S. Newcomb—Mean Motion of the Moon. 409 
Correcting Hansen’s term by this dnidivicad addition, we find 
that instead of 
15734 sin (A+-30°-2), 
the value given by Hansen, we shall have 
15”°3 sin (A—30°'6), 
as the result of observation 
sa test of this result, the sum of all the corrections here 
found to Hansen’s tables has been a and compare 
corrections given in column 1. It is to be remarked in the 
first place that the diminatiun of 10” a century in the mean 
motion of the moon involves a further correction of —0’”4 to 
the value of the sistas acceleration in order that the ancient 
observations may still, on the AYerAees be best represented. 
Thus the secular pray rt reduces 
87°45 
and the total correction to the accnieration of Hansen is 
—3"°76. 
We put V, for the empirical term of Hansen, 
217-47 sin (9SV—13E +274° 14’), 
the existence of which appears to have been entirely denis by 
the researches of Delaunay; and T for the time counted in 
centuries after 1800. Then the total corrections to the tables of 
ansen are as follows:— 
—V,~—1714—29717 T~3"-76 T? — 155 cos A. 
The following are the values of these corrections for the 
principal epoc ochs from 1625 to 1900. The computation and 
comparison with observation is given so fully that any explana- 
tion of the table appears to be unnecessary. 
1"-14 
—15"5 ; Observa- ‘ 
Epoch. —Ve iia i 2 ra Sum. pe th Diff. 
1625 | +17"1 =-10"°6 +38"4 +44"9 +50" +5" 
1650 21 “4 —15°0 34 +] 40 °5 —1°5 
1675 16°9 —14°7 29 °4 a1 6 3 +04 
1700 + 5:°2 — 9°5 24°3 20°0 21 +10 
1725 — 8°6 — 14 18 °6 8°6 7 —1°6 
1750 —18°9 + 7°38 12:6 + 0°9 0 —0'9 
1775 31-2 13 °6 + 5°9 — 1° 0 +1°7 
1800 —14°7 15 4 — I'l — O04 0 +04 
1825 — 2:1 12°4 - 8°7 + 1°6 0 16 
1850 +11 °4 6°3 —16°7 0-0 0 0°0 
1860 15 °7 + 1°8 —20°0 — 2°5 +1°5 +4°0 
1870 19-0 — 1% —23 4 — 671 —5°5 +0°6 
1880 20 °9 — 5-2 “—26°9 —11 "1 ae eae 
1890 21 °4 — 84 —30°4 —17 “4 Bee nape 
900 +20°6 —11°2 —34°] —24-7 Kees iua 
