Original 
Graduation: 
The Duke 
de Chaul- 
368 
As all the waxed pieces had their opposites cut in the 
other, it was not necessary to have 180 of them; for 
it is evident from the mode of procedure, that after the 
ones and nines had been put in, neither thesenor the _ 
nes’ method tens could be wanted. The semicircle of trial has yet 
of gradua- 
tion. 
Remarks on 
the Duke 
de Chaul- 
nes’method. 
Hindley’s 
method of 
graduation, 
upon it no divisions, and how (the waxed pieces being 
removed) it was divided from the other, has already 
been mentioned. ; > 
It is ‘observed, that when a circle is large enough to 
allow the microscopes to come so near each other as to 
bisect the arc of 10°, the numbers four and five may 
with advantage be substituted for nine and ten ; and 
when half degrees are required, it is proposed to bi- 
sect the are of 15°, and with this opening to put in all 
the half degrees, 
To subdivide the degree into five-minute spaces, the 
Duke de Chaulnes proposes to mount a telescope with a 
vertical wire in its focus, upon the centre arbor of the 
circle, so that it may either revolve with the circle, or 
concentric to it by itself, as the case may require ; and 
let a long beam of wood be provided, accurately divid- 
ed into 12 equal parts, and placed at such a distance as 
to subtend an angle of one degree ; a thin piece of brass 
is to be fixed upon the circle under the tracer; and as the 
telescope and circle are turned round,together, and the 
wire made successively to coincide with the divisions of 
the beam, the corresponding strokes are to be drawn 
upon the piece of brass: and lastly this piece is to be pla- 
ced under the fixed microscope, in order that by means 
of it and the tracer, every degree may be filled up. 
The ingenious inventor of the above method, like 
those who preceded Bird, has made no provision against 
the errors arising from expansion ; indeed, his tracer 
being fixed opposite to the point of trial, subjects his 
work to the greatest possible error in that respect ; and 
under this disadvantage, his division of the first semi- 
circle is no more than a copy of the wax-work ; and, 
again, the second semicircle. is, under the same disad- 
vantage, a copy from the first. 
The method of Hindley having been in part com- 
municated to Smeaton in 1741, and fully in 1748, 
might in our article have preceded some of the me- 
thods already noticed, but as he received it under the 
seal of secrecy, it was unknawn to the public until 
1785, in which year Mr Smeaton’s paper, before re- 
ferred to, concerning it, was read to the Royal So- 
ciety. 
Smeaton introduces this method under the full per- 
suasion that vision, even when assisted by glasses, can- 
not command a greater degree of accuracy than to the 
4000th part of an inch; and maintains, that by con- 
tact, the 60,000th becomes equally sensible. Were this 
true, and contact applicable to the graduation of instru- 
ments without drawback, a fine field of improvement 
would have been opened to the artist through the paper 
under consideration. 
Mr Smeaton says, “ It now comes to be time to open 
a principle, upon which there is a prospect of effecting 
such an improvement. I have shewn that a 4000th 
part of an inch is the ultimatum that we are to expect 
from sight, though aided by glasses, when observing 
the divisions of an instrument. But in the 48th vo- 
lume of the Philosophical Transactions, (p. 149 of this 
volume), I have shewn the mechanism of a new py- 
rometer, and experiments made therewith ; whereby it 
appears, that, upon the principle of contact, a 24,000th 
part of an inch is a very definite quantity. I remem- 
ber very well that I did not then go to the extent of 
what I might have asserted, being willing to keep with- 
in the bounds of credibility ; but on occasion of the 
4 
GRADUATION. 
resent subject, I have re-examined this instrument, 
nd Rioeie very well authorised to say, that a © 
60,000th part of an inch, with such an instrument, is ‘ 
a more definite and certain quantity than a 
of an inch is to the sight, conditioned as above s : 
fied.. The certainty of contact is, therefore, nD 
times greater than that of vision, when applied to the — 
divisions of an instrument: and if this. principle of cers 
tainty in contact did not take place, even much beyond — 
the limit I have now assigned, we never should have _ 
seen those exquisite mirrors for reflecting telescopes that — 
have already been produced. _ a (¢ 2 owt See 
These reflections apply immediately to. resent — 
subject, as Hindley’s method of Divtionimenade waa ' 
ly by contact, and that of the firmest kind ; there being — 
scarcely need of magnifying glasses in any part of the 
operation. ; egg +3 
In the year 1748, I came to settle in London; and — 
the first employment I met with was that of making : 
philosophical instruments and apparatus. In this si- 
tuation, my friend Hindley, from a principle the re. — 
verse of jealousy, fully communicated to me, by, letter, 
his method of division ; and though I was enjoined se- 
erecy respecting others, (for the reasons already men- 
tioned), yet the communication was expressly made — 
with an intention that I might apply it to my own pur- 
- The following are extracts from two letters, which 
contain the whole of what related to this subject ; and 
since I have many things to observe. thereon, so tl 
‘the paraphrase would be much greater than the text, — 
‘I think it best not to interrupt the description with any 
commentary, as perhaps his own mode of expression 
will more briefly and happily convey the general idea 
of the work, than any I can use instead of ‘it. e 
ae “Se 
«© My Dear Friend, ** York, 14th Noy. 1748. — 
«« As to what you was mentioning about my brother's 
knowing how I divided oy. engine plate, 1 willdescribe _ 
it as well as I can myself; (a0 fg will want a good 
many things to go through with it. The manneris _ 
this: first choose the largest number you want, and” 
then choose 4 long plate of thin brass; mine was about _ 
one inch in breadth, and eight feet in length, which I 
bent like a hoop for a hogshead, and soldered the ends 
together, and turned it of equal thickness, ges a block © 
of smooth-grained wood, upon my great lathe in the - 
air, (that is, upon the end of the mandrel); one Pie 
the hoop must be rather wider than the other, it & 
may fit the better to the block, which oh ae 
will be a short piece of a cone of a. \ 
large diameter: when the hoop was 
turned, I took it off, cut, and opened 
it straight again. 
The next step was to have a piece of 
steel bended into the form as per mar- 
gin; which had two small holes bored 
in it, of equal bigness, one to receive 
a small pin, and the other a drill of 
equal size. I ground the holes after 
they were hardened, to make them 
round and smooth. The chaps formed 
by this steel plate were as near together 
as just to let the long plate through. 
Being open at one end, the ch so 
formed would spring a little,and would 
press the long plate close, by setting in ; 
the vise. Then I put the long plate Lb 
to aright angle to the length of the steel chaps, and bored 
one hole through the long plate, into which I put the 
——== 
= >\) 
<== 
SSS 
—— 
=== 
———S 
