6 *^; " 



' through the vane at e, will see the reflected image of tiie 

 object c coincident with the object C : because in these dif- 

 ferent positions of the quadrant, the incident rays become 

 the reflected ones, and vice versa ; and the index glass in the 

 2ad position a, will be parallel to the same, as it was in the 

 1st position A ; as also the horizon glass b to B. 



But if the speculums A and B were not rightly adjusted 

 at right angles to each other, the reflected ray B E \a the 

 former position of the quadrant would not he parallel to the 

 incident ray C A, but these rays would make an angle, 

 equal, (suppose) to £ B M (or E B N) ; and consequently 

 this B M (or B NJ is the reflected ray, by which, and in 

 the direction of which, the image of the object C is seen : 

 then the object c must be placed at m (or n) in order to coin- 

 cide with the image of C, which appears only in the direc- 

 tion of M B (or N S), f,et them coincide in m ; and 

 let the quadrant no^v be turned half round, and put into 

 the position a p q ; in which the glasses a and A, and b and 

 B are parallel : the angle of incidence is now one half of the 

 angle m a d greater than half c a A or CAB by the angle 

 c a m; so that the reflected ray ad will fall without the angle 

 cab', and will therefore either fall quite without the hori- 

 zon glass b, or at least at a distance from its centre : in the 

 former case the image of c would not be seen by the eye at 

 c at all, unless the index glass were so long, and the object 

 c so near, that a ray in g could fall on it in an angle so 

 much less than the half of /« a d, as that the reflected ray 



