ioio THE SENSES 



' trail ' of a falling star, or the fiery circle traced in the air when a fire- 

 brand is rapidly whirled round. But the maximum retinal excitation 

 which a stimulus of given strength can call forth depends much more 

 closely upon the time during which the stimulus acts than the maximum 

 contraction does upon the length of the muscular stimulus. 



As the strength of the light increases in geometrical progression, the 

 time during which it must act in order to produce its maximum effect 

 decreases approximately in arithmetical progression (Exner) . For light 

 of moderate intensity this time is about second. Since for complete 

 fusion the stimuli must follow each other at a much more rapid rate 

 than four in the second, the intensity of the resultant sensation is 

 always less when a succession of similar stimuli are fused than when one 

 of the stimuli is allowed to produce its maximum effect. 



If the time of each stimulus is equal to the interval during which 

 there is no stimulation, the sensation, when complete fusion has been 

 reached, is the same as would be produced by a constant light of half 

 the strength employed. And, in general, if m be the proportion of the 

 time during which the eye is stimulated by a light of intensity 7, and n 

 the proportion of the time during which it is not stimulated, the resultant 

 impression is the same as that which would be produced by an un- 

 interrupted light of intensity ( Z~/^' This is Talbot's law, which 



may be expressed without the aid of symbols thus: When a light of 

 given intensity is allowed to act on the eye at intervals so short that the 

 impressions are completely fused, the resultant 

 sensation is independent of the absolute length of 

 each flash, and is proportional only to the fraction 

 of the whole time which is occupied by flashes and 

 to the intensity of the light. Talbot's law may be 

 readily demonstrated by means of a rotating disc 

 with alternate white and black sectors (Fig. 

 427), so arranged that the same proportion of the 

 circumference of each of the three concentric 

 zones is black. 



When the rotation is sufficiently rapid to give 

 Fig. 427. Disc for de- complete fusion (say 20 to 30 times a second), 

 monstrating Talbot's the whole disc appears equally bright. However 

 law. much the rate of rotation is now increased, no 



further change occurs. It has been shown that 



even for stimuli as short as the 8ooowo th of a second, repeated at 

 intervals of yigth second, Talbot's law holds good. So that not only 

 does a flash so inconceivably brief affect the retina, but it sets up 

 changes which last for a measurable time. For intense stimuli Talbot's 

 law ceases to be true: the field appears brighter than it should be 

 (Griinbaum) . 



Two chief theories have been proposed to account for the fusion of 

 intermittent retinal stimuli: (i) The persistence theory, according to 

 which the excitatory process in the retina remains for a short time at 

 the maximum reached when the light ceases to act. Steady fusion is 

 supposed to be obtained when the interval between successive stimuli 

 does not exceed this time. (2) The theory of Fick, who maintains that 

 as soon as the light is withdrawn the retinal excitation begins to sink, 

 at first rapidly, then more gradually. As the rate of stimulation is 

 increased the time allowed for the decline of the excitation is of course, 

 correspondingly shortened, and ultimately the oscillations become so 

 small that a continuous smooth sensation results Fick's theory 

 appears to explain the phenomena best. 



