8o REFLECTING TELESCOPE. 



in a spherical or hyperbolic mirror. From either of these, 

 the rays, which issue in a cone or pencil, from single, lumi- 

 nous, distinct points, in a very remote object, and fall on 

 them, will not conTerge again, to so many single points ; but 

 will, in the mean focus of the mirror,, be dispersed, and 

 blended together in a smajl degree, yet sirijicient to produce 

 an universal haziness and indistinctness, ove» the whole sur- 

 face of the object viev/ed in a telescope, having its large 

 mirror of these forms, because it occurs, with respect to 

 every point in such object ; of which the following are the 

 circumstances, 

 Effects of sphc- If the -mirror be spherical, those rays, nearly parallel of 

 rical mirrors. ^^^^ pencil, which fall on it, next to its centre, will conr 

 verge to a point more distant from the mirror, than the 

 focus of any rays, that fall between the centre and outer 

 edge of the mirror. And those, that fall on the outer extre- 

 mity of it, will converge to a different point, nearest to the 

 mirror : and the rays, which are incident on the several con- 

 centrical annuli, indefinitely narrow, of which the face of 

 the mirror is composed, will have an indefinite number of 

 points of convergence ; each annulus its own point, and all 

 lying in a series, in the axis of the pencil, between the 

 points, or foci, of the extreme, and of the innermost annu- 

 lus *. So that no entire incident pencil will, after reflec- 

 .tion, converge to one point, unless the radiant point were 

 in the centre of curvature of the mirror. 

 Contrary aber-' The property of an hyperbolic mirror is of the same na- 

 ration of the ture, but Avith effects reversed: for, in this, the rays parallel 

 L^:?!!?"^^*^ to its axis, which are incident on its outer annulus, will 

 converge to a point the most distant from it; and the rays, 

 falling on its innermost annulus, will have their focus the 

 nearest to it. And this is easy to comprehend : for, as the 

 curvature of the hyperbola continually diminishes from its 

 vertex, on each side, a parallel, or diverging pencil, falling 



* This property of a spherical mirror has never, so far as " Icnow, 

 been synthetically demonstrated, bf any optic writer, tfio j^. it is a 

 fundamental theorem in catoptrics. Mr. Robins derisively obj ed to 

 Dr Smith, that he had not demonstrated it. The Doctor, I beheve, 

 might have retorted the same charge on Mr. Robms. 1 have some 

 reason to think, it is difficult to give such a demonstration of it, and 

 that it will reflect credit on the person who furnishes it. 



at 



mirror. 



