ON SHOOTING STARS. 7 



If the area of the visible heavens is unity, the numbers in the third column give the 

 areas of the corresponding zones. The numbers of paths divided by the arms give quotients 

 proportional to the numbers of stars at different altitudes for any unit of surface. These form 

 the fourth column. The)' increase slowly to about 45°, and then rapidly diminish to the 

 horizon. 



The number of paths along an oblique line OA, (figure 2,) is greater than that along a 

 perpendicular line OZ. They must be very nearly as the cube of the length of the line, or, 

 disregarding the curvature of the earth, as sec 3 . 0:1. In the fifth column are given the cubes 

 of the secants of 5°, 15°, 25°, &c, these angles being the mean zenith distances for the 

 several zones. In the sixth column are the quotients arising from dividing the numbers in 

 the fourth column by those in the fifth. 



These numbers would be nearly constant if all the shooting stars in each direction were 

 visible. Their rapid diminution as increases corresponds very strikingly with the diminu- 

 tion of light as shown in the previous table. This correspondence may be better shown by 

 placing the numbers together in the same table, as below. In the first and second columns 

 marked I and I u are the numbers for the intensity of the light at different zenith distances. 



No. 



5— u, from table II. Dividing now n by I 



Area sec . ° J 



The next column, headed n, is the value of 



and Ij, we have the remaining columns. As the curvature of the earth is not taken into 

 account, the last line is of no importance: 



Table III. — Comparison of intensity of light of shooting stirs with the proportion visible, at different altitudes. 



Since the numbers in the last two columns are tolerably uniform, it appears that the 

 ratio of the shooting stars visible at different altitudes is very nearly as the intensity of their 

 light. Near the zenith the area of observation and the number of shooting stars actually seen 

 are so small that the law is less evident. But whether we consider the values of n, or n — I, 

 or n -f- Ij, or the numbers in the fourth column of the preceding table, it will be probably 

 admitted that 1800 is not far from the value to which n approaches as becomes zero. The 



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