ity that those venerable and .solid records of art 
Uhave left the spot where they had been so useful 
but as they were short. in comparison with the ea 
as, 
stand nearly in the direction of the radius... With re- 
spect to ms ing divigions ame the beam-compass, it 
may be doubted whether it was not a practice among 
instrument-makers, particularly upon chamfered edges, 
before the time that the Greenwich quadrant, was fi- 
nished ; and we have seen old works that indicated 
it. But there was another improvement of much, more 
i than either of the above, which. was. indis- 
of the quadrant into 96, which precludes altogether the 
practice of stepping, and has rendered essential service 
toastronomy. =) | Aetyh . . 
Graham's quadrant is described at length in Smith’s 
Opiics, and we barn Ayaiiee gnieivenc of ‘he process 
pursued in its graduation, y CO} ollowimMg ac- 
count from that. celebrated 2 Soper , . 
- There are 2 arches struck upon, the brass limb ; 
one with a radius of 8 feet, or more exactly of 96:85 
<,¢ inches; and the other with a radius of 95.8 inches. 
~ ‘This inner arch is divided into degrees, and 12th parts 
of adegree ; and the outward arch into 96 equal parts, 
which are severally subdivided into 16 equal parts. 
The beam of the compass which struck these arches, 
was secured from bending, by several braces fastened 
to it; and when an arch was struck, 60 degrees of it 
was determined, by placing one point of the compass at 
Fig. 1. Plate CCLX XXII.) and by making a stroke 
i the other at 6. This arch ad, was bisected in c, 
by drawing two small arches upon the centres a and 4, 
with such a radius as to cross the wd: cb, intwo 
ints as-near together as ible, without touchin 
oe other; then the sn interval between hem 
was bisected at c, by estimation of the eye, assisted by 
a magnifying glass. After this, the interval between 
the points @ and c, ore and}, was taken with the 
beam compass, and was transferred from 4 to d, which 
determined the Pago the quadrantal arch acéd. 
Every one of the arches being bisected in the 
ond mauner, the vere became divided into six 
ual parts, containing 15 degrees a piece ; and eve 
“x of these was divided into ae, equal parts, ef 
follows. To avoid making any false or superfluous 
ints. in the quadrantal 3 with its radius unaltered, 
ut upon any other centre, there was struck’ another 
GRADUATION. 
putably the invention of Graham); that is, the division, 
363 
faint arch, upon’ which the ehord of 15 degrees, already — Originai 
found,, was penal vale from the, quadrantal arch ; and Graduation, 
the third part of 15 degrees, being determined by trials ‘Aaaear 
upon the faint arch, was transferred back again upon Cohews 
the quadrantal arch ; which then was divided into 18 method of 
enon containing 5 degrees a piece ; and the 5th spaluating 
part of these was found, by, trials, as before, in dividing this qua- 
a separate arch, drawn upon a new centre for this pur~ drant. 
pose only. ‘Ihe subdivisions of the degrees into 12 
equal parts, were made by bisections and trisections, as 
before. ‘Thus was the whole quadrant divided. without 
any false or epee points. ' — ; 
See eee 
equal. , by no other met tof bisection, 
til 7 two thirds of the quadrant, became 
divided into 64, and the remaining third into 32 equab 
parts, which make 96 in the,whole, . And every one 
of these was also divided. into..16, equal parts by con- 
tinual bisections... These two sorts of divisions are a 
check upon each other, being in, effect two different 
uadrants; and the divisions in. one being reduced into 
the divisions of the other, by a table made :for that 
purpose, they are never found to differ, above five ox 
six seconds in any place of the limb, and when. they 
do, the preference ought to be given to the bisected div 
visions, as, being determined by. a.simpler operation: > 
The divisions hitherto mentioned being only very 
fine points in a fine arch-a 6d,' scarce, discernible by 
the naked. eye,. it) was necessary, as usual, to strike 
lines perpendicular to the arch, through every one of 
them. But since it is very difficult, and tedious: too, to: 
draw lines exactly through every point by the edge of ~ 
a ruler, the following method. was judged’ 
rate and expeditious. It was pv then to divide. 
any other concentric arch, fh t, by cross’stnokes, itito 
similar parts to those inthe given archacgehd. Take 
a small beam compass, and having: once fixed its: points: 
at any convenient interval ; upon the centres ¢, g, Sc." 
being the given points of the divided axch, strike the 
smal arches fi, Wk, &e. cutting the undivided>arch in 
Sh, &e.; then will the intercepted arches, asf; h, &e. 
be’similar to the arches e, g, &¢c. that.is, they will sub- 
tend the same angles a nem “penie ys 0. _ 
joining ef, gh, an of, oh, oe,0g, the triangles 
Sof; 8 eve be similar and equal to each. other ; 
every side in one being respectively equal toevery side 
inthe other.. Therefore, by taking away the common 
angle eoh, from the equal. angles, eof, gok, the -- 
angles eo g, foh, that remain, will also,be equal, 
If the triangles ¢ fo, ¢ ho, &e. be right angled at f 
and fA ; the dividing strokes fi, hk, &c. will, cut the 
quadrantal arch fi, at right angles also, at fand 4, 
&e,.” 
Respecting the means employed by Graham. in the /Remarks on 
division of the are of 90°, there is nothing in'them, ex- Graham’s 
cept what has already been noticed, that evinces supe=)™* 
rior contrivance ; it is to his accurate execution, and 
the invention of the continually bisectional are, that he 
owes. the well-deserved reputation which he . holds 
among those who have distinguished themselves in, the 
art of graduating astronomical instruments... 
Before the time that Bird flourished, there. is nota 
word. to be found in the history,of graduation about the 
dilatation and contraction, of metals in different tempera- 
tures; and it may be supposed, that as'Graham. made 
his quadrant of iron, and the limb of brass, he was un- 
acquainted with the different expansions of those me- 
tals. Our doubts, however, respecting the accuracy of 
that instrument, from this cireumstance, have been 
partly removed by the writer of this part of our article 
