THE LOCAL QUANTITATIVE EFFECT 119 



brighter. Sometimes the smaller appeared the larger. On approaching 

 the objects the difference in apparent brightness increased whilst the 

 sizes remained equal. Then followed a stage in which the difference in 

 apparent brightness diminished, the sizes remaining equal ; both might 

 even appear of the same brightness. On still further approximation 

 the difference in brightness again became manifest, and simultaneously 

 or shortly afterwards the larger object showed indefiniteness of the 

 edges and greater apparent size. In many cases the size and brightness 

 remained the same until the difference in size became distinguishable. 



Asher's explanation is as follows : So long as the objects subtend 

 so small a visual angle that they cover a single sensibility area 1 they 

 appear equal, since the same quantity of light acts upon the sensibility 

 area. With increase of the visual angle the influence of aberration 

 becomes manifest. The larger object has a larger light area which is 

 larger than a sensibility area, but the periphery of the light area has so 

 low an intensity that the effective light area is not larger than a sensi- 

 bility area. The smaller object, on the other hand, has a smaller light 

 area, the effective part of which, however, is as large as a sensibility 

 area. The ordinates corresponding to an effective brightness may extend 

 farther from the centre for the smaller than for the larger object, so 

 that the smaller may appear the brighter. So long as the relationship 

 of the objects is such that the sensibility areas of both cover one or 

 an equal number of sensibility areas they must appear of equal size, 

 though the aberration areas may be very different. The conditions 

 of light and contrast may easily be such that the smaller sensibility 

 area may belong to the larger aberration area. 



Asher denies that any proof has yet been given that it is possible to 

 produce a retinal image so small as to stimulate only one cone. 



Schoute 2 does not agree with Asher that it is impossible to stimulate 

 a single cone, and he holds that for single cone images the impression 

 of size is dependent solely upon the product of the area into the light 

 intensity. If only one cone is stimulated the object always appears 



1 Mach (18G6) first distinguished between the physical distribution of light over the 

 area of a retinal image and the physiological distribution of brightness over the same 

 area. If the retina be imagined flattened out and ordinates erected upon it, the lengths 

 of which correspond with the intensities of light at the given spots, the area obtained by 

 joining the summits of the ordinates will give an area representing the light intensity, or 

 more briefly a "light area." If the ordinates represent the apparent brightness of the 

 light at the spots as seen by the observer, the area will represent the sensibility and is 

 briefly termed a "sensibility area." 



2 Ztsch. f. Psychol. u. Physiol. d. Sinnesorg. xix. 252, 1899; Ztsck. f. Augenhlk. vm. 

 419, 1902. 



