The change of the temperature of the traveling air mass may be expressed in first approximation by dθ/dt=-α(θ-_??_), whereθ is the temperature of the air mass, _??_the temperature of the earth's surface, α a constant. Hence, the temperature of the air mass is calculated by giving initial air temperature θ₀ and distribution of the temperature of the surface. After some calculation we have θ=αθ₀+b_??_, where a and b are constants which depend on t. Putting α=1.4 day^-1 which is estimated by the analysis on synoptic chart, and t=24 hours we have θ(24h)=0.53θ₀+0.47_??_(24h).
That is to say, the temperature after 24 hours is given by averaging initial temperature of the air mass and the surface temperature at the point where the air mass will reach after 24 hours. And the above formula is confirmed by the actual data.
The maximum temerature in a day is predicted from the results of aerological observation in early morning. It is derived theoretically that the maximum termperature θ_m is given in good approximation by θ_m=θ_h+c where θ_h is the upper air temparature about 1000m above the earth surfce, c a constant which depends on weather. The results are also confirmed by the actual data.