167 



extremities, more and more straitened, as it unbends, while 

 the curvature, at the very middle, remains the same, it 

 will successively form these three curves, in the above or- 

 der. And, if concave mirrors had the same curvature with 

 them, they would have the following properties. 



If the speculum be of a parabolic form, rays of light, 

 falling on it, parallel to its axis, or issuing from a lumi- 

 nous point in the same, so very distant, that they may 

 l>e regarded as parallel, will converge, by reflection, to 

 one point in the axis; which point is the focus. Tlie 

 same is nearly true of rays coming from luminous points 

 not far from the axis, or lying in a very contracted field 

 of view, so as to make but a very small angle with the 

 axis: the rays, coming from each single distinct point in 

 the object, are converged to so many single distinct points 

 in the image, formed at the focus of the mirror. Hence, 

 the excellence of a parabolic mirror, for the larger specu- 

 lum of the Newtonian or Gregorian telescope.* 



Y 2 - If 



* But, because a parabolic mirror reflects, to one point, rays, that fall on 

 it pirallel to its axis, it follows, that it will not converge, to a point, rays, 

 that are diverging or inclined to its axis. The former, (if the point, from 

 whence they radiate, be .in the axis of the mirror,) would be rellected from 

 any line, drawn diametrically across the mirror, in a caustic curve double 

 and cuspidated: the latter, (being in the same plane in which is the radiant 

 point, infinitely distant, and the axis,) would form a curve nodated. So that 

 the excellence of a parabolic mirror is for viewing remote, but not near ob- 

 jects And a person might thus be deceived, who would judge of the good- 

 ness'of a telescope, only from its rendering print legible, at a small distance, 

 from whence the breadth of the great, mirror would subtend an angle of sen- 

 sible 



