THE DIOPTRIC SYSTEM. 1029 



The image of the anterior lens surface is too faint and ill-defined 

 to give satisfactory results by doubling, and Helmholtz determined 

 the curvature of this surface by making the lens and corneal images 

 of the same size. This was done by having luminous objects of different 

 sizes for cornea and lens. The size of a reflected image being proportional 

 to the focal distance of the reflecting surface, the radius of curvature of 

 the lens can be calculated from the sizes of the objects, and the known 

 radius of the cornea. When the eye is accommodated for distant 

 objects, it has been found to be about 10 mm., the figures of different 

 observers varying from 7"9 to 11 '9 mm. 



Position and curvature of the posterior lens surface. — The 

 position of the posterior lens surface is found by producing a light 

 reflection from the surface, and then exchanging the position of the 

 luminous object and the observing eye. In each case it is arranged 

 that the lens image shall be covered by a corneal reflected image, and 

 the position of the lens image will then be at the point of section of the 

 two lines of vision of the observer passing through the two corneal 

 images. The position of the latter being found, the position of the lens 

 image may be calculated, and is about 7*5 mm. behind the cornea. 



The curvature of the posterior surface may be found in the same 

 way as that of the anterior, or the apparent size of the reflected image 

 from the posterior surface may be measured, and the real size calculated 

 from the properties of the refractive media lying in front of it. 1 The 

 radius is about 6 mm., when the eye is accommodated for distant 

 vision. 



The cardinal points. — In addition to the above data, it is 

 necessary to know the refractive indices of the media. The index 

 of the aqueous is approximately equal to that of the vitreous, 

 measurements on fresh eyes by Hirschberg, using Abbe's refracto- 

 meter, giving that of the aqueous as 1*337, of the vitreous T336. The 

 index of the lens varies in its different layers, the refractive power 

 being greatest at the nucleus, and diminishing outwards. The mean 

 index adopted by Listing, derived from the results of Helmholtz and 

 Krause, was 14545 ; but other investigators have given smaller values. 

 In calculating the schematic eye, Listing used rather larger values than 

 those given above for the distances between the refractive surfaces and 

 for the radius of the cornea, and calculated the following positions of 

 the cardinal points : — The anterior principal focus 12-8326 mm. in front 

 of the anterior surface of the cornea ; the posterior principal focus 

 14 - G470 mm. behind the posterior surface of the lens; the first principal 

 point 2-1746 mm., the second 2 - 5724 mm., behind the anterior corneal 

 surface ; and the first nodal point '7580 mm., the second '3602 mm. in 

 front of the posterior surface of the lens. In the reduced eye, the foci 

 are the same as those of the schematic eye, while the single principal 

 point is 2-3448 mm. behind the anterior surface of the cornea, and the 

 single nodal point -4764 mm. in front of the posterior surface of the lens. 



Centre of rotation of eyeball.— This may also be found with 

 the aid of the ophthalmometer. The instrument is placed in the middle 

 of a graduated horizontal arc, along which a fixation point can be 

 moved. A fine hair is suspended vertically in front of the observed 



1 For more detailed description of these and the previous methods, refer to Arch. f. 

 Ophth., 1855, Bd. i. Abth. 2, S. 1 ; "Handbuch f. d. ges. Augenh.," 1874, Bd. iii. S. 

 204, etc. ; or "Traite complet d'opht.," by du Wecker and Landolt, 1880, tonic i. p. 738. 



