1 pin; then bored 
aed 
| on the outside of the 
_. [need not tell you, at ok 
- numbers ee retpleese nor that t 
» holes in the stee 
Jength of the hoop. 
ou may ask my brother what he knows about my 
the other hole ; and by 
ee chen e forward, and putting in 
the pin in the last hole, epee 1 hed divided 
ae the whole length of the p' 
The next thing was to make this into a circle again. 
then ed to join the ends, which I 
did thus : a mngmernets Seer brass plates, as I did 
the long one, and put one on the inside, and the other 
, whose ends were brought 
together ; and put two or three turned screw pins, with 
flat head and nuts to them, into each end, which held 
them er till L rivetted two little plates, one on 
ite After the was cut off at the end of the intended 
each side of the narrow plate, on the outside of the 
. Then I took out the screws, and turned my 
‘down, till the hoop would fit close on ; and by 
that means my right line was made into an equal di- 
vided circle of oh number I pleased. 
__ The engine plate was fixed on the face of the block, 
with a steel hole fixed before it, to bore through ; and 
I had a point that would fall into the holes of the divi- 
ded hoop ; so by cutting shorter, and turning the block 
less, I got all the numbers on my plate. 
as many prime 
e distance of the 
chaps must be proportioned to the 
method of dividing ; but need not tell him what I have 
said about it; for I think neither he nor John Smith 
knows so much as I have told you, though I believe 
they got some knowledge of it in general terms, I de- 
sire you to keep the method of dividing to yourself, 
and conclude with my best wishes. And am, dear sir, 
yours, &e. Henry Hinp.ey. 
Though the above letter was in itself very clear and 
explicit as to the general traces of the method, yet 
some doubts occurring to me, a farther explanation be- 
came n A copy of my letter not being pre- 
served, the purport of it may be inferred from the an- 
swer, which was as follows : 
Dear Friend, York, 13th March, 1748-9. 
; I think, in your last, you seem to be 
apprehensive of some difficulties in drilling the hoop 
for dividing: First, that the centre of the hole in the 
mom wien not be precisely in the centre of the hole 
of the steel chaps it was drilled in; but if I described 
fully to you the method I used, I can see no danger of 
error there ; for my chaps were very thick, and the two 
ing holes were a little conical, and ground 
with asteel pin; first one pair, and then the other, al- 
pag ill the pin would go the same depth into 
each. Then for drilling the hoop, I took any common 
drill that would pass through and borethe hole. After 
that I took a five-sided broach, which opened the hole 
in the brass betwixt the steel chaps, but would not 
touch the steel ; so, consequently, the centre of the 
holes in the brass‘must be concentric with the holes in 
the chaps ; and for alterations by air, heat, cold, &c. 
1 was not above two or three hours in drilling a row of 
holes, as far as I remember. 
2dly, For drilling, in a right line, I had a thin brass 
plate, fastened between the steel chaps, for the edge of 
the to bear against, whilst I thrust it forward from 
hole to hole. What you propose of an iron frame with 
a lead outside, will be better than my wooden block ; 
but considering the little time that past betwixt trans- 
VOL.X, PARF 1. : 
GRADUATION. 
$69 
ferring the divisions of the 2 to the divisions of my Original 
dividing plate, I did not suffer much that way. [t Graduation: 
was when I drilled the holes in my dividing plate that “~Y¥—" 
I used a frame for drilling, which had one part of it 
that had a steel hole ; that in lying upon the plane of 
the dividing plate, was fixed fast in its place for the 
point of the drill to pass through ; then, at the length 
of the drill, there was another piece of steel, witha 
hole in it, to receive the other end of the drill to keep 
it at right angles to the plane of the plate. This {piece 
- was a spring, which bended at the end, where it was 
fastened to the frame of the lathe, at about 18 inches 
from the end of the drill ; so it pushed the drill through 
with any given force the drill would bear ; and though 
that end of the drill moved in the arch of a circle, it 
was a very small of it, being no more than equal to 
the thickness of the dividing plate. My good wishes. 
Conclude me yours, EN. Hinpiey. 
_. Nothing ever surpassed in originality the method de- 
scribed sg the above letters, which is in no respect rer oa 
like any other. There is not a tool employed in it, ex- méthod of 
cept the lathe, but what may either be found in the ‘dividing. 
shop of the most common. worker in metals, or made 
by him, It is, however, like Hook’s and Roemer’s, a 
system of uncontroulled stepping; and, like theirs, if 
only applied to an arc, would have ended in the same 
uncertainty ; but being extended to the whole circle, 
it secures the intended number of divisions, and closes 
without a remainder, which is what theirs never could 
have done. 
To avoid errors occasioned by expansion, which 
Hindley seems not to have been aware of, Smeaton 
recommends that the work should be done when the 
air is of a moderate temperature ; and that, to prevent 
the materials from being heated, it should be carried 
on at short intervals ; but his chief improvement was di- 
rected to correct the effect of long continued stepping. 
Mr Smeaton would divide his circle into 1440 parts, or fr Smea- 
uarters of a degree. To effect the correction last men- ton’s me- 
tioned, two pieces of brass must be provided, in every thod of di- 
respect like that which is to be the hoop, except that Yiding- 
they need not be longer than is required to contain 30° ; 
these pieces, which are-called straps, he would drill in 
the manner that Hindley prescribes, and it should be 
mentioned; that the first hole in each must be made in 
a short piece of hardened steel, which in the first in- 
stance had been soldered to the ends of the straps. For 
the pu of obtaining the total length, the straps 
are Milled from end to. end; but no more than the 
first, middle, and last holes are used. The zero hole 
being made in the long, or hoop-piece, the middle holes 
of the straps are to be pinned to it on opposite sides, 
and the steel pieces directed forwards ; the three pieces 
extended in a right line are to be pressed together, and 
the 60th hole in the hoop-piece bored coincident with 
those of the straps. The straps are now taken off, and 
the 59 intermediate holes drilled by means of the chaps 
only. Again, the extreme holes of the straps are to 
be pinned to the zero holes of the hoop-piece, and ar- 
ranged as before, when the 120th hole of the latter is to 
be bored agreeable to the steel holes in the former ; and 
recourse again had to the chaps for the next 59 holes. 
As the process described above fills up as much of the 
hoop-piece as is equal to 30°, eleven similar double 
operations will complete the whole length ; and, as 
Smeaton observes, produce 12 master checks, and 12 
subordinate ones. The next thing to be done is to 
fasten the ends of the long piece together, so as to form 
3A 
