MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER. 215 



DIRECTIONS FOR THE COMPUTATION OF A GEOCENTRIC POSITION REFERRED TO 

 THE MEAN EQUINOX AND EQUATOR FOR THE BEGINNING OF THE YEAR, FROM 



M, 5 log r, AND 5,3. 



To the undisturbed g, i. e., the value taken directly from Table I, the perturbations no: 

 have been added to form the disturbed mean anomaly, 



M=nz = g + ndz. 



From M, the true anomaly./ 1 may be conveniently computed by means of Tietjen's "Tafe 

 zur Berechnung der Wahren Anomalie." " 



Compute the radius vector corresponding to f by the formula 



V 

 r = - 



1 +e cosy 



where p and e are to be found with the Auxiliary Quantities. 

 Compute /-, the disturbed radius vector by the formula 



r=r(l +v). 



Take from the table of the Constants for the Equator, Table VI, the values A', B' , C , log 

 sin a, log sin b, log sin c, for the beginning of the year and compute the heliocentric coordinates 

 by the formulae, 



x=r sin a sin (A' +j). 

 y = r sin b sin (B' +/')■ 

 z — r sin c sin ( C +f) . 

 Compute 



Ax = cos a dj3 

 Ay =cos b 5/3 

 Az =cos c dj3 



where cos a, cos b, cos c, are given in Table VI. 



Form the geocentric coordinates by the formulae, 



$=x + Jx + A 

 r l =y+Jy+T 



£=2 +AZ + Z 



in which X, Y, and Z are the solar coordinates at the date referred to the mean equator and 

 equinox at the beginning of the year. 



Compute a and d for the beginning of the year in the usual way from 



p cos 3 cos « = ? 



p cos d sin a = Tj 



psind =C 



EXAMPLE. 



As an example, the geocentric right ascension and declination of (179) IUytaemnestra will 

 be computed for September 26.5, 1907, Berlin mean time, referred to the mean equinox and 

 ecliptic for the beginning of the year, with the aid of the perturbations derived on page 206, etc 



a Veroffentlichungen des Koniglichen Astronomischen Rechen-Instituts zu Berlin. No. 1. 



