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[[centered]] 55. [[/centered]]

230 miles from sea-level, practically the limits of the Earth's atmosphere, requires under 90 lbs; and an altitude of 118 miles, close under the geocoronium sphere, only 38 lbs. First start at 15,000 ft., the masses are of course, less; namely 49.3 lbs. and 20.9 lbs., respectively.

The enormous difference between the total initial masses of wired for low-efficiency rockets, compared with those for high, may at first appear surprising; but they should be expected from the exponential nature of equations (6) and (7). Thus if the "effective velocity" is reduced from 7^[[,]]000 ft/sec. to half this value, the minimum masses for each interval, neglecting air resistance, will be those for 7^[[,]]000 ft/sec. [[underline]]squared[[/underline]]; and including air resistance, still greater. Similarly for an effective velocity of 960 ft/sec. which is that for reloading rockets having the same velocity of ejection at Coston ship rockets, the minimum masses will be those for 7^[[,]]000 ft/sec. [[underline]]raised to the 7.28th power[[/underline]]; and for bundles or groups of ship rockets, as shown in Fig. 22, the minimum masses will be those for 7^[[,]]000 ft/sec., raised to the [[underline]]27.2th[[/underline]] power. Even when air resistance is entirely neglected in the calculations for the last case, ^[[/the]] masses are of much the same magnitude, as shown in Table VII. The large values of the masses [[underline]]M[[subscript]]RI[[/subscript]][[/underline]] and [[underline]]M[[subscript]]R 2[[/subscript]][[/underline]] simply express the impossibility of employing rockets of low efficiency. Attention may be called to the particular case under [[underline]]M[[subscript]]R2[[/subscript]][[/underline]] (the groups of ship rockets indicated in Fig. 22) in which one pound is raised to the altitude of 1,228,000 feet (232 miles); the "total initial mass" in this case, even neglecting air resistance entirely, is 2.89 × 10^[[18]]. lbs., or [[underline]]over six fold greater then the entire mass of the earth[[/underline]].