Reflecting telescope. 85 



^erbola, when the precautions here given are obserYed. 

 Both t]icse may be done, by spreading the pitch on the polish- 

 er, to a greater or lesser extent. 



In the Gregorian telescope, the excess of curvature, in The defects of 

 the great mirror, may be remedied, by a defect of it in the the large spe- 

 „T,ij-iij. cuuim may be 

 little mirror, and vice versa. It must be desirable, to a compensated 



fabricator of this instrument, to understand why this is so; by the figure of 

 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 repeated, if 

 they arc made in the dark. I apprehend, that, in this kind 

 of telescope, the mirrors are commonly selected, out of a 

 number finished of each size, as they happen to suit each 

 other: and, if there should be but fcAV pairs in the assort- 

 ment, whose irregularities" compensate one another, few good 

 telescopes will be produced. This would be less frequently 

 the case, and the Gregorian telescope 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 uniform Popular obicr- 



in every part, being (in an arch of it, of a given length) so ^^^^^'^^ "P ^^* 

 •, ' => ^ ,, /, conic sections, 



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 parabola; and in this 



than in the hyperbola. So that, if we suppose a bow to be 



bent, at first, into an arch of a circle, and, when gradually 



relaxed, to become, towards its extremities, more and more 



straitened, as it unbends, while the curvature, at the very 



middle, remains the same, it will successively form these 



three curves, in the above order. And, if concave mirrors 



bad the same curvature with them, they would have the 



following properties. 



If the speculum be of a parabolic form, rays of light, The parabolic 



falling on it, parallel to its axis, or issuing from a luminous speculum is 

 " ' ^ ' " . ^ good for the 



pojnt * 



