On the Mechanifm of the Eyi, * 295- 



neceflary in order to produce it ; whether we fuppofe the radius of the cornea to be diml- 

 nifhed, or the diftance of the lens from the retina to be increafed, or thefe two caufes to 

 a(ft conjointly, or the figure of the lens itfelf to undergo an alteration. 



1. We have calculated, that when the eye is in a ftate of relaxation, the refraflion of 

 the cornea is fuch as to colledl rays diverging from a point ten inches diftant, to a focus at 

 the diftance of I3|- tenths. In order that it may bring to the fame focus, rays diverging 

 from a point diftant 29 tenths, we find (by Cor. 5, Prop. IV.) that its radius muft be 

 diminlflied from 31 to 25 hundredths, or very nearly in the ratio of five to four. 



2. Suppofing the change from perfeft vifion at ten inches to 29 tenths, to be efFefted by 

 a removal of the retina to a greater diftance from the lens, this will require, (by the fame 

 Corollary,) an elongation of 135 thoufandths, or more than one-feventh of the diameter of 

 the eye. In Mr. Abernethy's eye, an elongation of 17 hundredths, or more than oft^i 

 fixth, is requifite. 



3. If the radius of the cornea be diminiflied one-fixteenth, or to 29 hundredths, the eye 

 muft at the fame time be elongated 97 thoufandths, or about one-ninth of its diameter. 



4. Suppofing the cryftalline lens to change its form; if it became a fphere, its diamefet 

 would be 28 hundredths, and, its anterior furface retaining its fituation, the eye would 

 have perfe£t vifion at the diftance of an inch and a half. (Cor. 5 and 8, Prop; IV.) This 

 is more than double the aftual change. But it is impoflible to determine precifely how 

 great an alteration of form is neceflary, without afcertaining the nature of the curves- 

 into which its furfaces may be changed. If it were always a fpheroid more or lefs oblate, 

 the focal length of each furface would vary inverfely as the fquare of the axis : but, if the 

 furfaces became, from fpherical, portions of hyperbolic conoids, or of oblong fpheroids,, 

 or changed from more obtufe to more acute figures of this kind, the focal length would 

 vary more rapidly. DIfregarding the elongation of the axis, and fupppfing the curvature 

 of each furface to be changed proportionally, the radius of the anterior muft become about 

 21, and that of the pofterior 15 hundredths. 



VIII. I fiiall now proceed to inquire, which of thefe changes takes place in nature ;. and 

 I fhall begin with a relation of experiments made in order to afccrtain the curvature of the 

 cornea in all circumftances. 



The method defcribed \n Mr. Home's Croonian Lecture for 1795,* appears to be far 

 preferable to the apparatus of the preceding year if for a difference in the diftance of two 

 images feen in the cornea, would be far greater, and more confpicuous, than a change of 

 Its prominency, and far lefs liable to be difturbed by accidental caufes. It is nearly, and 

 perhaps totally impofHble to change the focus of the eye, without fome motion of its axis*. 

 The eyes fympathize perfe£lly with each other; and the change of focus is almoft infepar- 

 able from a change of the relative fituation of the optic axes; fo much, that if I dire£l both. 

 Hjy eyes at an objeft beyond their furtheft focus, 1 cannot avoid bringing that focus a little 



* Phil. Tranf. for HSo", p. 2, f Phjl. Tranf. for 1795, p. 13,. 



nearer-:. 



