C "5 ] 



rays reflected from the back-furface, will be to 

 double the inclination of the furfaces of the glafs 

 (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 refraction. Hence, 

 in rays failing 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, 7,13 or 26 times the incli- 

 nation of the furfaces, reflectively. 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 affected in the acquitment 

 of the infcrument, as in the obfervation. But, from 

 what has been juft laid down, this is far from being 

 the cafe, the deviation increasing according to the 

 obliquity with which the rays fall upon the index- 

 glafs j 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 lealt defect: in the parallelifm of the planes 

 of the two furfaces of the index-glafs may produce 

 a feniible error in the obfervation. 



What is here faid only takes place in the fulleft 

 extent, if the thicker! 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 Stands perpendicular to the plane of 

 the quadrant ; but, if^the common fection of the 

 planes is inclined to the plane of the quadrant, trie 

 error ariilng from the defect of the parallelifm of the 

 < Q 2 furfaces 



