No. 3.] MINOR PLANETS— LEUSCHNER, GLANCY, LEVY. 13 



and the arguments for the date of osculation: 



fl, = ^fo - 9' '^vhere g' = c' + [n'dz'] ; [n'dz'] = (9.5215) sin 1 15?326, (7) 



where the coefficient in parentheses is logarithmic in degrees. 



eo-^-osin £„ = r„: r = ^ £„ + ^„ + Jo (8) 



J„ = 215?8f)79 

 i'„= 28.9289 



(?„ = 223.23.34 (a) 



^c^-ic' + ln'dz']) =223.2445 (b) 



logw'„= 8.76072 ^ Co- c' = 223.5448 (c) 



See footnote.' 

 e, = 131?3236; r=145?0746 



With these initial quantities all the arguments and factors in Table LVI or F are computed. 

 The required function, w — Wg, is computed by successive approximations, the first approximation 

 being 



In the first trial the smallest terms and the last digit may be omitted; the second trial should 

 be accurate; a third trial, if necessary, will require only corrections to the largest terms. 

 The mean motion n is then given by 



2n' 



(10) Hygiea. 

 The three successive trials for w give 



Designating by Cand S series to be computed next from Table LVTI orG, it is evident bv 

 inspection of Table L\1I that 



C cos <1> + S sin <l> = Ic cos (^ + X) = Ic cos X cos ip—Ic sin X sin ^ 

 from which 



C=i:c cos X; 5= -Jcsin X (10) 



' Three numorlcal values for the argument 9, are given. According to the theory (sec footnote, Part 2, p. 147), (a) Is rigid; (6) Is rigid ivithin the 

 accuracy of the developments by v. Zeipcl; (c) is an approximation which v. Zclpel used and which is used here. The value (6) Is preferable. 



In equation (4), [n'hz'] — +0°.31 U and is the complete perturbation of Jupiter by Saturn taken from Hill; in all other parts of the computstlon 

 n'it'\ is only the long period term used by v. Zelpel. 



