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so; and how a change in the curvature may be effected: 

 for an artist cannot well execute a project, the design of 

 which is to him unknown; nor improve by trials, even re- 

 peated, if they are made in the dark. I apprehend, that, 

 in this kind of telescope, the mirrors are commonly se- 

 lected, out of a number finished of each size, as they hap- 

 pen to suit each other: and, if there should be but few 

 pairs in the assortment, whose irregularities compensate 

 one another, few good telescopes will be produced. This 

 would be less frequently the case, and the Gregorian te- 

 lescope be more improved, if a more certain method were 

 known, of giving, to each pair, their appropriate figure 

 at first, or of altering it in either, where it is defective. 

 Perhaps persons, not much versed in optics or geometry, 

 may be assisted, in discovering the evil, and the remedy, 

 from the following remarks; which are given in words, in 

 order to dispense with a diagram. 



The curvature of the circumference of a circle is uni- 

 form in every part, being (in an arch of it, of a given 

 length) so much the greater, as the radius is smaller, and 

 vice versa. But the curvature of the ellipse, parabola, and 

 hyperbola, is not uniform, but continually diminishes, from 

 the vertex of these curves, (which answers, in the present 

 case, to the center of the mirror,) to the extremity on each 

 side: but it diminishes less in the ellipsis than the para- 

 bola; and in this than in the hyperbola. So that, if we 

 suppose a bow to be bent, at first, into an arch of a cir- 

 cle, and, when gradually relaxed, to become, towards its 



extremities. 



