. 
DEGREE. 
The 
hat have their zeniths in a cirele, 1s rhe per- 
edie to the meridian, and pheroid a 
curve of double curvature, eu - the equator and the 
poles. At the equator it is the equator itfelf, and at the 
poles a meridian. For let A (Plate VI. Aftronomy, fiz. 47.) 
be aplace fituated between the poleand the taal and ABB 
be the perpendicular to the meridian i “he firft element, 
AMB, etermined 
eA 3. For the fame reafon, 
the fecond fide B B’ will be in the plane BM B’, BN 
being the ae . si point B, From the nature of the 
{fpheroid, CM i 
B 
N 
will be, the refore, inclined to the plane A MI 
s will 
likewife the line ’, which reprefents the jel goign 
of the line A B, bent in the dire of a ftra line pa 
rallel to B N._ It can be equally proved, that BB" feparates 
from the plane BN B’; , the four points 
BY, B”, B’’, are not a the fame plane. ‘Thus, finaily, 
the perpend: ei to the meridian is, in general, a curve of 
double curvatu 
T rees "OF ape which, on a {phere, would be 
equal, nee as they approach the pole on an oblate 
The ee of longitude are always equal on 
re) 
° 
5 
> 
a 
7] 
a 
5 
oe 
he {phere they decreafe as they recede from the 
equator, in the proportion of radius to ofine of the 
latitude. On a ipheroid, the degree of ongeae is equal to 
a de ree of a great circle perpendicular eridian, 
multiplied by the cofine of the latitude, as vill be canon: 
ftrated hereafter 
Meafurement of a Degree. 
by the meafurement of different degrees on the fur- 
face of te earth, that we acquire our knowledge of its 
magnitude and figure ; and as this problem a engaged the 
attentfon of mathema ican and aftronomers ‘in all ages, 
and i is, befides, one of ae important and eae ng in 
ere is ae reafon to bce 
pepe was attempted at a 
And if it be allowed to ee the filence of kite by 
oeieeiure we may p prefume that an attentive soeide ees 
me phenomena that firft indicated the fpherical W 
la 4 its fu 
ape to accomplifh this purpofe were, 
dosbilet, a sneer nd inaccurate ; but it is evident, that 
t and unexpected ftep was made in the progrefs of 
peas pom ee the moment a juft conception of this 
theory was obtained. 
Ic is in vain that we now inquire at Baise period this dif- 
covery was made; we know with what mytterious fecrecy 
the learned in thofe early ages veiled ee knowledge from 
ither becaufe thrir opinions were too much at 
d by 
their fecrets, whic ould: have reduced them nearer to the 
level of ordinary men. 
To what accuracy the ancients really did attain in their 
endeavours to meafure the magnitude of the ae is a dif- 
puted queftion among the learned to this day : 
Bailly, indulging in his favourite neg ie to pers 
fuade us thet traditionary meafures mu nave been tranf. 
mitted fro e antediluvian world 
of the aitronomers of the 
et 
mt. 
rs 
circumference 10r our defign to enter into this con- 
trover{y, or to treat with difrefpeét the opinions of a 
whofe talents were fo arid celebrated, and whofe ie 
‘4 fo juftly peer We fhall content otrfelves with obs 
ferving, that we can meet wich nothing on this fubjeé& fuf- 
ficiently authentic to merit the attention of the reader, pre- 
vioully to the elablifhment of the Alexandrian {chool, about 
ears before the Chriftian era 
ft meafurement we find upon record, to which trae 
dition has affixed the name of an individual, is that of Era- 
tolthencs of Alexandria, the fuccefior of Ariftarchus. 
regret that a more detailed oo of this celebrated opera- 
tion has not been tranfmitte us, 
ears that patie determined the difference of 
isanuae between Syene and Alexandria in Egypt to be 
7° 12’; aud this diftance having been previoufly meafured 
(as is faid) by the royal furveyors of Alexandria to be 5000 
adia, he concluded the circumference of the earth to be 
250,000 ftadia 
The length of this ftadium fs not exa&tly known. Some 
of the learned men who accompanied the French expedition 
into Egypt, have, by means of an ancient nilometer found 
of Elephantis, eftablifhed with great precifion 
ears to our 
= 
art 
as any 
We eran hae every per 
vert ‘s 
the fummer folftice, without any perceptible fhadow. 
latitude of Alexandria might, perhaps, be determined fome- 
what more corre@ly. But the amplitude of the whole are 
could {carcely be eftimated to within 10’ of the truth; fuc 
an error alone would produce a oe one of "above 
1000 toifes in the value of the degre 
the trigonometrical m eaten or we know ftilllefs, It 
habs certainly be avery favourable fuppofition, to admit it 
eto the one-hundredth part of the whole; and to this, like- 
wile, muft be added the siacertainty in determining the direc~ 
tion of one place, relative to the meridian of the other. All 
thefe circum {tances J adumesie we mult allow, that if the 
refult did not differ from the t 
the whole, it muft have been - a very fortunate compen- 
fation of errors. 
offidonius is the next aftronomer whofe name we find 
¢ 
connected with this fubjeé was a native of Apamea, 
in Syria, from whence he removed to Rome. He is faid 
ito have determined an arc the meridian, and to have 
eftimated the circumference of the earth at 240,000 ftadia. 
The filence of cotemporary writers relative to the derails. 
necelfi 
ary 
