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all parts of it as alike situated in the above respect, which 

 are equidistant from the center, or from the outer edge of 

 the polisher. 



To this purpose, let the surface 

 of the polisher, (supposed equal in 

 size to the mirror,) be represented 

 by the circle A B ; and its area be 

 conceived to be composed of an in- 

 definite number of concentrical zones 

 or annuli, a, b, c, d, See. Each of these 

 will sustain an uniform pressure, from 

 the mirror, proportional to its area; 

 because, the force impressed on the 

 mirror, and its attraction to the po- 

 lisher, is equably diffused on it. The areas of these an- 

 nuli, taken separately, are the differences of the two circles, 

 whose peripheries inscribe and circumscribe each of them ; 

 as the area of the annulus d (for instance) is the difference 

 of the circles, whose ;radii are a d and a c; and they are, 

 ■consequently, to each other, as the differences of the squares 

 6f their diameters, or as those of their radii; and the series 

 of them, fl, h, c, d, e, Sec. taken, in order, from the center 

 to the extremity, are strictly as a rank of figurate numbers 

 proceeding from unity, viz. the odd numbers 1, 3, 5, 7, &c. 

 But, since their breadth is supposed to be indefinitely small, 

 they may be taken as proportional to their mean diameters 

 or radii, i. e. as their distances from the center of the po- 

 lisher; which distances will, therefore, represent the pressure 



on 



