, three Degrees of the Meridian. 99 



the latitude vj/" is greater than ■!\!, and the inferior when it 

 is less. 



The correction dependent on the convergence of the me- 



ridiantor the azimuths is 65 = ( ; — - ) . { —,,^-~l-,i,)' 



\ Rl . sm. 1 / Vcos.if .cos.45>^ / 



Hence the azimuth of the first station seen from the 

 second and reckoned westward from the north, is 6' =180" 

 + fl + o9. 



If P" be put for the difference of longitude between two 

 points distant by an arc which measures m, we have sin. 



r,,, sin. m . sin. i , ■ , / "i \ K / m \, 



^ = -Tiir?-' ^°g- ^'"- "^ = '°s- (ri ) - -T ' W)^ 



and log. F'= log.(;-|;;^)+ J. (sin. P"). 



The arc of the meridian, beuveen Greenwich and For- 

 mentera, is so fortunately situated, that its middle point is 

 in latitude 4 5"^. Its whole extent measures 12° 48' 44", and 

 the distance between the parallels, in linear measure, was 

 found to be 730430,7 toises. Hence the mean degree, 

 corresponding to the latitude of 45^ 4' IS", is 57010,3 

 toises J and if we multiply this number by 90% we get 

 one-fourth part of the meridian of the earth. 



The correction to be deduced for oblateness is 58, 59, or 

 61 toises, according as it is assumed to be ^-^-g, 3-^5-, or 

 ' TTT' ^^'^ '^ ^^^ ^^^^ '•^'^ mean of these, we have the tourth 

 part of the meridian = 5130886 toises; and hence the 

 metre =44330867 lines ; so that the value of the metre 

 turns out to be almost entirely independent of the elliptical 

 form of the earth. 



The radius of the equator is derived from the expression 



log. a = log. C^) + K . (I . E + iV- ''^ i • '')' ' ^^'"S 

 the oblateness, and w the periphery of a circle =3,1416. 



In order to compare any degrees measured with those 

 obtained on the elliptic hypothesis, we have a very simple 

 formula. Let m and m' be the values of two degrees on 

 the meridian, of which the mean latitudes are \j/l and 4/2 ; 

 in comparing the analytic expressions for these two de- 

 grees, developing them, and then making ^--45°, we have 

 m'= ?«. (I— i .p.cos. 2^J/2 + ^. cos. '24/2), 771 = 57010,5 



n , , . , ,. sin. 1» , 15 , / sin. oo \ 



toi8es,/)=-e:*.(l4-f 6fM.-7- -, and e=-„- e*.( , ■ „ . ,„ )♦ 



And then we shall find that the oblateness -r^-J-jj- gives 

 57075,66 and 57192,38 toises for the degrees in England 

 and Lapland. 



G2 I bhali 



