ON SHOOTING STARS. 13 



and those visible somewhere over the earth lias been found to be for common meteors 

 1-r-lO-itiO. If the same ratio applies to telescopic meteors, (a supposition to which exceptions 

 may, it is admitted, be reasonably taken,) we have for the whole number of meteoroids 

 coming- daily into the air at least 1582x24x10-460, or four hundred millions. There is, 

 moreover, no reason to doubt that a further increase of optical power would reveal still 

 larger numbers of these small bodies. 



MEAN DISTANCE OF THE SHOOTING STARS. 



Although an exact determination of the mean distance of the meteor-paths from an 

 observer is not easily made, yet some idea of the limits of its value may be obtained. 



Suppose a small cone whose vertex is at the eye of the observer, whose axis is perpen- 

 dicular to the horizon, and whose semi-vertical angle is a. Let d be the mean distance from 

 the observer of the middle points falling within this cone, x the distance of an element of the 

 cone from the observer, and p the factor expressing the abundance of the meteor-paths in the 

 different elements; then by the same formula as for centre of gravity, 



_t/a 



x 3 dx 



" f\pa? 



x 2 dx 



where a and b are the heights of the limits of the meteor region. Using summation for inte- 

 gration, and taking the values of/?, a, and b, before given, we have, 



v - px 2 



fZ= -£ — 116.6 kilometres. 



b 



I px 2 



a 



Consider now the paths along a line OA, figure 2, inclined to OZ by any angle. Many of 

 those visible at points directly underneath them are invisible at 0, because of distance. It 

 seems reasonable that a larger proportion of the more distant than of the nearer ones should 

 disappear. If, then, it be supposed that the number of those which disappear from different 

 points along the line is always proportional to the actual number at each point, and the mean 

 distance be computed on this hypothesis, we shall have a result greater than the mean distance 

 of the paths actually seen. 



If the angle AOZ is 0, the mean distance of the paths in a small cone whose axis is OA is 



evidently d sec 6, on the above supposition. Representing by ip the numbers in the second 



column of table II, we have for an approximate expression for the superior limit of the mean 



distance of all visible shooting stars from an observer, 



d~<paec _„„ , ., 



% = 232 kilometres, 



where the summation extends to the several values of <p, and d has successively the values 



5°, 15°, 25°, &c. If the curvature of the earth had been considered, this limit would havo 



39 (303) 



