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44.

[[underline]] PART III. CALCULATION BASED ON THEORY AND EXPERIMENT [[/underline]].

[[underline]] APPLICATION OF APPROXIMATE METHOD [[/underline]].
 
As already explained this method consists in employing the equations

^[[M = R/a+g (e a+g/c(1-k)t -1) + e a+g/c(1-k) t, (6)
and M = e at/c(1-k), (7)]]

to obtain a minimum [[underline]] M [[/underline]] in each interval, where

M = the initial mass, for the interval, when the final mass is one pound, and

R = the air resistance in poundals over the cross section [[underline]] S [[/underline]], at atmospheric pressure. If we call, [[underline]] P [[/underline]], the air resistance per unit cross section, we shall have for [[underline]] R [[/underline]], ^[[PS S/S[[subscript]] o [[/subscript]] where [[underline]] S [[/underline]] is the density at sea-level,

a = the acceleration in ft. per second^2, taken constant throughout the interval,

g = the acceleration of gravity,

t = the time of ascent through the interval, and c(l-k) = what will be called the "effective velocity", for the reason that the problem would remain unchanged if the rocket were considered to be composed [[underline]] entirely [[/underline]] of propellant material, ejected with the velocity, c(l-k). It will be remembered that [[underline]] c [[/underline]] actually stands for the true velocity of ejection of the propellant, and [[underline]] k [[/underline]] for the fraction of the entire mass that consists of material other than propellant. The effective velocity is taken constant throughout any one calculation.