of the Angle jubi ended by Two Objects, See. 409 
theory. If the angle DFK (fig. 2.), being the inclination of 
the fixed plane of refieffion to the primitive fecondary be 
=■90°, and the arc KF, or the inclination of the reflectors to 
the plane of motion, be = 90° alfo, the conftruftion will be- 
come that of hadley’s inftrument (fig. 7.), whatever be the 
magnitude of the arc DF, that is, of the angle of incidence on the 
fixed fpeculum B : in this cafe the points F and O, and the points 
I and P, coincide. Here IF or PO meafures the inclination of 
the reflectors to each other ; and becaufe BF = FD, and BI ~ IE, 
by conftruftion, it follows, that DE=2PO, that is, the angle 
fubtended by the obferved objects is double to the angle at 
which the reflectors are inclined to each other. This is a known 
property of hadley’s inftrument, in which the vifualray, and 
the ray intermediate between the reflectors, are in the plane of 
motion,, which is alfo exprefled in the conftrudtion, DC and BC 
coinciding with the plane POC. 
15. BifeCt KO in F ; then will ;KFj= 45 0 (fig. 8.). The 
vifual ray CD being coincident with the plane of motion, let 
the inclination of the reflectors to that plane be equal to 
45 0 : moreover, let the angle * DFK — 180 0 ; fo fhall D coin- 
cide with O, and B withK : this will afford a good example 
to the general theory. Let the radius CP move into any given 
pofition, carrying with it the fpeculum C and its perpen- 
dicular Cl : here the obferved objeCt E and the point B are 
always equi-diftant from X ; and becaufe BI is half a quadrant 
by confiruCtion, it follows, that XE will be of the fame mag- 
nitude, BE therefore will be a quadrant, and confequently E 
-will coincide with P, being always in the plane of motion. 
The following properties are alfo derived from this conftru&ion. 
iff, The arc DE fubtended by the obferved objects is equal to 
the arc deferibed by the index or moveable radius CP from O ; 
. - * Compare fig. 2. 
differing 
