400 Mr. Atwood’s Theory for the Menfwatlou 
which the lines interfedfi the fpheres furface will give their re~- 
lative (filiations by the rules of trigonomety, 3clly, There 
will be no neceffity to reprefent the reflecting planes in the 
general confiruction, fince the portions of the perpendiculars 
to the planes will give the fituations of the planes themfelves. 
6. To determine by confirudtion the angle fubtended by the 
objedls T, S, from the data which have been defcribed, ler 
APOCQjhg. 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 difiance 
of the arc KF, = the meafure of the given inclination of the re- 
flecting planes to the plane of motion, defcribe a parallel or leffer 
circleFIM : with the poleF, and at a difiance 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 pafies through the pointO;- 
and draw the quadrant YF, which produce in the- direction YF:: 
from F on either fide of F fet off FD 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 difiance de- 
fended by the moveable radius CP from that pofition at which 
the refleCtors are parallel ; obferving that the arc OP be on that 
fide of the pointO which * correfponds with the conditions of the 
problem (art. 4.): through P defcribe the fecondary KP inter- 
fering the parallel FIM in the point I r 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 EG or recedes from it. 
the 
