132 Mr. Trgughton on dividing Instruments , 
its close contact with the limb of the circle does not allow it 
to return with the sector when the latter is set back at every 
course. Having in this manner proceeded, from one interval 
to another, through the whole circle, the micrometer at last 
will be found with its wire, at zero, on the dot from w'hich it 
set out ; and the sector, with its 16th division, coinciding with 
the wires of its microscope. 
Having now given a faithful detail of every part of the pro- 
cess of dividing this circle, I wish to remind the reader that, 
by verification and correction at every interval, any erroneous 
action of the roller is prevented from extending its influence 
to any distant interval. It will be further observed, that the 
subdividing sector magnifies the work ; that by means of 
its adjustable arc, it makes the run of the roller measure 
its corresponding intervals upon the circle ; and, without 
foreign aid, furnishes the means of reducing the bisec- 
tional intervals to the usual division of the circle. Further- 
more, the motion of the wire of the micrometer H, according 
to the divisions of its head and corresponding table of errors, 
furnishes the means of prosecuting the work with nearly the 
same certainty of success, as could have happened, had the 
256 points been (which in practice is quite impossible) in their 
true places. 
Now the whole of my method of dividing being performed 
by taking short measures with instruments which cannot 
themselves err in any sensible degree, and, inasmuch as those 
measures are taken, not by the hand, but by vision, and the 
whole performed by only looking at the work, the eye must 
be charged with all the errors that are committed until we 
come to cut the divisions ; and, as in this last operation the 
