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11.

for the interval in question. the "total initial mass" required to raise one pound to a desired altitude may thus be had as the product of the minimum [[underlined]] M's [[/underlined]] for each interval, obtained in this way.

From equations (6) and (7) we see at once the importance of high efficiency, if the"total initial mass"is to be reduced to a minimum.  Consider the exponent of [[underlined]] e [[/underlined]].  The quantities [[underlined]] a [[/underlined]], [[underlined]] g [[/underlined]] and [[underlined]] t [[/underlined]] depend upon the particular ascent that is to be made, whereas c(1-k) depends entirel y upon the efficiency of the rocket; [[underlined]] c [[/underlined]] being the velocity of expulsion of the gases, and [[underlined]] k [[/underlined]], the fraction of the entire mass that consists of loading and firing mechanism, and of magazine.  In order to see the importance of making c(1-k) as large as possible, suppose that it were decreased ten fold.  Then e a+g/c(1-k) t would be [[underlined]] raised to the 10th power [[/underlined]], in other words, the mass for each interval would be the [[underlined]] original value multiplied by itself ten times [[/underlined]].