586 



ON THE MECHANISM OF THE ETE, 



a focus at the distance of IS^ tenths. In or- 

 der that it may bring, to the same focus, rays 

 diverging from a point distant 29 tenths, we 

 shall find that its radius must be diminished 

 from 31 to 25 hundredths, or very nearly in 

 the ratio of five to four. 



2. Supposing the change from perfect vi- 

 sion at ten inches, to perfect vision at 29 

 tenths, to be effected by a removal of the re- 

 tina to a greater distance from the lens, this 

 will require an elongation of 135 thousandths, 

 or more than one seventh of the diameter of 

 the eye. In Mr. Abernethy's eye, an elon- 

 gation of 17 hundredths, or more than one 

 sixth, is requisite. 



3. If the radius of the cornea be dimi- 

 nished one sixteenth, or to 29 hundredths, 

 the eye must at the same time be elongated 

 97 thousandths, or about one ninth of its dia- 

 meter. 



4. Supposing the crystalline lens to change 

 , its form ; if it became a sphere, its diameter 



would be 28 hundredths, and, its anterior 

 surface retaining its situation, the eye would 

 have perfect vision at the distance of an inch 

 and a half. This is more than double the 

 Jictiial cliange. But it is impossible to deter- 

 mine precisely, how great an alteration of 

 form is necessarv, without ascertaining the 

 nature of the curves into which its surfaces 

 may be changed. If it were always a sphe- 

 roid, more or less oblate, the focal length of 

 each surface would vary inversely as the 

 .squareof the axis: but, if the surfaces be- 

 came, from spherical, portions of hyperbolic 

 conoids, or of oblong spheroids, or changed 

 from moie obtuse to more acute figures of 

 this kind, the focal length would vary more 

 rapidly. Disregarding the elongation of 

 the axis, and supposing tlie curvature of 

 each surface to be cli;«)ged proportionally. 



the radius of the anterior must become 

 about 21, and that of the posterior 15 hun- 

 dredths. 



VII. I shall now proceed to inquire, which 

 of these changes takes place in nature ; and 

 I shall begin with a relation of experiments, 

 made in order to ascertain the curvature of 

 the cornea in all circumstances. 



The method, described in Mr. Home's 

 Croonian Lecture for 1795*, appears to be 

 far preferable to the apparatus of the pre- 

 ceding yearf : for a difference in the dis- 

 tance of two images, seen in the cornea, 

 would be far greater, and more conspicuous, 

 than a change of its prominency, and far 

 less liable to be disturbed by accidental 

 causes. Ii is nearly, and perhaps totally, im- 

 possible to change the focus of the eye, with- 

 out some motion of its axis. The eyes sym- 

 pathize perfectly with each other ; and the 

 change of focus is almost inseparable from a 

 change of the relative situation of the optic 

 axes ; so much, that, in my eye this sympa- 

 thy causes a slight imperfection of sight ; for, 

 if I direct both my eyes to the same object, 

 even if it is beyond their furthest focus, I can- 

 not avoid contracting, in some degree, iheir 

 focal distance: now while one axis moves, it 

 is not easy to keep the other perfectly at rest; 

 and, besides, it is not impossible, that a 

 change in the proportions of some eyes may 

 render a slight alteration of the position of 

 the axis absolutely necessary. These consi- 

 derations may partly explain the trifling dif- 

 ference in the place of the cornea that was 

 observed in 1794. It appears that the expe- 

 riments of 1795 were matie with considerable 

 accuracy, and no doubt, with excellent in 

 struments ; and their failing to ascertain the 

 existence of any change induced Mr. Home 

 *-Phil. Trans. 1798. 2. f Thil. Trans. 1795. 13. 



