REFLECTING TELESCOPE. 43 



polish the fhlrror, most in the central part, and least towards 

 its edges ; thus giving to it a curvature, the reverse of a 

 conoid, which it ought to have, and which it can never at 

 first acquire correctly, by any other mode of polishing, but that 

 of wearing it most down (and thus reducing its curvature), ^ 

 towards its extremities.* 



Secondly. When there is a hole made through the center 

 of the polisher, or a void space left there, uncoated with 

 pitch, t 



In these circumstances, the pitch will have liberty to ex- — shewn in 

 pand itself (when yielding to the pressure of the mirror), ^^^ ^^ure pro- 

 towards the center, as well as the edges of the polisher : and, a polisher, 

 as the resistance and friction, in any annular tract of it, is as 

 the direct extent of pitch, bounding it on either side, it fol- 

 lows, from what has been laid down, that it will encrease in 

 any part, as the distance of the same annulus encreases, from 

 each extremity of the coating of the polisher ; and will be in 

 a ratio compounded of the distances, from the interior and 

 exterior margins of the pitch. So that, if the breadth orthe 

 polisher between these margins were, (for example,) 5 inches: 

 then the pressure and friction in the middle tract, equidistant 

 from the outer and inner edges, ^would be, to that prevailing 

 at the distance of half an inch from either margin, as 6| to 2|, 

 (nearly as three to 1 ;) and the same, at proportionate dis- 

 tances, in polishers of any other size ; which unequal pres- 

 sure could never produce, in the mirror, a regular curvature 

 of any species; and, in the spaces nearer to the margins, the 

 inequality of pressure would be still greater. Whence may be 

 conceived the impossibility of figuring mirrors correctly, on 

 polishers disposed in this manner, without some remedial con- 

 trivance ; whether the face, or area of them, be of a circular 

 shape, as directed by Mr, Mudge and others, or oval, as pro- 

 posed by Mr. Edwards : for the mirror would be thus least 

 reduced, and left of a spherical form, at the middle and edges; 

 and be worn down, and hollowed into a diiFerent and irregular 

 curvature, in the intermediate tract. 



*lt will be hereafter shewn, for what particular purpose, solely, 

 such a poljsher may be employed. 



t There ought always to be a hole made through the polisher 

 to prevent the confinement of air or water, near the centre of it. 



