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51.

Thus, in order that the initial mass for [[underlined]] s [[/underlined]][[subscript]] 7 [[/subscript]] shall be a minimum, the acceleration must become very large, with consequent severe strains in the rocket apparatus and instruments carried by the rocket; to say nothing of the difficulty of firing with sufficient rapidity to produce such large accelerations. It thus becomes advisable to choose a moderate acceleration in [[underlined]] s [[/underlined]][[subscript]] 7 [[/subscript]] and [[underlined]] s [[/underlined]][[subscript]] 8 [[/subscript]], and not to assign a velocity, [[underlined]] v [[/underlined]][[subscript]] 1 [[/subscript]], as was done in the preceding intervals. Two accelerations are chosen, 50 ft/sec[[superscript]] 2 [[/superscript]]. and 150 ft/sec[[superscript]] 2 [[/superscript]]., respectively. The interval [[underlined]] s [[/underlined]][[subscript]] 9 [[/subscript]], also calculated for assigned accelerations, will be explained in detail below. In all cases, when either one of these accelerations is mentioned in connection with [[underlined]] s [[/underlined]][[subscript]] 6 [[/subscript]] and [[underlined]] s [[/underlined]][[subscript]] 9 [[/subscript]], this acceleration will be understood as having been taken also in the preceding intervals, beyond [[underlined]] s [[/underlined]][[subscript]] 6 [[/subscript]]. 

In order to see how far the effective velocity, c(1-k) may fall short of 7,000 ft/sec. and still not render the rocket impracticable, a few additional columns for [[underlined]] M [[/underlined]] are calculated. 

In the first of the additional columns, [[underlined]] M [[/underlined]][[subscript]] 2 [[/subscript]], the effective velocity is taken as 3,500 ft/sec., namely, half that of the preceding calculations. This allows of considerable inefficiency of the apparatus, in a number of ways. For example, the product 

c(1-k) = 3,500,

may be given by the same proportionality, [[underlined]] k [[/underlined]], as before, but with a velocity of ejection of the gases as low as 3,750 ft/sec. On the other hand, the velocity of ejection may be as large as before i.e., (7,500 ft/sec.); and the proportionality, [[underlined]] k [[/underlined]], increased to 0.533; meaning, of course, that the rocket now consists of more mechanism than of propellant. 

The second additional calculations, [[underlined]] M [[subscript]] RI [[/subscript]][[/underlined]], are carried out under the assumption that a reloading mechanism is used, with [[underlined]] k [[/underlined]] as