io Mr. 8m eaton’s Obfervatlons on' the 
means of checking the diflan t diviiions, in ref peel of each 
other, it is very probable that no one has followed his fteps, 
in cafes where great accuracy was required, in a confiderable 
number of divifions. For in reality this method is likely to fall' 
far (ho it of Df Hook’s ; as Dr. Hook’s divifions being cut in 
a fimilar fuc'ceflive manner, by the rotation of the fharp edge of 
the threads of a ferew again. ft the exterior edge of the limb of 
tiie inftrument, a very flight degree of preflu re will bring a 
fine ferew of thirtythreads in an inch (which he preferibes), to. 
touch again ft an arch whofe radius is four or five feet iu more, 
than one, two, three, or four threads at once; fo that the. 
threads fupporting one another, a fmall extuberance, or even a 
fmall hard particle in the metal, will be cut through or re- 
moved by the grinding or rather flawing motion of the ferew ; 
and which, in regard to its contact, being in reality an edge^ 
will be much more effectual (that is, more firm) in its reten- 
tion than a mere Ample point : and a repetition of the opera- 
tion, from the fupport of the threads to each other, will tend 
to mend the firft traces; whereas, in Roemer’s way, a repeti- 
tion will make them worfe ; for, whatever drove forward or. 
backward the point on firft entering, will, from the doping o£ 
the point, be confirmed and increafed in driving it deeper. 
When Dr. Halley was chofea Aftronomer Royal (IVhv 
Flamsteed’s inftruments being taken away by his executors),. 
Mr. Graham undertook to make a new mural quadrant, about 
the year 1725 ; who, uniting all that appeared valuable in the. 
different methods of his predeceffors, executed it with, a degree 
of contrivance, accuracy, and precifion, before unknown : and 
the divifion thereof he performed with his own hand. The 
model of this quadrant, for ftrength, eafy management, and 
convenience, has been ever fince purfued as the moft perfedfc. 
1 What 
