of the Angle fubtended by Two Objects , &c. 401 
the arc of a great circle RIE, and in it take El equal to IB: 
through D and E draw the arc of a great circle DE : the arc 
DE will be the mealure of the true angle fubtended by the 
objects obferved, according to the data of the problem. 
Previous to the demonftration of this conftruCtion, the appli- 
cation of it to the method of obfervation by two reflections 
fiiould be defcribed. 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 reflectors at C and B will then be parallel. 
Join CD, and produce it to a very diftant point S r and: 
through R draw GBS parallel to CDS \ the refleCtors C and B 
being parallel, and their perpendiculars coinciding with CF and 
BR, let a ray SC impinge on the refleCtor C : becaufe FC is the 
perpendicular to the fpeculum C and the arc DF — FB by con- 
ftruCtion, thefe arcs being in the plane of the fame great circle 
DBQ^, it follows, that the ray SC will be reflected from C in 
the direction CB, impinging on the fpeculum B at the angle of 
incidence CBR ; and fince DC and BG are parallel by eon- 
ftruCtion, and the parallel lines FC BR fall on them, the 
angles RBG, FCD, will be equal, and FCB or CBR = RBG. 
CB therefore being the ray incident on the fpeculum B will be 
reflected in the direction BG parallel to SC ; and a ray SG com- 
ing direCtly from S will be feen coincident with the reflected 
ray BG. Here we obferve, that the planes of reflection at C 
and B, that is, the planes DCB and CBG coincide, the re- 
flectors being parallel. 
