422 ‘ Prize Queftions by 
but without fuccefs, to fubjeét the obfervations made of that 
comet to the laws of parabolic motion, Profperin and 
Pingré employed themfelves particularly im this refearch, 
and mathematicians are indebted to Dufejour for an im- 
portant piece of labaur, in which he has reduced to Jefs than 
a degree the maximum of the errors of the parabolic hypo- 
thefis, Lexell was able to reprefent with precifion thefe 
obfervations in an ellipfis deferibed in the courfe of five 
years and a half; but as this comet was not feen before 
1770, and has not appeared fince, fo rapid a revolution 
feems inadmiffible; unlefs we fuppofe that the comet ex- 
perienced, before its appearance, very {trong perturbations, 
which brought its aphelion much nearer to the fun; and 
that, after its difappearance, it experienced contrary pertur- 
bations, which removed that aphelion to a very great diftance. 
We find, indeed, that, in the ellipfe alluded to, the comet 
pafled very near to Jupiter at thefe two epochs. Thefe fup- 
pofitions, however, are very improbable; and ought not to 
be admitted until we are well aflured that the obferved 
motion of the comet cannot be reprefented in a non-re- 
entering orbit (orbite non rentranfe) or at leaft one very 
much elongated. . 
To clear up this remarkable phenomenon in the fyftem of 
the world, the Inftitute propofes : 
1. To difeufs all the obfervations which can be found of 
the comet of 1770, by determining, if neceflary, the pofi- 
tions of the fiars with which it was compared. 
2. To examine, with care, whether the obfervations can 
be reprefented 1 in a non-re-entering orbit. 
3. Should that be found impoffible, to determine the 
elements of the elliptic orbit, which correfpond moft exadlly: 
with thefe obfervations, But to give to the calculations all 
the precifion neceflary, and to leave no_doubt of the juftnefs 
of the confequences deduced from them, it will be abfolutely 
gequired that attention be paid to the following points: 
1, To free-the obferved longitudes and latitudes from the’ 
' effecla 
