130 Mr . Troughton on dividing Instruments . 
would go undiminished to the account of error. The micro- 
scope I is also fastened to the main frame ; but it is only re- 
quired to keep its position unvaried, while the divisions of the 
sector pass once under its notice ; for it must have its wires 
adjusted afresh to these divisions at every distinct course. 
The microscope I has two wires, crossing each other at an 
angle of about 40° ; and these are to be placed so as to make 
equal angles with the divisions of the sector, which are not 
dots, but lines. The sectorial arc must also be adjusted to its 
proper radius by the screw E, Fig. 5 ; i, e. while the main 
frame lias been carried along the circle through a mean in- 
terval shewn by H, the sector must have moved through 
exactly i6|- of its divisions, as indicated by I.* 
Things being in this position ; after having given the parts 
time to settle, and having also sufficiently proved the perma- 
nence of the micrometer H and the cutting frame with respect 
to each other, the first division may be made ; then, by means 
of the screw for slow motion, carry the apparatus forward, until 
the next line upon the sector comes to the cross wires of I ; you 
then cut another division, and thus proceed until the 16th divi- 
sion is cut, = i° 2o' : Now the apparatus wants to be carried 
* For the sake of simplicity, the account of the process is carried on as if the roller 
measured the mean interval without error : But it was said ( Page 107) that the roller, 
in a continued motion quite round the circle, would in some part of its course err by 
30" or more ; therefore, when that is the case, an extreme run of the roller cannot 
3 o" 
agree with a mean interval of the circle nearer than = o",23 ; and most probably 
this kind of error will on some intervals amount to double that quantity. It there- 
fore becomes matter of prudent precaution to examine every interval previous to 
ipaking the divisions ; and, where necessary, to adjust the sector, so that its arc may 
exactly measure the corresponding interval as corrected by the tabulated errors. 
