255 



density combined in a very complicated manner. Krause's measures 

 of the curvature of the surfaces of the lens confirm the inadmissibi- 

 lity of the all but universal opinion of the variation of density of 

 the crystalline being intended to correct the aberration of spherical 

 surfaces, when, in reality, no such surfaces exist. We arc quite un- 

 able to trace the exact course by which the rays of light are focalised 

 on the retina, since it depends on the internal constitution of the 

 lens that they do not meet very far behind it ; and it still remains 

 at least doubtful how the adjustment to distinct vision of objects at 

 different distances is effected. 



" Finally, the question of achromatism of the eye has its own diffi- 

 culties. It is not now contended that the eye has the power of con- 

 verging equally rays of different refrangibilities ; but it is not un- 

 reasonable to suppose that the chromatic aberration is at least par- 

 tially corrected. One result of the calculations into which I have 

 entered (which were first in part undertaken at my request, by Mr 

 James Clerk Maxwell, and since entirely repeated and extended by 

 myself), is a clear exhibition of the physical conditions of perfect 

 achromatism in the eye. The form is simpler than I have else- 

 where seen, and may at once satisfy any reasonable person of the 

 possibility that the eye might be rendered achromatic, at least for 

 objects at a certain distance ; to prove which, so much has been 

 written, and at so great length. The result may be stated in two 

 lines. If we calculate the effect upon the final focal distance of the 

 whole refracting system of the eye (^"), of a variation in the re- 

 fractive index of each of its three humours (denoted by /tj, (j,^, //,.). 

 We find this equation when the incident rays are parallel, or reach 

 the eye from a very distant object : — 



dq"=l-579 dfi, + l-150 3/4^-2-788 dfi^. 



Let the coefficients dft,^, dfi^, d/Ji.^ denote the dispersion or differ- 

 ences of the indices of refraction for extreme rays, corresponding to 

 the three media, then it is evident, from the negative sign of the 

 third term on the right hand, that they may be so chosen as to annihi- 

 late the second side of the equation, or make the variation of focal 

 distances nothimj, for the difl'ercntly refrangible rays. 



" If the rays proceed from a point 10 inches distant from the eye, 

 the equation for the variation of the focus will be 



67"- 1-873 3/1*. + 1-402 0^,-3-298 5/*i 



