It should be noticed that when we grow plants in a closed room like a glasshouse, their environment is quite different from that out of doors. Regarding the concentration of carbon dioxide in the air, it is increased in the glasshouse to get more harvest in recent experiments. But most glasshouses and phytotrons in this counntry maintatin the supply of carbon dioxide by ventilation. A study on this matter was made earlier by MORRIS et al. (1954). Since then, this problem has not been developed further. MORSE and EVANS (1962) designed the CSIRO Phytotron using MORRIS' hypothetical minimum ventilation rate. Furthermore, MORSE (1963) calculated the ventilation rate of the growth cabinet, assuming that the plant net assimilation rate was constant in spite of the large decrease in carbon dioxide concentration in the air. In the present paper, our study is to improve the methods used by MORRIS and MORSE, and to demonstrate the close relationship between the plant net assimilation rate and the ventilation rate in wide range of values of parameters. We assume that the plant net assimilation rate has a linear relation with the concentration of carbon dioxide in the air, i. e., a=C-Cc/C0-Cc-a0, C≥Cc, where a is the rate of net assimilation in the glasshouse per unit area per unit time (g/m2hr), C is the concentration of carbon dioxide in the glasshouse per unit volume (g/m3), Cc is that of compensation point (g/m3), C0 is that out of doors (g/m3), and a0 is the rate of net assimilation out of doors (g/m2hr). In Fig. 1, the line (A) is used by us, and the other (B) was shown by Morris et al. We also assume that the concentration of carbon dioxide in the atmosphere near the ground is constant in the daytime, the molecule of carbon dioxide in the glasshouse is always mixed uniformly, the influence of the temperature coefficients of respiration and assimilation are small, and the concentration of carbon dioxide is the limiting factor of plant photosynthesis. In this paper we shall confine the discussion to the simple problem of the soil free carbon dioxide in the glasshuose.We calculated the efficiency of plant assimilation rate in two ways. One isa/a0=m·z+2m/m·z+2m+1, where m is ce·v/a0·s, z is ventilation rate (1/h), v is the glasshouse air volume (m3), Ce is C0-Cc, s is growing area (m2), and a is (a0+ai)/2. This equation was solved using a linear approximation in the change of carbon dioxide concentration. The other is the strict solution of this problem, that is, ai/a0=1-a0/ce·j·z+a0{1-exp[-(z+a0/ce·j)t]} where j is V/S, t is time, ai is the plant net assimilation rate in the glasshouse. If a0 and Ce are fixed at 5.0g/m2hr (MORSE and EVANS, 1962) and 0.394g/m3 (Egle 1951) respectively, the ratio aj/a0 is the function of t with parameters i and z. Suppose the obtainable values of j are from 1 to 15 and that of z are from 1 to 100, the computation of this equation is very complicated, Taking t from 0.05 to 0.5 at the interval of 0.05 and from 0.5 to 5 at the interval of 0.5, j as integer, and z from 1 to 20 continuously, 25, 30, 40, 50 and 100, we calculated this equation using the electric computer at the Computation Centre, University of Tokyo. Some of the typical exmples are shown in Fig. 3.

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