n8 Mr. Troughton on dividing Instruments . 
of the wire ; and distinct vision of the dots is procured by a 
similar adjustment of the whole microscope. 
The first step towards sizing the roller, is to compute its 
diameter according to the measure of the circle, and to reduce 
it agreeably thereto, taking care to leave it a small matter too 
large. The second step is, after having brought the roller 
into its place in the Plate B B, to make a mark upon the sur- 
face of the circle near the edge, and a similar one upon the 
roller, exactly opposite each other ; then carry the appa- 
ratus forward with a steady hand, until the roller has made 
sixteen revolutions : If, now, the mark upon the roller, by 
having over-reached the one upon the circle, shews it to be 
much too large, take it out of the frame and reduce it by 
turning accordingly: When by repeating this, it is found to be 
very near, it may be turned about .001 of an inch smaller on 
the lower edge, and so far its preparation is completed. The 
third and last step is, the use and adaptation of the two micro- 
scopes ; one of these must take its position at H in Fig. 1 , 
viewing a small well defined dot made for the purpose on the 
circle ; the other, not represented in the figure, must also be 
fixed to the main plate of Fig, 1, as near to the former as pos- 
sible, but viewing one of the divisions on the roller. With a 
due attention to each microscope, it will now be seen to the 
greatest exactness when, by raising or depressing the roller, 
its commensurate diameter is found. 
Fig. 3 is a representation of the apparatus for transferring 
the divisions of the roller to the circle. It consists of two 
slender bars, which, being seen edgewise in the figure, have 
only the appearance of narrow lines ; but, when looked at 
from above, they resemble the form of the letter A. They 
