new, dividing by the roller, and I have been 
that it aleo occurred long ago to Hook, Sisson, 
others; but, as Hatton on watch-making says, “ I 
do not consider the man an inventor, who merely 
thinks of a thing. To be an inventor, in my opinion, 
he must act successfully upon the thought so as to 
make it useful.” I had no occasion, however, to have 
“made an for acting upon a thought, which, 
unknown ‘to me, had been previously conceived by 
___ others; for it will be seen in the sequel, how little the 
roller has to do in the result, and with what extreme 
caution it is found necessary to employ it. 
When a roller is Properly proportioned to the radius 
e,de- of the circle to be divided, and, with its edge, made a 
_ small matter conical, so that one side may be too great, 
and the other side too little, it may be adjusted so ex- 
actly, that it may be carried several times around the 
cece, without the error of a single second ; and it acts 
with so much steadiness, that it may not omy: be 
considered as a wheel and pinion of indefinitely high 
numbers. Yet, such is the imperfection of the edges 
of the circle and roller, that, when worked with the 
t care, the intermediate ; on a radius of two 
eee will sometimes be unequal to the value of half a 
_ minute or more. After having found the terminating 
point of a quadrant or circle so permanent, although I 
owas not to expect perfect equality throughout, 
et I was much mortified to find the errors so great, at 
st ten times. as much as I oars 3 which fact indi- 
cated, beyond a doubt, that if the roller is to be trusted 
astbe at all, it must only be trusted through a very short arc. 
ti Had there been any thing slippery in the action, which 
would have been indicated by peenarng the same part, 
| at different times, differently, there would have been an 
end of it at once; but this not being the case in any 
sensible degree, the roller becomes a useful auxiliary 
to fill wp short intervals, the limits of which have been 
__ corrected by more certain means.* 
nd’sme- ——- Bird, who enjoyed the undisputed reputation of neieg 
od of divi- the most accurate divider of the age in which he lived, 
was the first who contrived the means how to render 
the usual divisions of the quadrant bisectioual ; which 
rty, except his being unusually careful in avoid- 
the effects of unequal expansion from change of tem- 
perature, chiefly distinguished his method from others 
who divided by hand. This desirable object he ac- 
complished by the use which he made of a finely divi- 
ded scale of equal parts. The thing aimed at was, to 
te Bere 4 
. the roller should, in d 
nion, the cases are not very 
same effect. Brass unhammered is always porous; and the 
to ploughed ground. 
care, we may not be able to avoid it al 
sible 
. Now, were the materials perfect] 
peculiar kind of indentation that al 
surface on which it acts, which m 
many courses. 
GRADUATION. 
871 
obtain a point upon the are at the highest discctional Original 
number of divisions from 0, which in his eight feet qua- Graduation. 
drants was 1024 = 85° 20’... The extent of the beam “¥~" 
compasses, with which he traced the are upon the limb 
of the instrument to be divided, being set off upon that. 
arc, gave the points 0° and 60° ; which being bisected, 
gave 30° more to complete the total arc. A second or- 
er of bisections gave points at 15° distance from each 
other: but that which denoted 75° was most useful. 
Now, from the known length of the radius, as measured 
upon the scale, the length of thechord of 10°20’ was com- 
puted, taken off from the scale, and protracted from 75? 
forwards ; and the chord of 4° 40’, being ascertained in 
the same manner, was set off from 90° backwards, meet- 
ing the chord of 10° 20’ in the continually bisectional 
arc of 85° 20’... This point being found, the work was 
carried on by bisections, and the chords, as they be- 
came small enough, were set off beyond this point, to 
supply the remainder of the quadrantal arc. My bro- Mr Joha 
ther, whom I mentioned before, from mere want of a Troughton’s 
scale of equal parts upon which he could rely, contri- pars a 
ved the means of dividing bisectionally without one. stiianatie 
His method I will briefly state as follows, in the man- without a 
ner in which it would apply to dividing a mural qua- scale. 
drant. The ares of 60° oak 380° give the total arc as 
before ; and let the last arc: of 30° be bisected, also 
the last arc of 15°, and again the last are of 7° 30’: 
the two marks next 90° will now be 82° 30’ and 
86° 15’, consequently the point sought lies between 
them. Bisections will serve us no longer ; but if we 
divide this space equally into three parts, the most 
forward of the two intermediate marks will give us 85°, 
and if we divide the portion of the arc between this 
mark and 86° 15’ also into three, the most backward of 
the two marks will denote 85° 25’. Lastly, if we di- 
vide any one of these last spaces into five, and set off 
one of these fifth parts backwards from 85° 25’, we shall 
have the desired point at 1024 divisions upon the arc 
from 0°. All the rest of the divisions which have been 
made in this operation, which | have called marks, be- 
cause they should be made as faint as possible, must be 
erased ; for my brother would not suffer a mark to res 
main upon the arc, to interfere with his future bisections. : 
Mr Smeaton, in a paper to be more particularly woti- S™eaton’s 
ced presently, justly remarks the want of a unity of Arsene 
principle in Mr Bird’s method ; for he proceeds partly py the com- 
on the ground of the protracted radius, and partly upon puted chord. 
that of the computed chord ; which, as Smeaten ob- 
t * There are two things in the foregoing account, of the action of the roller, which have a tendency to excite surprise. The first is, that 
ifferen t parts of its journey round the circle, measure the latter so differently. Qne would not wonder, however, if in 
taking the measure across a ploughed field, it should be found different to‘a parallel measure taken upon a gravel walk; and, in my opi- 
dissimilar. Porosity of the metal, in one part of the circle more than in the other, must evidently have the 
part which has felt the effect of two blows, cannot be so dense as other parts 
which have felt the effect of three; and, should the edge of the circle be indented by jarring turning, it would produce a visible similitude 
Every workman must be sufficiently upon his guard against such a palpable 
ther. The second is, that, notwithstanding the inequality above-mentioned, the roller 
reached the point upon the circle from which it set out, should perform a second, third, &c. course of revolutions, without any sen- 
deviation from its former track. This is not, perhaps, so easily accounted for. 
' circle should be turned rounding, presenting to the roller a convex edge, the radius of curvature of which is not greater than one-tenth of an 
source of error; yet, perhaps, with our 
It must be mentioned, that the exterior border of the 
depth, Pine Sage ce he to the ver, sin. of half that arc, or yys5th of an inch; and that the circle has always hold of the roller by near- 
