PROFESSOR AT HEIDELBERG 189 



and fatigue. Neither of these processes is in its time-relations 

 directly conditioned by the action of light. For when the light 

 is cut off, excitation of the points of the retina previously 

 stimulated still persists for a recognizable time in the dark 

 field, and on testing with renewed and equal illumination of 

 the field traces of fatigue are visible for a long time as negative 

 after-images. We can also see how these conditions gradually 

 disappear while the eye is resting in the dark, when they 

 decline very fast and perceptibly at the outset, but the residue 

 subsequently vanishes very slowly. As a rule, indeed, excita- 

 tion dies out more quickly than fatigue. My conclusion is 

 that persistent processes obtain in the living eye, even during 

 the action of light, which tend to abolish both excitation and 

 fatigue; the simplest mathematical expression of this fact is 

 that the velocity with which the excitation 5 disappears, or, if 

 the time be denoted /, the negative differential quotient of s 

 with respect to the time, is proportional to the total strength 

 of excitation at the moment, provided there be no simultaneous 

 action of light. In the same way I assume for the alteration 

 of fatigue / that so long as there is no augmentation by 

 simultaneous excitation we have a differential equation of the 

 same form between / and /. On the other hand, the sensation 

 may of course be reinforced by a new impression of light. 

 This increase as a rule is not sudden, since the fresh exciting 

 impression is added at each moment to the residue of the 

 previous excitation. We may take the consequent incre- 

 ment of excitation as proportional to the luminous intensity 

 of the impression. Further, this rise of excitation is conditioned 

 by the concomitant fatigue, and the increment is less in pro- 

 portion as the fatigue is greater. If we take/= i as the 

 maximum value of the fatigue when the new impression 

 fails to produce any effect, we may take that portion of 

 the differential quotient of s with respect to /, produced by 

 the new light of intensity /, as mi (i /), so that this differen- 

 tial quotient = as + mi (i /). Fatigue is correspondingly 

 augmented by excitation in proportion to the magnitude 

 of stimulus, and this increment may be taken as proportional 

 to the excitation ; hence the complete expression of the 

 alteration of fatigue will be the differential quotient of / 

 with respect to /, viz. bf+ns. The two equations then 



