G RADUATION. 



^ual portions of die circle, yet, when the roller was proper- 

 ly adjufted to raeafure the whole circle without a remainder, 

 it was found to pofTefs tlie dehrable property of accommo- 

 dating itfelf to the fame track again, as often as the circuit 

 was repeated, and confequently of arriving at the point 

 7.ero again without the leaft fenfible deviation. This cir- 

 cumftance, which may be confidered as a plienomenon in 

 mechanics, reproduced the hope of fuccefs, which the w-ant 

 of perfeft regularity in mcafuring the intermediate portions 

 of the circle was calculated to dlfcouragc : and a remedy, 

 hereafter defcribcd, was fuccefsfuUy employed to equalize 

 tlie meafui-ements, nav, fo exaftly was the courfc of the 

 roller found to be identically the fame in every part of its 

 circuit, that, when duly adjufted for diameter, the devia- 

 tion at any individual point, from the iirft meafure, would 

 not exceed a _/eron^/. This uniformity in the mode of the 

 roller's travelling furniflied the means of correftiug its own 

 inaccuracies of meafuiement, feeing that thefe inaccuracies, 

 once afcertained, always remained the fame at tlie fam.e points 

 of the circle, provided that zero of the roller llarted from 

 7,ero of the circle, at the commencement of its lirft circuit. 

 We cannot convey an adequate conception of the mechanical 

 application of a roller to the diviiion and fub-divilion of a 

 circular inllrument, without a reference to drawings of the 

 apparatus aftually ufed ; nor can we defcribe that appara- 

 tus better than in the words of the author himfelf The in- 

 itrument, of which he has defcribed the graduation, is a 

 four feet meridian circle, at prcfent the property of Stephen 

 Groombridge, efq. of Blackheath. 



" The fuiface of the circle, which is to receive the divi- 

 fions," fays Mr. Troughton, " as well as its inner and outer 

 edges, but efpecially the latter, ftiouldbe turned in the moll 

 exatt and careful manner ; the reafon for which will be better 

 uuderftood when we come to defcribe the mode of 

 applying tlie roller : and as no projeftion can be admitted 

 beyond'the hmb, if the telefcope, as is generally the cafe, 

 be longer than the diameter, thole parts which extend fur- 

 ther mull be fo applied, that they may be removed during 

 the operation of dividing." Plates XIX. and XX of JJro- 

 hom'ual Injlrumcnls exhibit the principal parts of the appara- 

 tus ; Jjg. I. Ihews the plan, and fg. 4. the elevation of the 

 revolving parts of the mechanifm, in both of which the 

 fame letters of reference are affixed to correfponding parts, 

 and both are drawn to a fcale of half dimenhons. A A is 

 a part of the circle, the furface of which is feen in the plan, 

 and the edge in the elevation. B B B is the main plate of the 

 apparatus, relling with its four feet a, a, a, a, upon the fur- 

 face of the arc ; thefe feet, being fcrews, may be adjufted 

 fo as to take equal (hares of the weight, and then are faften- 

 ed by nuts below the plates, as (hewn in Jig. 4. C C and 

 D D are two fimiiar plates, each attached to the main 

 plate, one above, and the other below, by four pillars ; and 

 in them are centered the ends of the axis of the roller E. 

 F and G are two friftion wheels, the latter firmly faftencd 

 to B, but the former is fixed in an adjuftable frame, by 

 means of which adjultment thefe wheels and the roller E may 

 be made to prefs, the former on the interior, and the latter 

 on the exterior edge of the circle, with an equal and con- 

 venient force ; namely, by the bending of the pillars of the 

 lecondary frame, and of the axis of the roller. At the ex- 

 tremities of the axis of the roller, and attached to the mid- 

 dle of the plates C and D, are two bridges, having a fcrevi' 

 in each, by means of which an adjultment is procured for 

 railin"- or lowering the roller refpefting the edge of the cir- 

 cle, whereby the former having its diameter at the upper 

 cd"-e about .001 of an inch greater than at the lower edge. 



on account of its being a little conical, may eafily be brought 

 to the pofitlon where it will meafure the proper portion of 

 the circle. 



Much experience and thought upon the fubjeft have taught 

 me, that the roller flould be equal to one-Gxteenth part of 

 the circle to be divided, or that it fliould revolve once in 22*^ 

 30', and that the roller itfelf fliould be divided into fixteen 

 parts, no matter whether with abfolute truth, for accuracy 

 is not at all efTential here. Each of fuch divilions of the 

 roller will correfpond v/ith an angle of i 24' 22 .5,or ^-i^th 

 part of the circle. This number of principal divilions was 

 chofen, on account of its being capable of continual bifec- 

 tions, but they do not fall in with the ultimate divilions of 

 the circle, which arc intended to be equal to 5' each. 



'I'he next thing to be coniidered is, how to make the 

 roller meafure the circle. As two microfcopes are here 

 necefiary, and thofe which I life are very fimple, I will in 

 this place give a dcfcriotion of them. i-ig. 3. is a feftion of 

 the full fize, and fufiicir.ntly explains their conilruttion, and 

 the polition of the glalTes ; but the micrometer part, and 

 manner of mounting it, are better (hewn at H mjigs. I and 

 4. The m.icrometer part confills of an oblong Iquare 

 frame, which is foldered into a flit, cut at right angles in the 

 main tube ; another fimi ar piece, nicely fitted into the 

 former, and having a fmall motion at right angles to the ax;s 

 of the microfcope, has at one end a cylindrical guide-pin, 

 and at the other a micrometer icrevv ; a Ipring of ileel wire 

 is alfo applied, as feen 111 tlic fedlion, to prevent play, by 

 keeping the head of the micrometer in clofe contatl with the 

 fixed frame. This head is divided into one hundred parts, 

 which are numbered each way to fifty ; the ufe of which 

 will be (hewn hereafter. A fine wire is ftretched acrofs the 

 moveable frame, for the purpofe of bifefting fine dots. 

 Two of thefe microfcopes are necefiary ; alio a third, which 

 needs not have the divided head, and which mull have in the 

 moveable frame two wires crofling each other at an angle of 

 about 30"; this microfcope is ftiewn at I, fig. 1. In the two 

 firft micrometers a divifion of the head is of the value of about 

 o .2, and the power and diftinftnels fuch, that when great 

 care is taken, a much greater error than to the amount of 

 one of thefe divifions cannot well be committed in fetting 

 the wire acrofs the image of a well-made dot. The double 

 eye-glafs has a motion by hand, for producing diftintt vi- 

 fion of the wire ; and diflinct vilion of the dots is procured 

 by a fimiiar adjuftmcnt of the whole microfcope. The firlt 

 ftep towards fizing the roller is to compute its diameter ac- 

 cording to the meafure of the circle, and to reduce it agree- 

 ably thereto, care being taken to leave it a fmall quantity 

 too large. The fecond ftep is, after having brought the 

 roller into its place in the plate B B, to make a mark upon 

 the furface of the circle, near the edge, and a fimiiar one 

 upon the roller, exaftly oppofite each other ; then carry the 

 apparatus forward with a fteady hand, until the roller has 

 ir.ade fixteen revolutions ; if now the mark upon the roller, 

 by having over-reached the one upon the circle, fiiews it to 

 be much too large, take it out of the frame, and reduce it by 

 turning accordingly : when, by repeating this, it is found to 

 be very near, it may be turned about .001 of an inch fmalier 

 on the lower edge, and fo far its preparation is completed. 

 The third and laft ftep is the ufe and adaptation of tke two 

 microlcopes ; one of thefe mull take its pofition at H i^Jig. 

 I, viewing a fmall well-defined dot made for the purpofe on 

 the circle ; the other, not reprefented in the figure, mull alfa 

 be fixed to the main plate o{ Jig. i, as near to the former as 

 poflible, but viewing oiic of the divifions on the roller with 

 a due attention to each microfcope, it will now be feen to 



the 



