8 ON SHOOTING STARS. 



product 1S00 X sec 3 . 5° X .01519=27.67 would then give the number of shooting stars, out 

 of 1393, that should be seen within 10° of the zenith. This is equivalent to one in 50.35. 

 That is, not quite one in fifty of all the shooting stars seen at a place should have the middle points 

 of their apparent paths ivithin 10° of the zenith. 



NUMBER OF SHOOTING STARS THAT COME INTO THE ATMOSPHERE EVERY DAY. 



Shooting stars are seen in all countries, and any differences of number for different 

 countries thus far detected may be easily explained by the personal equations of observers, o 1 

 by differences in the clearness of the atmosphere. It will be assumed that for a given consid- 

 erable period of time the meteors are equally abundant over all parts of the earth's surface. 



Their frequency at different altitudes from the earth's surface, however, varies. If we 

 suppose p x to be the number of the middle points of visible paths that fall in any given period 

 of time into a cubic unit of the space of the region of meteor-paths, we should have f> 1 a func- 

 tion of the altitude above the earth's surface. Let x represent the altitude, and R the earth's 

 radius. Suppose now an inverted cone whose vertex is at the eye of the observer, whose axis 

 is a vertical line, and whose semi-vertical angle is 10°. In general, shooting stars which have 

 the middle points of their paths within this cone will have the middle points of their apparent 

 paths within 10° of the zenith.* The number in this cone in the given time will be expressed 

 very nearly by the formula, 



' />, tau 2 10° x 2 dx, 



£ 



where a and b are the values of x for the lower and upper surfaces of the region of meteor- 

 paths. 



On the other hand, the total number of shooting stars in the given period over the whole 

 earth will be equal to 



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 mis 

 the number in a given period visible in one place, and N the number that would be visible (except 

 for daylight, clouds, moon, &c.,) through the whole earth in the same period, we should have, 



J' 4 - !> x (It + a;) 2 dx 



I K pi tan 10° x dx 



or since 



4 



50.35 tan 2 10" = 2,5 ° 5 ' 



we have 



i / /'i • l ' 2 <%x + 211 J pi x dx + R 2 I ,"i dx f 

 I == 2.555 m •{ - ,.i, (■ 



N: 



J />i X 2 dx ! 



"The average apparent distance of the true centres of the meteor-paths from the centres of the apparent paths is about 1U' 

 oi aie. Tin- error resulting from the above supposition is therefore exceedingly small. 



(298) 



