8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 66 



even the first term is sufficient for several hundred kilometers. In 

 consideration of the various uncertainties, the application of a cor- 

 rection for refraction will seldom be of any advantage, except that it 

 may be done in cases of very large distances. 



If we desire to consider the weight when we unite the individual 

 determinations of the Hi's to an average value, then we must 

 consider carefully the weights of the observed values of the hi's that 

 have been adopted, generally these weights cannot easily be estimated. 



Large differences in the altitude above sea level of the individual 

 places of observation are easily allowed for. 



B. THE DETERMINATION OF THE APPARENT POSITION OF THE RADIANT 



The data hitherto useful can be given in dift"erent fomis, viz. : 



1. The co-ordinates (A, h or a, 8) of the beginning and end of the 

 apparent path. 



2. Any two other points of the path, or even one point only, when 

 it does not lie too near the assumed terminal point already well estab- 

 lished. To this also belongs the indication of the direction of motion 

 by means of some distant stars. 



3. The apparent inclination to the vertical of a portion of the orbit 

 at the terminal point, or the position angle with respect to the vertical. 

 This I think can also be given for any other well-established portion 

 of the path. In the case of paths that have a culminating point, the 

 apparent altitude of the culmination is often sufficient, but the azi- 

 muth less frequently. Very often it is possible to utilize a determina- 

 tion, that is better than a mere estimate, of the apparent node of the 

 orbit at the horizon or the apparent direction of motion with refer- 

 ence to some point in the horizon. 



The utilization of the items mentioned under this latter subdivision 

 No. 3, assumes that the terminal point has already been determined 

 from other data. Sometimes, for instance, in the case of very short 

 paths, these data are more useful than the co-ordinates of the begin- 

 ning and end of the path. In such cases graphic sketches of the 

 observed path are always a desirable addendum. 



At first from the known position and altitude of the terminal point 

 its apparent equatorial co-ordinates for the individual places or obser- 

 vations are calculated and in case i are taken instead of the observed, 

 in case 2 they are taken for the co-ordinates of the unspecified 

 terminal point. 



In the cases mentioned under item 3, these computed co-ordinates 

 serve for the two ends of the given apparent arc of the orbit. If A'"' 



