914 CONCENTRATION FACTORS CHAP. 27 



interference of the openings. He calculated that interference should be 

 inversely proportional to the square of the distance between pores, d: 



logQ/Qi = -k/d^ 



where Qi is the diffusion rate at d = oo . This equation agrees well with 

 experimental results of Verduin (1949) and Weishaupt (1935). At a given 

 ratio of pore diameter and pore distance, the interference must be stronger 

 the smaller the pores. The stomata are so small that the diffusion through 

 each of them is reduced significantly by interference — ^sometimes by > 50% 

 of the theoretical value for an isolated opening of the same size. As 

 stomata close gradually, interference weakens; and the diffusion rate 

 therefore declines slower than proportionally to the open area. 



These experiments and their theoretical interpretation explain how the 

 tiny stomata can allow a large volume of carbon dioxide to diffuse into the 

 leaf, thus permitting a high rate of photosynthesis. We now turn to the 

 second question; does the resistance of the stomata impose a significant 

 limit on the carbon dioxide supply and, with it, on the rate of photosynthe- 

 sis? Closed stomata undoubtedly must curtail photosynthesis drastically 

 (restricting it to the utilization of the carbon dioxide that can reach the 

 chloroplasts by diffusion through the cuticle, or is produced in the leaf by 

 respiration). The question is: How far must the stomata be open to 

 cease exercising a restrictive influence on photosynthesis? May this 

 restriction be significant even when slits are fully open? Are they the 

 bottlenecks responsible for the "Blackman features" of many carbon 

 dioxide curves? It will be recalled that, in the preceding chapter, it was 

 shown that the restrictive influence of a reaction step generally becomes felt 

 long before the rate of the over-all process closely approaches the "ceiling" 

 imposed on it by this step. Therefore, the resistance of the stomata may 

 affect the shape of the carbon dioxide curves even when the rate of photo- 

 synthesis is not more than one half or one quarter of the maximum possible 

 flow of carbon dioxide through the stomata. 



For an experimental study of the influence of stomata on photosynthesis, 

 one must measure the rate of photosynthesis under constant external con- 

 ditions, but with varying apertures of the stomata. Unfortunately, treat- 

 ments used to enforce partial closure of the stomata (such as incubation in 

 darkness or in dry air) may also directly affect the efficiency of photosyn- 

 thesis, so that caution is required in the interpretation of the results. In 

 order to arrive at reliable conclusions, the width of the stomata and the 

 rate of photosynthesis must be determined with the same leaf^a condition 

 that has not always been fulfilled. 



The relation between stomatal openings and the rate of photosynthesis 



