Graduation of Afronomical Injlrumenis. - 
In my Introdudion to M. Roemer’s Method of Divifion, I 
have fhewn, that diviffons laid off in fucceffion, by the fame 
opening of the compafles, either in a right line, or in the arch, 
of a circle, being in its Idea geometrically true, and in itfelf the 
moft fimple of all procefles, it has the faireft chance of being 
mechanically and practically exadl, . when cleared of the difturb-. 
ing caufes. The objection therefore to his method is, the gieat 
number of repetitions, which depending upon . each other in 
fucceffion (requiring no lefs than 540 to a quadrant, when fub- 
divided to ten minutes each), the fmalleft error in each, repeated 
540 times, without any thing to- check.it by the way, may arife. 
to a very fenfible and large amount : but in the method I have- 
hinted,, this objedion. will not lie; for, in the firfl: cafe, the, 
affumed opening is laid off but five times ; and in the latter cafe 
but four times ; ,no.r does this repetition ari fe out of the nature of 
the thing ; for, if you like it better, you may, in the. former cafe, 
at once compute the chord of 64° ; and . in the latter that of 
85° 20', and then proceed wholly by bifedion ; fupplying what 
is .wanted to make up the quadrant, from the bifeded divifions s . 
as they arife. Mr. Bird prefcribes this method himfelf,. for the 
divifion of Hadley’s. fextants and odants. 
He, I fupppfe, was the firft, who conceived the idea of laying 
off chords of arches, whofe fubdivifions ffioukl be come at by 
continual bifedion ; but why he mixed therewith divifions that 
were derived from a different origin (as prefcribed in his method 
of dividing) I do not eafily conceive. He fays, that after he had ■ 
proceeded by the bifedions, from the arc of 85° 20', the feveral 
points of 30°, 6o°, 75 0 , and 90°, (all of which were laid down 
from the principle of the chord of 6o° being equal to radius), 
fell in without fenfib J e inequality ; and io indeed they might ; but 
yet it does not follow that they were equally true in their places 
