GRADUATION. 



'••'hicli therefore admitted of better adjuftment for the vorti- 

 cal motion than the mural arc was capable of; and which 

 may be confidered as the firft tranjit Itijlrument that properly 

 deferves fuch a name. In dividing his arc, Mr. Roemer dif- 

 rcgardcd the total length, with refpcdl to an exatl number 



the greated precaution taken in drawing the dividing line»^ 

 or in marking the dividing points. The fcrcw for flow mo- 

 tion was alio ufod for dividing the vernier fcale in a proper 

 way, after its value was afcertained ; and its perfection was 

 cnfured, with refpeit to the due inclination of its threads all 



of degrets, and lacked more particularly to the equality of round, as well as to the equality of their fpsces : and laflly. 



the divifions, which were convertible into degrees and mi 

 nutes, by a table calculated for this purpofe. The me- 

 thod he made choice of, for rendering his divifions equal, 

 was to begin at one end of his arc, and to proceed by ilep- 

 ping, and by marking the dividing points with a proper prcf- 

 fure at each ftep, till the whole arc was finifhed : for this 

 purpofe he diJ not depend on a pair of dividers, however 

 ilrong their legs, but two fine pointed pieces of ftrong tem- 

 pered fteel were tied, or otherwife fixed together in Inch a 

 way, that the diftance between the two points was f'-th or 

 -TTth of an inch, and the radius of the arc to be divided was 

 lo proportioned, from 2| to 3 feet, that this diftance made a 

 fpace very nearly equal to lo' ; whether exaftly fo, or not, 

 did not fignify, as the difference was allowed for by the cal- 

 culated table, when an angle had been read by the divided 

 fpaces ?.s numbered. It is eafy to conceive that this mode 

 of meafuring an angle would be as accurate as any other, 

 after the due allowance was made, provided the fpaces were 

 perfectly equal to each other ; but the theory of this me- 

 thod is more perfeft than the praftice ; for none of the mix- 

 ed metals is fo perfeclly uniform in its denfity, and fo free 



in order that the advantage of continual bifeaion might be in 

 troduccd as a chtcL on the degree fpaces, the quadrant wa« 

 divided in 96 fpaces, with fub-divifions, in a fcparate 

 d the rea;!:!!^' from Uie <)6th arc were a conilan 



arc : 

 a conilant tell 



and tile re3;!:!!gj from Uie 96th arc were 



of the readings by the 90 , when converted into degrees 



and minutes by calculation, or by a table iifed for that 



purpofe. 



As it is not our iiitewtion to defcribe here the ftnifiure of 

 Graham's quadrant, but merely to defcribe liis method of 

 graduating the limb of bnifs, which was laid over the iron 

 frame, we fliall fatisfy ourfelves by dating that two feparate 

 arches were ftruck by a beam-compafs, fecured from bend- 

 ing by feveral bracing pieces ; the refpoftive radii of wliich. 

 were 96 85, and 95.8 inches. The inner arch was dinded 

 into exaft degrees, and twelfth parts of a degree, or 5' fpaces; 

 but the outer one was divided, as we have faid, into 96 equal 

 parts, and each of tliefe again fub-divided into 1 6 equal parts, 

 fo that the fub-divilions were to each other as 1080 : 15^6, 

 or in fmaller number, as 25 : 32. To convey to the reader 

 an idea how the arcs were divided, fuppofe the quadrant to 

 be rcprefcnted by_/?;/^. 1. of Plate XV' III. of AJlrmomical In 



from hard particles, occafionally met with by the ftepping JlrumnUs, and thjt the occult line a b ilhe required to be di- 



points, as to enfure the perfect equality of the divided fpaces, vided into degrees by points iiiferted thereon, as centres for 



however carefully the ftepping points are prefied in a verti- cutting the dividing lines from ; the known property of the 



cal direftion ; the fmalleft deviation on making the firft circle, that the chord of fixty degrees is always equal to the 



imprefllon becomes greater by preffure, and an attempt to radius, afforded the means of laying down the total arc of 



reftify any erroneous points can never be depended upon : 90 in the firft place ; thus, from the point a, or zero of the 



but, what is worfe, every individual deviation from perfect 

 equality is charged on the whole arc, which therefore will 

 be either longer or fticrter than the true length, by the ag- 

 gregate of ail the pofitive, or negaiive quantities, that pre- 

 dominate in the inequalities of the individual fpaces thus di- 

 vided ; and the longer the arc is from the firft point, when 

 any angle is meafured, the greater is the error of the mea- 

 furement in all probability, becaufe the greater is the proba- 



arc, the point b was marked by meafurement of the fame 

 points of the beam-compafs unaltered, that ftruck the occslt 

 line ; and this arc of 60° was bifecled at c by an extent nearly- 

 equal to the chord of 30 from the points a and b refpeCt- 

 i"ely ; the extent, however, being a trifle lefs than the chord 

 of 30 , the two fweeps did not interfeCi each other, but ap- 

 proached fo nearly together, that the fmall fpace between 

 the fweeping lines was bifected bv a point put in bv hand. 



ble ao-gregate of the deviations from perfect equality in the by the alfiftance of a magnifying eyc-glafs : the di dance of 



fpaces. The total arc thus dirided was about 75° ; but as this point c from a or from b being the chord of 30°, was 



Roemer apphed no correclion to the errors of the dil'ant laid along the hmb from b to d, the extreme point of the 



divifions of this arc, no dependence could be placed on the whole arc of 90 , and when this operation was fo carefullir 



ivfult of the readings, even when converted into degrees and performed, that the arcs a c, c b, and b d were prccifely of 



minutes bv his table, which fuppofed the arc perfedlly di- the fame length, when compared with each other, the total 



vided. ^"""^ might fafely be depended on, as being of its true dimen- 



The next ingenious artift who diftinguiflied liimfelf in the fions. During tliis nice operation, it was pr.^fumcd, that the 



art of graduating aftronomical indruments, was the cele- length of the dividing beam had not altered by any variation 



brated Graham. At the appointment of Dr. Halley to the of temperature. Tiie next ftep was to bififft each of thofc 



Roval Obfervatorv of Greenwich, Flaniftead's indruments three arcs of 30 into fix of 15- each, in the fame manner as 



a b, the arc of 60 , was bifeifled into a c and c l< : but the 

 arcs of 15 ' were not divlhble into a lower number tlian tlirae 

 parts of each 5 ; in order to tripartite each arc of iy\ a 

 feparate arc was nfed, as an arc of trial, defcxibed'Uy the 



Avere removed by his executors, and in the year 1725, Gra- 

 ham undertook the condruClion of a new mural quadrant, 

 which remains as a ftanding proof of his (kill, to this day, 

 in the faid obfervatory. This artift availed himfelf of every 



contrivance that had been praftifed by his predecedbrs, and original radius unaltered, and 15 were transferred to it, and 

 invented fuch a ftrong, and, at the fame time, fight method divided by trial till one-third of it was afcertained to moa- 

 of conftrnfting the frame-work of the iron quadrant, con- furc exactly thedilVunce lietween tlie two points of the com- 

 ilructed bv .Jonathan Siflon, as evinced his fuperior know- pafs ; this diftance 'wai then l.iid off each way Irom each of 

 ledo-e of mechanics, as well as Siffon's precifion in the work- the aforefaid paints of the arcs of 15", and tlie fecond fpace 

 manfhip. The diagonals were now rejefted, as being inca- of each being found equal to tlieir contiguous firit .-ind third 

 pible of being read by a fiducial edge with requifite exaft- 

 iiefs, and the vernier fcale was fabftituted as much prefer- 

 able in this refpecl, and the beam-compafs, with equal ad- _ , , , - 

 vantao-e, was fubftituted for the ruler and dividing knife, the arc of trial, was alcertained by repeated adjudtr.ents and 

 which were liable to coafidcrable parallax, notwithllanding examinations, and then inferted within the divifions of the 

 Vol. XVI. 3 Y divide* 



fpaces thus meafured, tlie whole arc was lub-«.livided into 18 

 equal arcs of 5=" each : in the fame manner, a fiftli part of 

 one of the arcs of 5 , firft transferred upon another part of 



