BELL. — THE PHYSIOLOGICAL BASIS OF ILLUMINATION. 85 



/ in terms of what one may call the admittance of the pupil, then 

 approximately 



u = c \/7, 



assuming that / is within ordinary ranges of intensity ; that is, the eye 

 works most efficiently at moderate illumination. The adverse factors in 

 lowering the illumination are the optical errors introduced by increase 

 of pupillary aperture and the general failure of shade-perception and 

 acuity as the illumination falls below about 10 meter-candles. Spheri- 

 cal aberration and astigmatism increase rapidly at large apertures, so 

 that definition of objects is much impaired. This doubtless plays its 

 part in the failure of acuity in very poor light, although a more promi- 

 nent fact is the increase of acuity as the eye is stopped down at illu- 

 minations considerably above the critical value at which the eye comes 

 into normal working condition. 



This critical value to which shade-perception, acuity, and pupillary 

 reaction all point relates, it must be remembered, to the illumination 

 received from the objects viewed considered as secondary light-sources. 

 In too strong light thus received the eye is as seriously dazzled as if 

 the source were a primary one, and the usual effects of after images 

 and other evidences of retinal exhaustion and irritation at once appear. 

 In very insufficient illumination there is failure to see contrast and 

 detail, and there is an instinctive effort to push the eye near to the 

 object at the risk of straining the mechanism of accommodation se- 

 riously. The familiar success of this expedient opens up some of the 

 most curious questions of physiological optics. 



Suppose, for instance, that one is viewing white letters -on a dark 

 ground. Evidently the letter acts as a secondary source of illumina- 

 tion, which proceeds from it, following the law of inverse squares. Now 

 by halving the distance to the eye the intensity at the pupil is quad- 

 rupled, and at first thought one would infer that inspection of the 

 shade-perception and acuity curves would give ample reason for the 

 gain in visibility. But at half the distance the object subtends double 

 the visual angle, and the retinal image is therefore quadrupled in area, 

 leaving the luminous energy per unit of area the same as before ; why, 

 therefore, any gain in visibility ? A similar question in a more aggra- 

 vated form arises in accounting for improved vision through night 

 glasses. 



The key to the situation is found in the fact, put on a sound experi- 

 mental basis by Dr. Charpentier, 8 that for the visible brightness of 



8 " La Lumiere et les couleurs," p. 138 et seq. 



