4,20 Capt, H. Kater’s improved method of dividing 
complicated, and others so incapsible of the necessary adjust- 
ments, that his method of dividing never has been, nor ever 
can be introduced into practice, and indeed was intended by its 
author merely to form a model, which was to be employed as 
part of a dividing engine. 
The method which I am about to describe requires no other 
apparatus than two pieces easily made, which I shall call 
adjustable dots; three microscopes, (two furnished with mi- 
crometers) and a cutting point with its frame. 
The general principle of this method consists in viewing the 
two micrometer microscopes, as the points of a pair of beam 
compasses, and the moveable dots as divisions, capable of the 
nicest adjustment previously to their being transferred to the 
limb of the instrument. Its principal advantages are its sim- 
plicity, and the exclusion of all errors, excepting such as may 
arise from careless execution, the imperfection of vision, or 
the instability of the apparatus employed. 
The adjustable dots are represented at plate XV. figs. 1,2, and 
3. a, a, j, a, fig. 1. is a flat piece of brass, intended to rest on 
the face of the arc to be divided, and to be clamped to it by 
means of the screw C, fig. 3, where the adjustable dot is re- 
presented in perspective. The piece c r, slides smoothly in a 
dove-tail groove, formed by the pieces b, b, and is moveable 
by the screw d, e, fy slides in like manner in a dove-tail 
groove beneath, and at right angles to the piece c r, and is 
moveable by the screwy. That part of the clamp which bears 
against the edge of the arc, should be curved in such a manner 
as to have only its two extremes in contact with the edge, by 
which means the motion of the sliding piece c c, will always 
be in the proper direction. A very thin and narrow tongue 
