ON SHOOTING STARS. V 



Now ,o, is a function of x, and assuming as heretofore that the observed altitudes are fair 

 examples of the real altitudes, we shall have f' 1 =J>p where k is a constant depending for its 

 numerical value on the period of time assumed, the unit of space assumed, and the abundance 

 of meteors during the given period. As we have assumed an equable distribution over the 

 earth's surface, this constant may be removed outside the integral sign. Again, we may, with- 

 out great error, use finite summation for integration-, and drop the common factors k and dx. 

 The equation then becomes, 



2 r x 2 + 2R 2'" px + It 2 2 

 N = 2.555 m 



I 2 (^ 



Iii this summation x is to be taken successively J (30 + GO), }, (GO -f- 90), &c, that is, 45, 75, 

 105, 135, and 165 kilometres, and p is 111, 243, 277, 10G, and 57. Hence 



2 p = 797, 



a 



2 px = 76155, and 



2 / oai 2 = 8135325. 



The mean value of R is G370 kilometres, and therefore 



N = 10460 m; 

 that is, the number over the whole earth is to be considered as 1 0460 times the number visible at one 

 •place. 



To obtain this result it was assumed that the shooting stars were uniformly distributed 

 over the earth's surface, and that the conditions of visibility were uniform. If, however, we 

 regard the actual instead of the theoretical case, we find that the numbers vary through the 

 hours of the night. Hence for a fraction of a day, at least, the distribution is not uniform. 

 The rapid diminution towards the horizon already shown indicates the influence of mists, &c, 

 in absorbing the light of these bodies. But for this, more would be seen within 10° of the 

 horizon than in the whole of the rest of the heavens; whereas, of 1393 only 31 were seen in 

 this part of the sky. These mists, of course, vary in different climates. Hence the numbers 

 visible in different places may reasonably be expected to differ. Let, however, a locality have 

 an atmosphere of mean purity, let it in other respects be one of medium character with 

 respect to the number of visible meteor-paths, and let n be the mean hourly number of shoot- 

 ing stars seen in a clear sky at that place, then we may consider that the whole number that 

 under clear skies could be seen over the whole earth in one hour would be 10460ra. 



The value of n is of course to be found by observation. It varies for different hours of 

 the night, but may be found either by counting the numbers that appear throughout the 

 night, or by counting at or near midnight. 



Mr. E. Bouvard, in the year from October, 1840, to October, 1S41, observed at Paris on 



(299) 



