REFLECTING TELESCOPE, 



93 



toward the edges. I believe, that (for the reason before 

 given) the uncoated space, at the center, oiigM always to 

 be as much smaller, on every side, than the perforation in 

 the mirror, as the greatest range of the strokes, in polish- 

 ing, advances the centre of the mirror beyond that of the Experience 

 polisher, having the same shape as the polisher itself; and ^°°^^™^ '^" 

 that it ought to be smallest, or no other than as just men- 

 tioned, when there is no hole in the mirror. 



I have, in this method, with certainty of success, as veri- 

 fied by examination oi" the progressive change of curvature 

 in the mirrors, from a greater degree to a less, and vice versa, 

 effected the desired configuration of them : which serves to 

 confirm me in the belief, that the circumstances, above pro- 

 posedj are those which are really operative, in communicat- 

 ing the diversity of figure to telescopic mirrors; and that 

 neither the direction of the strokes in polishing, the size or 

 form of the polisher, consistence of the pitch made use of, 

 or other accidents, are of any farther moment in the pro- 

 cess, than as they serve to modify the resistance of the pitch, 

 in the several parts of the surface of the polisher. Whe- 

 ther, by attention to the principles here laid down, it would 

 be possible to produce an hyperbolic form, in the convex 

 mirror of the Cassegrain telescope, I have been prevented 

 from endeavouring to ascertain by experiment, from those 

 casualties, affecting my situation in life, which I have already 

 intimated. But it should seem, that it would, to a certain 

 degree, be practicable, from the means I have suggested, of 

 producing a progressive, specific alteration in the figure of 

 the polisher; if I have judged rightly of the existence and 

 cause of that alteration. 



And if it should be found possible to give, to a convex Proposed im- 

 speculum, an hyperbolic curvature, the same could be done reft-acdng xdz- 

 to the convex object glasses of dioptrical telescopes ; which scopes. 

 is a property still wanting to them ; a want which makes 

 them inferior to reflectors, even when they have been ren- 

 dered achromatic, if the aberrations from their spherical 

 figure remain, after those from refrangibility are removed: 

 which aberrations, taken laterally, as they always ought to 

 be, are as the cubes of the apertures. So that, if the lineal 

 aperture be doubled, and the light admitted, which is as the 

 Bcjuare of the aperture, quadrupled, in order to increase the 



magnifying 



