314 Hastings — Error of Collimation in the Human Eye. 



will lie on the line Gb, which is essentially parallel to n y a, at 

 a point midway between C and the surface of the cornea. 

 Now if the center of the pupil were on the line of vision n 1 a, 

 it would appear displaced towards the temporal side by a dis- 

 tance equal to the interval separating n x a and Cb, or by n x C 

 sin a. In the schematic eye the distance from n x to C is 

 0'0861 cm . Since a is known for all the eyes observed, the 

 relation of the position of the center of the pupil to the point 

 where the line of vision pierces the plane of the pupil is readily 

 determinable. 



The results from the forty-eight eyes thus investigated ap- 

 peared highly irregular. Yet a careful analysis brings us to a 

 conclusion which may be stated with considerable precision. 

 There were only two eyes in which the centers of the pupils 

 were found to be quite certainly, although by a small amount, on 

 the temporal side of the axis of symmetry, and these belonged 

 to different individuals. On the other hand, only a single eye 

 was found to have the center of its pupil quite distinctly on 

 the nasal side of the line of vision, a peculiarity not shared by 

 its companion. In this exceptional case the apparent displace- 

 ment towards the nose was strikingly obvious to every casual 

 observer. The mean position of all the forty-eight was almost 

 exactly midway between the axis of symmetry and the line of 

 vision. This relation, so simply stated, was not dependent 

 upon the value of a. This was proved by the fact that when 

 all the observations were arranged in three equal groups 

 according to small, medium and large values of the constant of 

 collimation, each group was found to yield almost exactly the 

 same rule. 



The center which has been determined is, of course, the 

 center of the virtual image of the pupil as seen through the 

 cornea ; but the rule holds true also for the real position of the 

 pupil. It is not improbable that the center of a dilated pupil 

 is not in quite the same place as one adjusted to a well-lighted 

 room, but that is of minor importance in the questions which 

 have led to this investigation. 



For a further study of certain phenomena of vision I shall 

 assume, as a generalization of the schematic eye of Helmholtz : 



1st. That its constants as regards accommodation and wave- 

 lengths are defined by the tables given in the preceding num- 

 ber of this Journal. 



2d. That the collimation error is 4°'2 on the nasal side. 



3d. That the pupil is centered on a line which bisects the 

 angle between the axis of symmetry and the line of vision. 



Yale University, March, 1905. 



