1. The author proposed the model of diurnal course of air temperature which is required to analyze a crop growth. The relationship between air temperature (x) and time (t) is shown by the following “modified sine-curve (MS-curve)”, x=f(t, A, B, H, k)=(B-A)sin2(πt/2H)+A+k(B-A)sin2(πt/H), for |k|≤1/4 (1)where A is the minimum air temperature, B the maximum one, H the period between emergence times of A and B, and k the modification coefficient which shows the ratio of deviation from sine-curve.The two models of diurnal course of air temperature were devised from MS-curve. The one is “two-half cycle model” which simulates the rising course of the air temperature in a day by the half cycle of x=f(t, A1, B, H, k1) and the descending course by that of x=f(24-t, A2, B, 24-H, k2). The other is “one-half cycle model” which expresses the mean diurnal variation of air temperature by the half cycle of x=f (t, A, B, 24, km). In these equations, A1 and A2 are the morning minimum air temperature and that of the next day, and k1 and k2 are the modification coefficients to the periods A1 to B and B to A2, respectively, km is the daily mean modification coefficient shown by km={k1H+k2(24-H)}/24.2. The air temperature in 1968-1977 at Morioka in Japan was analyzed using these models. The following seasonal values were obtained;k1=-0.01-0.08, k2=-0.20-0.10, km=-0.13-0.05, H=8.4-10.0 hours, and tA=4.2-5.5, where tA is the emergence time of minimum air temperature. It was found that k1 and k2 values investigated for instance at Sapporo, Tokyo and Fukuoka were roughly similar to those values at Morioka. Then, the emergence time periods of classified air temperature, which were calculated from the reverse function of MS-curve using these coefficient values, agreed very well with the observed values.3. The daily mean air temperature θm which is estimated from the integration of MS-curve is shown as follows;θm=(A+B)/2+km(B-A)/2. (2)On the other hand, the daily mean air temperature θn which is obtained from the observations of several times a day is shown as follows;θn=(A+B)/2+lm(B-A), (3)where (A+B)/2 is the average air temperature and lm the coefficient of diurnal range of air temperature to convert (A+B)/2 into θn. The convenient equations of km and θm at Morioka were obtained from Eq. (2). Eq. (3), and the values observed at intervals of three hours as shown below, km=2lm-0.034, and (4)θm=(A+B)/2+(lm-0.017)(B-A). (5)