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47.

interval of altitude, and [[the Greek letter rho]] ^[[ ρ [[subscript]] 0 [[/subscript]] ]]  the density at sea-level, the right member of (8), on being multiplied by [[underlined]] S [[/underlined]] and ^[[ ρ/ρ [[subscript]] 0 [[/subscript]] ]], will give the air resistance, [[underlined]] R [[/underlined]], experienced by the rocket.

A curve representing the relation between density and altitude up to 120,000 ft. is shown in Fig. 21. This curve is derived from a table of pressures and temperatures in Arrhenius' "Lehrbuch der Kosmischen Physik". The ordinates of the curve are the numbers ^[[ρ/ρ[[subscript]] 0 [[/subscript]].]]

Beyond 120,000 ft. the density is calculated by the empirical rule which assumes the density to become halved at every increase in altitude of 3.5 miles. A comparison was made between the values obtained in this way and those obtained from the very probable pressures deduced by Wagener, in the following way: The mean density between two levels for which Wagener gives pressures was obtained by multiplying the difference in pressure by 13.6, and dividing by the difference in level in cm. A comparison showed that the densities used in the present calculations beyond 125,000 ft. were from three to twenty fold larger than those derived from Wagener's data, so that the values used in the present case were doubtless perfectly safe.

Densities beyond 700,000 ft. within the geocoronium sphere, must be negligible; for not only is the density very small but the [[underlined]] resistance to motion [[/underlined]] is very small -- due, according to Wagener, to the properties of geocoronium -- a conclusion which is supported by the fact that meteors remain, for the most part, invisible above this level. 

Transcription Notes:
The measure of air density is symbolized by the Greek letter rho or ? . At sea level density is denoted as ? with a subscript of 0.