( *59 ) 
and not being in Plano is not to be exactly defcribed but 
in the Spherical or Conical Surface. How to find the Points 
of this Curve in all Cafes is taught by P. Cottrfier , in a ve- 
ry fcarce Latin Book printed at Dijon in Burgundy, and 
publifhed at Paris in the Year 1663: nor do I hear of any 
other Author that has handled the fame Subjed fince, 
though capable and worthy of further Improvement. By 
what he there delivers. Prof. 11. 12. Lib. I. it will be eafi- 
ly underftood, that the Convexity of fo fmali a part of 
the Earths Surface as the Shadow commonly occupies, can 
produce but an inconfiderable Effed ; fo that without fen* 
fible Errour we may take it for a Plain, and the Sedion 
for a true Apollonian Ell ip (is, whofe tranfverfe Axis, by 
reafon of the fmallnefs of the Angle of the Cone, will be 
to its Conjugate nearly as Radius to the Sine of the Sun’s 
Altitude at its Center, efpecially if he be confiderably ele- 
vated. But when he is near the Horizon, it will be ne- 
cefiary to have regard to the true Figure, by reafon of 
the great Length to which the Tranfverfe Axe is extended, 
and particularly when the Shade is entring upon or leaving 
the Earth’s Disk; Of thefe perhaps a fuller Account may 
be given upon a further occafion. 
As to the Pofition of the Axis of the Shadow, it is ma° 
nifeft that it muft always lie in the Plane of a great Cir- 
cle of the Earth palling through tbs Axis of theCone of the 
Shade: and therefore it will be only requifite to obtain the 
Azimuth and Altitude of the Sun at the Place where the 
Center of the Shade at any time is found, to determine 
the Situation of the Axe and Species of theEllipfe required. 
Thus the middle of the Eclipfe at London having been ob- 
ferved at 9 b . 10'. 45", by the given Latitude and Decli- 
nation we find his Azimuth about 59°. 00 '• and Altitude 
40°. 46'. that is juft 40 Degrees high at the Center of the 
Shadow. Wherefore the Tranfverfe Axe of the Ellipfe 
was to its Conjugate very near as Rad. to the Sine of 40°, 
S f z or 
