GRADUATION. 



fent any number of equal parts upon the inllrument, whofe 



fub-divifions are to be 5' each ; for is cxaftly 



16J, therefore fo many divifions are exa&Iy equal to a mean 

 fpace between the dots, whofe errors have been tabulated. 

 Let therefore the arc of the feftor be divided into 1 6 fpaccs, 

 of I" 20' each, and let a fimilar fpace at each end be fub- 

 divided into eight parts of 10' each, as in Jig. 6 ; we fliall 

 then have a fcale, which furnifhes the means for making the 

 true divillons, and an intermediate examination at every 

 bifeftional point. 



I have always divided the feftor from the engine, becaufe 

 that is the readiefl method, and inferior to none in point of 

 acGiu-acy, where the radius is very fliort ; but as it is more 

 liable than any other to centrical error, the adjuftment of 

 the arc by the fcrew E becomes neceflary ; by that adjuft- 

 ment alfo any undue run in the aftion of the roller may be 

 reduced to an infenfiblc quantity. 



When the utmoft degree of accuracy is required, I give 

 the preference to dividing by lines, becaufe they are made 

 with a lefs forcible effort than dots are, and alfo, becaufe if 

 any fmall defeft in the contexture of the metal caufes the 

 cutter to deviate, it will, after pafTing the defective part, 

 proceed again in its proper courfe, and a partial crookednefs 

 in the "line will be the only confequence : whereas a dot, 

 under fimilar circumftances, would be altogether difplaccd. 

 Bat, on the contrary, where accuracy has been out of the 

 queftion, and only neatncfs required, I have ufcd dots ; and 

 I have done fo, becaufe I know that when a dot, and the wire 

 which is to bifeft it, are in due proportion to each other, 

 the wire covering about two-thirds of the dot, the niceit 

 comparifon poffible may be obtained. It may be further 

 obferved, that divifion by lines is complete in itfelf ; whereas 

 that by dots requires lines to diftinguifh their value. 



On the upper fide of Jig. i . is reprefented the apparatus 

 for cutting the divifions. It confifts of three pieces, J, K, L, 

 jointed together, fo as to give to the cutter an cafy motion 

 for drawing lines dircftly radiating from the centre, but in- 

 flexible with refpecl to lateral preffure ; J, d, are its handles. 

 The cutting point is hidden below the microfcope H; it is 

 of a conical form, and were it ufed as a dotting point, it 

 would make a puncture of an elliptic fliape, whofe longer 

 diameter would point towards the centre. This beautiful 

 contrivance, now well known, we owe to the ingenuity of 

 the late Mr. Hindley of York; it was borrowed by Mr. 

 Ramfden, (fee Engine for diviiling,) and applied with the 

 beft effeft to his dividing engine. 



Previoudy to cutting the divifions, the parts now defcribed 

 muft be adjulled. The cutting apparatus mull be placed 

 with the dividing point exaftly at tlie place where the firft 

 line is intended to be drawn, and clamped, fo that the ad- 

 iufting fcrew may be able to run it through a whole interval. 

 The microicope H muil be firmly fixed by its two pillars 

 b, b, to the main frame, with its micrometer head at •z.cro ; 

 and with its only wire in the line of tlie radius, bifedting tlie 

 firft of the 256 dot.s. And it ftiould be obferved tiiat the 

 cuttiiig frame and this muft not vary refpeiling each other, 

 during- the time that the divifions are cut ; for any motion 

 that look place in either would go uudimiiiillied to the 



account of error. The microfcope I is alfo faftened to the 

 main frame, but it is only required to keep its pofition un- 

 varied, while the divifions of the fcctor pafs once under its 

 notice, for it muft have its wires adjufted afrelh to ihefc 

 divifions at every diftinft courfe. The microfcope I has 

 two wires, crofting each other at an angle of about 40 ; 

 and thefe are to be placed fo as to make equal angles with 

 the divifions of the feftor, which are not dots but lints. 

 The feftorial arc muft alfo be adjufted to its proper radius 

 by the fcrew ^, fg. 2. i. e. while the main frame has been 

 carried along the circle through a mean interval (hewn by 

 H, the feftor muft have moved through exactly i6j of iti 

 divifions, as indicated by I. 



Things being in tliis pofition, after liaving given the parts 

 time to fettle, and having alfo fulTiciently proved th^- per- 

 inanence of the micrometer H, and the cutting frame, 

 with refpeiSt to each other, the firft divifion may be made; 

 then, by means of the fcrew for flow motion, carrj- the 

 apparatus forward, until the next line upon the fcAor coiqcs 

 to the crofs wires of I ; you then cut another divifion, and 

 thus proceed until the i6th divifion is cut := i' 20': now 

 the apparatus wants to be carried further, to the amount of 

 |ths of a divifion, before an interval is complete, but at this 

 laft point no divifion is to be made; we are here only to 

 compare the diviiiou on the feclor with the corrcfponding 

 dot upon the inllrument: this interval, however, upon the 

 circle will not be exactly meafured by the correfponding 

 line of the fedor, which has been adjufted to the mean in- 

 terval, for the fituation of the dot i .4 is too far back, as 

 appears by the table of real errors, by —4.8 divifions of the 

 micrometer head. The range of the fcrew for flow motion 

 muft now be reftorcd, the crofs wires of H fet back to 

 —4.8 divifions, and the feftor moved back by iiaiid, but vmX. 

 to the divifion o, where it began before ; for, as it left oft" in 

 the firft interval at ^ths of a divifion, it has to go forwards ^th 

 more before it will arrive at the fpot where the i 7th divi- 

 fion of the inftrument i' 25' is to be made, fo that in this 

 fecond courfe it muft begin at ^th ftiort of o: go through 

 this interval as before, making a divifion upon the circle at 

 every one of the fixteen great divifions of the fe(^tor ; and H 

 ftiould now reach the third dot, allowing for a tabular 

 error of — 10.2, when the divifion fths of the fedlor reaches 

 the crofs wires of I. It would be tedious to lead the reader 

 through all the variety of the fedor, which confifts of eight 

 courfes; and it may be fuflicient to obicrve, that at the 

 commencement of every courfe, it muft be put back to the 

 fame fraftion of a divifion which terminated its former one; 

 and that the wire of the micrometer H muft always be fet 

 to the tabular error belonging to every dot, when we end 

 one interval and begin another. The eight courfes of the 

 fedlor will have carried us through ,\d part of the circle 

 !!■ 15', and during this time the roller will have proceeded 

 through half a revolution: for its clofe contact witii th>- 

 limb of the circle does not allow it to return witli the feeder 

 when the latter is fet back at everj- courfe. Having in this 

 manner proceeded from one interval to another, tlirough the 

 whole circle, the micrometer at laft will be found with its 

 wire at ■x.cra, on the dot from which it fet out; ;i;id the fee- 

 tor, with its i6tli divilion, coinciding with tht wires of it* 

 niicrolcope." 



3Z2 



T.<RL* 



