Mr. Troughton on dividing Instruments. 131 
further, to the amount of \ of a division, before an interval is 
complete ; but at this last point no division is to be made ; we 
are here only to compare the division on the sector with the 
corresponding dot upon the instrument : This interval, how- 
ever, upon the circle will not be exactly measured by the 
corresponding line of the sector, which has been adjusted to 
the mean interval, for the situation of the dot T,4 is too far 
back, as appears by the table of real errors, by — 4,8 divisions 
of the micrometer head. The range of the screw for slow 
motion must now be restored, the cross wires of H set back 
to — 4,8 divisions, and the sector moved back by hand, but 
not to the division o where it began before ; for, as it left off 
in the first interval at ^ of a division, it has to go forwards f 
more before it will arrive at the spot where the 1 7th division 
of the instrument i° 2 g is to be made, so that in this second 
course it must begin at short of o : Go through this interval 
as before, making a division upon the circle at every one of 
the 16 great divisions of the sector; and H should now reach 
the third dot, allowing for a tabular error of — 10,2 when the 
division fths of the sector reaches the cross wires of I. It 
would be tedious to lead the reader through all the variety 
of the sector, which consists of eight courses ; and it may be 
sufficient to observe, that at the commencement of every 
course, it must be put back to the same fraction of a division 
which terminated its former one ; and that the wire of the 
micrometer H must always be set to the tabular error belong- 
ing to every dot, when we end one interval and begin an- 
other. The eight courses of the sector will have carried us 
through -j- part of the circle, 1 T 15', and during this time, 
the roller will have proceeded through half a revolution ; for 
S 2 
