98 FIGURE OF TftE EARTH. 



Formula em- (K being the modules of the table of logarithms, so that log. 



plovedinthe K = Q,6377843.) 



preceding 



computation. By means of the logarithmic sine of the base, and the angles 



of the triangles, considered as spherical, the logarnhmic sines 



of the sides in the series were next computed, and then 



reduced to logarithms of the arcs themselves by the formula 



i i . K sin. U 

 log. « = log. sin. s H gg — 



For the purpose of making this las! reduction, it is sufficient 

 to take a single value of R, corresponding to the mean latitude 

 of the entire arc 52 2' 20". It was thus that the table was 

 formed of logarithmic sides considered as arcs. 



Let 7/2 be one of these arcs, and let us represent by ^ arsci 

 o\J/' its value reduced to the meridian, the one in toises, the 

 other in seconds of a degree, and we shall have the following 

 formulae ; 



*-«•«*•- (— 5K— ) -tang .+_(-__ ) . (— R -) 



. (1+3 tan. ^) 



ty '= L, **':, ) + f . y t| J . e« . (1 + e 2 ) . cos. 2 4- . 5 1 + 

 VR • sin. i / ' \R. sin, 1 / v r C 



( 3ta " , . T \ . (~) i : the superior sign being taken when the 



latitude ■]," is greater than ^, and the inferior when it is less. 



The correction dependent on the convergence of the meri- 

 dian for the azimuths is £0 = (p ,' *■'" ' ,„) . ( J" ,', ' II /l V 



V R1. sin. 1"/ v cos.'4/ . cos. £ ©y"/ 



Hence the azimuth of the first station seen from the second 

 and reckoned westward from the north, is fi' = 180' + 9 

 + Jfl. 



IfP" be put for the difference of longitude between two 



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



sin. m . sin. , . . /w\ K/m X(> , 



= -st-' 1o§ ' 81 "' 8,=1 "8' vr.' — t • W) • and 



The arc of the meridian, between Greenwich and For- 

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

 latitude 45°. 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' 18', is 57010,5 toises j and if we multi- 

 ply 



