2 2j.o Mr. Daley’s Deduction of the 
The length of the whole meridional arc between Greenwich 
and Paris on this ellipfoid is fix fathoms greater than the mea- 
fared arc ; the degree in latitude 48° 43", 16 fathoms lefs; ir 
latitude 45°, 10 fathoms lefs; in- 43 0 , 13 fathoms greater 
and that in latitude 39 0 12% 54 fathoms greater. The degree; 
at the equator and polar circle are confiderably lefs than th« 
meafured ones, conformable to the hypothefis. 
Suppofe CE, CP (fig. 1.), are the greater and lefs femi 
axes of the ellipfoid; G Greenwich; PGE its meridian ; PI 
the meridian of Dunkirk ; and let GBA be perpendicular t< 
the curve of the meridian at G ; then GA will be the fhorte 
axis of the elliptical fedion which is the perpendicular to thi 
p C ~ | | 
at P, G, E, will be as PC% GB^ and — , becaufe at the point E (or equa| 
V'i-* 1 
pc 
tor) the line fo drawn will become the radius of curvature itfelf, or — . Therd 
fore GB 3 : 
PCM 3 
CE 
:: rad. curv . at G : rad. curv. at E :: length of a deg . in t\ 
lat. of G : length of a deg . at E, the equator. Let the arc ERL be defcribt* 
with the radius CE; draw CR parallel to GB, RS parallel to PC, and join CK; 
then, by the nature of the ellipse, CR (CE) : CK :: GB : half the parameter , <j 
therefore CE 3 : CK 3 :: GB 3 : S£-| :: 60844. : 60344 ( fuppofng the U 
CE CE 
of the point G to he 50° ff), or CE (CR) : CK :: 60844I3- : 60344)1 ; b 
CP> 
■ ■■ x 
3 X cofne lat • j 
fine SKC ; hence the angle SCK is given (50° therefore, as tai\ 
SCK ; tang. lat. (SCR) :: SK ; SR :: lejfer femi- axis CP \ greater -C E. Andputti;; 
dzz 57.2937 79, Sec. the degrees in the circular arc which is equal to the radius ) vc Q ha: 
tan?. lat 
tang. SCK 
x 60344^ ~ 3489932 fathoms the longer fend -axis ; al 
tan?, lat. 
'- - • ".T X 60344 d~ 34736 56, the {hotter* 
tan 
meridii) 
