1801.] 
fuperior to the others, which is acknow- 
ledged over India, as it is the material of 
the fineft muflins, and which gives it 
the preference in the Englifh markets; 
but that the reafon of its depreciation in 
France (which is almoft always at leaft 
15 per cent. below the price of the Fer- 
nambouc and Marignan) is that the 
French manufafturers are ignorant of the 
precife manipulations which the Englith 
and Indians know fo well how to turn to 
account. 
C. Levavasseur, a Correfponding 
‘Member, and General of Artillery, pre- 
fented to the Society a work of high im- 
portance and utility, entitled, «© A Table 
of the Correfponding Proportions of the 
New Syfiem of Univerfal Weights and 
Mealures adopted at Paris and in the Na- 
tional Eftablifhment, with the Old French 
Meafures; to which is added, Logarith- 
micalT ables of thefe Propertions..”. The 
author obferves, that as ail the new Frerfch 
metrology is founded on decimal arithmetic 
as well as on the fyftem of logarithms, 
and as the latter affords the fimpleft, moft 
convenient, and expeditious mode of cal- 
culation, he confidered the ufe of loga- 
rithms as preferable to every other me- 
thod for converting the old meafure into 
the new, and vice werfa. This may be 
performed, it is well known, by the com- 
mon rule-of-three; but it then requires 
both a multiplication and a divifion, often 
long and tedious ; whereas in working by 
logarithms nothing more is required than 
to take out of the common tables the lo- 
garithms of the number fought for, and 
from thofe of General Levavaffeur the lo- 
garithm of the correfponding number, 
and to add them together, which is by far 
more fimple and expeditious. He hasalfo 
confiruéted feveral tables, containing a 
variety of proportional calculations of a 
more complicated nature, but fuch as will 
conftantly eccur, as long as the inconve- 
nience confequent to 2 change of the whole 
fyftem of weights and meafures will con- 
tinue. Forexample, he has forined thefe 
logarithmical tables to procure, by a 
fingle addition, the anfwer of fuch quef- 
tions as the following :—‘* What will be 
the coft in francs of 27 metres of cloth, at 
7 liv. ros. the Paris ell?” ; 
C. Depitton has given to the Society 
a new demonftration of the propofition, 
¢* that of all regular z/operimetrical figures, 
the circle is that which has the greateft 
fuperficies.”” 
C. L’Hoste, who was required to ex- 
_gmine this new demonitration, after men- 
Proceedings of Learned Societies. 
157 
tioning that which ts furnifhed by elemen- 
tary geometry, declares that this given by 
C. Depillon appears to him no lefs in- 
terefting, as it may throw new light upon 
one of the moft beautiful theorems in geo- 
metry ; may affilt the minds of thofe who 
are not fully fenfible of the force of the 
ancient demonftration, may be applied in 
a variety of cafes, and may induce the au- 
thor not to abandon the theory of i/operi- 
meters to which the Bernouillis and Euler 
did not think it ufelefs to dire&t their 
ftudies. ) 
The procefs of C. Depillon is the fol- 
lowing :—He begins by feeking the ana- 
lytical expreflion of the area of the poly- 
gon, and caufes to enter into it the tan- 
gent of the angle at the centre of the poly- 
gon: this area being a maximum, its 
differential is none. Hence by a feries of 
calculations, the author is led to the con- 
clufion, that the fine of the angle in the 
centre of the polygon is equal to the area 
which fubtehds it. - The polygon, there- 
fore, becomes cofifounded with the circle, 
ay thus the circle is the maximum fought 
Ore 
SOCIETY of ARTS aud AGRICULTURE at 
BOULOGNE. 
This Society held its fecond public 
meeting on the 1ft Fruétidor, year 8, 
(Auguft 19, 1800.) The Prefident, C. 
DoLeT, opened the fitting with a {peech . 
in favour of thefe Agricultural Societies, 
_ and the advantages likely to’ accrue from 
them, and pointed out a number of im- 
provements entirely owing to the united 
labours of zealous citizens in the laudable 
object of the agricultural art, A medal was 
decreed to C. Maurice Remand, for the moft 
fatisfaétory anfwer to the prize-queftion 
of the preceding year, which was, “* What 
is the fafeft; moft convenient, and Jeaft 
expenfive method of preventing the acci- 
dents to which the fhaft-horfe of a wag- 
gon is expofed on going down hill.’ 
The prizes propofed for the enfuing 
year were the following:—** What are 
the beft means for employing the local ad- 
vantages and the induftry of the inhabi- 
tants of the diftriét of Boulogne, to pro- 
mote the commerce and welfare of this mas 
ritime town, 
The Society, flruck with the inconve- 
nience which arifes in elevated countries, 
and efpecially the Haut Boulonnais, from 
lang droughts, propoles as a prize-quef- 
tion :—“* What are the bef methods of 
procuring, to farms and villages placed in 
, elevated 
