THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 29 
Now let 
Qe wy | @) =m ¥ 
(let SS ae Ge (GA) Ge 
Coe) ee eC) Se 
(6.W=¥%+% G)=%—Pa 
Then 
3(@ + 2c) = (0.6)+ (2.8) + (4.10) 
HGE—Le)= Gl B.O)4- Gy) 
3(@+ e%)= (0.6)—[ (2.8) + (4.10) | sin 30° 
3(@— «)=[(1.7)+ (6.11) ] sin 30°— (3.9) 
K(S.+ sy) = ae 7)— (5.11) )| cos 30° 
B(Sss— S)= (2. 8)— (4. 10) | cos 30° 
314+ G)= () +[( 2) — (4s) | sin 30° 
3(— 65) =| (4) — G4) | cos 30° 
6.¢ = ()—)+ Go) 
3(s,+ 85) =|) + Gy) ] sin 30° + (8) 
3(s:— 33) =| (2) + (tp) | cos 80° 
6.8, = (%)—(G) + Gy): 
The values of these coefficients can be easily verified by finding the values of 
each one from the sum for all the different values of Y’ as given in the series for 
DE Atle) epi (eM ne eer 
When we divide the circumference into sixteen parts, each division is 22.°5. We 
find the values of ¥, Yi, Y.,.... Yis, as in the case of twelve divisions. To find 
the values of ¢, and s,, in the case of sixteen divisions, we put 
CO gare 8) Se 
(Loe) ie ase 285 () = 14 16 
(Beal) = Y2+ Yio (Zr = ¥,— Vu 
(c= SE V5 Gy = Na oe 
