173 



nuli, and, consequently, nearer to the little minor than 

 those; the rays, issuing from it, to this mirror, \vill not 

 be reflected by it, to the same point with those of the 

 other annuli, unless the curvature of the corresponding 

 annulus, of the little mirror, be encreased, in the propor- 

 tion of its radius to that of the great mirror: for, then 

 only will the focus of rays, reflected by this annulus of 

 the little mirror, be shoitened, as much as, by the effect 

 of tliat of the same annulus,. of the great mirror, it 

 would otherwise be lengthened. The same is true, vice 

 versAj if the focus of any ii annulus, of the great tnirror, 

 be shorter than those of the other annuli. 



Foiuthly. That, if there be any excess or defect, in 

 the curvature of tlie great miiTor, from that of a para- 

 bola, (and, consequently, a contraction, or elongation, 

 of the foci, of the extreme rays of the reflected pencils,) 

 there is no remedy, Avhile this I'emains, but to make the 

 little mirror so much deficient, or excessive in curvature, 

 from that of an ellipse, (and, consequently, to lengthen 

 or contract the foci of the extreme rays of the pen- 

 cils reflected by it,) as its focus is, in proportion to the 

 focus of the great mirror; there being no other means of 

 reducing all the rays, of each pencil, to one point, at the 

 second or conjugate focus of the little mirror: by which 

 alone, the second image, consisting of such points, can be 

 formed, and vieAved distinctly, through the last eye-glass. 

 - From all which, it is manifest, that, if the curv^ature 

 of the great mirror be hyberbolical or doticicnt, then that 



VOL. X. z of 



