DEGREE, 
“met with ; and when, thle are wanting, gal erected to 
ane their place. ‘By means of thefe a ai of 
triangles are formed, by which Aa B are c 
each “other, and with the bafe line ad, as in fig. re 
rc, it ig not unufual to meafure a 
of verification near the other extremity, and to compare its 
length by actual meafurement with that’ deduced by com- 
putation by means of the intervening triangles. is is an 
excellent teft of the accuracy of the trigonometuical 
¢ bafe jaa cereene ae os bas and angles of the 
triangles deter entirely aftro- 
teal, are rete pee comic e of proceis. The 
ference of latitude of the extreme fHations muft be dete 
dii- 
nates Sufficient data are now o ne or 
g the perpendicular diftance of each ation from the 
ere MN; as pp’, gq’, a and BRS and alfo the 
diftance of each perpendicular from A, a ae: ae Se ae 
d Bx being thus eae the dittance 
metry. The latitude of the other point x, which is uled 
i. find: ing the amplitude of ce arc A x, 1s deduced a the 
obferved latitude o t is at this can only be 
done rigoroufly by a f herical  eaicoa: the {mall arc 
x, ae in toifes or feet, being converted into minutes 
and feconds of a degree To do this, we muft fuppofe 
known the very thing we are in fearch of, that is, the relation 
the degree bears to our so ta meafures. ie as the arc 
x is always taken mall, compared with 
— ie avsicnee! is ond to arife fon this pron 
It a appea s then, ie the whole procefs confifts of four 
diftin® pee anoni meafurement cf a bafe ; the deter- 
mination of the angles i a feries of triangles, fo cont acied, 
as to connect the extreme ftations, both with the bafe and 
with each other on ermination the latitudes, or, 
at leaft, the differe latitude of the extreme ftations; 
O 
and, laftly, the oe bearing of one ftation with the meri- 
dian of the other 
rom ce varied and uneven nature of the a of the 
earth, feveral complicated confiderations arife in practice, 
that have the preceding defcrip- 
, if we fuppofe triangles to be formed by lines joining 
no two tri 
angles, Sonebly, lying in oe fame plane. ‘Bee 
muft al th 
furface Saat furface is Pita lly fup 
level of the fea). rig. 50. intended to iia c oan 
of thefe reductions. , &, are the elevated fig- 
nals; a, 5, ¢, d, e, their staces reduced for computation. 
o have an accurate idea of this reduction, we may fuppofe 
tines drawn from the centre of the globe to the vertices of 
the ftations : the points formed by the interleétion of thefe 
‘fines with the imaginary fpherical furface, every where level 
with the fea, are ae fe which are to be ufed in the fub- 
feat ealculat 
The aaegiea raed by thefe points may either be con- 
L. XI. 
Gyo ones, he was defirous of verifying it by dire& 
Pp meal 
fidered as oo - Bean in one cafe, their fides are 
chords paflisg through the earth; in the other, cuived 
lines eae over is Gas 
may here likewife me the principle of another 
method, which hereafter we fhall have occafion to defcri' ¢ 
with the adjoining {tation is afcert ained. 
Let P (fg. 51.) be the pole of the earth, A any place 
whofe latitude is known, oe a os ation vifible from Aj; av ob- 
por ang gle PAB, the angie 
a ion oe ane the 
be 
triangle PA B, PA is known ee € 
tude of the place; and the two angles being known, the 
fide A B may be found; and thus the value of a degree, or 
an ob! ‘que circle, obtained, 
oO 
veny 
thefe we may § nd the value of Ap, which tsa 
portion of the great a perpendicular to the meridian. 
And this are Ap may be always knawn in lincar mealure, 
by the rules of plane trigonomeiy 
It is evident that on a {phere all thefe degrees fhould be 
equal, 
We may now return to the hiftorical part of our fubjec, 
and refume the narrative of the operations of Picard, who, 
as was before flated, was entrulted Lge the meafurement of 
a degree pl Paris and Amien A.D. 1699. 
I. fig. 52, may be fren . e general ae = 
In Plate 
Picard’s NC gles were meafure 
drant of fhed with two Meera 
€ an 
three a radius, “faci 
the one fixed, other meveable. 
He began his operation by meafuring the diftance be- 
tween Villejuive and Juvefy, which places being nearly joined 
b € thought moftt eligible tor his 
inning at efy, he 
at Vilicjuive, that terminated his bafe, made with the fteeple 
at Bri e angie made the pe t lefcopes was 95° 
’55". He then carried the inftrument to Villejuive, and 
there directing one telefcope .of the quadrant to a fignal at 
Juvefy (which formed the other extremity of his bale ), and 
e other to the fteeple at ea e found the angle fub- 
tended by thefe two objcés t 9 4' 35”. With thefe 
m Villejuiv = 
nee a was verified by taking the inftrument to Brie, and ob- 
ferving the third angle of the ela which appeered by ob- 
fervation to be the fame as it fhould have been by computation 
e 
a ie ee The third and fourth ae were ok 
formed on this bafe ; one was limited 
tower of Montjay, the ane on he fout 
e the diftances from Montlhery to 
nefe triangles the diftance from 
sie a to Mareuil was cladad to be 31,897. 
determined this great triaugle by means of the 
rGe 
