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In taking the back-obfervation, obfervers have been 
advifed either to turn the quadrant about upon the axis 
of vifion, or, holding the quadrant upright, to turn them- 
felves about upon the heel, indifferently. The true date 
of the cafe is this ; that, in taking the Sun’s altitude, 
whether by the fore or back-obfervation, thefe two 
methods muft be combined together ; that is to fay, the 
obferver mud turn the quadrant about upon the axis 
of vifion, and at the fame time turn himfelf about 
upon his heel, fo as to keep the Sun always in that 
part of the horizon -glafs which is at the fame didance 
as the eye from the plane of the quadrant: for, un- 
lefs the caution of obferving the objects in the proper 
part of the horizon-glafs be attended to, it is evident 
the angles meafured cannot be true ones. In this 
way the reflected Sun will defcribe an arch of a 
parallel circle round the true Sun, whofe convex fide 
will be downwards in thefore-obfervation, and upwards 
in the back-obfervation, and confequently, when, by 
moving the index, the lowed point of the arch in 
the fore-obfervation, or the uppermod point of the 
arch in the back-obfervation, is made to touch the 
horizon, the quadrant will dand in a vertical plane,, 
and the altitude above the vidble horizon will be 
properly tibferved. 
The reafon of thefe operations may be thus ex- 
plained: the image of the Sun being always kept in 
the axis of vidon, the index will always fhew on the 
quadrant thedidance between the Sun and any objeft 
feen diredtly which its image appears to touch j there- 
fore, as long as the index remains unmoved, the 
image of the Sun w,ill defcribe an arch everywhere 
equididaat fpom the Sun in the heavens, and confer 
quently 
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