Bauhaus-Universität Weimar

Helmholtz's treatise on physiological optics. Volume 1. Edited by James P. C. Southall. Translated from the 3rd German edition
Helmholtz, Hermann von
11, 12.] 
>2. Sclerotica and Cornea 
division, etc. In this way a series of cor¬ 
related values is obtained for x and a, 
from which h and n may be calculated by 
a suitable process of elimination. If 
many observations are to be made, it is 
well to prepare a table for E for every 
degree from 0° to 60°.1 
The same adjustment of the double 
images that is found for a rotation of a 
degrees occurs also for a rotation of —a 
and likewise for (180° —a) or (a —180°). 
In order to eliminate errors in the disc 
scale and in the parallelism of the faces 
of the glass plates, it is advisable to repeat 
each measurement in these four positions 
and to take the average of the four results 
thus obtained. 
One of the most important advantages 
of the ophthalmometer is that the linear 
magnitude of the apparent distance of its double images is independent of 
the distance of the object, so that it is not necessary to know the latter in 
order to make the measurements. 
If the instrument described is used for the measurement of a corneal 
image, small movements of the head of the subject do not introduce a dis¬ 
turbing factor, inasmuch as both images will always move in the same way, and 
their relative positions will not be altered. If at the same time the object 
which is responsible for the corneal image is far enough away, so that small 
movements of the head are negligible in comparison with its distance, the size 
of the image also will not be noticeably affected by these movements, and the 
head can be kept steady enough by providing an easy support for the chin. 
A bright window may be chosen as object for the image in the cornea. If 
the parallel boundaries of two images of such a bright surface are adjusted in 
contact in the ophthalmometer, the eye of the observer will be quite sensitive 
to any overlapping or separation of the two images, which will be noticeable 
at once in virtue of a white or black line between the two uniformly illuminated 
fields. On the other hand, a scale placed far enough away from the eye may 
be used as object if one of its divisions is marked by a small lamp and another 
preferably by two such lamps placed close together. The measurement in this 
case consists in adjusting one of the images of the single lamp midway between 
that of the pair of lamps. This method of adjustment is capable of great 
accuracjq as has been observed by Bessel in the measurement of stellar 
parallaxes with the heliometer. 
The calculation of the radius of curvature of the cornea is very simple 
provided the reflex image as measured is relatively small in comparison. In 
this case the size of the object is to its distance from the eye in the same ratio 
as the size of the image is to half the radius of curvature; so that the latter 
may then be calculated from this proportion. The ellipticity of the cornea 
may also be determined in this way, by measuring the size of the reflex image 
in each position of the eye when, by appropriate variations of the point of 
fixation, the eye is made to turn through successive known angles, both later¬ 
ally and vertically. (Thus the various values of the radius of curvature over 
the different parts of the cornea are calculated first of all, whence are computed 
the elements of the ellipsoid which the cornea approximately resembles in 
1 In the first edition h occurs here instead of E, evidently an error in the manuscript 
or a typographical error. N. 
Fig. 6.


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