98 Olservations on the Measurement of 



the resulu to which I have come in the foregoing Memoir. 

 The demonstration of ihenn is to be found in the work of 

 M. Delamhre on the Meridian. 



In the firsi place, let a be the radius of the equator, e the 

 eccentricity, 4* the latitude of one extremity of a side, or 

 arc, in any series of triangles, and 9 the azimuth of that 

 side. The radius of curvature of this ^rc will be e:;pressed by 



/ e2 



■^e ^ 





and 



Rl R R a ' 



Hence we see that R is the radius of the arc a( right an- 

 gles to the meridian. One may in general neglect the 

 azimuth, and take the last radius for the radius Rl. Now, 

 in computing the arc between Clifton and Dunnose, 1 have 



supposed the oblateness to be — - or e-= „ , and log. o = 



6,5147200 expressed in toises. 



The latitude of the southern extremity of the base is the 

 samt- as that of Clifton, and its azimuth, if we choose tQ 

 attend to it, is nearly 335- 23'. 'I'his base, consideied as 

 an arc of a circle, is reduced to its sine by the foimula 



e = log. e— --^^ , (K beirfg the modules of the table of lo- 

 garithms, so that log. K=9.fi377843.) 



by means of the logarithmic sine of the base, and the 

 angles of the triangles, considered as spherical, the lo- 

 garithmic sines of the sides in the series were next com- 

 puted, and then reduced to logarithms of the arcs them- 

 selves by the formula log. e = log. sin. s 4- — "^|^ ,' - \ 



For the purpose of making this last reductiouj it is suffi- 

 cient to take a single value ot 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 m be one of these arcs, and let us represent by &4f 

 and t'\)" its value reduced to the meridian, the one in loises, 

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

 following formulns; 



5vl;=:m . COS. fl-.(-^-) . tang.^I,-(-^^ ).(-^^) 



. (1 +3- tan. 'rj/) 



C'~~2~) ' \~R/ ] * ^^^^ superior sign being taken when 



the 



