PHYSIOLOGICAL STUDIES 47 



ring. As we have seen in Chapter 2, the diffusion path be- 

 tween the assimilating cells and the external medium varies 

 considerably in different plants, and thus the concentration 

 of carbon dioxide at the assimilatory centres will vary in 

 different plants even for a fixed external concentration. In 

 Chlorella the difference between the 'internal' and the exter- 

 nal concentration of carbon dioxide is very small, so that the 

 experimental curve might be expected to approximate to the 

 Michaelis type. In a water plant of more complex structure 

 the diffusion path for carbon dioxide may be much longer, 

 especially in the experiments of Blackman in which some 

 shoots of Elodea were placed on top of others. In such a case 

 we must combine with the Michaelis equation, which ex- 

 presses the rate as a function of the 'internal' concentration, 

 a second expression derived from Pick's law relating the 

 'internal' to the external concentration. If the length of the 

 diffusion path is L, the coefficient of diffusion K, then if C 

 is the concentration in the external medium and Cg that 

 where the reaction takes place, the rate of diffusion per unit 



area will be -y(C-Cs). In addition to this supply of carbon 



dioxide there will be that from respiration and we shall con- 

 sider only the simplest case in which all the carbon dioxide 

 from respiration is assumed to be immediately available to 

 photosynthesis. In the steady state the rate of consumption, 

 i.e. the rate of photosynthesis, must equal the total rate of 

 supply of carbon dioxide, so that if the relation between rate 

 of photosynthesis {R) and concentration of carbon dioxide 

 at the reaction centre is of the Michaelis type, then 



when r is the rate of production of carbon dioxide in respira- 

 tion. Hence 



LR''-R[KC+L.r+KKc+Rco-L]+Ra,[K.C+L.r]=o 

 When the diffusion path becomes very long the term -j^c 



