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^[[TL 782 G63 1919 NASMRB]]

i.

[[underline]] OUTLINE [[/underline]]

A search for methods of raising recording apparatus beyond the range for sounding balloons (about 20 miles) lead the writer to develope a theory of rocket action, in general (pages 5 to 11); taking into account air resistance and gravity. The problem was to determine the minimum initial mass of an ideal rocket necessary, in order that on continuous loss of mass, a final mass of one pound would remain, at any desired altitude.

An approximate method was found necessary, in solving this problem (pages 9 to 11), in order to avoid an unsolved problem in the Calculus of Variations. The solution that was obtained revealed the fact that surprisingly small initial masses would be necessary (Table VII, page 53) [[underline]] provided the gases were ejected from the rocket at a high velocity [[/underline]], and also provided that [[underline]] most of the rocket consisted of propellant material [[/underline]]. The reason for this is, very briefly, that the velocity enters [[underline]] exponentially [[/underline]] in the expression for the initial mass. Thus if the velocity of the ejected gases be increased five fold, for example, the initial mass necessary to reach a given height will be [[underline]] reduced to the fifth root [[/underline]] of that required for the lesser velocity. (A simple calculation, page 58, shows at once the effectiveness of a rocket apparatus of high efficiency.)

It was obviously desirable to perform certain experiments; first with the object of finding just how inefficient an ordinary rocket is, and secondly, to determine to what extent the efficiency could be increased in a rocket of new design. The term "efficiency" here means the ratio of the kinetic energy of the expelled gases to the heat energy of the powder; the kinetic energy being calculated