12 ON SHOOTING STARS. 



THE MEAN LENGTH OF APPARENT PATHS. 



To obtain the mean length of the apparent paths I have computed, or measured, the 



lengths assigned in 213 European and 803 American observations. The aggregate sum of the 



lengths is 12804°, which g*ives an average of 12°. 6. As the observations were made by a large 



number of persons, this result will be nearly free from the individual peculiarities of observers. 



NUMBERS OF TELESCOPIC SHOOTING STARS. 



Shooting stars are of all degrees of brilliancy, and there are many very faint ones. 

 Almost every hour that a man watches he sees, or thinks he sees, flights which are yet so 

 faint as to leave him in doubt whether they are shooting stars, or only illusions. We may 

 therefore reasonably conclude that large numbers of shooling stars are invisible to the naked 

 eye which yet are visible through the telescope. 



This conclusion is verified by observation. In 1854 Messrs. Pape and Winnecke ob- 

 served* at Gottingen for 32 hours, on nights between the 24th of July and the 3d of August. 

 Pape saw with the naked eye 312 shooting stars, and Wixnecke saw 45 during the same time 

 through a comet-seeker. The diameter of the field of view is not given, but in observations 

 made at the same time diameters of 53' and 36', with powers of 30 and GO, were used. 



If the apparent length of a meteor-path is I, and the breadth of the field of view of a 

 telescope is b, and if the axis of the telescope is directed towards any part of the area whose 

 length is I and breadth is b, the meteor-path would cross the field of view. If all paths were 

 of the same length b, and were equally distributed over the whole heavens, then would a 

 telescope command a portion of the heavens expressed by the fraction lb -4- surface of sky. 

 Meteor-paths diminish somewhat in length as they diminish in brightness. On the other 

 hand, a path may be longer when viewed by aid of the telescope than when seen by the naked 

 eye. Hence for the approximate mean value of I may be taken 1 2°. 6, the mean value of the 

 length of the apparent meteor-paths visible to the naked eye. Let b be 53', and the ratio of 

 those actually seen through one telescope to all those which are bright enough to be visible 



in it is 



180 

 53 X 12.6:360 X 60 X — , or 1:1853. 



I have selected the larger diameter of the telescope, that the ratio may be too small rather 

 than too large. For the same reason I prefer to reject in the divisor that part of the surface 

 of the sky which is within 15° of the horizon. This makes the ratio 1:1371. 



We have" seen that according to Bouvard's observations one person should see an average 

 of 8 shooting stars per hour. Hence if -j*^- is taken as the ratio of the number of those seen 

 in a comet-seeker to that of those seen by one person with the naked eye, there should be in 

 each hour 8x 3 \VX 1 371, or 1582 shooting stars hourly that might be visible through a comet- 

 seeker if the whole heavens could be watched. The ratio between those visible at one place 



* Astiouotuiscbe Nachrichten, xxxix, 113. 

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