of long period in the mean motion of the Moon. 191 
will be about right, and we have for the excess of computed 
times 
ast s observations, + 7° 
Pou + 27 
Wiainatend’s + 30+ 
I infer from these results that the correction to Hansen’s mean 
longitude at the epoch 1715 is about +11”. 
Comparing the corrections thus found for the epochs 1680 and 
1715, we find they are substantially those required to reduce 
ansen’s mean longitude to Burckhardt’s. 1 conclude, there- 
fore, that no egregious systematic error has crept into the re- 
searches by which Burckhardt sought to show that the epoch of 
his tables was substantially correct during the latter half of the 
seventeenth century, and that the difference between the mean 
longitude of Hansen and Burckhardt during that period repre- 
sents approximately, at least, errors of Hansen’s mean longitude. 
he observations of the moon made at the observatories of 
Greehwills and Washington during the last ten years, indicate 
a tabular deviation of a eae tigtte character. From 1850 to 
1862 we find the moon slowly running ahead of the tables, 
until the latter required a correction of plus two seconds in lon- 
gitude to make them agree with observa ee But this correc- 
tion, instead of continuing to increase as all analogy would 
have led us to anticipate, suddenly ean to diminish, so that 
since 1862 the moon seems to have been falling behind the 
tables at the rate of a Baty a year. This is shown by the fol- 
lowing exhibit of the corrections to Hansen’s mean longitude, 
or right- -ascension, deduced from the meridian observations of 
the two observatories. 
Correction given by , 
Year. | Greenwich. Washington. Mean. Corr. mean. 
di 
1850 +03 ie 60 ote 
+15 +0°6 +13 eae 
52 +0°9 ee, +09 +24 
56 +10 er +10 414 
BT +155 sare 415 414 
a Beer +15 +18 +13 
62 +24 + +24 +0°9 
+2°2 +12 +14 +05 
64 +0°1 —1¢9 a uf S 
eS —24° | -17 —21 
el By —41 —40 —3'6 
68 —4°4 —4°5 4:5 as 
~=<s —55 —55 —43 
The corrections here given as those of Greenwich are, previ- 
ous to 1859, derived from the comparison found in the Green- 
