Hl, A. Newton on Shooting Stars. 199 
_ If the sphere attracts the small bodies, it may be shown that 
2 
instead of *R2nv we should have xR2nv +e), when v, is 
_ thevelocity of a particle falling by the attraction of the sphere 
ftom rest at infinity, to the surface of the sphere. If the sphere 
has an uniform motion the same formula applies by making v 
y 2 2 y 2 
Aen ( 1 +55 )-baRen’o"( 7) ae (ey ete, 
Vv 
Call this N’ and we may write, 
N=ake(En'v'-+0225), 
: where the summation indicated by S extends to all the systems 
_ of bodies, 
i ? ? 
3s the sum of n'+n" +n’ +&c., then 
., DSn'v' nv. 
The remaining term is the sum of fractions whose denomina- 
lors vary. We may, however, write, 
‘ If v is the mean value of v’, v’, &c., for all the bodies and n 
, 2 
vgsi= (1 7 6), , 
_ Where # is a number and is evidently positive. If the values of 
¥, 0,0", &., do not vary widely, 4 will be small, Making these 
substitutions, we have 
via (v2 +0 2+60,?). 
attrac: ght : h 
earth, On from infinity to a distance R from the centre of the 
N’ the avérage number of meteoroids coming into the 
2 ae 
