\ Academy. of Sciences at Berl elim. 99 
ing confiderations :—In regard to obfervations of the obli- 
‘quity of the ecliptic, aftronomers do not appear to be yet 
fully agreed. The academy wifhes, therefore, that’ thefe 
obfervations may be carefully examined, and particularly 
that the following queftion may be explained: How far can 
the old obfervations be employed with advantage, and | how 
far back may we venture to go in making ufe of them ?—In 
regard to the theory, one of its moft important principles, 
without doubt, is to determine the maffes of the perturbing 
planets, and efpecially of Venus. The academy defires that 
thefe may be deduced from principles independent of the 
obliquity of the ecliptic; and, above all, that the candidates 
will endeavour ta difcover how the mafs of Venus may be 
determined from confidering the motion of the nodes, not- 
withftanding the difficulties which the movement of the 
ecliptic oppofes to this refearch ; and alfo how a {maller mafs 
affigned to Venus than that found by M. de la Grange, 
would agree with the motion of the apogeum of the fun, as 
the contrary feems to arifé from the formule of that great 
geometer. Laftly, how far Herfchel’s obfervations of the 
fatellites of Uranus are fufficient to determine the maf of 
that planet.—The application of the general folution of the 
problem, would become much more ufeful, if none of the 
planets were omitted to be taken into confideration ; for in 
that cafe the equations, which arife, might be compared 
with thofe obtained by M. de la Grange, by his folution. 
And, on this occafion, the queftion propofed by himfelf will 
occur, viz. Whether the maffes of the planets, let them be 
what they may, provided they are pofitive, will give the equa- 
tions at all times with pofitive and unequal roots ?—In regard 
to the mean values, the maximum and minimum, the petite 
of ‘the variation, &c. fhould any direct method be difco- 
yered of determining them, it would be neceffary that the 
author, confidering the complex nature of analytical ex- 
preflions, fhould be as accurate in his calculations as pof- 
fible; but if they are determined by repeated trials, it is 
Ha required 
