NO. 2 METHOD OF REACHING EXTREME ALTITUDES 55 



and also the equation relating " parabolic " velocity to distance from 

 the center of the earth 



36,700 _ / 20,900,000+ H 



u 



/ 20,900^00+ H . s 



\ 20,900,000 ' ^ 



On putting the values of u and H, from (ii) and (12), in (13), 

 we have 



Y'2o,90o,ooox 36,700= (vi + at) V 21, 400,000 + Vj^t + ^-at'. (14) 



Equation (14) is a biquadratic in t, from which t may easily be 

 obtained (by trial and error). The values of t, for the two accelera- 

 tions chosen, given in table V, enables u and the initial masses for s^, 

 to be at once obtained. 



The effect of air resistance in Sj, is negligible, if we accept 

 Wegener'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 Sg (500,000 ft.) 

 to 1,000,000 ft. (beyond which the density is negligible). This is 

 shown in Appendix F, page 64. 



The " total initial masses," to raise one pound to an " infinite " 

 altitude, for the two accelerations chosen, are given in table VIL 

 It will be observed that they are astonishingly small, provided the 

 efficiency is high. Thus with an " effective velocity " of 7,000 ft./sec, 

 and an acceleration of 150 ft./sec.^, 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 decreasing efficiency, for, 

 with but half of the former " effective velocity " (3,500 ft./sec.) the 

 " total initial mass," even for a start irdm 15,000 ft., is 351,000 lbs. 

 The masses would obviously be slightly less if the acceleration 

 exceeded 150 ft./sec.^ 



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 be difficult to foretell, 

 even approximately, the direction in which it would be most likely to 

 appear. 



The only reliable procedure would be to send the smallest mass 

 of flash powder possible to the dark surface of the moon when in 

 conjunction (i. e., the " new " moon), in such a way that it would be 



