404 Mr. ativood’s Theory for the Menfuration 
ED : through I and F draw the arc IF : then the given arc 
KF or KI, and the angle IKF, measured by the given arc PO, 
define the triangle IKF, and in it, therefore, the fide IF and 
and the angle IFK arc determined. If from 1FK, the given 
angle DFK, meafured by the arc XY, be fubtra&ed, the re- 
mainder IFD, and 1FB its fupplement to iSo~ will be defined : 
the given arc FB, with the angle 1FB and the arc IF, deter- 
mine the angle IBF, and the arc IB, or its double BE : and the 
given arc BD, the arc BE, with the contained angle DBE before 
determined, define the arc ED, which is therefore the true mea- 
fure of the angle fubtended by the objeftsobferved under the 
conditions fulfilled in the con {fruition. 
7 . The computation of the obferved angle DCE being for 
the prefent omitted, fome confequences which follow from the 
conftruftion may be inferted in this place, being either corol- 
laries, or fuch truths as admit of eafy geometrical dedudtion 
from the general propofition. The line DC will always be the 
pofition of the vifual ray or line of collimation of the telefcope 
ufed in the obfervation, and the inclination of it to the plane 
of motion will be meafured by the complement of the arc DK 
to a quadrant. The line BC will be the pofition of the ray 
which pafles between the refle&ors B and C, and the inclina- 
tion of it to the plane of motion will be meafured by the com- 
plement of the arc BK to a quadrant. Thefe arcs are left out 
of the figure, that the more material parts of the conftru&ion 
might not be confufed by them. 
8 . Every thing elfe remaining, let the parallel FIM (fig. 3 .) 
be projected on the plane of motion QOP. Through the 
points F and I draw the arc of a great circle NIFR. The ob- 
ferved * objects T and S, or, which is the fame thing, the points 
of mterfeflion at the fphere’s furface E and D will be at equal 
* Compare -fig. 2. 
perpen- 
