GRADUATION. 



either of the SifTons, as the real contriver of the metliods 

 here adverted to. SiiTon (the younger) rcjefled the arc of 

 96, as being only a help to a bad divider ; but Bird uft-d to 

 retort on him, by faying, that good dividing wa3 not afraid 

 of fuch a teft of its accuracy. 



It is the charafteriftic of a great genius in mechanics, not 

 to tread too clofely in the licps of his predccefTors, but, 

 avaihng himfclf of any hints tliat may have been prcfented 

 to him, to mark out a more diredt and even path for him- 

 fclf, that (hall throw in his way fewer obilacles to impede 

 his progrefs. This was the cafe with Mr. Bird, who, hav- 

 ing been brought up a cloth-weaver in the county of Dur- 

 ham, and having noticed fome very coarfe divifions on the 

 face of a clock that fell in his way, immediately fet about 

 dividing one himfelf, in a much neater manner, and was fo 

 pleafed with his fuccefs, that in the year 1740 he came to 

 London, and was in bufinefs for himfelf as an inftrument- 

 makcr, only five years afterwards. After having made him- 

 felf acquainted with the methods at that time in ufe of 

 dividing a circle, he faw that no one had guarded again 11 

 the errors produced by the effedls of variable temperature 

 on the beam of the compafs, as well as on the metal of the 

 fcales and circles to be divided ; he alfo faw that bifeftion 

 of an arc had fo much advantage over trifefiion, or quin- 

 quefeftion, that he abandoned the latter modes of dividing 

 altogether, and was the firll probably to compute chord- 

 lines, to be taken from a good vernier (what he calls iio- 

 riius) fcale, by the beam-compafs, in order to determine 

 fuch points in an arc of 90°, as may enable a divifion by 

 continual bifeftion to be adopted, and at the fame time fuch 

 as may be laid down without lofs of time, or, in other words, 

 without fenfible change of atmofpheric temperature. 



We cannot better defcribe Mr. Bird's method of dividing 

 ailronomical inilruments than by uilng his own words. " The 

 requifites," favs he, " for the performance of this work are as 

 follow : A fcale of equal parts, by which the radius may- 

 be meafured to o 001 of an inch mull be provided. My 

 tcale is 90 inches long, each inch divided into 10, conti- 

 guous to which are nonius (vernier) divifions, viz. 10. 1 

 inches divided into 100 equal parts, fhewing 0.00 1 of an 

 inch, and by the aflillance of a magnifying glafs, of one 

 inch focal length, a third of ocoi may be taken off by 

 eftimation. 



" Provide fine beam-compafles, to which magnifying 

 glafTes of not more than one inch focal length Ihould be 

 applied. Let the longell beam be fufficient to draw the 

 arcs, and meafure the radius ; the zd to mealure tlic 

 chord of 42' 40' ; the 3d to moafure the chord of 30 ; 

 ihe 4th, 10 20'; the 5th, 4' 40' ; and if a lixth, to mea- 

 lure I y', be made ufe of, fo much the better. 



" The radius of the arc of 90" at the points is equal 

 10 95.938 inches, from which the following numbers were 

 computed, vi-z. 49.6615 inches r= chord of 30°; 25.0448 

 inches z= chord or 15 ; 17.279047 inches = chord of 

 10^20'; 7.81 186 inches ::= chord of 4° 40 ; and 69.80318 

 inches =: chord of 42' 40'. Having drawn the fevcral 

 arcs, between whicli the divifions were to be cut, the radius 

 and the lengths of the above chords were taken by the 

 beam-compafles, which, together with the fcale, were laid 

 upon the quadrant, where they remained till the next morn- 

 ing ; daring which time, the door of the room was kept 

 locked. Before fun-rife I re-meafured the radius, which 

 required fome correction ; the beam being of wliite fir, and 

 the fcale of brafs, which probably contrafted, while the 

 beam remained unaltered : the oilier beani-compafies alto 

 required correction. Now tiie quadrant and feale being 

 of the fame temperature, tlie faint arc i /I fjl£. 2. of 



Plate XVIII. of /IJronomicnl Injlrumeiiis,) was ftruck, and 

 with a very fine prick-punch (pointril) the point a wa« 

 made ; with the fame beam-compafs unaltered I laid off 

 from a X.O e the cliord of 60'', making alfo a fine point ; 

 witli the chord of 30" a e was bife£led in r. Now one point 

 of the beam-compalTes containing 60' was fixed in c, and 

 with the other was marked the point r or 90" : next, with 

 the bcam-compaffes containing 15% was bifeftcd e r\n n or 

 75'; from n was laid off the chord of 10' 2o' ; and from 

 r, 4 40'; which two lall chords joined exaftly in ^, being 

 the point of 85' 20' : now each degree being to be divided 

 into 12 parts, or every 5', thcref^ire, 85 x 12 + 4 = 1024, 

 a number divifible by continual bifedions. The lall chord 

 computed was 42^ 40', with which a g was bifedled in ; 

 a and g were bifedled by trials : but, whoever under- 

 takes to divide a large quadrant, will do well to compute 

 alfo the chord of 21° 20' ; but for this chcrd any of the 

 beam-conipaffes already provided, which will take in the 

 length, may be ufed. Tiie point g, being forrred as above, 

 I proceeded, by continual b feclions, till I had the number 

 required, viz. 1024. To fill up the fpace betn-ecn^ and r, 

 containing 56 divifions, the cliord of 64 divifions was laid ' 

 off from g towards d, and divided like the rcfl by co.itinual 

 bifeftions ; as was alio from a towards b. The points 30', 

 60, 75", and 90', fell in without any fenfible ineqHality." 



So much will lufRce for giving a general idea of Bird's 

 proceedings, in di'oiding his ailronomical inilruments ; but 

 his method of transferring the divided points into dividing 

 lines was equally original, and guarded alfo againft errors 

 that might ariie from the handling of the beam duriiiir the 

 operation, by variable temperature ; before, however, we 

 proceed to detail this procefs, it may be proper to obferyc,- 

 that the points made on the faint circle were inferted by a 

 pointril, or piece of ileel-wire, with a conical point made 

 fail into a piece of cylindrical brafs rounded at the upper 

 end : the fteel part was -^x.\\ of an inch thick, and ^ths of an 

 inch long, and the brafs part 2 f long, and 'th of an inch ir» 

 diameter. The angle of the fteel conical point was from 

 2Q^ to 25 ^ and the point fome what above a fpring temper, 

 fo that the point made in the circle did not exceed o.coi 

 of an inch ; as it was fliarpened on an oil-done while tiuTi» 

 ing round, and while drawn in a dircclioii outwards from 

 the point itfelf, the furfacc partook of the nature of a 

 counter-fink, and, as it were, drilled a diminutive hole of a 

 conical fhape when gently prelfed on, as it revolved in the 

 point of bifeCVion, which point, by reafon of the four an- 

 giilar burs made by the inlerfetling lines, could he f:!t as 

 well ^•ifeen. The poii.ts of the lieam-compaffes were never 

 made to approach nearer to each other than two or three 

 inches, but at the ends of th.e arcs fpring dividers, witW 

 conical points, were fubllituted to meafura fmall arcs. 

 Another precaution was, that in all bifeclioiis, the place to 

 be pointed was laid off from left to right, and tlien from 

 right to left, from the refpcctive central points. 



As the maxim, " tiiat an arc may be bifc3ed, but not 

 praftically trifeded or qutnqueftfied with certainty," was th? 

 maxim adopted by Bird, when lie introduced the ufe of hi* 

 fcale for meafuring the chords, fo the maxim, " that a right 

 line cannot be cut on brafs, fo as accurately to pafs through 

 two given points, but that a circle maybe defcribed from 

 any centre, to pafs accurately through a given point," was 

 taken up by him when he adopted the beam-compafs, as 

 Graham and SilFon had done, for cutting tlie fmall portions 

 (if a circle, indead of perfectly liraight lines, as boundaric* 

 of the divifions. His plan of doing this, however, was new, 

 as may be feen from his own words. 



" The next llep," fays he, " is to cut the linear dinfion* 

 3 Y i from 



