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50.

[[underlined]] without [[/underlined]] overcoming [[underlined]] R [[/underlined]] and [[underlined]] g [[/underlined]]; [[underlined]] and the entire calculation must be repeated until a minimum value of this ratio is obtained [[/underlined]], -- when the corresponding mass, [[underlined]] M [[/underlined]], will be the minimum mass for the interval in question. These minimum [[underlined]] M [[/underlined]]'s are marked in the tables by a start (*).

This process is carried out for each interval beginning with the first. 

It should be noticed that, although [[underlined]] R [[/underlined]] and the density are not constant in any interval, the result obtained by taking the mean of the quantities must nevertheless give results close to the truth, owing to the fact that [[underlined]] R [[/underlined]] increases during the ascent whereas the density decreases. 

[[underlined]] EXPLANATION OF TABLES V and VI. [[/underlined]]

It should first be explained why no minimum [[underlined]] M [[/underlined]] has been calculated for the intervals [[underlined]] s [[/underlined]][[subscript]] 7 [[/subscript]] and [[underlined]] s [[/underlined]][[subscript]] 8 [[/subscript]], only for extremely high velocities, v[[subscript]] 1 [[/subscript]]; although for [[underlined]] s [[/underlined]][[subscript]] 7 [[/subscript]] a secondary minimum occurs for v[[subscript]] 1 [[/subscript]] = 8,000 ft/sec. Even for v[[subscript]] 1 [[/subscript]] = 30,000 ft/sec. the minimum has not yet been attained for this interval, although the acceleration required to produce this velocity is 6,000 ft/sec.[[superscript]] 2 [[/superscript]]. The reason for this state of affairs is evident at once from the fact that the density ratio, s/so, is very small for [[underlined]] s [[/underlined]][[subscript]] 7 [[/subscript]], and also from the fact that [[underlined]] a [[/underlined]] occurs in the denominator of the term containing [[underlined]] R [[/underlined]] in equation (6), so that the large acceleration counterbalances the increase in [[underlined]] R [[/underlined]].