NO. 2 METHOD OF REACHING EXTREME ALTITUDES 69 



The sum of these separate probable numbers is the number 1.23 X lo'", in 

 Appendix G. 



In general, for any values of v and V, the meteors reaching the spherical 

 body at successive instants come from a spherical surface of increasing radius, 

 Vt, with moving center distant vt in front of the initial position of the 

 spherical body. 



it should be explained that when v differs but little from V, the relative 

 velocity of the body and meteors is small enough to be neglected, for meteors 

 on this expanding spherical surface lying outside a certain cone, the vertex 

 of which coincides with the moving center of the spherical body. 



Also, if v exceeds V, the only part of the expanding spherical surface which 

 is to be considered is that lying outside the contact circle of the tangent cone, 

 the vertex of which also coincides with the moving center of the spherical 

 body. 



Attention is called to the fact that, even if meteor swarms were not avoided, 

 the probable number of collisions would be reduced if the direction of motion 

 were substantially that of the swarm. 



^ No difference in the calculation would be necessary if the radius of the 

 sphere were to be increased by the diameter of the meteors, these being then 

 considered as particles. 



