1797+] 
titude of the Inftitute will, doubtlefs, 
not forget their names in the fuure col- 
le€tion of its labours. et thofe, in the 
mean time, who cherifh letters and hu- 
manity, Know, that not only private in- 
dividuals—not only numerous coalitions 
of enlightened men, but even foreign 
governments, particularly that of Spain, 
‘have given frefh proofs of efteem to the 
French nation, by applying to the Infti- 
tute for its decifion upon feveral fubjects 
relating to Arts and Sciences.—Let them 
know, that war itfelf has not proved an 
impediment to thofe men, in whom Eu- 
rope prides itfelf; that country which 
gave birth toa Newton, ftill fees feveral 
members of its Royal Society, efpecially 
its celebrated prefident, endeavouring, 
by his truly fraternal communications, to 
diminifh the horrors.of that fcourge 
which has fallen fo long, and fo heavily, 
on two great and illuftriotis nations.— 
Thanks tothe Genius of fcience, which 
is alfothat of nature, peace, and virtue | 
May this fentimental alliance—this fa- 
créd union of all thofe who have dedi- 
cated themfelves to literature, become 
daily clofer, and contribute to reftore 
peace to unhappy Europe !. May France 
become the centre of this pacific, ufeful, 
and glorious intercourfe! After having 
received fo many laurels from the hands 
of victory, let her only hold out the olive 
to the furrounding nations—let her be 
ambitious of no other triumphs, rhan 
thofe of labour over time—of intelli+ 
gence over fpace—and of art over na- 
ture. 
———— 
NOTICE OF MatTHEMATICAL 
Me- 
MOIRS BY PRONY, ONE OF THE 
SECRETARIES, 
LAPLACE read a memoir on the fe- 
cular equations of the motion of the 
nodes of the apogee of the lunar orbit, 
and on the abberration of the ftars.— 
This learned member had, in a preced- 
ing memoir, publifhed in 1786, obferved, 
that the motions of the nodes, and of 
the apogee, were fubjeét to inequalities 
fimilar to thofe of the mean motion of 
the moon—inequalities that are very ex- 
actly determined for this latter motion, 
regard being had only to the terms de- 
pending on the firf& power of the pertur- 
bating force; but in refpeét to the’mo- 
tion of the apogee, a half of it only is 
obtained through fthe means of this firft 
power, and the other half is principally 
due to the terms depending on the fe- 
cond power. Lapuiace has according- 
dy found, that the refylts proceeding 
Important Proceedings of the National Inftitute. 
28y 
from each of thefe powers, do not differ 
from each other .},, and that their to-~ 
tal produces nearly ,!., the motion ob- 
ferved. 
It follows, from his refearches, that 
while the motion of the moon is acceler- 
ated, that of its apogee is lefened, a de 
lay, which is 24 of the acceleration of 
the mean motion of the moon; and 
that the fecular equation of the anoma- 
ly is 3% of the equation of the mean 
motion; which muit have a very fenfible 
influence on the calculation of ancient 
obfervations. 
By introducing the fquare of the per- 
turbating force into the calculation of 
the motions of the nodes, Laplace finds 
their. fecular equation to be J1 of that of 
the mean motion, and to coincide witia 
the obfervation within nearly 545... The 
motion of the nodes, and that of 
the apogee, are leflened, when the mean 
motion 4s accelerated; and thefe three 
motions are to-eech other inthe conftane 
proportion of 11, 36, and 16. 
Thefe great inequalities muft one day 
produce variations, equal at leaf to the 
40th of the circumference in the feculae 
motion of the moon, to the 18th in the 
fecular motion of its apogee, and the 
primitive order, or fituation, will not 
return for millions of years. 
Paft obfervations have made known 
the fecular equation of the mean motion, 
fuch as it is concluded to be from univer. 
fal gravity; but notice has not been 
taken of the fecular equation of its ano~ 
maly, of which the exiftence is afcer« 
tained by the calculations that Bouvard 
has made of all the eclipfes, tranfimitred 
by Ptolemy and the Arabians, and of 
which, the introduction evinces the ne- 
ceffity of an alteration in calculating the 
motion. of the moon's anomaly. La- 
PLACE, applying to former obfervations 
the confiderations refulting from his re- 
fearches, finds that thete obfervations 
prove inconteftibly the exiftence of the 
fecular equations of the moon’s motion 
and of its anomaly, the neceflity of at- 
tending to it, and of accelerating the 
motion of the anomaly giveneby the ta- 
bles. He does not hefitate to propofe to 
aftronomers, to increafe this motion 
about 5’ 49” every hundred years, and to 
apply it to an additional fecular equa- 
tion, equal to 34, which is that of the 
mean motion. ‘Thefe correétions will 
infallibly conduce to augment the exact- 
nefs of the lunar tables, which are of 
fuch importance to navigation and geo- 
graphy. 
LAPLACE, 

ee 
== SSS SSS 
