78 PROCEEDINGS OF THE AMERICAN ACADEMY. 



range over a long scale of values of luminosity. Whatever the absolute 

 values of the light reflected, the relative values expressed by the coeffi- 

 cients of reflection range from about 0.80 to about .01, very few sub- 

 stances returning more than the former or less than the latter percentage 

 of the incident light. 



The fundamental fact at the basis of vision is that the eye can per- 

 ceive, -^vithin a very wide range of absolute intensity, a substantially 

 constant fractional difference of luminosity. This is the purport of 

 Fechner's law, and the fractional diff"erence mentioned is well known 

 as Fechner's fraction. Its numerical value for normal eyes and ordinary 

 intensities of illumination is from .02 to .0055. The importance of this 

 law in practical seeing is enormous, for in a room well lighted by diffuse 

 daylight the illumination may vary from 100 meter-candles down to 10 

 or 20 in different parts of the room or at different times; and if power 

 of discriminating difference of luminosity changed much with the illu- 

 mination, one would be purblind most of the time. In some abnormal 

 eyes Fechner's fraction, with vision otherwise nprmal, is considerably 

 increased, with serious results. A case is cited by Krenchel in which 

 a patient was unable to get about in full daylight without stumbling 

 over things. His condition was most puzzling until a test showed 

 Fechner's fraction at a value of 0.1. At this value one could not dis- 

 tinguish between dark and light shades of brown and gray, having 

 coefficients of diffuse reflection of say .15 and .25 respectively, and 

 ordinary shadows on neutral surfaces would therefore disappear en- 

 tirely. With Fechner's fraction at 0.5 no contrast less than that be- 

 tween white and very dark pigments would be easily distinguished. 



Now while Fechner's fi-action is fairly constant over a wide range of 

 intensities, one easily realizes that as twilight deepens his power of dis- 

 criminating shades is seriously impaired. It is this variation of Fech- 

 ner's fraction with the illumination which determines the minimum 

 amount of artificial (or natural) light which is effective in enabling one 

 to see things en masse in their natural relations. For general vision 

 any illumination above that required to bring Fechner's fraction for 

 the normal eye up to its steady value is needless, and, as we shall pres- 

 ently see, may be injurious. 



Human vision, however, is frequently concerned with the observation 

 of fine details both far and near, and the power of seeing these is within 

 wide limits independent of the capacitj^ of the eye for distinguishing 

 small differences of luminosity. In the case mentioned by Krenchel 

 this visual acidty was normal in spite of the extraordinary lack of sen- 

 sitiveness to variations of light and shade. Acuity seems to depend on 

 the structure of the retina and the quality of the eye as an optical in- 



