NO. l6 METEOR-ORBITS IN THE SOLAR SYSTEM — VON NIESSL 9 



is the inclination of the apparent orbit to the vertical through the 

 terminal point (Ac, ho) in the incomplete observation as given, while 

 A'' is the inclination to the horizon at the apparent node of the orbit 

 and Ak, the azimuth of this node, then we have 



cos A'' = sin N' cos he, ] 

 tan / = tan A^' sin he, I (9) 



Ak = Ae±f, J 



where the plus or minus sign is taken according as the movement of 

 the meteor is in the direction of increasing azimuth or in the opposite 

 direction. 



In a similar way the relations are obtained when the angle with the 

 vertical at any other point of the orbital path has been observed, and 

 for which either the azimuth or altitude or distance from the terminal 

 point along the path must be given. 



In cases i and 2 the two given points on the path are computed 

 from the co-ordinates at', 8/, and a/', hi", and then for the great circle 

 thus determined is computed the right ascension at of the ascending 

 node on the equator, and the inclination / to the equator. 



With *^"^'=^. we have 



tan 8'^ 



/ , . .Ssin(a" — a^) 



tan (a -a,,) = ' „ ,. 



I— JCOS(a — a) > 



^ , tana' tan 8" 



tan / = 



(10) 



sin(a' — a/c) sin (a"— ttfc) 



ak must thus be chosen so that the two equations for / are satisfied. 



These determinations can be made rapidly and with sufficient 

 accuracy by the use of a spherical net work or chart on the gnomonic 

 projection and a correspondingly large scale. 



This method is also to be used in the third case. Finally, every sta- 

 tion of observation that furnishes usable data should employ a great 

 circle drawn through a/c and / with the appropriate direction of motion 

 to determine the radiant. If these apparent orbits were free from 

 error, then by extending them backward, they would all intersect at 

 the radiation point {a, d), that is to say the equation 



sin(a — aA:i)tan/( = tan d (11) 



would then be satisfied for each value of i from / to n. 



But since this cannot be the case because of the errors of observa- 

 tion, we must apply corresponding corrections to the observed orbit 

 paths. In doing this and ignoring certain exceptional cases, it will 

 be assumed that the co-ordinates a", 8" remain unchanged and there- 



