52 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 71 



Some means will, of course, be necessary to check the velocity of 

 the returning instruments. It might not appear, at first sight, that a 

 parachute would be operative at a velocity of 10,000 ft./sec. or more ; 

 but it should be remembered that this velocity will occur in air of 

 very small density, so that the pressure, or force per unit area of the 

 parachute, would not be excessive, notwithstanding the high velocity 

 of the apparatus. The magnitudes of the air resistance will, of 

 course, be much larger than would be indicated from the values of 

 R in tables V and VI, from the fact that, for motion with the para- 

 chute, the cross-section will be much larger in proportion to the mass 

 of the rocket than for the cases presented in these tables. 



If the parachute is so large that the velocity will be decreased 

 greatly when the denser air is reached, the descent will be so slow 

 that finding of the apparatus will not be so easy as would be the case 

 with a more rapid descent. For this reason, part of the parachute 

 de!vice must be lost automatically when the apparatus has fallen into 

 air of a certain density ; or else the parachute must be small enough 

 to facilitate a rapid descent, with additional parachute devices ren- 

 dered operative as the rocket nears the ground. Such devices are 

 not described in the present paper, but can be of simple and light 

 construction. 



The effectiveness of a parachute of even moderate size, ©"perating 

 in a region where the density is small, may be demonstrated by the 

 following concrete example. Suppose that an apparatus weighing 

 one pound and having a parachute of one square foot area descends 

 from the altitude, 1,228,000 ft. (over 200 miles), and does not en- 

 counter any atmospheric resistance until it is level with the upper 

 limit of Sq (125,000 ft.). This condition will not, of course, be that 

 which would actually obtain in practice, for a continually increasing 

 resistance will be experienced as the apparatus descends ; but if a 

 sufficient braking action can be shown to exist in the present example, 

 the parachute device will a fortiori be satisfactory in practice. 



The velocity acquired by the apparatus in falling freely under the 

 influence of gravity between the two levels is 



V64X 1,103,000=8,400 ft./sec. 



Now the air resistance in poundals per square inch of section at 

 atmospheric pressure for this velocity is, from the plot of Mallock's 

 formula, 360x32 poundals per square inch, making the value of R 

 for the area of the parachute 



R= 1,653,000 poundals/in.- 



