. Longitudes of Dunkirk and Paris. 237 
to r". The determination of M. Beccaria is not.brovight into 
the comparifon, becaufe his meafured degree in latitude 44° 44/ 
is longer than the meafured 1 one in latitude 45 0 . 
The longitude of Dunkirk on this ellipfoid is found to be 
9 m. 29.8 s. in time ; and confequently that of Paris 9 m. 
20} s., which is about 1 1 s. more than that inferred from 
the value of the meafured arc between Goudhurft and the 
meridian of Botley Hill ; and therefore the fum of the two 
horizontal angles at thefe flations would, on this ellipfoid, be 
only about 4" lef than thole found by a&ual obfervation. 
Method of computation. 
On an ellipfoid, where the degrees of the meridian at tire 
equator and polar circle are 60481 and 61194 fathoms refpec- 
tivelv, the degree in latitude 9 2 (the middle latitude be- 
tween Greenwich and Paris) will be 60981 fathoms, exceeding 
the meafured degree by 140 fathoms (Val. LXXX. p. 225.) ; 
therefore, if each of the former degrees, was about 140 fa- 
thoms lefs, the computed and meafured arcs in latitude 50 9 f 
would be nearly the fame. But, that they alfo may nearly, 
agree in latitude 45 0 , let the degrees at the equator, and in 
latitude 50° 9T, be taken 60344. and 60844; then, from thefe 
two degrees., the ratio of the axes will be found, as the tan- 
gents of the arcs 50° fi and 50° P 35' Is aud the femi-axes 
3489932 and 3+73656 fathoms *. T 
- 
* Determined thus : If righ t tines are drawn perpendicular to the curve of a conic 
fiBion to meet the axis, it is known, that the radii of curvature at the points in the 
curve from whence thefe lines are drawn, will he as the cubes of thefe lines. Hence, if PC, 
GB, EC (Tab. VII. fig, 1.), are perpendicular to the curve, the radii of curvature 
at 
