SPECULUM. 



all the fand-holes and inequalities were taken off; and then 

 a fmaller grinding-ftone, or a piece of one, was fhaped fo 

 convex as to fit the brafs co'^cave pattern, on which the 

 metal was again grouiid, when fixed upon a block, with a 

 little emery and water, till the gauge fitti d it. The dia- 

 meter of the rough ftone was to the diameter of the fpe- 

 culum as 6 to 5. When the ilrokcs in grinding were made 

 in a circular direftion, they diminifhed the edges of the 

 ftone ; but when made acrofs, they made it flatter, fo that 

 it might be made a portion of either a fmaller or larger 

 fphere, by the mode of working, and coiifequently mi^ht 

 be made to grind the cor.cave fpeculum accordingly. But 

 care was taken that as little of the external hard cruft was 

 ground away as pofiible, when the figure was once com- 

 plete, and the furface even. When the rough grindmg was 

 finifhed, various other tools were ufed, not only with the 

 fpeculum, but with each other, to infure an uniformity of 

 fhape. A brafs concave tool, fhaped like the fpeculum, 

 but of larger diameter, was worked on a marble convex 

 tool, on which were bedded by cement a number of fmall 

 blue hones, like a pavement ; fo that the working of the 

 brafs concave tool on this pavement made a convex curve 

 over the furface of the pavement, which was thus prepared 

 to fmooth the fpeculum ftill further, as well as to improve 

 its figure, by varying the mode of applying the grinding 

 ftrokes. Again, a polilhing tool made convex, of glafs or 

 fine marble, and brought to its figure by the brafs concave 

 tool, was covered with a piece of fine even farcenet, and 

 laced tight behind, on which a folution of pitch in fpirits 

 of wine was fpread evenly with a varnifh brufli, till its con- 

 fidence was uniform, and thick enough to receive a portion 

 of fine putty powder, when another tool, made concave of 

 brafs, called a bruifer, was ufed to rub down the gritty 

 matter of the putty occafioually, as well as to grind fome- 

 times the bed of hones, when its figure began to alter too 

 much. During the grinding, a wooden handle was ce- 

 mented on the central part of the fpeculum, to move it by. 

 It would be tedious to detail all the variety of precautions, 

 with the fucceffion of circular, fpiral, and crofs Itrokes, re- 

 commended for giving perfcftion to the figure and polifh of 

 the metal ; all which the reader may find in Smith's Optics, 

 from page 301 to page 312, together with the author's 

 mode of examining both the exaft length of the focus, 

 and the figure of the curve, by the rcfleftcd light of a 

 candle. 



In reflefting telefcopes of various lengths, a given nbjeft 

 will appear equally bright and equally diftinft, when their 

 linear apertures, and alto their linear amplifications, or mag- 

 nifying powers, are as the Iqnare-fquare roots of the cubes 

 of their lengths, agreeably to both fir Ifaac Newton and 

 Dr. Smith. For example, fuppofe that a reflefting tele- 

 fcope, with an aperture of 2.448 inches, have a fpccuhim of 

 two feet focal length, and an eye-glafs of .-jVijth-of an inch 

 focus, wlicre the power will be -3?,,V = 102, and that it be 

 required to have another made of three feet focal length, 

 that fhall produce the fame brightnefs and diitinftnefs in the 

 objeft viewed ; firlt we fliall have 2 X 2 x 2 = 8 for the 

 cube, and the fquarc root of 8 = 2.83, and again the 

 fquare root of 2.83 = 1.68 ; then 3 X 3 X 3 = 27 is the 

 cube of the new focal length, and 5.2 its fquare root ; and 

 again, the fquare root of 5.2 will be 2.28 ; hence, as 1.68 

 : 2.28 :: 102 : 138 ; therefore 138 will be the magnifying 

 power of the enlarged telefcopc, 0.261 the focua of its eye- 

 piece, and 3-312 inches its corrcfponding aperture; for as 

 1.68 : 2.28 :: 2.448 : 3-3l2> &c.; and alfo ,:',V ~ O.261. 



The following table, couftrufted on this propoCtion, 

 was calculated by Dr. Smith, which we infert, as being in 



a form more intelligible to a common workman, than the 

 one we have before inferted from the calculation of fir Ifaac 

 Newton. 



This table is adapted for telefcopes of the Newtonian 

 conltruftion, in which the figure of the great metal is fup- 

 pofed to be truly fpherical ; but it is prefumed, tiiat when 

 tliis table fuppofes the conftruftioii to be of the Gregorian 

 kind, the focal length is the fum of the focal lengths of 

 both the fpecula, or the diltance that the rays pals after 

 both refleftions, before they come to the eye-glafs; and 

 that the large fpeculum is parabolical. 



Short. — We do not find that any optician didinguifhed 

 himfelf in tlic art of making fpecula for reflefting telefcopes, 

 after Dr. Smith's time, till we come to Mr. James Short, 

 whofe compofition was beautiful, and whofe ])olilh, as well 

 as parabolic figure, were excellent ; nay, have been con- 

 fidered as llandards of perfeftion for even fublequent opti- 

 cians to imitate. We have, however, to regret that this 

 confummatc workman not only kept his procels a fecret 

 from the other opticians, but, in order to fecure to himfelf 

 the fame he had acquired of being the firlt in his line of 

 mainifaftory, fome little time before his death, as we arc 

 credibly informed, he employed his founder, Mr. .lurticc 

 Blackburgh, to deftroy all hi* tools, lell they (hould fall 

 into fome perfmi's hands, who might avail himfelf of their 

 ufe ; and accordingly they were all melted into a liquid mafs : 

 and his long and luccelsful experience has no further bene- 

 fited polterity, than as it left fpccimons of workmanfhip to 

 (hew what Ikilful perfevcrance could cflcft. 



Short Ibft beliind him, however, a table of the apertures, 



powers. 



