Cdpt, Katek’s improved Method of dividing 
the upper surface of the piece G, and connected with a handle, 
ihight be used with advantage. The length of that part of the 
cutting point which projects beneath the piece G, may also 
prove a source of error; but this may be easily obviated by 
making the piece G, much thicker, and passing the screw 
through it, as represented in the profile. 
An arc of cast iron or brass must be provided, of about 120 
degrees in length, and of a radius rather greater than that of 
the instrument to be divided. Its breadth may be about two 
inches, and its thickness should be fully sufficient to ensure its 
not bending. This arc, which is designed to carry the three 
microscopes, is to be fastened at its extremities by clamps, 
screws, or otherwise, to the framework of the instrument to 
be divided, in such a manner as that the microscopes may 
project over its limb, and be at a proper distance above it for 
distinct vision, and that the surface of the arc may be parallel 
to the face of the instrument. The manner of fastening this 
arc must be left to the ingenuity of the artist. In some in- 
stances it may perhaps be found convenient to construct a 
temporary frame for the reception of the instrument during 
the operation of dividing, but in whatever manner the arc is 
applied, it is absolutely necessary that it should be so secured 
as to be perfectly immoveable. 
I shall now proceed to detail the manner in which this ap- 
paratus is to be employed in dividing a circle, wliich 1 shall 
suppose to be tw'o feet in diameter. The first operation ne- 
cessary is to describe on the face of the instrument the circles 
which are to limit the divisions. This may readily be done 
by causing a fixed point to press on the surface of the circle, 
whilst it is made to revolve on its axis. The support carrying 
