Imperial Institute of France. 309 
posed about the same time; and which was fixed upon by him- 
self in his first researches. He remarked in his preface, that 
time alone could decide upon a point so delicate. 
But whatever is to be obtained in a long interval of time, and 
by more numerous and more precise observations, may likewise 
be obtained, at least in a certam degree, by redoubling present 
vigilance, multiplying calculations, and employing more correct 
data. This is precisely what M. Burckhardt has attempted. 
He began by calculating 36 years of observations from 1774 to 
1810, in order without inconvenience to be able to dispense with 
the small equation of the latitude of the sun, which ought to 
pass several times over all the values of which it is susceptible, 
in this double revolution of the nodes of the moon. He em- 
ployed besides 310 observations of Bradley in 1752. By this 
means he gained eight years, which have elapsed since the con- 
struction of the last tables. To calculate these observations, he 
took a mean between the corrected right ascensions of Maskelyne 
and those of M. Bessel. The author of the tables had employed 
the right ascensions of Maskelyne corrected by his own observa 
tions in 1800. And for 1752 he had taken the right ascensions 
of Bradley, newly corrected by Hornsby, Bradley’s editor. From 
these changes, which the researches and observations made of 
late years rendered possible, there ought to result a difference 
in the mean motion, and probably likewise in the value of the 
quantity of matter in the planets. 
M. Burckhardt finds 3:8” to be added to the motion for 49 
years, which gives 7'7” for the secular motion. This motion is 
the mean between that of Zach and that published by La Caille 
about 56 years ago. Mayer, who attempted to correct this mo- 
tion, considerably increased the small error in it. Lalande di- 
minished Mayer’s motion 20”, and gave 2 quantity 8” greater 
than that now given by Burckhardt. 
We see at least that in these oscillations the error is always 
diminishing, and that, if we have not yet obtained the true quan- 
tity, we have made an approach to it. The mean length of 
the year, according to M. Burckhardt, is 365 days five hours 
48' 49-7”. The author of the tables made it 51:5”. But in 
the second volume of his Astronomy, which was published about 
a year ago, we find that he inclines to 50”, and was therefore 
himself approaching to the new determination. The difference 
is now only 5-3”, a quantity respecting which it will be always 
difficult to decide, 
The author of the tables had found for the lunar equation 7°55 
La Caille supposed 7:05”, Maskelyne 7-1”, M. Burckhardt 6:8"; - 
The mean will be 0°15”. So that the uncertainty is reduced to 
a small fraction of a second, 
U3 M. Burek- 
r 
