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65.

The effect of air resistance, in [[underlined]] s [[/underlined]] [[subscript]] 9 [[/subscript]] is 
negligible, if we accept Wagener's conclusions, above mentioned, concerning the properties of geocoronium. But even if we use the empirical rule of a fall of density to one half for every 3.5 miles we shall find the reduction of velocity very small on passing from the upper end of [[underlined]] s [[/underlined]] [[subscript]] 8 [[/subscript]] (500,000 ft.) to 1,000,000 ft. (beyond which the density is negligible). This is shown in Appendix F, p. 79.
 
The "total initial masses", to raise on pound to an "infinite" altitude, for the two accelerations chosen, are given in Table VII. It will be observed that they are astonishingly small; [[underlined]] provided the efficiency is high [[/underlined]]. Thus with an "effective velocity" of 7,000 ft/sec., and an acceleration of 150 ft./sec[[exponent]] 2 [[/exponent]], the "total initial mass", starting at sea-level is 602 lbs; and starting from 15,000 ft. is 438 lbs. The mass required increases enormously, with descreasing efficiency; for, with but half of the  former "effective velocity" (3,500 ft/sec.) the "total initial mass", even for a start from 15,000 ft., is 351,000 lbs. The masses would obviously be slightly less if the acceleration exceeded 150 ft./sec.[[exponent]] 2 [[/exponent]]

It is of interest to speculate upon the possibility of proving that such extreme altitudes had been reached even if they actually were attained. In general, the proving would be a difficult matter. Thus even if a mass of flash powder, arranged to be ignited automatically after a long interval of time, were projected vertically upward; the light would at best be very faint, and it would difficult to foretell, even approximately, the direction in which it would be most likely to appear.