of the Angle fubt ended by Two Objefils, Set. . 407 
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 fines 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. -I " 
1 2. Since the angle fubtended by the obferved objects' (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 elle remaining 
the fame ; becaufe neither the fine of IF, nor the cofine of DL, 
is affeCted by this change. For this reafon in any conftruCtion for 
meafuring angles by two reflections, the pofition of the * vifual 
ray may be altered into that of the ray BC palling between the 
refleCtors, which will become in that cafe the fituation of the 
vifual ray, this alteration noways affeCting the obferved angles. 
13. While the perpendicular Cl (fig. 2. and 5.) deferibes the 
parallel FIM, the angle of incidence on the moveable fpeculum 
C 4 that is, the angle ECI or ICB, meafured by the arc BI, 
continually increafes until it arrives at a certain limit. This 
limit is determined by drawing through the points B and 1C 
the arc of a great circle BKM. When the perpendicular Cl 
arrives at M, the arc BM is the greateft poflible, which wilt 
therefore be the meafure of the greateft angle of incidence on 
the moveable fpeculum, according to this conftruCtion, the 
radius CP having then deferibed from O an arc which is the 
meafure of the angle FKM. Now it is plain, that if the arc 
MB ftiould be greater than a quadrant, there can be no vifion 
by two reflections, when the perpendicular Cl coincides with M 
(fuppofing the moveable fpeculum to reflect on one fide only) 
becaufe the angles of incidence and reflection on any fpeculum 
* The pofition of the ray DC is the fame with that <of the ray BG parallel to 
it, when referred to diftant objedts. 
H h h 2 muft 
