jo Mr. Smeaton’s Ohfervations on the 
hold of fifteen teeth or degrees together : this* in effeO:, becomes 
a pair of compaffes, 24 removes of which complete the whole 
circle* and produce 24 checks in the circumference : and whoever 
confiders the very exquifite degree -of truth that refults from 
the grinding of furfaces in contaft, as already noticed, muft 
expeCt a very great degree of rectification of whatever errors 
might fubfift in the wheel after its firft cutting. 
What degree of truth it might in reality be capable of upon 
its firft produdlion and adjuftment, is not now to be afcertained, 
he never having ufed it for the graduation of any capital inftru- 
ment. Thofe that he made with a view to an accurate meafure 
of angles, he always made with a fcrew and wheel, or parts of 
circles cut by his engine into teeth, and ground together as 
before-mentioned; but I have reafon to think, that its per- 
formance, if put to a ftriCt teft, was never capable of that 
accuracy that he himfelf fuppofed it to have. 
The method itfelf, however, from its fimplicity, and eafe 
of execution, feems to me to be a foundation for every thing 
that can be expe&ed in truth of graduation ; and in confe- 
quence for reducing inftruments to the leaft fize that is ca- 
pable of bringing out all that can be expeCted from the largeft ; 
when it ftiall, like manual divifion, have received thofe advan- 
tages that the joint labours of the moft ingenious men can 
beftow upon it. That I may not appear to be without grounds 
for my expectations, I will beg leave to propofe, what near 
forty years occafional contemplation has fuggefted to me on 
the fubjeCt ; and as I can defcribe the procefs I would purfue, 
where different from Hindlby’s, in fewer words than I could 
make out a regular criticifm upon his letters, I will imme- 
diately proceed to the defcription of it. 
4 
Propofed 
