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[[centered]] 54. [[/centered]]

Obviously if the start is made at a high elevation, the "total initial mass" required to reach a given height will be less than for a start at sea-level; due not only to the fact that the apparatus is not raised through so great a height, but also to the fact that the denser part of the atmosphere is avoided. Table VI gives minimum masses, [[underline]]M[[/underline]], calculated for a start with zero velocity from the beginning of interval [[underline]]s[[/underline]][[subscript]]3[[/subscript]] (i.e., 15,000 ft.); The effective velocity being 7,000 ft/sec., as in Table V.

It happens that the velocity [[underline]]v[[/underline]][[subscript]]1[[/subscript]] for minimum [[underline]]M[[/underline]] in the interval [[underline]]s[[/underline]][[subscript]]6[[/subscript]] of Table VI is the same as the [[underline]]v[[/underline]][[subscript]]1[[/subscript]] for the same interval in Table V. The calculations that have been made for the intervals beyond [[underline]]s[[/underline]][[subscript]]6[[/subscript]] apply therefore to the present case, and the only difference between the two cases is that the masses required to reach [[underline]]s[[/underline]][[subscript]]7[[/subscript]] will be greater, for the start at sea-level, then for the start at 15,000 ft.

The calculations, beginning at 15,000 ft. have been carried out in Table VII for all but the lowest "effective velocity"; and it will be observed that the start from a high elevation becomes important only for the lower "effective velocities".

The most striking as well as the most important conclusion to be drawn from Table VII is the small "total initial mass" required to raise one pound to very great altitudes when the "effective velocity is 7^[[,]]000 ft./sec; the mass for the height of 437 miles (2,310,000 ft.) for example, being but 12.33 lbs., starting from sea-level. [[underline]]even for "effective velocity" of 3^[[,]]500 ft/sec.[[/underline]], which allows of considerable inefficiency in the rocket apparatus, [[underline]]the mass is sufficiently moderate to render the method perfectly practicable,[[/underline]] for in this case an altitude of over