10 



are uncovered, the eye may see the image of w, (by rays in*- 

 cident on a and g in the mirror a, and on d and h in the 

 mirror 6,) in different places, whose angular distance is amg; 

 and if the sight vane or hole at e be of any breadth, the 

 second reflected image may be seen in two extreme places, 

 whose distance will be as near to that anglie as the breadth of 

 the vane and of the horizon glass will allow, and it may be 

 also seen coincident with the direct image C, because the 

 unsilvered part of the glass b extends- across its whole 

 breadth, so that in whatever part of it the reflected image 

 appears, the sight may be directed through that part to C. * 



angles would make do issue parallel to be;- But if tHe speculums were uncovered, thedif. 

 ference only of the angles amg and cam would require to be corrected by an angular 

 motion of the speculum b,. which would be half of this difference ; and this being done 

 the image of m would be seen in the direction ft e by the ray m g, wliile the same image' 

 would be visible at an angular distance equal to a m g, by the ray m a; so that the 

 image of c or m might be- seen in different places under the same inclination of the 

 glasses; i. e. the adjustment would be uncertain.. 



* To shew that what is here stated is applicable to observations made with the quadrant, 

 let d (fig, 2.) be a luminous body, from which light falls on the mirror a b with an angle 

 of incidence «f/ e : its image will be visible to an eye at e in the direction e/, when 

 the angle efc is equal to c/rf; Let the mirror be turned on its axis/, carrying the 

 perpendicular/ c with it : when this has arrived to the position/g-, the angle of incidence 

 will be encreased hy cfg; and the angle of reflection must be augmented by the same, 

 so as now to be equal to dfg: if therefore the image is to be seen still in the point /i 

 and no other point in the speculum, the eye must be placedat A ; when g-/A will be 

 equal to g f d; in which case the angle efh will be equal to twice tjie angular motion 

 af i of the speculum, or of its perpendicular c/, which is the same ; i. e. ef h will be equal 

 to twice cfg. If the eye may be shifted, from the place h to a different place, as n, 

 by looking through a hole or vane, whose breadth is equal to the interval h n, the imag»^ 

 of the object d may be seen by reflection from the mirror i A: in a different place or di- 



