THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 159 
We first form a table giving the integrating factors. From log. n’ = 2.4758576, 
log. n = 2.9823542, we have “ = 0.34954524, 
° *, e °, nv ° * nv 1 ° ° * n’ ° *, nv 1 
= =o = ary, L = og, = OF amar iy 
4 vl a+r = Log. (‘4 a a Log-() CU) Cao Log (i+7 =) Log. (7) 
—2 — 1| —2.34954 0.37098n 9.62902 3 — 3} +1.95136 0.29034 9.70966 
—1 — 1} —1.34954 0.130187 9.869827 4— 3} +2.95136 0.47002 9.52998 
Q — 1) — .34954 9.54350n 0.45650 5 — 3] 3.95136 0.5968 9.4032 
1—1} + .65045 9.813217 0.186783 Th 2) SIE TESTL 9.60008 0.39992n 
2—1} +1.65045 0.21760 9.78240 2—4| + .601819 9.77946 0.22054 
3 — 1} +2.65045 0.4233 9.5767 3 — 4} +1.601819 0.20461 9.79539 
4—1} +3.65045 0.5624 9.4376 4— 4) +2.601819 0.41528 9.58472 
2) 1.69909 0.230217 9.76979n 5— 4) +3.601819 0.5565 9.4435 
0 — 2} — .69909 9.84467 0.1554n 6 — 4; +4.601819 0.6630 9.3370 
1 — 2) + .30091 9.478423 0.521577 2=—5) | 2522974 9.40187 0.59818 
2 — 2} +1.30091 0.11425 9.88575 3 — 5| 1.259974 0.09770 9.90230 
3 — 2} +2.30091 0.86190 9.63810 4— 5) --2.952274 0.385268 9.64737 
4 2} +3.30091 0.5186 9.4814 5 = |) =3.2520714 0.5122 9.4878 
5 — 2) +4.30091 0.6336 9.3664 }/6 —5| +4.252274 0.6286 9.3714 
0 — 31 —1.04864 0.020627 9.97938n 138 — 6] + .902729 9.9556 0.0444 
1 — 3) = .04863572 8.6869553n 1.3130447n ||4— 6] -+1.902729 0.2794 9.7206 
2— 3) + .95136 9.97835 0.02165 5 — 6| +2.902729 0.4628 9.5372 
In regard to this table we may add that the form of the angles is (¢g + vg’) = 
(i 14 2) g= (7 4 ) nt. he differential relative to the time is (2 414 “) ndt. 
g n 7 
t 
The preceding table is applied by subtracting the logarithms of the column headed 
, 1 
log. (i aE “), or by adding the Jogarithms of the column headed log. (aa): 
nN 
We will now give the values of —— W, and ——, remarking that in the inte- 
nat cost 
grations the angle y is constant; after the integrations it changes into g. 
