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1808.) 
_ Metres (cr $2,555 toises) in length. 
FRENCH BOARD OF LONGITUDE. 
REPORT on the MEASUREMENT of the anc 
of the MERIDIAN from BARCELONA to 
_ FORMENTERA, 
2 Ress Board having appointed a com- 
mittee of its members to examine 
and calculate, with the greatest care, the 
observations relative to the continuation 
of the meridian in Spain, as far as the 
Balearicisles; they delivered in a report 
containing the following resulis of their 
Jabours :— 
The new measurement reaches from 
+ Fort Montjuy, at Barcelona, to the 
smal) island of Formentera, in the Medi- 
terranean. ‘ The extent of the arc in the 
direction of the meridian, from the sig- 
nal-post of Matas to that of Formentera, 
is 315,552 metres. As the whole of it is 
On the sea, it was measured bya series of 
triangles along the coast of Spain, from 
Barcelona to the kinsdom of Valencia, 
and joining the coast of Valencia to the 
islands by an immense triangle, one of 
the sides of which is more than 160,000 
At 
such distances day-signals would Have 
been invisible: they therefore had re- 
course to night-signals, formed by reflect- 
ing lamps, with a current of air, which 
were kept lighted at the different stations 
from sun-set to sun-rise. The angles 
Were measured with a large repeating 
‘circle of the workmanship of Lenoir, ad- 
_ding every practicable kind of verifica- 
tion. The triangulation was begun in 
the winter of 1806; that being the enly 
season of the year when the weather is 
‘sufficiently clear for the observing of large 
triangles. At the close of the summer 
“ot 1807 all the geodetic operations were 
‘finished. 
The latitude of Formentera, the south- 
ernmost point of the arc, was ascertained 
that winter by means of 2,558 observa- 
tions of the polar star, in which they used 
one of Fortin’s repeating circles with a 
fixed level. The greatest deviation of 
the partial series, from the mean.of the 
whole, is four sexagesimal seconds; and 
this happens only twice in a contrary di- 
rection. In all the other series the ex- 
' treme aberration is two seconds. ‘hese 
‘deviations are the same that Bradley 
found in his researches on the mutation, 
in making observations near the zenith 
with large sectors. They seem to be ow- 
ing to the variety of refractions produced 
the changing forms of the layers of 
. ‘Monqury Mac., No, 177. 
a! 
[ 359 J ns 
_. PROCEEDINGS OF LEARNED SOCIETIES. 
———— i 
* 
clouds. But from their smallness we , 
may confidently conclude, that the lati- 
tude laid down from a-mean of all the. 
observations is exact, ¥ 
This latitude in decimal 
degrees, or in grades, is - 
That of Dunkirk, observed 
by Delambre, and laid. down 
only from the observations of 
the polar star, is - 56,760652. 
Difference, or arc of the 
meridian between Dunkirk . 
and Formentera - - 13,744875 
By means of these results we may ye- 
rify the metre which serves as the unit of 
mensuration.. The metre adopted by the 
laws of France is equal to 443 296: lines . 
of the toise of Peru, taken at 10° of the 
centesimal thermometer. This length 
was. determined according to the first 
measurement by Méchain and’ Delam- 
bre of the meridian: between Dunkirk 
and Barcelona; and they supposed it 
equal to a quarter of the terrestrial meri- 
42,961777 
dian, considered as an elliptic. Ifthe earth 
were exactly of a spherical form, every 
decimal degree, or every grade, would 
contain 100,000 metres; and thus, if 
the celestial are measured, be multiplied 
by 100,000, we should obtain the dis- 
tance from Dunkirk to Formentera in 
metres—which would be 1374487,50. 
But the flattened form of the earth 
renders it somewhat less. To calculate 
the correction thence resulting, we shall 
suppose the flattening to be s4,, which is 
given by the theory of the moon. This 
evaluation is the most. probable of all, be- 
cause it belongs to the whole of the earth’s 
figure, independent of its small irregutari- 
ties, which disappear at the distance 
where the moonis placed. We thus find 
that 48,37 metres must be deducted from 
the arc, and the result. will be the real 
distance between Dunkirk and Formen- 
tera on the spheroid, viz. 137445913 
According to the measure- : 
ment of “the triangles the 
distanceis == - 
. 
1374438,72 
Diterence - ,041 
That there should be so small an error 
inso large an are 8 truly astonishing ; 
as it is far less than might reasonably be 
attributed to unavoidable errors in the 
observations. It might have been’ forty 
or fifty times more considerable, withotit 
any sensible inconveriience thence re- 
sulting in the nicest operations of the 
arts. On calculating whatwould have 
Zz been 
