from Solar Reflexion. 289 
earth to form a true cone aQa’, on the principle of similar tri- 
angles we have the proportion 
BA=418,550: BC=95,000,000 : : EC=3950: EO 
= 855,660 miles, 
Fig. 1. 
the length of the axis of the shadow from the centre of the earth. 
And the diameters aa’, 6 L!, &c. are in proportion to the distances 
Ow, Ox, &e., as the diameter r7/=7900 miles to the whole 
length EO, &. Now EC =E w=8950 miles ; and let wx=200 
miles, then we have 
855,660 : 7900 :: O#=851,510 : 7862 miles =d0'; 
similarly, a a! =7863} miles; and calling wz=8000 miles, we 
have dd'=7790 miles ; and if w y=38931, then c c'=7831 miles. 
I have taken wz =200 miles, that being considerably over 
the average distance of shooting-stars whose distances have been 
pretty accurately determined by Heiss, Brandes, Benzenburgh, 
Twining, and Quetelet; w is the situation of the supposed ob- 
server at midnight, near the equator at the time of the vernal or 
autumnal equinox. From the above it will be seen that at a 
distance of 8000 miles from the spectator at w, the cone of the 
earth’s shadow or umbra would have a breadth of not less than 
7790 miles. 
On referring now to fig. 2, which is merely a portion of fig. 1 
enlarged for the sake of convenience, it will be easy to ascertain 
the minimum distance we at which a shooting-star m could be 
visible outside the cone of shadow to a spectator at w, the angle 
awy being = 90°, and wa=wy=38931 miles; then as cy 
= 25 _ 29153 miles, 
*, we= 7 (39152 + 8931%) =5547-97 miles, 
the angle awc being consequently just over 45°, 7, e. a distance, 
