430 Capt. Kater's improved Method of dividing 
dot in tlie intersection of the cross wires of A, taking care, by 
examining the dot under B, to ascertain that the circle has not 
in the mean time suffered any change of position. Bring the 
dot which w'as last placed, and which is now under A, to the 
intersection of the wires of B, when it is evident if the wires 
of the microscopes A and B, are at the required distance from 
each other, the next division of the instrument, or zero, will 
now pass precisely through the intersection of the cross wires 
of A. But should this not be the case, the distance may be 
measured by means of the micrometer, and thecross wiresof A 
must be removed one third of this distance from their first 
position towards the side opposite to that on w'hich the divi- 
sion appears in the microscope. The line of reference must 
then be brought again to the wires of the fixed microscope, 
and the w hole operation repeated as before, till the intersec- 
tions of the w ires of A and B, are at the proper distance from 
each other. 
In order to cut the divisions ; having ascertained that the 
line of reference, the division wdnch is under B, and the 
adjustable dot under A, are accurately in the intersection of 
the wires of their respective microscopes ; turn the circle till 
A and B, have each an adjustable dot in the intersection of 
their cross wires, and cut a division ; move the circle till an 
adjustable dot is in the intersection of the wnres of B, and a 
division in that of A, and trace another line with the cuttinsT 
O 
point. It is now evident, that one of the primary divisions of 
seventy-two degrees is trisected. Take off the adjustable dots, 
W'hich are now no longer necessary, and bringing eadi of the 
new divisions, as well as the primary ones, successively under 
the intersection of the wires of the microscope A, trace a new 
