156 HERMANN VON HELMHOLTZ 



mathematical basis for the whole structure of physiological 

 optics. After a masterly anatomical description of the eye, 

 Helmholtz divides the theory of visual sensation into three 

 sections, dealing with the path of light in the eye, the sensa- 

 tions of the optic nerve, and the interpretation of visual 

 sensations or visual perception. In the part first published, 

 he is principally concerned with the problem of the refraction 

 of the light-rays, or the dioptrics of the eye. He begins 

 with a simpler and more comprehensive account of refraction 

 in centric systems of refracting and reflecting spherical sur- 

 faces, than that given by Gauss, and then applies the theorems 

 to the refraction of light-rays in the media of the eye, where 

 he makes the interesting point that the distance between the 

 principal points in the crystalline lens is less than it would be in 

 a lens of the same form with the refrangibility of the nucleus : 

 at the same time he is led by measurements carried out upon 

 the living eye, to doubt whether the form and focal length of 

 a dead lens are the same as in the living eye accommodated 

 for far vision. He examines the different reduction methods 

 of Listing, and, after defining accommodation, discusses its 

 mechanism, and the theory of diffusion-images upon the retina, 

 with the aid of all the measurements previously made by others 

 and by himself with different optometers. He makes some 

 excellent observations on astigmatism and the entoptic phe- 

 nomena of the eye, but in this first section touches the question 

 of colour only in so far as it relates to the dispersion of colours 

 in the eye. His estimation of brightness in the diffusion-area 

 produced by dispersion of a single luminous point, as also at 

 the edge of an evenly illuminated surface, is interesting, and 

 he goes on to explain why the chromatic dispersion of images 

 in the eye interferes so little with the acuteness of vision; 

 a combination of lenses designed to make the eye achromatic 

 had no perceptible effect on the clearness of vision. Lastly, 

 he works out the refraction at the vertex of an ellipsoid with 

 unequal axes, and investigates pencils of rays falling obliquely 

 upon a spherical surface. 



In order to establish the mathematical theory of the lumi- 

 nosity of the eye, and of the ophthalmoscope, Helmholtz develops 

 some more general theorems than those already published 

 in his work on the ophthalmoscope, the following of which 



