b802. ] 
problem of the. chainette, it was quickly 
perceived that this returned curve was 
that of the equilibrium for a vault com- 
pofed of -arches infinitely fmall, and of 
equal gravity. David Gregori firft re- 
marked this identity. It is deduced ftill 
more direétly from a method given by 
Jacques Bernoulli. A fecond method of 
the fame author, corrected by Citizen 
Boffut, leads likewife to the fame con- 
clufion. 
La Hire, proceeding fram fome experi- 
ments, gave, in 1712, a method which, 
from its great facility, was adopted by the 
builders, who did not give themielves the 
trouble to inquire whether it was appli- 
cable to all cafes. Not content with tol- 
lowing it for the concavities of their 
vaults, they applied it likewife to domes, 
although the equation of equilibrium, 
in this cafe, be of the third degree, and 
not of the fecond degree only, asin the 
preceding cale. 
CouPLer has treated of the projecting 
force of vaults ez berceau, and of the 
thicknefs of their uprights, firft confider- 
ing the arches as infinitely polifhed or 
fmooth, and not experiencing any refiftance 
on the part of friétion; he has next en- 
deavoured to correct what there was 
defective in that fuppofition; but he 
goes no further than La Hire and Parent, 
Boucuér has treated of vaulted 
domes: he has fhewn that an infinite num- 
ber of curves may be ufed therein, among 
which he enumerates the moft advantage- 
ous. But he has not calculated the pro- 
jecting force, he has not examined the 
law of the forces which are to act on the 
arches when the generative curve is fub- 
jected to given.conditions ; a matter fruit- 
ful in curious and ufeful problems. 
Citizen Bossur undertook, in 1770, to 
treat the queftion at large, as well for 
vaults ex berceau, as: for thofe that are ex 
dome. He examined all that regards the 
‘figuie and the projecting force of vaults. 
His Memoirs were printed in the voluines 
of the Academy of Sciences for the year 
1774 and 1776. 
MascCHERONI, whom we have feen at 
Paris a Deputy of the Cifalpine Republic, 
for fixing the unity of the new meafures, 
and who, laft year, was loft to the {ciences, 
had made, in 1785, fome new inveftiga- 
tions on this fubjeét, and had given fome 
beautiful propofitions on the equilibrium 
of vaults in dome, with circular, elliptical, 
and polygonal bafes. 
After many new refleCtions, and a num- 
ber of experiments, which may be of the 
greatelt utility in practice, Citizen Boffut 
Proceedings of Learned Societies. 
485 
has lately refumed his two Memoirs. He 
has moulded them afreth, by fimplifying his 
calculations in many places. He has like- 
wife made a great number of theoretical 
and praétical additions, in fo much, that 
the whole now forms a work which may 
be confidered as new. hs 
Citizen MessseEr read a Note on the 
Comet which he difcovered the 23d of 
Jaft Meffidor, about half paft eleven at 
night: in 41 minutes time it had 24/40! 
of direét motion in right afcenfion, and 
6’ 38” in boreal decreafing declination. 
This fame comet was feen on the very, 
fame day, and almoft at the fame inftant, 
by Citizens Mecuain and Bouvarp; 
this laft had even obferved it at rth 57’ 4g" | 
of true time. The right afcenfion was of 
11° 13’, and the boreal declination of 
6g? go! 
We have fince learned, that Citizen 
Pons had obferved it the fame day at 
-Marfeilles ; he had even perceived it on 
the preceding evening ; but the clouds had 
not allowed him to fatisfy himfelf then by 
regular obfervations, whether it was a co- 
met, or merely a nebulous fpot. 
Objervations of the Summer Solftice of the 
Year 9. 
Citizen Duc La CHaPELLE, an Affo- 
ciate-member, has communicated the re- 
fult of the Obfervations which he made at 
Montauban. : 
By a medium between nine days’ ob- 
fervations, he finds 23° 28’ 9" for the ap- 
parent obliquity, by fuppofing 15! 48" for 
the femi-diameter of the fun, and 44° of | 
52" for the latitude of his obfervatory. 
Thefe obfervations were made with the 
fextant of LacaiLLE3 and it would, per- 
haps, be advifeable to take, in the Tables 
of that aftronomer, the diameter of the 
fun, and the refraétions which he had de- 
termined with the fame inftrument, as 
his ‘Tables include, at the fame time, the 
errors of the fextant. By this means, 
the obfervations of Citizen Duc la Cha-: 
pelle would agree very. well with ours. 
By a medium between 18 ‘days’ obferva- 
tions, made with acircle of Borda, he 
‘found 23° 28’ 82; Citizens Mecuain 
and Le Francats found only from 6 to 
7. Tt is extremely difficult to avoid fuch 
{mall differences. In confolidating his 
obfervations for three years, he’ fourid 
by a medium 23° 28' 6"4 for the appa- 
rent obliquity of the folftice of the year 8, 
or 23°27' 58" for the mean: obliquity. 
The obferyations of BRaDLEY, Mayer, 
Lacatibtyand-LeGEenTIL, gave, as near 
as poffible, 28% 28! 18” for 1750; it 
would appear hence, that the fecular dimi- 
2R2 nhution 
