84 On dividing Instruments. 



been an end of it at once ; but, that not being the case in 

 anv sensible degree, the roller becomes an usetii! auxiliary 

 to 'fill up short intervals, whose limits have been corrected 

 by more certain means*. 



i;ird, who enjoyed the undisputed reputation of being the 

 most accurate divider of the age in which lie lived, was the 

 .firsi who contrived the means how to render ihe usual divi- 

 sions of the quadrant bisectional ; which property, except 

 his being unusually careful in avoiding the eflects ot unequal 

 expansion from change of temperature, chiefly distinguished 

 his method fr >n) others who divided by hand. This desi- 

 rable object lie accomplished by the use which he made of a 



* There are two things in the foregoing account of the action of the roller 

 which have a tendency to exciie surprise. The first is, that the roller should, 

 indifFerent parts of its journey round the circle, me.'.sure the latter so difFe- 

 renily. One would not won<Jer, ho\ve\ cr, if in taking- the measure across a 

 plcugtieu licld, it siiould be found ditTtrcnt to a parallel measure taken upon 

 a orave! walk; and, in my opinion, i he cases are not very dissimilar. Poro- 

 sity of the metal, in one part of the circle more than in the other, must evi- 

 dently have the same effect; brass nnhammered is always porous; and the 

 part, which has felt the tfFect of two blows, cannot be so dense as other parts 

 Vfhich have felt the eftect of three ; and, should the edge of the circle be in- 

 dented by jairin^-liiriiirp:, it would prcduce a visible similitude to ploughed 

 ground. Every workman must Iv. sufficiently upon his guard against such a 

 palpable source of error ; yet, pcrliaps with our greatest care we may not be 

 able to avoid jt altogelhtr. The second is, that notwithstanding the ine- 

 quality above mentioned, the roller having reached the point upon the circle 

 from whence it set out, should perform a second, third, &c., course of revo- 

 lutions, without any sensible deviation from its former track; this is not per- 

 h-ipsso easily accounted for. It nius; lie mentioned, that the exterior border 

 of the circle should be luntfd tonmhui;, presenting to the rollera convex edge, 

 whose radius of curvature is not greater than one-tenth of an inch. Now, 

 vverethe matcri.,ls perfectly inelastic and impenetrable, the roller could only 

 touch the circle in a poinl, and in passing rounu the circle, it could only oc- 

 cupy a '"'f '^'f <^""f^<^'' '1^'^ '" practice is not the case; the circle always 

 marks the roller with a broad list, and thereby shows that ihcre is a yielding 

 between them to a considerable amount. The breadth of this list is not less 

 than one-fiftieth of an inch ; and it follows, that at least 12" of the circle's 

 ed"-e must be in contact at the same time,; that the two surfaces yield to eacli 

 Other in depth, by a quantity equal to the ver. *;?!. of half that arc, or -j-j^^th 

 of an inch; and that the circle has always hold of the roller by ne.irly i" of 

 the edge of the laltcr. Whoever has examined the surfaces of metals which 

 ha\e replied against each other, must have observed that peculiar kind of in- 

 dentation that always accompnin'es their action; and there can be no doubt 

 that the particles o. a roller, and those of the surface on which it acts, which 

 mutually indent each other, will, upon a second course begun from the same 

 point, indent each other deeper : this is not, however, exactly the case in 

 qiies'ion; for, whatever of fitting inight have taken place between the sur- 

 faces of our roller and circle in the first revolution of the former, one should 

 imagine would be oblilerattd by the fifteen turns which it must repeat over 

 fresh ground. Experience shows, however, as every one will find who tries 

 the experiment with good work, that on coming round to the point of com- 

 mencement, the roller has the disposition to regain its former track; for, 

 were this not the case, alihoui^h the commensurate diameter; were adjusted 

 so exactly as to be without sensible error in one course, yet a less error thaa 

 that which j» »« woold become visible, when repeated through m;\nv courses. 



