insects depend largely on their visual powers.^ 
* ‘Proc. Eoy. Soc.,’ vol. xxvii. p. 261. 
