ON SHOOTING STARS. 11 



a second system, n!" bodies of a third system, and so forth, and let the bodies of the first 

 system move in one direction with a velocity v' relative to the sphere; let the bodies of the 

 second system move in another direction with a relative velocity v", &c, , then will the 

 number of bodies which the sphere intercepts in each second be equaj to 



*RV <-'(l + ^ + ,Kn"c"(l +jj) + 7 rRW'(l + ^) + &c. 



Call this N 1 , and we may write, 



where the summation indicated by I extends to all the systems of bodies. If V is the mean 

 value of v', v", v'", etc., for all the bodies, and n is sum of n', n", «"', &c, then fn's'^nV, 

 The remaining term is the sum of fractions whose denominators vary. Wo may, however, 

 write 



^4=^(1 + ^ 



when 6 is a number, and is evidently positive; for the mean value of fractions having the 

 same numerator is greater than the numerator divided by the mean value of the denominators. 

 Moreover, if the values of v', v",v'", &c, do not vary widely, 6 will be small. Making these 

 substitutions, we have, 



N 1 = T JL^L {V 2 + v* + r 2 ). 



This formula expresses the number of meteoroids which the earth intercepts, by considering 

 the earth with its atmosphere as the supposed sphere, R its radius measured to the upper 

 part of the region of meteor-paths, V the mean relative velocity of the meteoroids when they 

 come into the earth's attraction, v Q the velocity acquired by a body falling from infinity to a 

 distance R from the centre of the earth, N 1 the average number of meteoroids coming into the 

 atmosphere in a second, and n the mean number in a cubic unit of the space the earth is 

 traversing in the given period. 



If m be the average number visible at one place in a unit of time, we have found that 



N= 10460m. The volume of a sphere whose radius is R is f ^R 3 . Let M be the number of 



meteoroids in a space equal to the volume of such a sphere; then M= | ;rnR 3 , and 



r> T\r 

 10460™ = -.— (V 2 + r 2 + OvJ), 



or 



„ 4 10460 wiRV 

 M: 



V 2 + r 2 + v 2 ' 



where m denotes the average number (or fraction of a number) seen in one place per second. 

 If the hourly number is, as before assumed, 30, then m is ^27, and 



M= 116.2 (^ ?^ Y 



(301) 



