l64 On dividing Instruments. 



Having now compleled the two first sections of my me- 

 thod of dividing ; namely, the first, which consists of 

 waking 256 small round dots; and the second, in finding 

 the errors of those dots, and forming; them into a table; — I 

 come now to the third and last part, which consists in 

 using the erroneous dots in comparison with the tabulated 

 errors, so as ultimately to make from them the true di- 

 visions. 



It will here be necessary to complete the description of 

 the remaining part of the apparatus. And first, a little in- 

 strument which I denominate a subdividing sector presents 

 itself to notice. From all that has hitherto been said, it 

 must have been supposed that the roller itself will point out, 

 upon the limb of the instrument to be divided, spaces cor- 

 responding to others previously divided upon itself, as was 

 done in setting off the 236points : but, to obviate the diffi- 

 culty of dividing the roller with sufficient exactness, re- 

 course was had to this sector; which also serves the equally 

 important purpose of reducing the bisectional points to the 

 usual division of the circle. This sector is represented in 

 half dimensions by Fig. b: it is formed of thin brass, and 

 centred upon the axis at A, in contact with the upper sur- 

 face of the roller : it is capable of being moved round by 

 hand ; but, by its friction upon the axis and its pressure 

 upon the roller, it is sufficiently prevented from being dis- 

 turbed by accident. An internal frame B B, to which the 

 arc C C is attached, moves freely in the outer one, and by 

 a spring D is pushed outwards, while the screw E, whose 

 point touches the frame B, confines the arc to its proper 

 radius. The arc of this sector is of about four times greater 

 radius than the roller, and upon it are divided the spaces 

 which must be transferred to the instrument, as represented 

 on a magnified scale by Fig. 4. Now, the angle of one 

 of the spaces of the circle will be measured by sixteen times 

 its angular value upon the sectorial arc, or22°30'; bui 

 this does not represent any number of equal parts upon the 

 instrument, whose subdivisions are to be 3' each ; for 



1° 24' 11" 5 



is exactly l6-|-ths, therefore so many divisions are 



exactly equal to a mean space between the dots whose er- • 

 rors have been tabulated. Let, therefore, the arc of the 

 sector be divided into IQ spaces of P 20' each, and let a 

 similar space at each end be subdivided into eight parts of 

 lo' each, as in Fig. 4; we shall then have a scale which 

 furnishes the means for making the true divisions, and an 

 immediate examination at every bisectional point. 



I have 



I 



