54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. JI 



is evidently well suited for such a purpose, in that the time of rise 

 and fall would be short, so that the apparatus could easily be found 

 on the return. Thus the expense wo*uld be slight, being simply that 

 of a fresh magazine of cartridges for each day. 



For this work, as well as for that previously described, the head of 

 the rocket should be prevented from rotating, by means of a gyro- 

 scope, such as is explained in United States Patent, No. 1,102,653. 



CALCULATION OF MINIMUM MASS REQUIRED TO RAISE ONE 

 POUND TO AN "INFINITE" ALTITUDE 



From the fact that the preceding calculation leads us to conclude 

 that such an extreme altitude as 2,310,000 ft. (over 437 miles) can be 

 reached by the employment of a moderate mass, provided the effici- 

 ency is high, it becomes of interest to speculate as to whether or not 

 a velocity as high as the " parabolic " velocity for the earth could be 

 attained by an apparatus of reasonably small initial mass. 



Theoretically, a mass projected from the surface of the earth with 

 a velocity of 6.95 miles/sec. would, neglecting air resistance, reach 

 an infinite distance, after an infinite time ; or, in short, would never 

 return. Such a projection without air resistance, is, of course, impos- 

 sible. Moreover, the mass would not reach infinity but would come 

 under the gravitational influence of some other heavenly body. 



We may, however, consider the following conceivable case: If a 

 rocket apparatus such as has here been discussed were projected to 

 the upper end of interval Sg, either with an acceleration of 50 or 150 

 ft./sec.^, and this acceleration were maintained to a suificient distance 

 beyond j-^, until the parabolic velocity were attained, the mass finally 

 remaining would certainly never return. 



If we designate as the upper end of S9 the height at which the 

 velocity of ascent becomes the " parabolic " velocity, it will be evident 

 that this height will be different for the two accelerations chosen, 

 inasmuch as the " parabolic " velocity decreases with increasing dis- 

 tance from the center of the earth. 



If we call u = the " parabolic " velocity at a distance H above the 

 surface of the earth, 

 V, =:the velocity acquired at the upper end of interval s^, 

 Soothe height of the upper end of Sg above sea-level, 

 we have, taking the radius of the earth as 20,900,000 feet, 



u = Vi-|-at, (11) 



H = So-(-Vit + iat2, (12) 



