eA eee 
PROCEEDINGS OF PUBLIC SOCIETIES, 
: 
mat? 7 ee 
NATIONAL INSTITUTE OF 
FRANCE. 
NOTICE of the LABOURS of the CLass of 
MATHEMATICKS and NATURAL PHI- 
LOSOPHY, during the second TRiMES-~ 
TRE (quarter) of the YEAR 83 read at 
ibe PUBLIC SITTING Of the 15th GER- 
MiINAL (4th April) by c. LEFEVRE 
GiNgau the SECRETARY. 
MATHEMATICS. 
IT. BRISSON prefentéd a new edi- 
Ky tion, with confiderable additions, of 
his <* Diétionnaire de Phyfique,”’ before 
the other “proceedings were entered 
upon. 
Several aftronomers of the Inftitute had 
previoufly communicated, during the for- 
mer trimeftres, their obfervations upon the 
paflage of Mercury over the fun, the 18th 
Floreal (gth May) year 7. C. Delambre 
now read a long memoir upon the fame 
phenomenon. He gave an account of the 
precautions he took to prepare himfelf for 
what he was going to do, and of the ob- 
fervations he made. He fubmitted thofe 
obfervations to ca}culatian, compared them 
with other faéts in Germany, Hungary, 
and France. He then deduced the correc- 
tions neceffary to apply to the tables of 
Mercury, in order that the refults which 
they gave might coincide with thofe of the 
oblervation. The precautions he took, 
and which he developed in the general pre- 
paratory calculations, form anew and com- 
plete theory of thefe kind of phenomena,’ 
eftablifhing a method equally applicable to 
the paflage of Mercury and of Venus; and 
for calculating the movement of Mercury 
in particular, they lay down fermulas by 
“which the errors of the tables may be 
found out before obfervation. 
The obferyations which C. Delambre 
compared with his own, and which he dif- 
cuffed, were made at Berlin, at Vienna, 
and in, feveral ether cities of Germany ; 
at Buda, at Mirepoix, and at Paris; thefe 
Jatt were made by his countryman Meffier. 
According to the time that Mercury tock 
up in entering and quitting the fun’s difk, 
it appears-that the diameter of this planet 
was well known; but there are trifling 
~ corrections to be made in the other refults 
attorded by the tables, in order that they 
may agree with the obfervations.—C, La- 
fande has written a memoir upon the fame 
phenomenon, in which he compares the laft 
paffage of Mercury to that of 1786. By 
a method peculiar to himfelf, he calculates 
the longitude of the planet, and of that of 
its aphelion, paying due regard to the agi- 
tations or aberrations caufed by the at- 
tractions of Venus and the Earth, and even 
to the errors of the fun’s tables, which he 
determined by obfervations. He found that 
the longitude calculated by the tables differ- 
ed only 13” from the obferved longitude. 
C. Rochon, who has been long em- 
ployed in the compofition of lenticular 
glafles, propofed in a memoir the con- 
ftruction of a new compound burning 
glafs, which he calls Joupé a@ échelons, 
whofe diameter of all the zones is not to 
exceed two metres (6 feet, 1 inch and 
a fraction). The effect produced by 
a lens of this dimenfion, he affirms, will 
be quintuple that of any of thofe already 
in ufe, which neverthelefs have arrived to 
fo great a degree of power as to volatilife 
gold and decompofe diamond, and thereby 
to determine the nature of the conftituent 
principles of that precious ftone. 
C. Laplace read’ a memoir upon the 
movements of the orbits of the {atellites 
ef Saturn and Uranus. His obfervations 
fhewed that the ring of Saturn and his fix 
firftt fatelltes moved nearly on the fame 
plane; but that the feventh departed from 
that order; that its nodes have a retro~ 
grade movement upon the plane of the 
orbit of Saturn, on account of the nodes of 
the rings. C. Laplaceis defirous of knows 
ing what the theory of univerfal gravity 
will afford with regard to this. He has 
“already proved in the sth book of «* Me~ 
canique célefte, that the rings are kept in 
the plane of the equator of Saturn, hy the 
attraction of this planet; the fame caufe 
Keeps the orbits of the fix firft fatellites in 
the fame plane; but the attraction of the 
fuh upon the feventh, which is much more 
diftant from Saturn than the other, pro- 
duces effects comparable to thofe of Sa 
turn, the rings and the fix interior fatel- 
lites united : and thereby deftroys the 
equilibrium neceflary for maintaining the 
orbit in the plane of the equator of Saturn,’ 
By.a curious analyfis he proves that the 
inclination of the orbit of the feventh 
fatellite upon the equator ef Saturn de- 
pends upon the flattening of this planet, 
the aflemblages of rings, and of the inte- 
rieg 
