264 ADAPTATIONS TO SPACE AND MOTION 



The 'ganoids', too, need more attention. Hess was unable to detect 

 any accommodatory changes in the sturgeon. The eyes of the spoonbills 

 (Polyodon and Psepburus) have not been studied from any standpoint, 

 to say nothing of accommodation. In the holosteans (Amia, Lepisos- 

 teus), there is an ectodermal lens-muscle, but it is not known whether 

 it is homologous with that of the elasmobranchs or with that of the 

 teleosts; nor is it even certain whether it pulls the lens forward, or back- 

 ward and sidewise. 



Matt hies sen's Ratio — The optics of the fish eye — of whatever tax- 

 onomic category — was exhaustively studied years ago by Matthiessen. 

 This worker found that the fish eye is more thoroughly standardized 

 than any other. The refractive index of the lens nearly always varies 

 parabolically from 1.51 at the center to 1.38 (as in mammals) at the 

 surface, giving it a higher effective index (1.649—1.653) than that of 

 any other vertebrate type. The lens is a sphere, and the optical properties 

 of the other media are constant, the indices of the humors low (about 

 equal to water — 1.33+), so that the difference between lens- and humor- 

 indices is maximal. Thus the fish eye should always have the same pro- 

 portions regardless of its size — and indeed Matthiessen found close 

 agreement to exist between the theoretical and the actual. The distance 

 from lens center to retina, for instance, should ideally be 2.55 times the 

 radius of the lens, and it rarely actually differs from this figure, known 

 as Matthiessen's ratio, by more than one or two integers in the last deci- 

 mal place — even in the tubular eyes of deep-sea forms, which were once 

 called telescopic because they were thought to be radically different from 

 ordinary fish eyes in their optical principles. 



Optical Elimination of the Cornea — The conformation of the fish 

 cornea is of no consequence whatever, since its refractive index is so near 

 to that of water that it has no focusing power. It is not surprising to find 

 that the piscine corneal epithelium is often irregular in thickness, the 

 cornea sometimes having concentric ridges and the like which would be 

 fatal to clear vision in a land animal. All responsibility for image-for- 

 mation rests on the lens, which, for the sake of periscopy, must lie against 

 the cornea and even project from the level of the head surface if this is 

 feasible. This necessity has kept the fishes using their ancient methods of 

 accommodation; for until, in land animals, the cornea came to share in 

 refraction, thus allowing the lens to be drawn back farther into the eye, 



