12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 66 



the direction of the path are of course indeterminate because of the 

 inequaHty of the aspect. The correcting of a, 8' according to these 

 suggestions is easily done, but is only necessary when the problem is 

 sufficiently trustworthy to allow it to be applied to the determination 

 of the altitude of the initial visibility and of the real length of the path. 



C. THE LOCATION OF THE ORBIT RELATIVE TO THE EARTH ; THE LENGTH 

 OF THE PATH ; THE ALTITUDE OF THE INITIAL VISIBILITY 



If for the terminal point {Le, <f>e), finally settled upon, the values 

 for the azimuth and altitude of the radiant, referred to the horizon 

 of the terminal point, are calculated from the equatorial co-ordinates 

 of the determined radiant (a, d) with the aid of the meteor's time of 

 fall corresponding to this meridian, then the first corresponds also to 

 the azimuth of the linear meteor path, and the latter corresponds to its 

 inclination relative to the horizon of the terminal point. The azimuth, 

 which specifies the projection of the orbit upon the surface of the 

 earth, can be taken from the chart or computed from the places above 

 whose zenith the meteor passed, and the inclination in connection with 

 the altitude of the terminal point gives the linear altitude which the 

 meteor had at any point in its orbit above the earth's surface. In 

 general we can neither speak of the true length of the meteor's path 

 in the atmosphere, nor of the altitude of the beginning, because as 

 has been remarked, observers very frequently catch difiPerent phases 

 of motion. Since the length of the linear path in connection with 

 the estimated duration allows us to deduce approximately the geo- 

 centric velocity, therefore the real orbital length must be obtained 

 especially for those observations that give estimates of the duration. 

 The altitude of the first visibility can then always be assumed to be 

 that which results from the longest well-observed path. 



In order to determine these quantities, however, all data are given 

 as soon as the above-mentioned projection of the true orbit on the 

 earth's surface and the inclination are well established. For each of 

 the places of observation the corrected position (a, 8') of the first 

 visible point in the orbit will now come into consideration. The 

 corresponding azimuth then gives us the initial direction in the 

 trajectory of the orbit, whence by the use of the inclination of the 

 orbit to the horizon we get both the corresponding length of the orbit 

 and the altitude of the meteor above this point. 



D. THE GEOCENTRIC OR RELATIVE VELOCITY 



If Li and ti are associated values of the length of the true orbit 

 as computed from the observations and of the thence estimated 



