408 Hastings — Optical Errors of the Human Eye. 



men ted. By isolating small pieces of colored paper by a black 

 border from the red background I Lave been able to show the 

 peculiar shifting in question for various hues of green, blue, 

 and ultramarine blue. Sometimes when not obvious to direct 

 vision it becomes striking to averted vision. 



The explanation, it seems to me, may be found in the differ- 

 ing angular velocity with which the images of different colors 

 move over the retina. This difference can be readily calcu- 

 lated in the following method. 



Let the object move so that its image (fig. 2) in red light 

 shifts its position from r 'to r' ; the corresponding image in 

 blue light will shift from b to b\ while the center of the diffu- 

 sion circle on the retina, supposed to be at r for convenience, 

 shifts from r to b\. It is at once obvious that rr' /bb' — n^r/njb ; 

 also W/rb/ = irjb/ir^r ; whence rr ! /rb x f = n^r . irjb/nfi . ir 2 r. 

 From the table of dimensions given above this ratio is found 

 to equal 1*0072 ; that is to say, when an object having red 

 points is shifted in the visual field, the red points seem to have 

 an angular velocity and an angular acceleration about three- 

 fourths of one per cent greater than that of accompanying 

 blue points. Thus, when the red surface described in the 

 experiment is suddenly set in motion, the eye, for an instant 

 fixed, judges of its acceleration and of the less acceleration of 

 the green ; then, following it in its motion until it is arrested, 

 concludes that the more refrangible color is left behind — a 

 false judgment which is corrected by the sense of a gradual 

 approach of the green to its true position of rest, just as when 

 the eyes, observing a procession of points passing fixed points, 

 corrects a false judgment as to the place of the former, when 

 the motion suddenly ceases, by an apparent temporary motion 

 in the opposite direction. Of course, if we gain our notion 

 of the angular velocity of the green areas from sharp visual 

 perceptions of their boundaries, the illusion ought not to 

 appear; it is only when the position of the colored area is 

 recognized by its color alone that the effect becomes striking ; 

 hence the significance of faint illumination. 



