12 6 Mr. Troughton on dividing Instruments. 
Respecting the angular value of the numbers in these tables, 
it may be worth mentioning, that it is not of the least import- 
ance ; 100 of them being comprised in one revolution of the 
micrometer screw ; and, in the instance before me, 5,6 of 
them made no more than a second. It is not pretended that 
one of these parts was seen beyond a doubt, being scarcely 
of an inch, much less the tenths, as exhibited in the 
tables ; but, as they were visible upon the micrometer heads, 
it was judged best to take them into the account. 
Having now completed the two first sections of my method 
of dividing ; namely, the first, which consists of making 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 divisions. 
It will here be necessary to complete the description of the 
remaining part of the apparatus. And first, a little instrument 
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 corresponding to 
others previously divided upon itself, as was done in setting 
off the 256 points : but, to obviate the difficulty of dividing 
the roller with sufficient exactness, recourse 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 full dimensions by Fig. 5: 
it is formed of thin brass, and centred upon the axis at A, in 
contact with the upper surface of the roller : it is capable of 
