244 Mr. Dalby’s Deduction of the 
axis, will be 3499798 fathoms*, which, divided by 57.295779, 
&c. (the degrees in the circular arc which is equal to the radius), ; 
gives 61083 fathoms for a degree on this ellipfe, confidered as 
a great circle perpendicular to the meridian at the point H on : 
the ellipfoid ; and fiuce the length of this arc (HD) will be 1 
nearly the fame as that of the parallel, or 9 1176 fathoms, its j 
value will be i° 29' 33".6 (the arc DH, or rather the angle 
DWH). Hence, as rad. cotang. i° 29' sf'-h (HWD) :: fine. 
38° $6' 24.". 4. (HWP) : cotang. 2° 22' 26 // .8, the longitude 
of D, or Dunkirk, the fame as before, very near •, hence the 
longitude of Paris will be 2° 20' 4^.9 . But the fame may be 
obtained from the mean diftance of the meridians of Green- 
wich and Paris, or 537950 feet. See p. 599. in the Appendix 
to Vol. LXXX. 
It appears from the foregoing hypothefis, that the meafured de- 
grees of the meridian in middle latitudes will anfwer nearly on an f 
ellipfoid whofe axes are in the ratio affigned by Sir Isaac New- 
ton. But this will receive further confirmation from the fifth: 4 
ellipfoid in the fecond Table, p. 232. (Vol. LXXX.), where the 
near agreement between the computed and meafured arc of the 
meridian between Greenwich and Perpignan (differing but about 
52 fathoms in the extent of 8° 46' 44") would be fomewhat 
extraordinary, were we certain that the latitude of Perpignan^ 
(42 0 41' 56 // ) is correct ; but this is fufpe&ed by M. de la 
% It is not neceflfary to determine the axes of this ellipfe, becaufe when HW 
is perpendicular to the curve of the meridian, it will (by the nature of the figure) 
be the radius of curvature of the arc HD at the point H. Hence, if we put v 
for the cotang, and c for the cojine of the latitude of the point H, and let a denote 
CE sl 
the fine of an arc whofe tang, is — x v; then - X CE=HW, by the properties 
of the ellipfe, 
Caille* 
