86 PKOCEEDINGS OF THE AMERICAN ACADEMY. 



objects giving images less than about 0.15 mm. in diameter the simple 

 la^w of inverse squares holds. In other words, for weak stimuli at least, 

 the visibility of small objects is determined by the total light emitted 

 and by the distance and not by the surface brilliancy. It is as if 

 a retinal area of about 0.15 mm. diameter acted as a visual unit, all 

 stimuli acting upon this as a whole. As Charpentier (loc. cit.) puts 

 the case with reference to distance, " In a word, the apparent brightness 

 of a luminous object varies, other things being equal and within the 

 limits indicated, in inverse ratio with the square of its distance from 

 the eye." 



As the eye then approaches a luminous object its apparent brightness 

 increases, and it is distinguished more plainly so long as its image di- 

 mension is anywhere within the limit mentioned. As this corresponds 

 to an object 2 mm. long at a distance of about 20 cm., the rule holds 

 for reading type and the observation of small objects generally. The 

 cause of this phenomenon is somewhat obscure. The natural suppo- 

 sition that it migiit well be due to spherical aberration and faulty 

 accommodation in an eye with its pupil expanded, fails, as Charpentier 

 (loc. cit.) shows, in two ways. First, the circle of diffusion in the eye 

 due to spherical aberration is much smaller than the critical diameter 

 in this case, and second, the phenomenon occurs when the eye is stopped 

 by a diaphragm. I have tried it with a wedge photometer provided 

 with a pair of 2 mm. apertures in line and separated by 6 mm., so 

 that the ray pencil was of very narrow aperture, and find it still very 

 conspicuous and apparently unchanged. 



Charpentier and others are disposed to think its origin purely retinal, 

 resulting from the spreading of the stimulus over retinal elements ad- 

 jacent to those immediately concerned, and closely allied to the phe- 

 nomenon of irradiation. 



This latter phenomenon, however, is charged by Helmholtz largely to 

 aberrations and dioptric faults generally. One of the best sources for 

 studying irradiation is an incandescent lamp filament. At a distance 

 of say 2 meters the apparent diameter of the filament at full incandes- 

 cence is 4 or 5 mm. Using the wedge photometer upon it, the diminu- 

 tion of apparent diameter is at first rapid, until it falls to about 0.5 

 mm., at which it remains nearly constant until it completely vanishes. 

 Stopping down the pencil of rays to 1 mm. or so cuts oif most of the 

 irradiation, but this seems to act in the main merely as a reduction of 

 intensity, since the same effect is produced by a similar reduction in 

 intensity by the wedge retaining the full aperture of about 5 mm. At 

 a few hundredths of a meter-candle most of the irradiation has disap- 

 peared. The apparent breadth of the filament decreases without any 



