S. Neweomb—Mean Motion of the Moon. 401 
Art. XLVIL—On the Mean Motion of the Moon; by Stwon 
NEWCOMB. 
For some time after the appearance of Hansen's Lunar Tables, 
it was very generally considered that the theory of the moon, 
aftcr occupying the attention of the mathematicians and astron- 
omers of every century for two thousand years, was at length 
complete, and that the motion of that body could now be pre- 
dicted with entire confidence. That Hansen’s computation of 
the Seats of short period pies d mE the sun not only 
Seiirerlen’s of modern sironomy, I conceive can hardly be 
ou i 
agreement with Pebets from 1750 to 1860, it was there 
shown that this agreement had been obtained b sacrificing the 
agreement before 1750, and that the moon had then begun to 
tinue satisfactorily to represent the observations. During the 
entirely confirmed. So far as can be j y the most recent 
observations, the i of the tables now seh A ten seconds, 
d is increasing at a rate of not less than half a second a year. 
Shortly after Ne phere yeti of the short paper to which I 
have alluded, it was made a part of my official duty to investi- 
gate this question. In accordance with this arrangement, I 
have aimed at the complete discussion of all recorded observa- 
tions of any astronomical value before the year 1750. These 
researches now being brought substantially to a close, so far 
as the din Maas are Sass the object of the present 
article is to ome account of them , and of their results. 
The material peoalete in brief, e every observation of an eclipse 
or an occultation previous to 1750, which appears to be worthy 
of confidence, and calculated to throw any light upon the ques- 
tion of changes in the moon’s mean motion. The available 
data may be Classified as follows :— 
ccounts of ancient historians from which it has been i ae 
ferred that the shadow of the moon pet over certain points 
of the earth’s surface during certain total eclipses of the sun 
f Thales, of Lari, and of Agathocles 
have been very estan Sy discussed py Professor Airy i 
7: ee Sct. heer, Vot. XIV, No. 83.—Nov. 
