VOL. LXVII.] PHILOSOPHICAL TRANSACTIONS. I67 



figure; and indeed nothing else is expected from this method, as very evidently 

 appears by the experiment recommended to ascertain the truth of the figure. 

 You are directed to place a small luminous object in the centre of the sphere of 

 which the metal is a segment, and then having adjusted an eye-glass at the 

 distance of its own focal length from the object, and so situated that the image 

 of the object formed by the speculum may be visible to the eye, you are to judge 

 of the perfect figure of the metal by the sharpness and distinctness with which 

 the image appears. Hence it is very evident, that as the object and image are 

 both distant from the metal by exactly its radius, nothing but a true spherical 

 figure of the speculum can produce a sharp distinct image; and that the image 

 could not be distinct if the figure of the speculum were parabolic. Con- 

 sequently, if the same speculum used in a telescope were to receive parallel rays, 

 there would necessarily be a considerable aberration produced, and a consequent 

 imperfection in the image. Accordingly, there never was a good telescope made 

 in this manner; for if the number of degrees, or the portion of the sphere of 

 which the great metal is a part, were as considerable as it ought to be, or as 

 great as Mr. Short allowed in his metal, the instrument would bear but a very 

 low charge, unless a great part of the circumference of the metal were cut off 

 by an aperture, and the ill effects of the aberration by that means in some 

 measure prevented. If ever a finished metal turned out without this defect, 

 and has been found perfectly sharp and distinct, it must have been owing to an 

 accidental parabolic tendency, no ways the natural result of the process, and 

 therefore quite unexpected, and most probably unknown, to the workman. 



Having made many efforts in the former method, which by no means pleased 

 me for the reasons abovementioned; and having observed, from some of 

 Mr. Short's telescopes which fell into my hands, that the high lustre of the 

 polish could never have been produced in the manner above described, but by 

 some softer and more tender substance; and at the same time recollecting that 

 Sir Isaac Newton had given an account in his Optics of his having finished 

 some metals, and considerably mended the object-glass of a refractor, by work- 

 ing both on a tool whose surface had been covered with common pitch about 

 the thickness of a groat; reflecting on these matters, coarse and uncertain as 

 this method appeared at first sight, I was determined to try whether I could not 

 get rid of my embarrassment, by a mode of operation somewhat similar. 

 Accordingly, shortening Dr. Smith's process, I made a set of tools in the 

 manner before described, except that I was obliged to make some subsequent 

 alteration in the polisher which I shall presently describe. Having given a good 

 spherical figure to the brass tool and the bruiser, as well as to the metal on the 

 hones, and made the brass convex tools so hot as just not to hurt the finger, I 

 tied a lump of common pitch (which should be neither too hard nor too soft) in 



