f 84 On a Method of examining 



be ^ 4£ = 2s at 180^; --- 4- ^- x 4s = 3£ at 90" j 



2i 3 1 2 3—2 



— 4--^- X 45 = 3-33a at6(P;--.X 2s + -^ X4 X 



5f = 4sat 120\ The greatest error must therefore lie 

 betwixt 90 and 120'% aiuT nearer to the extremity of the 

 latter ihan of ihe former arc. At 103^ it will be d'dOs; 



at 11 F it will be 5*506 ~y . 1,3£ + ^^ x 4 x 2£ = 



9,70 £ \ and at 1 1 1^ lo' it will be 9,70 ^ — -- • 1,0 4c (the 



excess of the error at IIP above that at 112^) + 3*33 e = 

 •J2-86£, which will he found to be the greatest error l)et\vixt 

 105 and 120% and of course the greatest in the tirst semi- 

 circle. In the other semi-circle, the process being the 

 same, the possible errors must necessarily be the same at 

 the same distances from the tirst point, reckoning the con- 

 trary way upon the circle. 



I'he magnitude of the quantity e will of course vary upon 

 circles of the same radius, according to the excellence of 

 the glass employtd, and the accuracT of the examiner's 

 eye. It will seldom, however, exceed one second upon a 

 circle whose radius is one foot; and in general it will not 

 amount to sd much. I find that 1 can read off, to a certainty, 

 within less than three fourths of a second ; and hence I 

 conclude, that I could examine the divisions of my circle 

 without being liable to a greater error than ^'^3 seconds, 

 and those of a circle of three feet radius wiuDut the risk of 



greater error than 3*21 seconds 



'o those people who are accustomed to entertain such 

 exalted notions of the accuracy with which astronomical 

 instruments can v^ith a certainty be divided, this error, f 

 dare say, will appear very considerable; but for my part, 

 I am perfectly satisfied that it bears but a small pro- 

 portion to the accumulated error which may take place, in 

 spite of tlie utmost vigilance of the artist, in an instrument 

 divided according to any metliod which has hitherto been 

 made public. I wfnidi not, however, remark upon the very 

 great iniprobability that the error of examination should 

 ever attain, or ap[)roach, to its extreme limit, as this must 

 be sufficiently obvious to any person who is in the least 

 degree conversant with the doctrine of chances ; but it may 

 be proper to observe, that we have it in our power (and in 

 this respect the examiner possesses a most iniportant ad- 

 vantage over the divider of an instrument) to diniinish its 

 probable amount, as nnich as we please, by bringing the 

 jjfioveablc wires of the micrometer and microscope several 



timvs 



