430 Mr. R. Templeton on the received value of [i, 



value of fj, from the centre of the lens to the surface is quite un- 

 known*, the form of the caustic of refraction, as it really exists, 

 quite untraced ; we are hence unable to form the slightest con- 

 jectures in explanation of the diversified forms of the eye in the 

 lower animals, or of the extraordinary variety in the comparative 

 distances of the arched surfaces from each other, and that, too, 

 under circumstances in which no reason can apparently be as- 

 signed why they should not be as identical in form and position 

 as they are similar in function. 



18. The curvatures which generate these surfaces are so nearly 

 circular arcs, in those portions at least which receive, or through 

 which pass the rays of light, that the eye, armed with powerful 

 glasses, can detect no deviation from perfect conformity; yet it 

 may readily be accepted that they are not so simply curved. 

 What, then, is their form ? and what also are the modifi- 

 cations which the index of refraction undergoes as we pro- 

 ceed from order to order, and family to family, in the brute 

 creation ? 



19. We find in the human eyef the retina comparatively far 

 distant from the back of the lens, and with a radius of curvature 

 about half the entire horizontal axis; in the elephant, with a 

 lens not much differing in form, the retina is half as close again 

 to the leus, and the radius of curvature considerably greater than 

 the entire axis. Is the value of \x i then, in this latter case, so 

 very much greater than in the human eye ? or what can be its 

 law of decrease that will admit of a caustic of refraction of such 

 unwonted flatness ? a flatness with nothing like it, as far as is 

 known, except in the whale (Balana Mysticetus), in which like- 

 wise the centre of curvature is in front of the cornea. 



20. In Sgualus Acanthias and Hystrix cristata, creatures dif- 

 fering entirely in habit from each other, the eyes scarcely differ 



* Assuming the curvatures to be arcs of circles, if z be the arc mea- 

 sured along the curvature of the cornea from its centre (or point traversed 

 by the axis of the eye), and ju, the index of refraction of the lens, then the 

 value of fi for values of z up to 30° (corresponding to the largest size of the 

 pupil) will be tolerably well represented by log ju = '16555 — '0020434 sm 2 '55z. 

 On the other hand, if the curvatures be generated by parabolas differing 

 insensibly from circular arcs, a constant value of \i (1*4388) will convey 

 the refracted rays into a focus at the retina, at least with 4-figure logarithms j 

 but making the subnormals vary a little with sin z, any degree of precision 

 required can be attained. The change of value of fx involved in the case of 

 circular arcs is very great, far beyond the limits of probability ; we may 

 more reasonably suppose it intermediate betwixt the conditions indicated 

 above ; but we really know nothing about it. 



f Vide Detmar Wilhelm Soemmering de Oculorum Hominis Animalium- 

 que Sectione horizontali Comment atio. In the comparisons instituted in the 

 text, the distance from the cornea along the axis to the rear of the lens (in- 

 cluding all the refracting surfaces) is assumed equal to 10. (See also infrh, 

 p. 432.) 



