NO. l6 METEOR-ORBITS IN THE SOLAR SYSTEM VON NIESSL 1 5 



circles. On the other hand, we have, however, never absolute cer- 

 tainty that the paths taken into consideration do actually belong to the 

 same radiant, wherefore the application of the rigorous method loses 

 in value. 



In the case of observations made at one place the geographic loca- 

 tion and the altitude of the terminal point of a path cannot be given. 

 Hence we do not have the correction to the terminal position a", 8" 

 referred to in the appropriate portion of the previous section, which 

 terminal position, therefore, is only of about the same value as a, 8'. 

 Hence it is natural to distribute the corrections uniformly and to 

 undertake the necessary rotation of the arc about the center of the 



. / 

 sm — 



orbit. The factor for the equation of error will therefore be -. — j-. 



sm / 



where V denotes the distance of the center of the orbit from the pre- 

 liminary radiant point. Otherwise we may af ply the same method 

 as in the other case and indeed by the ordinary preferable graphic 

 determination in which the observations are entered on squared paper. 



R. Lehmann-Filhes ^ develops the method of deducing the apparent 

 radiant for star shower observations made at one place, from the 

 apparent paths each of which is determined by some point a, 8 in the 

 path and its position angle relative to the declination circle through 

 this point. If the observer has a free choice of this point, then he will 

 frequently fix it more accurately in the neighborhood of a star that 

 is well known to him, and if the attention is not too much taken up by 

 the exact locating of the beginning and ending of the path, then the 

 direction of the path and thus also of the angular position is probably 

 more accurately known than by locating each of the two points which, 

 in observations made at one place, can only be approximately located, 

 if in general we desire to consider them at all. 



Equations 14 to 17, in which occurs the position angle P relative 

 to the hour circle of the preliminary radiant ao, do and therefore not 

 that determined for any other arbitrary point a, 8, can very easily be 

 applied in this method of solution. 



Let W be the angle of position determined for a. 8 where these 

 co-ordinates, therefore, must be indicated, then aj- can be found at 

 once from 



tan (a — ttfc) = tan W • sin 8, 



r)/ COS 8 • TT/ 



smP = — -.- sm W, 

 cos 80 



T, COS(ao — ajc) rrr 



COS P= V^ ^ COS W. 



COS(a — afc) 



(19) 



*R. Lehmann-Filhes, Astr. Nachr. 96 (1880), p. 241. 



