[ 3 * ] 
with the plane BCD, it is manifefi: that BCD will 
be its ecliptic, making the angle of obliquity B1E 
with its equator EAK (whofe pole is P) ; and if B 
be the place of the fun in this ecliptic, at any given 
time, the arc BI will be the diftance of the fun from 
the neareft equinoctial point I ; and the arc BF his 
declination at the fame time. 
COROLLARY III. 
If the plane POG, which pafles through P, the 
pole of the fpheroid, be perpendicular to the plane 
LPH, it will alfo be perpendicular to any other plane 
BOD, which palfes through A, the interfedtion of the 
equatorial plane EAR, with the plane LPH j there- 
fore the angle ACO being a right angle, it is evi- 
dent that AC will be the femi-tranfverfe, and CO 
the femi- conjugate axis of the elliptic fedtion BOD. 
* 
COROLLARY IV. 
Hence it appears, that the tranfverfe axis of any 
elliptic fedtion BOD, made by a plane palling through 
the center of the fpheroid, will always be equal to 
the equatorial diameter of the fpheroid, but the con- 
jugate axis will be longer or fhorter, according as the 
inclination of the planes LPH, BOD, is more or 
lefs. 
PROPOSITION II. 
Fig. 2 . To find the length of the femi-conjugate 
axis CO, of the elliptic fedtion AO b, formed by a 
plane cutting the given prolate fpheroid POG through 
its center C, and making the angle PCO with the 
axis CP. 
Let 
