Mr. Troughton on dividing Instruments. 12 7 
being moved round by hand ; but, by its friction upon the 
axis and its pressure upon the roller, it is sufficiently pre- 
vented from being disturbed by accident. An internal frame 
B B, to which the arc C C is attached, moves freely in the 
outer one, and by a spring D is pushed outwards, while the 
screw E, whose point touches the frame B, confines the arc 
to its proper radius. The arc of this sector is of about four 
times greater radius than the roller, and upon it are divided 
the spaces which must be transferred to the instrument, as 
represented on a magnified scale by Fig. 4,. Now, the angle 
of one of the spaces of the circle will be measured by sixteen 
times its angular value upon the sectorial arc, or 22 0 30'; but 
this does not represent any number of equal parts upon the 
instrument, whose subdivisions are to be 5' each ; for l _ 2 ^ 22 . 5 
is exactly 1 6%, therefore so many divisions are exactly equal 
to a mean space between the dots whose errors have been 
tabulated. Let, therefore, the arc of the sector be divided into 
1 6 spaces of T 20' each, and let a similar space at each end 
be subdivided into eight parts of 10' each, as in Fig. 4; we 
shall then have a scale which furnishes the means for making 
the true divisions, and an immediate examination at every 
bisectional point. 
I have always divided the sector from the engine, because 
that is the readiest method, and inferior to none in point of ac- 
curacy, where the radius is very short ; but, as it is more liable 
than any other to centrical error, the adjustment of the arc 
by the screw E becomes necessary: by that adjustment, also, 
any undue run in the action of the roller may be reduced to 
an insensible quantity.* 
* See note page 130. 
