H. A. Newton on Shooting Stars. 197 
b 
J mg , tan?10°x?dz, : 
a 
where a and 8 are the values of x for the lower and upper sur- 
faces of the region of meteors. 
On the other hand, the total number of shooting stars within 
the given period over the whole earth will be equal to 
b 
: i [sx0s(R+2)2de. 
__ The whole number visible at one place is 50°35 times the 
number seen within 10° of the zenith, and therefore 50°35 times 
_ the number within the above described cone. Hence if m isthe 
_ humber in a given period visible at one place, and N the num- 
ber that would be visible (except for daylight, clouds, moon, 
s 99 through the whole earth in the same period, we should 
have, 
> 
b 
z | ni [0B + 2)dz 
‘eo 5035 7% 
- [ae tan? 10retde 
9 a 
_ ‘Me earth’s surface, this constant may be removed from the in- 
“etal sign. Again, without great error finite summation may 
a the Bae of integration, in which ease the equation easily 
? 
(2 ex? ORS’ or + RS’ 0 
N= 2:555 mi —* —— f° 
a” ga? 
Taking x successively 45, 75, 105, 185, and 165 kilometers, 
| oP 114, 243, 277, 106, and 57, and R equal to 6370, 
number visible at one place. . 
obtain this result, it was assumed that the shooting stars 
* 
Sin, ee 
