of long period in the mean motion of the Moon. 187. 
to the first per his result is 
2 sin (—J—167'+187"4-35° 20-2) 
a result potas identical with that of Hansen. The ulterior 
approximations change it to 
16-34 sin (—J—16/++-187"+-35° 16'°5), 
so that they increase the coefficient instead of diminishing it as 
- In Hansen’s theory. e difference is however so small that 
the results may be regarded as identical. 
But, in the case of the second inequality instead of reproduc- 
ing the result of Hansen, he finds a coefficient of only 0-27, a 
tity quite in significant in in the present state of the question. 
Wel have thus an irreconcilable difference on a purely theoreti- 
cal question. 
I propose to inquire whether we have in either theory an en- 
tirely satisfactory agreement with observation. As a prelimin- 
ary step to this inquiry I have prepared the following ‘ehte of 
the mean longitude of the moon from the tables of Burekhardt 
and of Hansen respectively, for a series of equidistant dates, the 
interval being 86525 days, and the epoch 1800 Jan. 0, Greenwich 
mean noon. ese dates are marked by the year near the 
Next is given the acceleration of the mean temgibads deduced 
from Table xLvint. The inequality of long period is from Table 
xLix. The sum of these ae quantities gives the corrected 
mean longitu 
Hansen's ee longitude and secular acceleration are deduced 
in the Page way from the elements given on page 15 of his 
ables de la Lune. His terms of long period are deduced from 
Tables XLI and XL, ae aa constants es ate and the re- 
mainder reduced to are by being mu tiplied the factor 
0004703. The iat column'of the ele gives the « 
this difference is really the mean difference ‘ors: the 
longitudes of the moon deduced from the two tables is shown 
