between Comets and Meteors. 191 



nuence upon whatever streams of meteors may have overtaken 

 it than upon those which came in the opposite direction. The 

 earth exerts an attraction which is competent to turn aside a 

 meteorite of the former class through an angle of 50°. and to 

 alter entirely its periodic time, but is too feeble to impress 

 more than a trifling change on either the direction or period of 

 bodies rushing past it with the speed of meteors moving in re- 

 trograde orbits*. Those chance meteors, therefore, which the 



* The extreme cases will arise when a meteor passes the earth, either in 

 precisely the same direction as the earth is moving, or in the opposite di- 

 rection. In the former case it will approach the earth (assuming that the 

 meteor moves in some large orbit, which is necessary, since it is only the 

 great planets of the solar system, Jupiter, Saturn, Uranus, and Neptune, 

 which can bring a swarm of meteors permanently in) with a relative velo- 

 city of about 0*4, in the latter case with a relative velocity of about 2*4 

 times the velocity of the earth in its orbit. Hence the relative orbit which 

 the meteor will describe under the influence of the attraction of the earth 

 will be hyperbolic ; and the amount of deflection may be found as fol- 

 lows : — 



From the equation of hyperbolic motion 



Y2 2fxm , \xm 



r a 



it follows that _ \xm 



y- 



where a is the semiaxis major of the hyperbola; /x the coefficient of attrac- 

 tion, m the mass of the earth, and V the velocity of the meteor at a suffi- 

 cient distance from the earth to render — negligible. 

 In the case of retrograde meteors 



V=24, 



taking the velocity of the earth in its orbit as the unit of velocity. Again 

 using the radius of the earth -f the height of the earth's atmosphere as 

 our unit of length, the distance of the sun is about 22400. Hence from 



the equation V 2 = ^— for the earth's motion round the sun, we find 

 r 



22400 



Tvr 

 and, again, — (the ratio of the sun's to the earth's mass) is about 324000. 

 m 



Introducing these numbers, we find that 



_ 22400 J_ _J_ 

 a 324000' (2-4) 2 83* 



Now the deflection of a meteor's path in its relative orbit =2cosec —1 



-, and will of course be greatest when the meteor almost grazes the earth's 



atmosphere, i. e. when c— a=l. 



Therefore the maximum deflection =2 cosec -1 84 = 1° 22'. This is the 



