of the Angle fubt ended by Two Objects, &cc. 40 y 
fecondary KO, or at right angles to it, the perpendiculars DL, 
DV, become equal in both cafes, which is obvious from the 
equality of the triangles DVF, DLF ; it follows, therefore, 
(art. 10.) that the flies of FI and FU, and the cofines of DL, 
DV, being equal, the arcs DE, DW, will be equal in thefe two 
extreme cafes, but in no other. 
1 2. Since the angle fubtended by the obferved objedts (art. 
jo.) depends only on the fine of IF and the cofine of DL, it 
is plain, that if the points D and B be interchanged, (fig. 2,3,4.) 
the angle obferved will not be altered, every thing elfe remaining 
the fame ; becaufe neither the fine of IF, nor the cofine of DL, 
is affedled by this change. For this reafon In any confiruction for 
meafuring angles by two refledlions, the pofition of the * vifual 
ray may be altered into that of the ray BC paffing between the 
refledlors, which will become in that cafe the fituation of the 
vifual ray, this alteration noways affedting the obferved angles. 
1 3. While the perpendicular Cl (fig. 2. and 5.) defcribes the 
parallel FIM, the angle of incidence on the moveable fpeculum 
that is, the ahgle ECI or ICB, meafured by the arc BX # 
continually increafes until it arrives at a certain limit. This 
limit is determined by drawing through the points B and K 
the arc of a great circle BKM. When the perpendicular Cl 
arrives at M, the arc BM is the greateft poffible, which will 
therefore be the meafure of the greate.fi: angle of incidence 011 
the moveable fpeculum, according to this confirudfion, the 
radius CP having then defcribed from O an arc which is the 
meafure of the angle FKM. Now it is plain, that if the arc 
MB Ihould be greater than a quadrant, there can be no vifion 
by two refledlions, when the perpendicular Cl coincides with M 
(fuppofing the moveable fpeculum to refledt on one fide only) 
becaufe the angles of incidence and refledtion on any fpeculum 
* The pofition of the ray DC is the fame with that of the ray BG parallel to 
It, when referred to dillant objects. 
H h h 2 mufi 
