ON DIVIDING INSTRUMENTS. 5 



Bird, who enjoyed the undisputed reputation of being Bird's meth-d 

 the most accurate divider of the a;^e in which he lived, was 

 the tirst who contrived the me^ns how to render tlie usual 

 divisions of the quadrant bisectional ; which property, ex- 

 cept his being unusually careful in avoiding the effects of 

 unequal expansion from change of temperature, chiefly dis- 

 tinguished his method from others who divided by hand. 

 This desirable object he accomplished by the use which he 

 made of a finely divided scale of equal parts. The thing 

 aimed at was, to obtain a point upon the arc at the highest 

 bisectional number of divisions from 0, which in his eight 

 feet quadrar>ts was 1024, n 85° 20'. The extent of ' the 

 beam compasses, with which he traced the arc upon the 

 limb of the instrument to he divided, being set off upon 

 that arc, gave the points 0° and 6o°; which, being bisected, 

 gave 30° more to complete the total arc. A second order of 

 bisections gave points at 15° distance from each other; but 

 that which denoted 75° was most useful. Now, from the 

 known length of the radius, as measured upon the scale, 

 the length of the chord of 10° 20' was computed, taken off 

 from the scale, and protracted from 75° forwards; and the 

 chord of 4* 40', being ascertained in the same manner, was 

 set off from 90° backwards, meeting the chord of 10' 20' in 

 the continually bisectional arc of 85° 20'. This point being 

 found, the work was carried on by bisections, and the 

 chords, as they became small enough, were set off beyond 

 this point, to supply the remainder of the quadrantal arc. 

 My. brother, whom T mentioned before, from mere wnnt of Mr. John 

 a scale of equal parts upon which he qould rely, contrived ni'e°tho'd of *di- 



course begun from the same point, indent each nther deeper : this is not, 

 ho'sever, exactly the case in question j for, whatever of fitting might 

 have taken place between the surfaces of our loUer and circle in the first 

 revoUuion of the former, we should imagine would be obliierated 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 commencemeai, the roller 

 has the disposition to regain its former track 3 for, were th'i-r, not the case, 

 although the commensur^jte diameters were adjusted so exactly as to be 

 without sensible errour in one course, yet a less errour than that which 

 is so would become visible, when repeated through many couries. 



the 



