S. Newcomb on the apparent inequalities, etc. 183 
higher value in one compound than in another, remains to be 
accounted for, although upon this point, perhaps, Buff’s idea 
that the different degrees of quantivalence of an element in its 
various compounds, cause the differences in its atomic volumes, 
may prove correct.* 
But at all events, whether the theory which I put forward 
turns out true or false, it may, perhaps, by lending some system 
to the study of atomic volume, pave the way for something of 
greater value. 
Boston, May 30th, 1870. 
period in the mean motion of the Moon; by Stmon NEWCOMB, 
[Read to the National Academy, April, 1870.] 
ART. XIX.—Considerations on the apparent inequalities of long 
B 
THE problem of determining the motion of the moon around 
the earth under the influence of the combined attraction of the 
it successfully completed in its simplest form, in which the earth, 
the moon, and the sun are considered as material points, mov- 
ing under the influence of their mutual attractions. The satis- 
factory solutions are due to the genius of Hansen and of De- 
launay. orking independently of each other, each using a 
method of his own invention more rigorous than had before 
been applied, they arrived at expressions for the longitude of 
the moon which, bane compared, were found to exhibit an av- 
erage discrepancy of less than a second of arc. No doubt could 
remain of the substantial correctness of eac 
The solutions here referred to exhibit only inequalities of 
short period in the motion of the moon, But, it has long been 
a, from ict hs ae er the mean motion of the moon is 
subject to a nt changes of very long period, and especiall 
to pete ocslaeiunn fy seh % artes gradually Riscbas- 
ing, from century to century, since the time of the earliest re- 
corded observations. If we eee into the problem of these 
iti i all find it seemingly no nearer 
a final solution than it was left by La Place, observation 
having since added more anomalies than theory has satisfacto- 
rily shown to exist. 
The first inequality in the order of discovery was the secular 
acceleration. This was discovered about the middle of the last 
century by a comparison of ancient eclipses with modern ob- 
* See Buff’s paper in the Annalen d. Chem. u. Pharm., 4th supplement 
1865-6, Or, see his “Grundlehren der theoretischen Che sae pplement vol., 
