408 S. Newcomb—Mean Motion of the Moon. 
hypothetical errors of the earth’s rotation which it is necessary 
in order to reduce them to. a perfectly uniform measure of 
time. The sign + indicates that the mah is abead of its mean 
rotation, and the sign — that it is behind it. For some years 
truth it would be no longer possible to predict the apparent 
motion of the moon, since the changes in the rotation of the 
It is therefore extremely gratifying to find that the compari- 
sons we have just given lead to the hope that these deviations 
may, after all, be due to the action of some of the bodies of the 
not very far from 260 years. Now, it is remarkable that this 
_ differs very little from the period of Hansen’s first Pe bam oe 
which is 273 years. The question therefore arises whether 
deviations in question may not be explained by a ibe in 
the constants of this inequality. The result is very surprising. 
By merely diminishing the argument of Hansen’s first ine- 
quality by 60° 48’ without changing the co-efficients at all, the 
observations from 1625 to 1875 may all be 2 i pany within 
the limits of error. In fact, we see that the numbers in col- 
umn (3) may be very nearly "represented by the formula 
t~ 1800 
— 5”°04—107°14 a — 15750 cos A, 
in which we have placed, 
A=18V-16E-g, 
V being the mean longitude of Venus counted cet the equinox 
of 1800, E that of the earth counted in the same way, and g 
the mean anomaly of the moon. The com abot in question 
is shown in the following tables; the fourth column of which 1s 
taken from the corresponding column of the preceding table. 
The residuals still outstanding are shown in the last column. 
Epoch. Pe paseo terms. Observ. Diff. 
1625 ~47°-0 +3 +6"1 +3"9 
1650 —14 -0 aid fs —6°9 —2 2 
1675 +19 ‘0 snl all hy —0°3 
1700 52 0 ~4°5 —3 6 +09 
1725 85 -0 +1°3 —O 3 —1°5 
1750 118 -0 +1°3 +64 —0°9 
1775 151 ‘0 +110 +125 +1°5 
1800 184 -0 +104 +11 1 +0 °7 
1825 217 0 4°8 +3°0 —1°8 
1850 250 -0 —4°3 —4°6 +0°2 
1875 283 -0 —160 —165 °8 +0°2 
