. 139 



' 'In these circumstances, the pitch will have liberty to 

 expand itself (when yielding to the pressure of the mir- 

 ror), towards the center, as well as the edges of the po- 

 lisher: and, as the resistance and friction, in any annu- 

 ■lar tract of it, is as the direct extent of pitch, bound- 

 ing it on either side, it follows, from what has been 

 laid down, that it Avill encrease in any part, as the dis- 

 tance of the same annulus encreases, fjom each extre- 

 mity of the coating of the polisher; and Avill be in a 

 ratio compounded of the distances, from the interior and 

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

 the polisher between these margins were, (for example,) 

 •5 inches: then the pressure and friction in. the middle 

 itract, equidistant from the outer and innef edges, would 

 he, to that prevailing at the distance of half an inch 

 from either margin, as 6"i to 2i, (nearly as three to 1;.) 

 and the same, at proportionate distances, in polishers of 

 any other size; Avhich unequal pressure could never pro- 

 duce, in the mirror, a regular curvature of any species ; 

 and, in the spaces nearer to the margins, the inequality 

 oi' pressure would be still greater. Whence may be con- 

 ceived the impossibility of figuring mirrors correctly, ou 

 polishers disposed in this manner, without some reme- 

 dial contrivance; whether the face, or area of them, be 

 of a circular shape, as directed by Mr. Mudge and others, 

 or oval, as proposed 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 



