allowing for a 
ow reach the 
a 
It w 
e variety of 
iety 
ion of a division which termi- 
part of the circle, 11° 14’, 
_. and during this time the roller, will have proceeded 
_ through half a revolution ; fur its close contact with 
the limb of the circle does not allow it to return with 
sector when the latter is set back at every course. 
‘Having in this manner proceeded, from one interval to 
, through the, whole circle, the micrometer at 
Jast will be found with its wire at zero, on the dot 
from which it set out; and the sector, with its 16th 
‘division, coinciding with the wires of its microscope. 
S . Having now-given a faithful detail of every part of 
* the process of Sividing this circle, I wish to remind 
_ the reader, that, by verification and_correction at every 
“TT ‘interval, any erroneous action . of the roller is prevent- 
_. ed from extending its influence to any distant interval. 
Tt will be farther observed, that the subdividing sector 
; aaities the work ; ae. by means of its adjustable 
arc, it makes the run of the roller measure its corre- 
Spaiing intervals upon the circle; and, without fo- 
reign aid, furnishes the means of reducing the bisec- 
tional intervals to the usual division of the circle.. Far- 
- thermore, the motion of the wire of the micrometer H, 
_ according to the division of its head and correspond- 
‘ing table of errors, furnishes the means of prosecut- 
‘ing the work with nearly the same certainty of success, 
as could have happened, had the 256 points been (which 
in practice is quite impossible) in. their true places. 
y term Now, the whole of my method of dividing- being 
ividing “performed by taking short measures with instruments 
ne eye; which cannot. themselves err in any sensible degree, 
arg as those measures are taken, not by the 
hand, but by vision, and the whole performed by only 
looking at work, the eye must be charged with all 
© ‘the errors that are committed until we come to cut the 
> divisions ; and, as in this last operation the hand has 
a ‘no more to do than to guide an apparatus so perfect 
__. in itself, that it cannot be easily made to deviate from 
its proper course, I would. wish to distinguish it from 
| ‘the other methods, by denominating it, dividing by the 
2. © ‘ 
*- The number. of persons at all capable of dividing 
originally have hitherto been very few : the practice of 
-_ it being so limited, that in less 
n twice seven years, 
- 
coincidence 
bao 
VOL. X. PARTI. 
GRADUATION, 
877 
aman could hardly hope to become a workman in this _ Original 
most difficult art. How far. I. shall be considered ag Graduation. 
having surmounted these difficulties, [. know. not; but “7Y7"™ 
if, by the method. here revealed, I have not rendered 
original dividing almost equally-easy with what copy- 
ing was before, I have spent much labour, time, and 
thought in yain. 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 following the steps here marked out, be able to di- 
vide it, the first time he tries, better than the most’ ex 
perienced workman, by any former method. 
If, instead of subdividing with the roller, the same Subdivision 
thing be performed with the screw, “it will not give to with the 
dividing by, the eye any very distinctive character: I screw in- 
haye practised this on arcs of citcles with success, the stead of the 
edge being slightly racked, the screw carrying forward ™le™* 
an index with the requisite apparatus, and having a di- | 
vided micrometer head ; the latter answers to the sub- 
dividing sector, and, being used with a correspondin 
table of errors, forms the means of correcting the pri- 
mitive points ; but the roller furnishes a more delicate 
action, and is by far more satisfactory and expeditious. 
It is known to many, that the six feet circle, which six feet cix- 
I am now at work upon for our Royal Observatory, is cle for the 
to be divided upon a broad edge, or upon a surface at Royal Ob- 
right angles to the usual plane’of division: the only al- Svs" 
terations which will on this account be required, are, j., alae 
that the roller must act upon that plane which is usual- 
ly divided upon; which roller, being elevated or des. 
pressed, 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 immoveably to the frame which supports 
the circle: its position must be at the vertex, where 
also I must have my station; and the instrument it-. 
self must be turned around its axis, in its proper yer- 
tical position, as the work proceeds. The above may 
suffice, for the proeats to gratify those who feel them- 
selves interested upon a subject which will be better 
understood, if I should hereafter have the honour of 
laying before the Royal Society a particular description 
of the instrument here alluded to ; a task which I mean 
to undertake, when, after being fixed in the place de- 
signed for it, which I hope will be effected at no very 
distant period, it shall be found completely to answer 
the purposes intended. See Circe, Vol. I. p. 485. 
Should it be ‘required to divide a circle according to 4 circle 
the centesimal division of the quadrant, as now recom- may readily 
mended and used in France, we shall have no difficul- be divided 
ty. The 100° of the quadrant may be conveniently ae ls 
subdivided into 10 each, making 4000 divisions in the "47 Sm. 
whole round. The 256. bisectional intervals, the two j.on way. 
tables of errors, and the manner of proceeding an : 
acting upon them, will be exactly the same as before, 
*1 must here remark, that Smeaton has represented the greatest degree of accuracy that can be derived from vision, in judging of the - 
wer of the 
sensible to 
Foounth part of an inch. Were materials'infinitely hard, no bounds could be set to the precision of contact; but taking things as 
the it deg: 
