number in this co 
196 H. A. Newton on Shooting Stars, W 
portional to the numbers of stars at different altitudes to any 
unit of surface. These form the fourth column. They increase 
slowly to about 45°, and then rapidly diminish to the horizon, 
The number of paths along an oblique line is greater than 
that along a perpendicular line. They should be very nearly as 
the cubes of the lengths of the lines, or, disregarding the curva: — 
ture of the earth, as sec?6:1. The cubes of the secants of 5° — 
15°, 25°, &., are given in the fifth column, these angles being — 
taken as the mean zenith distances of the zones. In the six 
column are the quotients of the numbers in the fourth column — 
divided by those in the fifth. ’ 
Under any reasonable law the numbers in the last column 
should diminish from the zenith. . The deviations from this unt 
} 
of shooting stars out of 1,893 that should be seen within 10° of d 
py 
a 
Their frequency at different altitudes from the surface 0 
earth varies. If we suppose e, to be the number of 
t x represent the altitude, and R the earth’s radius. Supp 4 
now an inverted cone, whose vertex is at the eye of the 0D a 
_ Whose axis is a vertical line, and whose semi-vertical angle t 
10°. In general, shooting stars which have the middle Aer ne, : 
luminous parts of their trajectories in this cone will hav ne! 
middle of their apparent paths within 10° of the zenith, very 
ne in the given time will be expressed re -] 
nearly by the formula, pe, 
