DEGREE, 
t 7 
menue) ¥ p fin. 4L! —jq fin. 6 
— é 
L + &c.; confequently the 
the latitudes L‘and L’ 
c § — S! comprifed between 
will be ae by the equation 
= m(L—L’) — fa (fin. 2L — fin. »L) +p 
ony 
(fin. 4 L —41L9—4¢(fn.6L—6L') + 
=m(L— ae roi E)c sees eon Z p fin. 
re L’) —¢ viet L') cof. 3 
go°; and equation (13) gives 
= = mor. 
Dividing thie | by the preceding 
os: yo? 
S—S (L—-L’)-™& 
a 
2 sfin.2(L— Look (L+ L) — 3 £fin. 3 (L — L) 
col. 3(L + L’.) 
But, (rejecting the terms above e* *) 
m=aI+> 
4 
[xpi were 
Il 
ning 
S| 
(S — S‘) go° 3. ,) fin. (L — L’) cof. 
an Sa (4 tes fe) teat 
(LL _ 15 afin. 2 (L— Ly cof 2(L— LL) 
. op 5). 
To ploy an a which a Q in the fame mea 
fure as ae ar S’ (and in which the two terms of fhe 
fraGtion 92 
LL 
fhould be reduced into parts of the radius, and 7 
1.5707963 267) oe - 8 
When L + L! = 90° — + Li= O, and then 
without fenfible error gif ———> ) 90" 3 
ought to be of the fame kind) L—L 
m~ (or 
that is to fay, 
that the value of the quarter of the mevidian is independent 
of the ellipticity, and ‘that Oa degree at 45° is very nearly 
the goth part of the quadra 
Ia the fame reali ae equation (14) gives 5 — S’ 
— (x = e”’) m mL M 
And Q= e)s 
Exterminating m ; ae aun af the equator being re- 
prefented by unity 
Q=ir fees _ ae — e) (16). 
ee ee 256 
The fame as may be obtained by formule (13), by making 
L090" 
To ufe the above formule, it is neceflary previoufly to 
determine the elements they contain; thefe are, the eccen- 
tricity. é, or the compreffion, & : and a ag formule are 
relative to an eliipfe whofe greater axis is 1, they muit be 
se by the equatorial ae expr in fome ftan- 
—_ 
fin, (L—L’) cof.(L + L’) + 3 
dard meafure, as feet or metres, &c. whenever we apply them 
to the terreftrial meridian. 
And firft to find the compreffion Oe 
Let g, g’ be the meafured value of two degrees, let L, L! 
exprefs the angles which the refpeclive normals paffin 
“through the centres of thefe degrees make with the greater 
axis — ~ the circumference of a circle whofe radius = 1, 
R, R’, the radii of curvature we have by formula (12). 
all —~o (2 —3 fin.’ L’) 
R’ = a(1 —a(2 — 3 fin L’) 
The femi-cireumference of which R is the radius = w Ry. 
and it intercepts 180°, confequently, 
Se 
&= T80% = T80 laaes 
gia (2 —3 fin L) 
g 1—a@({2— 3 fn?L’) 
Reducing this fraction, and negle€ting the terms a, &c. 
z =1—3e(fin’ L — fin? L’) 
From whence the value - oe 16 a 
fi) 
55 ia — fin.’ L’.) 
The equation « = ey: 
2s gives g" = § (i + 3% 
fin.? )L”, if we take ve _ wee 3 fin’? LY = 3; then g” =e 
c Au 3 9) ; and this degree multiplied by go will give the 
value of a quarter of the meridian. From thefe a : 
a aaa thatthe increafe of the degree from the equat 
the poles is aad uel proportional to the fquares of ie 
fine of the latitu 
If the fare mentured in Peru be employed with that 
meafured in France by Mechain and mere in the above 
333 
— 7 
formule, the compreffion « will be oT and 2’ 
andi — J*=— . 
2 
Therefore *? = 1 — (=) = 0.005979058, which 
quantity has for its log. 7.7766329. Toifes, 
The equatorial is is ome ecim. Ddexag. 
fuppofed = oy 8 
And the degree at 45° - - — -51307-4 = 57008 
For the equation « = i aa gives g” = go (14+ 3 
e fin? L”) and when L” = 45° fin.? L’= 3 ..9”= 51307.4 
decimal = 57008 toifes {-xagefimal. 
From equat. (14), 1 == rooCeCcoO metres; a = 
TOOCO000 4 
—_——-— (tier La 4 2S 6), and fncee = 
z T 256 
20 — a, it follows that @ expreffed in metres 
TOOCOCOO I 
=—— (1 tiatsie co) irom 
wh'ch log. a = 6. 452 c. &e. 
It with ee value of the degree at the equator we deduce 
ite radius of abe R, we may, by fubltituting its value 
n equatio on (12), find the equatorial paused ae a, as 
likew ife d, With he above data theie appear : 
a= 32271226 toifes re ee 
= 6375737 metre gx. 6,804.5304 
= 20918230 Englith feet Low. 763205255 
== 3201432 toiles 6.5134C83 
= 6356049 metre ne 6.8032283 
== 20555922 Englifhfeet Leg. 743192234 
