6 ADAPTATION OF THE EYE TO DISTINCT VISION AT DIFFERENT DISTANCES. 
the crystalline intended to correct spherical aberration, this condition presumes 
the sphericity of the surfaces. If the surfaces have the curve of no aberration, 
for instance, an ellipsoid, with its longer axis parallel to the incident rays, any 
variation of density of the medium is not only useless but hurtful, producing a 
contrary error, and causing the central rays to converge too fast. On the con- 
trary, if the variable density of the matter of the crystalline exist (which is an 
undoubted fact), and has been so arranged for a distinct purpose, the form of the 
surface of no aberration adapted to it will be a peculiar one, and, very probably, 
will be more convex towards the lateral parts than even the sphere, much more 
than the ellipsoid already mentioned, which is the curve of no aberration for a 
lens of uniform density. 
Having perceived this result, it was with no small satisfaction that I found, 
on examining M. Cuossat’s paper, that whilst for the cornea (where the refrac- 
tion is from air into the uniformly dense medium of the aqueous humour), the 
surface is that of an ellipsoid, with the longer axis in the direction of the incident 
rays, and which, therefore, destroys aberration by the appropriate curvature,—in 
the lens, the figure is that generated by an ellipse revolving round its lesser axis, 
and therefore possessing a contrary property to that ordinarily required for cor- 
recting aberration; the curvature being greater for the lateral than the central 
parts of the lens. This is surely an unanswerable proof, that the opinion main- 
tained by, I believe, every modern writer on optics, without exception, namely, 
that the variable density of the lens is intended to correct spherical aberration, is 
a fallacy, since we find it combined with an appropriate figure for destroying its 
aberration, in which the peculiarities of spherical refraction are exaggerated. 
The measures and drawings of M. Cuossat appear so minute and correct, as 
to leave no doubt of the fact of this antagonism to the common opinion.* Accord- 
ingly, neither by himself, nor by the few authors who have quoted this singular 
circumstance, has any explanation been given. 
On our theory it is simple. The gradation of density has been provided for 
the mechanical purpose of varying the elasticity of the lens in different directions ; 
and the form of its surfaces has been then determined so as to render the lens 
aplanatic. 
* M. Cuossat’s experiments were made on the lens of an ox; but Dr ALLEN THomson tells me 
that, without knowing his results, he had arrived at a similar conclusion, as to the opposite kind of 
curvature in the cornea and in the lens of the human eye; the surface of the former lying without, 
and the latter within the surface of the osculating sphere. 
EDINBURGH, 20th December 1844. 
