GRADUATION. 



fcription of the manner in wliicli Copernicus, long after- 

 wards, had his aftrolabe and meridian quadrant graduated, 

 though we have fhcwn under our article Chicle that his pa- 

 ralladical inftrument, with which his altitudes were chiefly 

 taken, had its limb divided by equal divifions that were the 

 fubtenfes of 3' 49. "137 each. 



Tvcho Brahe's intiruinents had the advantage of along 

 radius, which rendered any incquaUties that might occur in 

 his^diviiiims of, Icfs value than they would have been in inllru- 

 nients of Ihort radii ; the fmalleft fub-divilions into wliich he 

 profcfTed to mark his fpaccs were 10' each, and the lingle 

 minutes and portions of a minute, even to 15" and 10", were 

 indicated by triangular diagonals ; but with what degree of 

 preciiionthc fub-divHionswerc effc<fled, and what dependence 

 could be placed on Iris diagonals, as to accuracy, at this dif- 

 tance of time, it is not an eafy matter to afcertain : it is re- 

 corded, however, that tlie operation of graduating his in- 

 ilrumcnts was performed by liis own manual labour. 



And what we have here faid of the inftruments of Tycho 

 Bralie, is equally true of the machiim ccchjl'n of Hevelius ; 

 whatever accuracy his apparatus pofTeiTed, was the refult of 

 his own perfevering induitry, but we are not aware that hi» 

 methods of proceeding have been particularly detailed. 



In Dr. Hook's Animadverlions on the Mach'ina CaJeJl'u of 

 Hevelius, 1 674, this very ingenious mechanift has publiflied 

 an account of iris metliod of racking the exterior edge of 

 the limb of his quadrant, as performed by Tompion, which 

 method, he fays, " does not at all depend upon the care and 

 diligence of the inftrument-maker, in dividing, graving, or 

 numbering the divifions, for the fame fcrew makes it from 

 end to end.'' But, as Smeaton has very properly obferved, 

 this inventive contriver has not given his reader any precau- 

 tions, or particular directions how the perfeftion of the 

 fcrew is to be eniured, or how the notches of the rack work 

 are to be rendered perfectly equal among themfelves, not- 

 withftanding the unequal denfities, and hardnefs of different 

 portions of the metal lo racked. The difficulties alluded to 

 here, were acknowledged by the due de Chaulnes, in a 

 memoir of the Royal Academy of Sciences at Paris, pub- 

 lilhed in the year 1765. Tlie doClor called the account of 

 his method, " an explication of the new way of dividing,' 

 and as an original invention, it may probably be called his 

 own, though the want of a perfect fcrew, with intervals 

 exaftly proportioned to the effective radius of his quadrant, 

 was a fource of error, that pollerior contrivances were re- 

 quired to remedy. See Encine (by Ramfden) fur cutting 

 the fcre-ws of the circular HiviJiiig engine. 



The ufe of Dr. Hook's fcrew for racking the limb of an 

 aflronomical inltrument was not, liowever, abandoned, witli- 

 out a fair trial of its accuracy in reading the quantity of the 

 angles fo meafured ; for Flamllead, (or Flamfleed,) on his ap- 

 pointment to the Royal Obfervatory in 1676, employed 

 Tompion to conilruft him a fextant of fix feet nine and a 

 quarter inches radius, at the expence of Jonas Moore, with 

 an endlefs fcrew of feventeen threads per inch, acting on the 

 racked edge of tlie limb, and with telefcopic fights, which 

 had not been before ufed : the refult of this trial was, that 

 fome (liake took place in tlie notches, that were worn by the 

 fcrew, and frequently an error of a whole minute in reading 

 anobfervation was unavoidably produced thereby. Toremedy 

 this evil, in tlie following year degree fpaces, with diagonal 

 divifions to read to the accuracy of 10", were added as a 

 check on the meafures of the fcrew, and a column, to contain 

 the check angle by diagonal lines, was filled up from the i ith 

 of September of the year 1677. Thefe additions, it appears, 

 from the Prolegomena of the H'tflor'ia Cahjlii, were inferted 

 bj- Flamllead himfelf, and a eomparifon of the fcrew with 



the diagonals proved that an error of as mtich as one m'lnuta 

 was frequently the rcfult of the reading by the fcrew. In 

 an obfervation of the moon, taken on tlie 9th of June 1687, 

 Smeaton fays, that on looking over the obfervations, he de- 

 tected an error of 55", which, upan a radius of fix feet nine 

 inches, he calculates amounts to more than J-^ih part of an 

 inch. The fcrew, however, was ufeful for giving a regular 

 flow motion to the telefcopic fights, and though its ufe, as 

 an accurate meafure of a large arc, was foon abandoned in 

 aftronomical inftruments, it has been retained as an excellent 

 mode of producing a flow motion, by the aid of a tapped 

 clamping piece, and has been applied with great fuccefs to 

 the limb of a dividing engine, which, being a complete circle, 

 admits of equalization of the contiguous notches, by a long 

 continued fimultaneous action of feveral threads of a very 

 perfedt fcrew, caiTied many times all round the circle, when 

 the cxait iituations of dillaut notches have been enfured by 

 the checks afforded by accurate divifions, previoufly mado^ 

 on its plane. 



Notwithftanding what we have above faid of the imperfefit 

 meafureraent of an angle by tlie fcrew, it was notrelinquillicd 

 without another trial in Flamllead's time, by Abraham 

 Sharp, his amanuenfis, to wiiofe fliill and dexterity in ma- 

 nual operations of a meclianical nature both Flamitead and 

 Smeaton have borne ample teilimony ; tlie latter of whom 

 fays, " I look upon Mr. vSharp to have been tlie firft perfon 

 that cut accurate and delicate divifions upon allronomical 

 inftruments.'' The inftrument at which Sharp laboured, 

 and to wliich he applied the fcrew in conjunction with the 

 diagonals of the divided fpaces, in 1689, was the mural arc 

 at Greenwich, of whicli the radius is fix feet feven inclies 

 and a half. " But yet," lays Smeaton, in his paper on this 

 fubjeft, read November 17, 1785, at the Royal Society's 

 room, " wlioever compares the different parts of the table for, 

 converfion of the revolutions, and parts of the fcrew belong, 

 iiig to the mural arc into degrees, minutes, and feconds, 

 with each other, at the fame diltance from the zenith on 

 different fides, and witli their halves, quarters, SiC. will 

 find as notable a difagreement of the fcrew-work from the 

 hand-divifions, as had appeared before in the work of Mr; 

 Tompion ; and hence we may conclude, that the method of 

 Dr. Hook, being executed by two fuch mafterly liands as 

 Tompion and Sharp, and found defective, is in reality not 

 to be depended on in nice matters.'' 



This inference of Smeaton obvioufly implies, that what 

 he calls the hand-dtvifiotis of the mural arc, are njore accurate 

 than the readings by tlie fcrew alone ; but, as he has given 

 no other teft of the accuracy of thefe hand-divifions, nor 

 has explained by what procefs they were inferted, tlie more 

 legitimate inference would have been, that either the fcrew, 

 or the hand-divifions may be faulty, or both may be fo in 

 their refpeCtive degrees. It is to be regretted that Sharp, 

 who was a mathematician as well as a mechanift, has not 

 publiflied the method he adopted of marking out and cutting 

 his dividing lines, which is more immediately the fubject of 

 our prefent article. Had he made his hand-divifions firft, 

 and checked his notches, made by the fcrew, thereby, as 

 Ramfden did with his engine afterwards, his meafures by 

 the fcrew would have been more perfect, though the centre- 

 work might have been hable to be galled by too much 

 preffure of the fcrew againft the notched edge of the inftru- 

 ment, when frequently ufed. 



Nearlyabout tlie time that the mural arc was fixed at Green- 

 wich, Olaus Rocmer, the Danifli aftronomer, fupplied his 

 domeftic obfervatory with an inftrument that had divifions 

 and telefcopic fights moving in the meridian, by means of a 

 long axis, common to both the divided arc and telefcopt-, 



wbicii 



