Longitudes of Dunkirk and Paris. 243 
of the point H ; and the former proportion would give the 
longitude of D, whether the figure was a fphere or fpheroid ; 
and the angle DWP (found by the latter proportion) would be 
the co-latitude of D fuppofing it a fphere, in which cafe the 
point W becomes the center; but this will not hold in a 
fpheroid, becaufe DW would not be perpendicular to the meri- 
dian at D. 
The forgoing method of computing the longitude from the 
xneafured arc of a parallel on a given ellipfoid (though evidently 
the dired one), will be tedious, efpecially when the lengths of 
the meafured arcs (GH, HD) are very confiderable. But when 
the latitude of the point H is determined from the meafured arc 
GH (on the known meridian), and the extent of the other arc 
(HD), or rather the angle HWD, is not more than two or 
three degrees, the fame conclufions, extremely near, may be 
obtained in the following manner, which is nearly the fame as 
the method ufed in computing the longitudes in the Table of 
General refults, p. 232. (Vol. LXXX.). 
Suppofe G and D (fig. 1.) to be Greenwich and Dunkirk ; PH, 
PD, their meridians, as before; and let HD (inftead of its being 
a parallel to the perpendicular at Greenwich) be an arc of ati 
ellipfe cutting the meridian of Greenwich at right angles, fuppofe 
in the point H. Then the arc GH being = 152549 + 50 feet 
nearly (becaufe the ellipfe which paffes through D, and is at 
right angles to the meridian PG, will fall about 50 feet to the 
fouth of the point cut by the parallel), therefore the value of 
the arc GH, or 25433 fathoms, will, on this ellipfoid, be 
25' 4". 4, and confequently the angle PWH, or the co-lati- 
tude of H, is 38° 56' 24 7/ -4. Now, the radius of curvature 
of this perpendicular ellipfe at H, the extremity of its lefler 
K k 2 axis, 
