406 Hastings — Optical Errors of the Human Eye. 



unilluminated portion of the retina, if it caused any visual 

 perception, would be interpreted as a line of more than abso- 

 lute external blackness. 



In the case of the model eye the breadth of the dark band 

 would be considerably less than one minute of arc and at a dis- 

 tance of about two degrees from the point of most distinct 

 vision, hence it is perhaps doubtful whether it could be per- 

 ceived as a black line. In the case of my own eyes the con- 

 stant of collimation is about half that of the normal eye and 

 the pupils are nearer the axis of vision. From these data we 

 may estimate the angular value of r J, for my eyes, as some- 

 thing less than one half minute of arc at the fovea centralis. 

 The value for the interval red-green may be regarded as half 

 this value ; and finally, at the eccentric position where the 

 strip on the retina is wholly unilluminated this must be again 

 reduced by an amount which could be determined accurately 

 only when the constants of the eye are known with a greater 

 precision than now attained. It is probable, however, that 

 this value would not be less than ten seconds of arc. Whether a 

 strip of the retina of a width only one sixth of the ultimate 

 perceptual elements of vision would, when deprived of light, 

 give rise to a conspicuous sensation, is a question which, as far 

 as I can find, has not been considered by investigators in this 

 field. It has been abundantly proved that the ultimate precision 

 of optical definition, under the most favorable circumstances, 

 is not less than 60" ; on the other hand, there is obviously no 

 minimum limit for the angular width of a bright line for visi- 

 bility, since this is only a question of the amount of light 

 received by the eye, or of its brightness. But the question of 

 how narrow a black line on a bright field can be seen is wholly 

 different. My own experiments, although of great simplicity, 

 seem to be perfectly adequate for our present purposes. I 

 found that I could see a black hair of a measured diameter of 

 0-0025 inch as a black line, against a sky of favorable bright- 

 ness, up to a distance of 300 inches. At the greatest distance 

 the angular width is only l //, 72. There is, therefore, no diffi- 

 culty in adopting the above explanation of the phenomenon 

 under discussion even if we were obliged to assume a much 

 smaller value for the area of unilluminated retina. 



A familiar example of this same phenomenon, if I am not 

 mistaken, is presented to us by the appearance of a red billiard 

 ball on a green table. Here the vertical contours of the ball 

 are astonishingly sharp as compared to that of the upper sur- 

 face, and also to what we might expect from the pronounced 

 chromatic aberration of the eye. 



