278 BOTANICAL GAZETTE [april 



Summation of light stimuli. — It is well known that stimvdij too brief to produce 

 a visible reaction, if repeated at intervals not too long, lead to a response, just as 

 continuous stimulation for a sufficient time does. Wiesner found that when 

 intermittent light stimuli followed each other within double the period of their 

 duration, reaction began as soon as though the plants had been continuously 

 stimulated. Generalizing from this he concluded that summation of the stimuli 

 occurred without loss during the intervals. Talbot's law, however, which 

 holds with extreme exactness for the human eye, indicates that the effect of an 

 intermittent light can only equal that of a constant one of lower intensity. Thus, 

 if a light of intensity i acts for x seconds, at intervals of 3.V seconds, its stimulating 

 effect will be equal to that of a light of i/4 intensity. Obviously if this law be 

 valid for heliotropic reactions of plants, reaction time, which alone Wiesner 

 determined, cannot be a correct index of the eflfects of light as a stimulus- 

 Nathansohn and Pringsheim showed that this is so, and further undertook to 

 make an extended comparison of the effects of constant and intermittent light 

 stimuli.8 Using such lights on opposite sides of seedlings of Brassica and 

 Avena, they find that Talbot's law is valid for heliotropic phenomena within 

 reasonable limits. Only when the frequency and duration of the illumination 

 was greatly reduced, as to i| minutes duration with darkness 3? minutes, did 

 the point of physiological indifference depart from the optical one (determined 

 by the photometer) in favor of the intermittent light. Thus they established 

 that there was, for plants as for the eye, a so-called critical periodicity. ^^Tien 

 mtermittent stimuli are too slow, the eye sees a flickering; the plant responds by 

 pendulum-like swings instead of a steady curvature. They also found the law 

 valid within wider limits with weaker illumination than with strong. 



In an elaborate theoretical discussion they propose to account for the obser\-ed 

 phenomena of summation thus : They assume, with Helmholtz, that the primar)' 

 excitation is photochemical, and that its effect is proportional to the product of the 

 intensity by the time of illumination. This produces a certain excitation, which 

 IS steadily maintained in constant illumination, but falls in the dark interval of 

 mtermittent illumination. In both cases a counter-reaction is assumed to be 

 released, which antagonizes the primary reaction, and must be overcome if the 

 atter is realized vasibly. With constant illumination the algebraic sum of the 

 light excitation and the counter-reaction determines the maximum effect. In 

 intermittent light the counter-reaction is effective in the dark intervals in reducing 

 the effect of each excitation, the remainder being added to by the next impulse, 

 which serves at the same time to heighten the counter-excitation, and so on. As 

 ^v-^ und erstand it, the case for constant illumination might be represented thus: 

 a b-c, a being the total direct excitation, b the total counter excitation, and 

 c the response, with intensity i. At the intensity 2/, and alternate equal periods 

 °^_|^g^t^d arkness, the case is this : {x-y) + [x-iy + k)]+n=c; where x is 



9 Nathaxsohx, a. und Pringsheim, E., Ueber die Summation intermittierende 



Lichtreise. 



Jahrb. Wiss. Bot. 45:137-190. 1907. 



