The upper atmosphere

The density calculations of the following paragraphs are based on the assumptions of diffusion as indicated by Table 3 and temperature‐distribution as shown in Figure 7. The calculations for the atmospheric conditions of summer nights are given in detail since it was considered these figures would be the most useful. The change in atmospheric pressure per centimeter can be calculated for any height Z by the equation or in words PZ+1, the pressure at altitude (Z+1), is equal to the pressure at Z minus the weight of one cubic centimeter of gas at Z. Equation (13) may be written then log PZ = log P0‐Σ0Z log [1 + (WZ/PZ)] but here W0, PC, T0, g0, and M0 represent the weight per cubic centimeter, pressure per square centimeter, temperature, acceleration due to gravity, and molecular weight of any given gas at the initial point, Z = 0, and WZ, PZ, TZ, gZ, and MZ represent the same quantities for the gas at altitude Z. In table 11, calculated values of WZ/PZ are given in column 1 and values of log (1 + WZ/PZ) in column 2 for altitudes from 0 to 100 km. The value of MZ/M0 was considered to be unity below the diffusion‐levels given in Table 4, column 4, for all gases; at these levels an abrupt change is considered to take place and for greater altitudes (MZ/M0) for a given gas is taken as the molecular weight of the given gas divided by 28.95, the molecular weight of air. The change in density is calculated separately for each gas for altitudes greater than 100 km. Table 12 gives values of W/P and log (1 + W/P) for altitudes 100, 500, and 1000 km for the condition of summer night based on the assumption of gravity‐equilibrium for each gas For these calculations (W0/P0), (T0/TZ), and (MZ/M0) are considered constants ; the only variable term in the value of (WZ/PZ).is therefore (gZ/g0), which maybe replaced by (r02/rZ2) where r0 and rZ are distances from the center of the Earth at sea‐level and at the height Z, respectively. The change in (WZ/PZ) is then very nearly linear for these altitudes.