ig4i Mr. Troughton on dividing Instruments. 
I have not rendered original dividing almost equally easy 
with what copying was before, I have spent much labour, 
time, and thought in vain. I have no doubt indeed, that any 
careful workman who can divide in common, and has the 
ability to construct an astronomical instrument, will, by fol- 
lowing the steps here marked out, be able to divide it, the 
first time he tries, better than the most experienced workman, 
by any former method. 
If, instead of subdividing with the roller, the same thing be 
performed with the screw, it will not give to dividing by the 
eye any very distinctive character : I have practised this on 
arcs of circles with success, the edge being slightly racked, 
the screw carrying forward an index with the requisite appa- 
ratus, and having a divided micrometer head ; the latter an- 
swers to the subdividing sector, and, being used with a cor- 
responding table of errors, forms the means of correcting the 
primitive points ; but the roller furnishes a more delicate ac- 
tion, and is by far more satisfactory and expeditious. 
It is known to many that the six feet circle, which I am 
now at “work upon for our Royal Observatory, is to be divided 
upon a broad edge, or upon a surface at right angles to the 
usual plane of division : The only alterations, which will on 
that account be required, are, that the roller must act upon 
that plane which is usually divided upon ; which roller, being 
elevated or depressed, may be adjusted to the commensurate 
radius without being made conical, as was necessary in the other 
case. The apparatus, similar to the other, must here be fixed 
immoveable to the frame which supports the circle ; its posi- 
tion must be at the vertex, where also 1 must have my station ; 
and the instrument itself must be turned around its axis, in its 
