MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER. 



327 



TABLES OF (101) HELENA. 



OSCULATING ELEMENTS. 



Epoch ami osculation, L877, Dec. 10.0, M. T. Berlin=1877.042, M. T. Berlin. 



o / // 



O = 99 46 33= 99?7757 



w=343 57 7=343.9519] 



fi=343 39 43=343. 6620 Mean equinox and ecliptic 1880.0. 



i= 10 9 51= 10. 1642 J 

 = 7 55 16= 7.9210 



n=854. "4377 = 0.23734381 



g and n are mean elements. 

 The elements are based on oppositions extending from 1868 to 1899 and on the perturbations of the first 

 order by Jupiter, as given on page 329. 



AUXILIARY QUANTITIES. 



loga=0.41222 

 log e=9.13928 



log 57 

 log p 



2958e=0.89740 

 =0.40389 



Log fi 



+e 



=9.93977 



NUMERAL DESIGNATION OF THE ARGUMENTS FOR TABLES II-V. 



1= g-ty' 



2= 9 

 3= g- 9' 



4= g-2g' 

 b=2g-Sg' 

 6= - ;,' 

 7=2g- g' 



8= g-ig' 

 9= 2g-bg' 

 10= Zg—4g' 

 11= Sg-bg' 

 12= 4g-:lg' 

 13= 3g-2g' 

 14=-jr- g> 



15= 4g-bg' 

 16= 4g-lg' 

 17= bg-4g' 

 18= bg-6g' 

 19= bg-Za' 

 20= -g-2g' 

 21= g—bg 



CONSTANTS TO BE SUBTRACTED FROM THE TABULATED PERTURBATIONS. 



c z =0?9227 c r =0.00224 c,j=0.00263 



Derivation of c-. c r , c. (See also page 208) 



c 2 =0?9227 



e r =0. 002185— (constant part of o log r+correction for difference between mean and 

 osculating values of semi-major axis) 

 =0. 002185-(-112".33+88 // .49)sin 1" Mod. 

 =0.002185+0.000050. 

 =0. 00224 



c„=0. 002540— (constant part oi Bp) 

 '=0.002540+0.000087 

 =0. 00263 



