120 Mr. Troughton - on dividing Instruments . 
lower end comes in contact with the circle; this will carry 
down the point, and make the first impression, or primary dot, 
upon the circle ; unclamp the apparatus, and carry it forwards 
by hand, until another division of the roller comes near the 
wire of the microscope ; then damp it, and with the screw 
motion make the coincidence complete ; where again press 
upon the feeler for the second dot : proceed in this manner 
until the whole round is completed. 
From these 256 erroneous divisions, by a certain course of 
examination, and by computation, to ascertain their absolute 
and individual errors, and to form these errors into convenient 
tables, is the next part of the process, and makes a very im- 
portant branch of my method of dividing. 
The apparatus must now be taken off, and the circle 
mounted in the same manner, that it will be in the Observa- 
tory. The two microscopes, which have divided heads, must 
also be firmly fixed to the support of the instrument, on op- 
posite sides, and their wires brought to bisect the first dot, and 
the one which should be 180° distant. Now, the microscopes 
remaining fixed, turn the eircle half round, or until the first 
microscope coincides with the opposite dot ; and, if the other 
microscope be exactly at the other dot, it is obvious that these 
dots are 180 9 apart, or in the true diameter of the circle ; and 
if they disagree, it is obvious that half the quantity by which 
they disagree, as measured by the divisions of the micrometer 
head, is the error of the opposite division ; for the quantity 
measured is that by which the greater portion of the circle 
exceeds the less. It is convenient to note these errors -f- or 
— , as the dots are found too forward or too backward, ac- 
cording to the numbering of the degrees ; and for the purpose 
