Quoted by O.F.F. Grünbaum, 'On Intermittent Stimulation of the Retina (Part II)', Journal of Physiology 22 (6) (1898), pp. 433-450
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'It is surprising that writers after Fick's explanation [of the cause of extinguish of flicker] did not adopt his view, since even if Exner's statement that under normal conditions the duration of the after-image of undiminished brightness is infinitely short, be disallowed, nevertheless the persistence-theory seems unsatisfactory; to illustrate this I cannot do better than quote a passage from Rood's [note: 'p. 207. 1879.'] Modern Chromatics. 

"The duration of the sensation of light or the duration of the impression of the retina, as it is called, varies with the intensity of the light producing it, and in the case of white paper is not by any means so great as with the coal of fire. According to an experiment of Helmholtz the impression on the retina lasts in this case with undiminished strength about 1/48 of a second; hence it is necessary for the disc to revolve 48 times per second in order to produce the appearance of a steady uniform ring of light. While as just stated the impression lasts for 1/48 sec., its total duration with decreasing strength is greater, being perhaps as high as 1/3 sec., though the interval varies with the circumstances and is a little difficult of determination.

"It is not however to be supposed that in the experiment the ring of white light will have the same luminosity as its source, viz.: the slip of white paper on the black disc; on the contrary the luminosity of the ring will be much feebler than that of the source. The reason is quite evident: we have virtually spread out the light of the spot over a much larger surface and it will be proportionately weaker, if the surface of the ring is one hundred times as great as that of the spot, then the luminosity of the ring will be exactly one hundredth that of the spot."

Assuming that the statements are correct the reason seems to me far from obvious. Remembering that the "duration of the impression with undiminished strength lasts 1/48 sec." and the disc rotates 48 times per sec., if the duration of exposure of the stimulus be sufficient for it to produce its maximum sensation, we should be led to suppose that the resultant ring would be as bright as its source, while if the duration of exposure be too short for the maximum sensation to be developed, then protracted observation would produce a gradual increase in the brightness of the ring owing to a summation of stimuli.' (444-445)