of the Angle fubt ended by Two Object^ &c. 401 
the arc of a great circle BIE, and in it take El equal to IB: 
through D and E draw the arc of a great circle DE : the arc 
DE will he. the meafure of the true angle fubtended by the 
objeds obferved, according to the data of the problem. 
Previous to the demonftration of this conftrudion, the appli- 
cation of it to the method of obfervation by two reflections 
ffiould bedefcribed. Join CP, Cl, and CF. To the extremity C 
of the radius CP let a plane fpeculum be affixed, Cl being' 
always- perpendicular to this plane : as PC revolves in the plane 
of motion, the perpendicular Cl will defcribe the parallel or 
lefler circle FIM, and when CP coincides with CO, CL will 
coincide with CF. Through B draw BR parallel to CF, and 
let a plane fpeculum be fixed at: B perpendicular to BR ; CF 
and BR being parallel when the perpendicular Cl coincides- 
with CF, the refiedors at C and B will then be parallel. 
Join CD, and produce it to a very diftant point S,- and: 
through B draw GBS parallel to CDS the refiedors C and B 
being parallel,, and their perpendiculars coinciding; with CF and: 
BR, let a ray SC impinge on the refledor C : becaufe FC is the 
perpendicular to the fpeculum C and the arc DF rrFB-by con-- 
Rrudion,., thefe. arcs- being in the plane of the fame great circle- 
DBQ^, it follows, that the ray SC Will be refleded* from C in: 
the diredion CB, impinging on the fpeculum B atthe anjgle of 
incidence CBR ; and fince DC and BG are parallel by con- 
ftrudion, and the, parallel lines FC BR fall oil therm, the 
angles RBG, FCD, will be equal, and FCB or CBR = RBG. , 
CB therefore being the ray incident on the fpeculum E-will be: 
refleded in the diredion BG parallel to SC ; and a ray SG com- 
ing diredly from S will be feen coincident with the refleded" 
ray BG. Here we obferve, that the- planes of refledion at C 
and B, that is, the planes DCB and CBG coincide^ the re- 
fledors being parallel. 
Lc'C*. 
