narrower, and finally the image shown in fig. 64 is obtained. Fig. 65 shows the appearance when the focal plane is behind the retinal image. The author's experiments lead to the conclusion that the dioptric apparatus of the Lampyris-eye is very similar in its effects to a system of two lenses on the same axis which are separated by a distance equal to the sum of their focal lengths. In the Lampyris-eye the two convex lenses are replaced by two cylindrical lenses, the Linsencylinder of Exner, which form the crystalline cone. The path of two pencils in a crystalline cone, according to this principle, is shown in fig. 66. The inverted image a, b, of the distant object a b, which gave rise to so much confusion in the physiology of the compound eye, is formed not at the vertex or behind the cone, but in front, where there can be no nervefibres. The rays m and n proceeding from a form an image at a1; similarly the rays p and q from b form an image at b. The image a, b, is formed between the focus on the hinder part of the crystalline cone and its vertex, so that the rays m, n from a,, on leaving the cone, are slightly divergent. Thus a, b, gives rise to the virtual image a, b The figure shows how the angle of emergence of a pencil to the axis is on the same side as the incident pencil, and that it is so much greater, as the incident angle is greater. The author has constructed a model of an insect eye on the above principles. It consists of ten pairs of convex lenses, each of focal length of 2 in. The two members of each pair are separated by 4 in., and the ten sets are arranged on an arc of 75 cm. radius. The formation of the inverted image which is seen when the concave side of the Lampyris-eye is turned towards the object is explained by fig. 67. The crystalline cone acts like an astronomical telescope adjusted for infinite distance. The deviation which a ray undergoes is shown in fig. 68. or, 1 sin a = 2 sin ẞ since a, ß are small. The rays incident on the eye will be deflected in each crystalline cone according to the above law, and by means of it the calculation of the image, optical constants, &c., follows in a way strictly analogous to that of an ordinary lens. Let bc (fig. 69) be the curvature of the eye, ap a radius from the centre of curvature a, pc a ray from the point p, which is deflected to d. Then by the above law, b2 |