_ DEGREE, 
In each of the right angled triangles, A 5B, M’ dD, two 
angles and the hypothenufe are known, and thus the fides 
B, M’ d, dD, may be found. Therefore the diftances 
of the points, B, D, from the meridian and its perpendicular 
are known 
Proceeding in this ~— in - triangle ACN 
obtain A Na N, the continuation of C D, 
nd in vi triangle DNF t o get the fide NF, and the 
aie NF, D FN, we fhall be able to determine the co- 
ordina 
The “dillanée FF; and the angles DF N, Bate Rs 
known, we have fF P= — DF NFF; 
fince all the horizontal angles about a given ies are to- 
gether equal to four right angles, 
Since two angles and a fide are known in the right angled 
triangle fF P, we may calculate the elle excefg and 
the angle F P fand the other fides f P, Then by re- 
folving the right angled triangle ¢ E z. 
of E with refpe& to the meridian A X, and its perpendicular 
A Y, may be found. It is advifable to make a {cale of the 
obferved chain of triangles, to fee if any fuch as ACN, 
'E P, which have been formed to facilitate the calcula- 
i may not be too obtufe or too acute to be employed with 
ety. 
This method may be very properly employed for deter- 
i the meridian, when the ie 
angles ine; and a 
azimuths of a great number hes fides are found, thele an = 
verified by dire&t obfervatio 
In a memoir of eri of whichthe following is an 
extraGt, he fhews a method of calculating a meridian line, 
without drawing Seredicalaie from the feveral itations. 
hen all the angles of the triangles are reduced to the 
eae and the correCtion neceffar to reduce the _ of 
he 
fidered as an extention of the furface of t . 
In this hypothefis, which feems the per for fim- 
plifying the calculation, the tria ee become f{pherical or 
plying to it a correction calculated from the known height 
of the two extreme points above the level of the fea. aa 
being granted, we may employ the theorem given in the m 
moirs of ae academy for the year 1787, to calculate the dif. 
ferent fides of the projeéted chain of triangles. Confequently, 
a in the propofed triangle the fum of the angles is 130 + w, 
uft take away 4 w from each angle to reduce the fum 
i ae This fubtration being made, we may proceed as if 
the given triangle was rectilinear. belie to fay, we may 
deduce this proportion: the fine o cae way ofite to a 
iven fide is to fide as the fine a ators ngle is to its 
e fourth a will be the ee . the fide 
of the fpherical nae we wih to refolve; and which can 
be found with as much faci lity, as if the a “OF trie 
angles was Grated entirely in the fame plane. It has been 
pofed to calculate the fame {pherical triangles by means of 
rectilinear triangles formed by reducing the ‘fides to their 
t for this method we mult 
ference between each angle of the {pherical triangle, and 
the correfpondieg angle of the rectilinear triangle, ae a fepa- 
rate cperation. It is evident that this method mult be leis 
fimple, and more fubje& to error than the one we have men- 
ione 
et A,B ,C,D,E, F, &c. (PA VII. fig. 61. ied tee 
tingle little diflant from the meridian, and traced upona 
rved furface, reprefenting the level of the fea. We fuppofe 
dis angles and fides of the ee known, y the operation 
already defcribed. We may y oblervation the angle, 
CAW , which meafures the azimuth of the fide, AC, or 
. inclination relative to the meridian. It is required to find 
he length of the meridian, x, orged til it meets the 
pose te L X, let fall from the laft point of the chain. 
or this purpofe we fhall follow the fame principles, as in the 
refolution of the triangles. But we may, according to cir- 
ances, find means to abbreviate, and to avoid the calcue 
kn me 
thi is triangle, muft 
M 
M, 
the triangle, D MF, muft then be oreo in which the 
fides, DM, DF, and | the included a 
ut pofe wem 
By ae means we trait find te fide, 
M F, and the two angles, DMF, DF M, to each of which 
mult add tq. Proceeding then to the triangle MFO, 
the fide, MF, and the two adjacent angles are known 5 
O, FO, and the angle, fF, may be 
In the triangle, O P H, 
remainder of the meridian, PX, may now be found 
refolution of th 7 ale eae : ; i ‘d 
to determine PX, by 
in this laft the hypothenule, LZ, the angle Z, a 
right angle, X, are known. Then after having determined 
the-valve of aw, proper for this triangle, it may be refolved 
bg the following oS 
Sine (go— 7 qw): Lz : (Col, a—} w): ae 
in the figure g 
can exift in ce Apes res of this method. 
cry {mall quantity, w, varies from one triangle to another, 
ee fhould bedetermined 2 priori, for each of the triangles ta 
be refolved. One-third of this quantity fhonld be fubtracted 
from each angle of the {pherical triangle, to enabie us te 
being found, we fhould ad one Jv “yu toe vey a 
have given an example of the relolation of a que rdrilateral 
figure, D MFO, in which two fides and three angles are 
known. As this eeueuny isa a more difficnlt than ors 
oy ones, it pa aes be av rclonging the two fides 
M, REN, and 
F N O. But a are a divee trie iia to be ean inftead 
of two, fo that the firlt method {eems preferable. By this 
operation the azimpths of many fides of the chain-are foun 
at the fame time, that ia, the angles which thefe fides make 
with the meridian. Ifthen thefe azimuths have age n bP aa 
Tt2 uly 
