from the measurement of an arc of the meridian , &c. 497 
Terrestrial arc in fathoms - - 178904,70 
Latitude of the middle point 16° 34/ 42" 
Mean degree in fathoms due to latitude 16 0 34' 42" 60512,78 
So that by the above comparisons it appears that the 
degree due to latitude - 9 0 34' 44" is - 60472,83 
the degree due to latitude 12 0 s' 55" is - 60487,56 
the degree due to latitude 16 0 34' 42" is - 60512,78 
It now remains to compare each of these mean degrees, 
first with the French measurement ; then with the English ; 
and lastly with the Swedish ; and by proceeding on the 
elliptic theory, deduce from these data three mean ellipticities, 
and from these three a general mean , which must give nearly 
the true compression at the poles. 
Previous to this determination, it will be necessary to inves- 
tigate the requisite formulas for obtaining the compression by 
a comparison of measured degrees in distant latitudes ; and 
first, by the measured degrees on the meridian. 
Let ml and m be the measured degrees, in latitudes 'l and /; 
and let a represent the equatorial diameter, and h the polar 
axis : that is, supposing the earth to be an ellipsoid, let a and 
b represent the transverse and conjugate axes of an elliptic 
meridian. Then it is known from conic sections and the 
nature of curvature, that -—r , — “ fv — rrrm is the radius 
5 -2 (Cos. 1 a r -f Sin. a V. 6 1 )-! 
of curvature of the ellipse at 'l; and that a b - c . v > 
r ’ 2 (Cos. 1 L a z + Sin. 1 1. 6 a )f 
is the radius of curvature of the same, or any other elliptic 
meridian, on the same ellipsoid, at the point L And since the 
degrees at 7 and l are as the radii of curvature at these points, 
we have ml: tn:: 
b* 
2 (Cos, 1 '/. a z + Sin. 1 '/. P)| * z (Cos. 1 /, a 1 + Sin. 1 L b 2 ) -| 
