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5.

By this means the large ratio of propellant material to total mass is kept sensibly the same during the entire flight. This last principle is obviously serviceable only when the most extreme altitudes are to be reached.  In order to avoid damage when the discarded casings reach the ground, each should be fitted with a parachute device, as explained in United States Patent No. 1,191,299.

Experiments will be described below which show that, by application of the above principles,it is possible to convert the rocket from a very inefficient heat engine into the most efficient heat engine that ever has be devised.

[[underlined]] STATEMENT OF THE PROBLEM [[/underlined]].

Before describing the experiments that have been performed, it will be well to deduce the theory of rocket action in general, in order to show the tremendous importance of efficiency in the attainment of very high altitudes.  A statement of the problem will therefore be made, which will lead to the differential equation of the motion.  An approximate solution of this equation will be made for the initial mass required to raise a mass of one pound to any desired altitude, when said initial mass is a minimum.

A particular form of ideal rocket is chosen for the discussion as being very amenable to theoretical treatment, and at the same time embodying all of the essential points of the practical apparatus.  Referring to Fig. 1, a mass [[underlined]] H [[/underlined]], weighing one pound is to be raised as high as possible in a vertical direction by a rocket formed of a cone, [[underlined]] P [[/underlined]], of propellant material, surrounded by a casing [[underlined]] K [[/underlined]].  The material [[underlined]] P [[/underlined]] is expelled downward with a