MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER. 



213 



ARRANGEMENT OF THE TABLES. 



'fable I gives the values of the mean anomaly g and of (g—g') for January 0.0 of every 

 common year and for January 1.0 of every leap year from 1865 to 19:50, and their changes for 

 the different months and days. 



Table II gives the coefficients a, and b, of the periodic parts of the perturbations ndz, with 

 the argument N, hi units of 0?001 and one decimal thereof, where 



N=(g-g') + J(g-g'). 



Table III gives the coefficients a, and b, of the periodic parts of the perturbations log 

 (1 +y) =o log r with the argument N in units of the fifth decimal place and one decimal thereof. 



Table IV gives the coefficients a, and />, of the periodic parts of the perturbations <5 ; ? with 

 the argument N in units of the fifth place and one decimal thereof. 



Table V gives the coefficients (Jb ) t , (Ja t ) t , and (J6,-)« of the secular parts of the perturba- 

 tions for all three components for the beginning of every second year from 1865 to 1930, together 

 with their changes for one year, thirty-one days, thirty days, twenty-eight days, and one day. 

 The coefficient (4b ) t for ndz represents the long-period term. 



Table VI gives the constants for the equator for the beginning of every year from date of 

 discovery to 1930, inclusively of cos a, cos b, cos c, by which the perturbations d.3 must be multi- 

 plied to obtain the corrections Jx, Jy, Iz to the heliocentric equatorial coordinates x, y, and z. 



Table VII gives the values of J(g —g') =e—g — ue sin s and the values of the reduction (s —g) 

 from mean to eccentric anomaly for the argument g. 



DIRECTIONS FOR COMPUTING THE PERTURBATIONS n,)z, o log r=log (l+u), and oj). 



Let t be the date for which the perturbations are to be computed. Let g' be Jupiter's 

 mean anomaly at the date. Let g be the planet's undisturbed mean anomaly at the date. For 

 the date / take g and g—g' from Table I. Greenwich mean time is used for this table. 



With g + -l~ as argument take J (g—g') and (e— g) from Table VII. 



Form the multiples of s up to 5s, where £ =g + (s — g). 



With N=(g -g')+J(g -g')+J- as argument take the coefficients a„ b t of the periodic part 

 of the perturbations from Tables II, III, and IV, where i has every value from to 5. 



For the date t take the coefficients (Ja,),, (Jb,) t from Table V for each of the three com- 

 ponents. Form the coefficients (a) i =a i + (Ja,) t and (b) i = b t + (Jb i ) t - 



By means of the traverse tables, Tables B, form the products 



[a,- + (Ja,) t ] sin is and [b, + (Jfr,)<] cos is. 



Form the sum of the products for each component. The resulting sums are the desired 

 values. of ndz, <Hogr, and d,3. The disturbed mean anomaly is M'=nz=g + ndz. 



EXAMPLE. 



As an example of the use of the tables, the perturbations of Minerva will be computed for 

 1874, January 15.0, Greenwich mean time. 



