NO. l6 METEOR-ORBITS IN THE SOLAR SYSTEM — VON NIESSL 7 



If He = Ho + ^Ho, and ALo cos </)o — a', ^^o — y, ^Ho = 2 in longitude 

 measure, while the corrections of the observed directions and the 

 observed altitudes hie are given in degree measure and if we put 



(tan Ate + sin ei)cos €i = Ki, 



cos- hir 



D o • =Vyi- cos hic = Fi 



R • arc I • sin ei 



(5) 



— FiK{ s'mA°ci=ai, 



— FiKi cos A°ci = hi, 



Fi = Ci, 



■ then the error equations which we determine from the directions 

 become 



Vi = ni + aiX + biy + CiS. (6) 



From these results again we obtain the normal equations and the 

 unknown quantities. 



This method should only be used with reliable altitudes and should 

 only be applied when those deducted from stations in the neighborhood 

 of the terminal point are to be compared with those further removed. 



If we desire to determine the linear altitude of the terminal point 

 separately on the basis of the geographical location of this point as 

 already determined, then we usually combine the individual distances 

 Die of the corrected terminal point with the corresponding observed 

 apparent altitudes hie in order to obtain individual values of He from 

 which an average value may then be determined. The distances 

 do not need to be newly computed when they are known from previous 

 work with reference to the preliminary terminal point, since they can 

 easily be corrected from the corrections already determined, viz. : 

 ALo cos cf)o and A<^o, and in fact with the help of the azimuth Aie they 

 can be easily reduced to the definitive point Le, 4>e, for 



. T^ _ _ AL^OS <^n __ _ Acjbo 



sin A°ie cos A°ie ' 



Since the reduction of the distance to the chord for such determina- 

 tions of altitude is generally unnecessary, we can adopt 



{hi + 



sm ^.., , 2 ^ 



Hi = Die ri —r- n • (7) 



COS(/li + £|) 



If we put hi-\- ^^ =hi then up to 10,000 kilometers the approximate 



height will be 



Ei=Diei^nhi^~^{Diei2inhiy, (8) 



