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



calculations, since in the gradual carrying- out of the observations an 

 approximate judgment must be formed of the location of the terminal 

 points. In all important cases that are worthy of a more thorough 

 treatment of the observations a preliminary idea of these quantities 

 will soon be obtained. 



With these approximate values we now compute approximate azi- 

 muths from Oi to E which will be denoted here by A°ie and also those 

 for the readily deducible directions from £ to Oi which we shall 

 denote by A'd. Furthermore, we find the approximate distances 

 OiE or the spherical amplitudes a and approximately the apparent 

 altitudes hie. The latter influence this determination only in so far 

 as even quite crude approximations suffice when we do not desire to 

 use observed quantities. 



Finally we must form the numerical values of all the differences 

 A°ie — A*ie = oii. If now we assume Le = Lo-f-ALo, </)e = ^o + A^o, in 

 which ALo and A<^o are the corrections to be determined for the pre- 

 liminary co-ordinates of the terminal point, then if Aie denotes the 

 actual value of the azimuth we shall obtain from the equations 



tan <^e cos <^i = cot^tc sin (Le — Li) -t-sin<^i cos(Le — Li), 



tan<^o cos<^i = cot^°ie sin(Lo — Li) -hsin <^i cos(Lo — Li), 



Aie=A*ie + Vi sec h 



in the usual way, the following set of equations for the errors : 



Vi = Oi + aiX + hiy, (i) 



X = ALo cos <^o, 3^ = A^o, 



where 



Oi = o)i cos hie, 



CLi ^ — . COS jTi ei, 



sm ci y 



bi=- S9lJli± . sin A\i =-ai tan A'a. 



sm ci 



(2) 



J 



The general factor cos hie is more important the more unequal 

 the distances are, so also are the hi/s because the errors of direction 



