Graduation of Afironomical Infir uments. 23 
coincidence with its index, can be replaced with any degree of 
certainty nearer than the 40oodth part of an inch, though 
aided by a magnifying glafs *•; 
A 4ooodth part of an. inch being then determined to be the 
minimum vfibile by the ftrokes of an inftrument, this will be 
lefs than one fecond of a degree upon a radius of four feet ^ 
and therefore, if the whole fet of diviiions upon the limb could 
be preferved true to this aliquot part of an inch,, the eight-feet 
quadrants of Greenwich might be expected to be true to half 
a fecond. How far they are from this, I do not exaftly know ;; 
but I have reafon to think they vary from it fome feconds : 
nay, I believe it is generally allowed, that our larged qua- 
drants, even when executed by the accurate hand of Mr. Bird, 
do not exceed thofe of a lefs fize, by the fame hand, in pro- 
portion to their increafe of radius: nor can it well be expected' 
that they Ihould y lince, as the weight neceflarily increafes in 
a triplicate ratio of the radius, the great weight of the Green- 
wich quadrants in moving and fixing them (as they could not 
be divided in their place) may eafily derange the framing ; or 
even the internal eJcfiidty of the materials may give way, by a 
change of pofition, to fo minute a quantity as a qooodth part 
of an inch. It therefore appears to me, that fince the divifions 
of a quadrant of four-feet radius are more than fufficient, and 
even thofe of three feet admit of ail the dlftinftnefs that in- 
other refpefts is wanted, a three-feet quadrant,, in point of 
* It will be to little purpofe to attempt it with a greater power. Double 
microfcopes can aoubtlefs be formed to magnify obje&s, far lefs than a 4Coodth 
part of art inch, to diilin6I: furfaces ; but then the advantage of fuch degrees of 
magnifying power is chiefly upon the organized bodies of nature. Let a dot, or 
the fined point that can be made by human art, be fo viewed, and it will appear 
notxourtdj but a very ragged irregular figure, 
fize* , 
