[ 116 ] 
furfaces will be leflened in the proportion of the 
fine of the inclination to the radius; fo that at laft, 
when the common fe&ion becomes parallel to the 
plane of the quadrant, the error intirely vanifhes. 
For thisreafon, Mr. Hadley very properly directed the 
thickeft and thinned edges of the index-glafs to be 
placed parallel to the plane of the quadrant. But, as it 
may well be queftioned whether this care is always 
taken by the inftrument-maker, and it cannot be fup- 
pofed that the glades can be ground perfedt parallel 
planes, it would certainly be an advantage acquired to 
the inftrument, could the error aridng from a want of 
parallelifm of the planes be removed in whatever 
pofition the common fedtion of the planes fhould be 
placed with refpeCl to the plane of the quadrant. 
This will be effected for celeftial obfervations, if the 
upper part of the index-glafs be left unfilveredon the 
back, and made rough and blacked, the lower part 
of the glafs being filvered as ufual, which mud: be 
covered whenever any celeftial obfervations are made. 
Then, if the telefcope be fufficiently raifed above 
the plane of the quadrant, it is evident that the ob- 
fervations will be made by the rays reflected from 
the fore-furface of the upper part of the index-glafs, 
and confequently, if the quadrant be adjufted by 
making ufe of the fame part of the index-glafs, the 
obfervations will be true whether the two furfaces 
of the index-glafs are parallel planes or not. The 
Sun or Moon may be thus obferved by reflection 
from the unfilvered parts of the index-gla:s and ho- 
rizon-glafs, fo that a paler darkening gla"s will fuf- 
fice, and they will appear much diftinCter than from 
an index-glafs wholly filvered with a deeper darken- 
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