Capt. Kater^s improved Method of dividing 
been minutely detailed, and on bringing the adjustable dot to 
the intersection of the wires of B, if the distance of the mi- 
croscopes be accurate, a division will be found precisely in the 
intersection of the wires of A, but should it not be so, the 
error in the distance of A and B, must be determined and cor- 
rected by means of the micrometer, as before described. The 
line of reference is then to be brought back to the intersection 
of the wires of the fixed microscope, and the trial repeated. 
When the distance of A and B, is found to be correct; the 
line of reference being brought to the intersection of the cross 
wires of the fixed microscope, and a division being in that of 
the microscope B, it is evident that the intersection of the 
wires of A must accurately bisect a division, or be four de- 
grees distant from the next division on the instrument. Bring 
up this division therefore to the intersection of the wires of A, 
and trace a line with the cutting point ; do the like with each 
division, or every eighth degree successively, and the circle 
W’ill be divided into parts of four degrees each, and by continu- 
ing to bisect in the same manner, the division of the circle is 
to be carried to thirty minutes. 
The last operation consists in trisecting the divisions of thirty 
minutes.* Bring the line of reference to the fixed microscope, 
and examine the adjustment of the cutting frame as before. 
Place the intersections of the wires of B and A, on any two 
divisions of the instrument, say ten degrees from each other, 
and increase their distance by advancing the intersection of 
the wires of A, by means of its micrometer screw, one third 
of a division, or ten minutes. Place an adjustable dot under 
• The method by which this trisection is effected is of very general application, 
and may be used with equal facility to divide an arc into any other number of parts. 
