400 Mr. atwood’s Theory for the Menfuratiou 
which the lines interfeCt the fpheres furface will give their re- 
lative fituations by the rules of trigonomety. 3dly, There 
will be no necefiity to reprefent the reflecting planes in the 
general conftruCtion, fince the pofitions of the perpendiculars 
to the planes will give the fituations of the planes themfelves. 
6. To determine by conftruCtion the angle fubtended by the 
objects T, S, from the data which have been defcribed, let 
APOCQj(fig. 2.) reprefent a great circle of the fphere to the 
furface of which the objects obferved, and the pofitions of the- 
incident and reflected rays, &c. are referred ; C being the cen- 
ter, CK the axis, and K the pole of this great circle; through 
K draw any fecondary KO, and from the pole K, at the diftance 
of the arc KF, = the meafure of the given inclination of the re- 
flecting planes to the plane of motion, defcribe a parallel or lefier 
circleFIM : with the poleF, and at a diftance equal to a quadrant, 
defcribe an arc of a great circle interfering the fecondary KO 
produced in the point X, and in this arc from X take XY = the 
meafure of the given inclination of the fixed plane of reflection at 
the fpeculumB to the fecondary which paffes through the point O; 
and draw the quadrant YF, which produce in the direction YF : 
from, F on either fide of F fet offFD equal to the meafure of the 
given conftant angle of incidence at the fpeculum B, and make 
FB (taken on that fide of F which is oppofite to D) equal to FD. 
Draw the radius CO : from O fet off an arc OP in the circum- 
ference OPA equal to the meafure of the angular diftance de- 
fcribed by the moveable radius CP from that pofition at which 
the reflectors are parallel ; obferving that the arc 0 P' be on that 
fide of the point O which* correfponds with the conditions of the 
problem (art. 4,): through P defcribe the fecondary KP inter- 
acting the parallel FIM in the point I : through B and I defcribe 
* It is fuppofed to be known, whether CP beginning its motion from the pofi- 
tion CO approaches towards the vifual ray BG or recedes from it. 
the 
