on the Mechanism of the Eye. 
53 
distance from the lens, this will require, (by the same Corollary,) 
an elongation of 135 thousandths, or more than one-seventh 
of the diameter of the eye. In Mr. Abernethy’s eye, an 
elongation of 17 hundredths, or more than one-sixth, is re- 
quisite. 
3. If the radius of the cornea be diminished one-sixteenth, 
or to 29 hundredths, the eye must at the same time be elon- 
gated 97 thousandths, or about one-ninth of its diameter. 
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 per- 
fect vision at the distance of an inch and a half. (Cor. 5 and 
8, Prop. IV.) This is more than double the actual change. 
But it is impossible to determine precisely how great an alteration 
of form is necessary, without ascertaining the nature of the 
curves into which its surfaces may be changed. If it were 
always a spheroid more or less oblate, the focal length of each 
surface would vary inversely as the square of the axis : but, if 
the surfaces became, from spherical, portions of hyperbolic 
conoids, or of oblong spheroids, or changed from more obtuse 
to more acute figures of this kind, the focal length would vary 
more rapidly. Disregarding the elongation of the axis, and 
supposing the curvature of each surface to be changed propor- 
tionally, the radius of the anterior must become about 24, and 
that of the posterior 1 7 hundredths. 
VIII. I shall now proceed to inquire, which of these changes 
takes place in nature ; and I shall begin with a relation of expe- 
riments made in order to ascertain the curvature of the cornea 
in all circumstances. 
The method described in Mr. Home’s Croonian Lecture for 
