KINETIC ANALYSIS OF PHOTOPERIODISM 461 



various times during a 16-hr night, which has followed an 8-hr photo- 

 period. The response was measured in terms of the floral stage at- 

 tained at the end of the experiment as observed by microscopic dis- 

 section. A completely effective flash is one which prevented any 

 development in the direction of a floral stage and the ordinant quanti- 

 ties would be zero. It is seen that the middle of the dark period is the 

 time at which the flash has its maximum effectiveness. It is less effec- 

 tive either before or after this period. This is in contrast to the 

 response of the hypocotyl hook of bean in which a single flash of 

 enerey has its maximum effectiveness at the bednning of a 20-hr 

 dark period, and flashes applied at later times are decreasingly effec- 

 tive because there is less time available for a growth response to occur. 

 One of the most amazing features of the photomorphogenic system 

 is the extreme range over which the response is proportional to the 

 logarithm of the incident energy. This is graphically shown in Fig. 8 

 for oat and bean seedhngs. The response is proportional to the 

 logarithm of the incident energy above a certain low value, and below 

 this point it is directly proportional to the incident energy. This is 

 shown by the curving of the straight line in the case of the bean hook 

 responses. In the hook response, which involves an inhibition of length 

 growth in the hypocotyl as a result of a photochemical reaction by 

 red energy, there is an extremely great range of linearity. In the graph, 

 the data are plotted for six orders of magnitude from 1 to 1,000.000 

 Mw/cm^. However, we know that this curve continues for at least two 

 more orders. This is an extremely wide range of stimulus value for 

 any continuous function. This has many characteristics of the Weber- 

 Fechner law, although here the logarithmic response seldom holds for 

 more than two orders of magnitude in animals. The equation for the 

 linear portion of these curves is given by: 



/3 = Mi\og)E/E^ (1) 



differentiating 



D(3 - A' de/e (2) 



where /3 is the response in terms of angle of hook opening or stimula- 

 tion of the epicotyl or inhibition of the growth of the hypocotyl, M is 

 the slope constant, E is the incident energy, and Em is the minimum 

 energy requirement which is the value of energy at zero response. This 



