' 171 



pencil will, after reflection, converge to one point, unless 

 the radiant point were in the center of curvature of the 

 mirror. 



The property of an hyperbolic mirror is of the same 

 nature, but with effects reversed : for, in this, the rays 

 parallel to its axis, which are incident on its outer an- 

 nulus, will cojiverge 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 con- 

 tinually diminishes from its vei'tex, on each side, a paral- 

 lel, or diverging pencil, falling at a distance from the 

 vertex, on a mirror of this form, must (as in the case of 

 a mirror of greater radius, i. e. of less curvature) have 

 its focus formed farther from it, than if it were incident 

 near the^ middle or vertex, where the curvature of the 

 mirror is that of a circle of lesser radius. 



And thus it is evident, that, as the several pencils, re- 

 flected by the great mirror, when it is spherical or hyper- 

 bolical, do not converge, each to a single point, but to 

 a series of, points, whWse length is the depth of the fo- 

 cus of tlie mirror; so, neither do these pencils, in pro- 

 ceeding on to the little min'or, divei'ge eaeh 'from a single 

 point, but from the same series * of ' points. So' that, 



-'•'■'-•'■ --'though 



had not demonstrated it. The Doctor, I believe,, plight have retorted the 

 same charge on Mr. Robins. I have some reason to think, it is difhcult to 

 give such a demonstration of it, knd that it will reflect credit on the person 

 who. furnishes it. 



