Measurement of three Degrees of the Meridian. 
Note. 
I shall now explain the formulas employed in deducing the 
results to which I have come in the foregoing Memoir. The 
demonstration of them is to be found in the work of M. De- 
lambre, on the Meridian. 
In the first place, let a be the radius of the equator, e the ec- 
centricity, 4, the latitude of one extremity of a side, or arc, in 
any series of triangles, and Q the azimuth of that side. The 
radius of curvature of this arc will be expressed by 
1 
R~i 
1 + TZ — . cos. *4" • cos. 
and 4 - = 
e t . sin. 
R R 
Hence we see that R is the radius of the arc at right angles 
to the meridian. One may in general neglect the azimuth 
and take the last radius for the radius Ri. Now, in compu- 
ting the arc between Clifton and Dunnose, I have v supposed 
the oblateness to be j- or e a = and log. a = 6,5147200 
33 ° 
expressed in toises. 
The latitude of the southern extremity of the base is the 
same as that of Clifton, and its azimuth, if we choose to attend 
to it, is nearly 33 5 0 23'. This base, considered as an arc of a 
K. 
circle, is reduced to its sine by tire formula e = log. e — - 
(K being the modules of the table of logarithms, so that log. 
K = 9,6377843.) 
By means of the logarithmic sine of the base, and the angles 
