[ IX 5 ] 
rays refle&ed from the back-furface, will be to 
double the inclination of the furfaces of the glals 
(which is here fuppofed to be but fmall), as the tan- 
gent of the angle of incidence out of air into glafs, 
is to the tangent of the angle of refradlion. Hence, 
in rays falling near the perpendicular, the deviation 
will be about three times the inclination of the 
furfaces; and if the angles of incidence be 50°, 
6o°, 70°, 8o° or 85°, the deviations of the reflected 
rays will be about 4, 5, 7, 1 3 or 26 times the incli- 
nation of the furfaces, refpedlively. Had the devi- 
ation been the fame at all incidences of the rays on 
the index-glafs, no error would have been produced 
in the obfervation ; becaufe the courfe of the ray 
would have been equally affedfed in the adjuftment 
of the inftrument, as in the obfervation; But, from 
what has been juft laid down, this is far from being 
the cafe, the deviation increaftng according to the 
obliquity with which the rays fall upon the index- 
glafs ; fo that in very oblique incidences of the rays, 
fuch as happen in meafuring a large angle by the 
fore-obfervation or a fmall angle by the back-obfer- 
vation, the leaft defedt in the parallelifm of the planes 
of the two furfaces of the index-glafs may produce 
a fenfible error in the obfervation. 
What is here faid only takes place in the fulleft 
extent, if the thickeft or thinned: edge of the index- 
glafs, or, to exprefs the fame thing in other words, 
the common fection of the planes of the furfaces of 
the index-glafs ftands perpendicular to the plane of 
the quadrant ; but, if the common fedtion of the 
planes is inclined to the plane of the quadrant, the 
error arifing from the defedt of the parallelifm of the 
Q 2 furfaces 
