( »4* ) 
hend an Angle double to that of the Inclination of 
the two polilh'd Surfaces. 
Fig. I. Let R F H and R G I reprefent the Sec- 
tions of the Plane of the Figure by the polifh’d Sur- 
faces of the two Specula BC and DE, ere&ed perpen- 
dicularly thereon, meeting in R, which will be the 
Point where their common Se&ion, perpendicular like- 
wife to the fame Plane, paffes it, and H R 1 is the An- 
gle of their Inclination. Let A F be a Ray of Light 
from any Point of an ObjeQ: A falling on the Point F 
of the firft Speculum B C, and thence refle&ed into 
the Line F G, and at the Point G of the fecond Spe- 
culum D E reflected again into the Line G K, pro- 
duce G F and K G backwards to M and N, the two 
fucceflive Reprefentations of the Point A j and draw 
R A, R M, and R N«. 
Since the Point A is in the Plane of the Scheme, 
the Point M will be fo alfo by the known Laws of 
Catoptricks. The Line F M is equal to F A, and the 
Angle M F A double the Angle H F A or M F H ; 
consequently RM is equal to RA, and the Angle 
M R A double the Angle H R A or M R H. In the 
fame manner the Point N is alfo in the Plane of the 
Scheme, the Line R N equal to R M, and the Angle 
M RN double the Angle MR I or I R N : Subftraft 
the Angle M R A from the Angle M R N, and the 
Angle A R 1SI remains equal to double the Difference 
of the Angles M R I and M R H, or double the Angle 
H R I, by which the Surface of the Speculum D E is 
reclin’d from that of B C ; and the Lines R A, R M 
and R N are equal. 
Co- 
