64 SAIITHSONIAN MISCELLANEOUS COLLECTIONS VOL. /I 



APPENDIX F 



PROOF THAT THE RETARDATION BETWEEN 500,000 FT. AND 

 1,000,000 FT. IS NEGLIGIBLE 



The falling-off of velocity, w, due to air resistance, is given by 



P -^ shrr^MoWi^ 



Po 



w^here P = the mean air resistance in poundals per square inch 

 between the altitudes 500,000 and 1,000,000 ft. from 

 the previously mentioned velocity curves, the pressure 

 being considered as atmospheric. 



p = the mean density over this distance, 



s = the mean area of cross-section of the apparatus through- 

 out the distance, taken as 25 square inches in view of 

 the average mass, Mq, throughout the interval, and 



h = the distance traversed: 500,000 ft. 



It is thus found that the loss of velocity w is less than 10 ft./sec. 



(for a=i50 ft./sec.) even when — - is taken as constant throughout 



Po 



the distance and equal to that at 500,000 ft. (i. e., 2.73 x lO"^). 



APPENDIX G 



PROBABILITY OF COLLISION WITH METEORS 

 The probability of collision with meteors of " visible " size is 

 negligible. This can be shown by deriving an expression for the 

 probability of collision of a sphere with particles moving in directions 

 at random, all having constant velocity, the expression being o'btained 

 on the assumption that the speed of the sphere is small compared 

 with the speed of the particles. 



If we accept Newton's estimate^ of the average distance apart of 

 meteors as being 250 miles, we have by considering collision between 

 very small meteors of velocity 30 miles/sec, and a sphere one foot 

 in diameter of velocity one mile/sec, moving over a distance of 

 220,000 miles, the probability^ as 1.23x10"**; which is, of course, 

 practically negligible. The value would be slightly greater if the 

 meteors were considered as having a diameter of several centimeters, 

 rather than being particles ^; but the probability would be less, how- 

 ever, if meteor swarms were avoided. 



^ Newton, En eye. Brit. 9 ed. v. 16. 



