402 Mr. atwood’s Theory for the Menfu, ration 
Let the radius CP move from the position CO, carrying with 
it the fpeculum C and its perpendicular Cl : then, El being 
equal to IB by oonftruCtion, a ray impinging on C in the di- 
rection TEC will be reflected in the plane ECB, and becaufe 
ECI — ICB, the reflected ray will coincide with the line CB, 
:and after reflection at B will * proceed in the direction BG, 
being coincident with the ray SG which comes direCtly from S. 
When the perpendicular Cl leaves CF, the plane of reflection 
ICB becomes inclined to the plane of reflection DCBG with 
which it before coincided ; but the pofition of the rays CB, 
BG, and of the perpendicular BR, remains unaltered ; for 
which reafon the plane GBCFD correfponds to the fixed plane 
of reflection defcribed among the conditions (art. 4.). When 
Cl was coincident with CF, the radius CP was coincident with 
CO, O being the initial point of the arc OP, defcribed by the 
radius 4 CP, denoting that when CP coincides with O, the re- 
fleCtors being then parallel, the inclination of the ray SC ob- 
fierved after two reflections, and SG obferved by direCt rays 
parallel to SC, is nothing : the great circle KO, therefore, 
which pafles through O and F, will be the fixed or primitive fe- 
condary to which the inclination of the fixed plane of reflec- 
tion at the fpeculum B is referred. 
The demon fixation of the conftruCtion , will confift of two 
parts. It mult be firft Ihewn, that the conditions or data of 
the problem are obferved in the conftruCtion. 2dly, That the 
magnitude of the arc ED, which meafures the angle fubtended 
by the obferved objeCts is limited or determined by them. 
Suppofing the angle TCS to be of any unknown quantity, 
it has appeared, that according to the conftruCtion, the rays 
which come from T, and are feen after two reflections at C and 
B, will be obferved to coincide with the rays which come 
* Supra. 
5 
direCtly 
