No. 3.] MINOR PL^VNETS— LEUSCIiNER, GLANCY, LEVY. 17 



The numerical coefficients in Table XXXV or A are niultijilied by their respective factors 



and the terms are then coUectod in the form 



nd2-[ndz] = ICl'^^ ii^e + j^ + U-lJ) (23) 



By expanding the trigonometric functions, the known pai t of the argument, namely, 



U-lI 



is incorporated in the coefficients, and the terms are collected in the form: 



ndz - [ndz] = la sin x + ~b fos x + (^^ - ''o) (^(^' si" X + -Sb' cos x) 



+ (t? -.?„)= (Ja" sin x + 2-i" cos x) (24) 



+ 



where 

 Let 



Then 



X^^i'^s+i^ (25) 



a = 7c cos K b =k sin K 



a' =-l'' sin IC h' =¥ cos K' (26) 



a"= k" cos K" b" = Jc" sin K" 



ndz-[ndz] = Ik sin (x+K) + (i}-d,) Ik' cos (x+ A'' ) 



+ (i? - ^,)'IJc" sin (x + A"') + 



(27) 



The tabulation of n8z — [ndz] for (10) Hygiea is given on page 27. 



Finally, the complete perturbation in the mean anomaly is: 



Tidz = [ndz] + {n3z - [ndz] ) (28) 



It is now possible to determine c by successive approximations from equations (20), (19), 



(IS), (21), (22), (27), (28). 



From equation (1), which holds for any time t, 



c = £i — e sin £, — ndz 



t = o (29) 



As a first approximation 



ndz = c = s, — esinjj 



Introducing this value of c in equation (19), a first approximation for ndz is made. For < = 0, 



(:-Co)=0 (30) 



(,?-«?„) =0 



Substituting the value of ndz in equation (29), and computing a new value of c, the procesa of 

 solution by trials is repeated until a satisfactory agreement is reached. 

 110379°— 22 2 



