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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 ftate 

 of the cafe is this j that, in taking the Sun's altitude, 

 whether by the fore or back-obfervation, thefe two 

 methods mull: be combined together; that is to fay, the 

 obferver muffc 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 diftance 

 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 the fore-obfervation, and upwards 

 in the back-obfervation, and confequently, when, by 

 moving the index, the loweft point of the arch in 

 the fore-obfervation, or the uppermoft point of the 

 arch in the back-obfervation, is made to touch the 

 horizon, the quadrant will fland in a vertical plane, 

 and the altitude above the vifible horizon will be 

 properly obferved. 



The reafon of thefe operations may be thus ex- 

 plained : the image of the Sun being always kept in 

 the axis of vifion, the index will always mew on the 

 quadrant the diflance between the Sun and any object 

 feen directly which its image appears to touch j there- 

 fore, as long as the index remains unmoved, the 

 image of the Sun will defcribe an arch everywhere 

 equidiftant from the Sun in the heavens, and confer 



quently 



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