434 Capt. Kater’s improved Method of dividing 
The microscopes must be perfectly free from parallax, and 
the vertical angles formed by the intersections of their cross 
wires, accurately bisected by the divisions which pass through 
them. The intersections of the cross wires of A and B must 
appear between the circles which limit the divisions, and be 
equidistant from the centre of the instrument to be divided. 
The dot on the cutting frame, if moved through the field 
of view, must always pass through the intersection of the 
wires of the fixed microscope ; and the motion of the cutting 
point must be in the diameter of the circle to be divided. 
When the line of reference is in the intersection of the 
wires of the fixed microscope, a division should always appear 
precisely in the intersection of the wires of the microscope B. 
Lastly, previous to cutting each new division, if two divi- 
sions do not appear precisely in the intersections of the wires 
of A and B, it is an immediate proof, (unless the microscopes 
may have suffered any accidental change of position ) of inac- 
curate execution in the former part of the work. 
From what has been said, it is evident that the microscope 
B might have remained stationary after having been placed 
over one of the primary divisions of seventy-two degrees, and 
perhaps in practice this may be preferable. My only reason 
for directing it to be removed was to obviate the effect of any 
expansion which might take place in that part of the arc which 
is between the tracing point and the microscope, by placing it 
as near as possible to the cutting frame; this, however, will 
probably be found to be an unnecessary refinement. 
This method of dividing is not confined to circles, but may 
be applied with equal facility and advantage to the division of 
straight lines and zenith sectors. For the last, it is necessary 
