364 
Original having heard Troughton say, that he had looked at it 
Graduation. with an eye to this matter ; that he is of opinion, from 
estimating ‘the elasticity of those metals at 8 or 10 times 
their difference of expansion, in such temperatures as 
they are exposed'to‘in the observatory, that the iron 
will command the brass, and little or no error will en- 
sue. The same artist also observes, that as the iron 
quadrant has long borne an additional are of 96°, divi- 
ded by Bird, and as there is no proof of its having 
changed its figure, since that are was put on, as the 
brass one has certainly done to the amount‘of 7 or 8 se- 
conds, for aught that is known to the contrary, the 
iron one may be the better instrument ; but as both of 
them are now superseded by the new mural circle, this 
uestion may, perhaps, remain for ever at issue, and its 
iscussion is now rendered of far less interest than it 
would have been 30 years ago. 
‘(Graham laid it down as a principle or maxim, “ that 
it is‘possible, practically, ‘to bisect an ‘arch or a right 
line, but not to trisect quinquisect, &c.” Bird not 
only acted upon this maxim, to the full scope of what 
been done by the’artist who ‘conceived it, but ex- 
tended it even to the division of the arc of 90°. We 
will not, however, ‘anticipate the method of Bird, 
which is in many respects original and ingenious ; for 
every one who dips into these matters, will derive the 
most satisfactory information from perusing his-own ac- 
count of it, as published by order of the Board of Lon- 
gitude in 1767, the whole of which is subjoined.' 
« The following method of dividing astronomical in- 
struments, &c. is collected principally from the expe- 
rience which I have gained in the space of thirty-four 
years ; and, in some parts, from the instructions which 
I received ‘from the late Mr Jonathan Sisson. 
‘What I call my own, I have distinguished by Italic 
‘characters. If any other instrument-makers have used 
the same method, it is unknown to me; and shall, 
therefore, :pay no regard to any pretensions unsupport- 
ed by evidence;—I mean, pretensions, without pro- 
ducing astronomical instruments superior, or, at least, 
equal to those which I have made. 
How far the lunar theory hath been improved by the 
observations of the late Dr Bradley and Mr Mayer, I 
leave to the decision of those who have tried it by ob- 
servations, in order to find the longitude at’sea, &c. I 
cannot help, however, being fully of opinion, that a still 
more perfect knowledge of the motion of the heavenly 
bodies may be obtained by future observations, skilful- 
ly made, with accurate instruments. 
I have been favoured with so distinguished a mark* 
of approbation from the Commissioners of Longitude, 
that nothing on my part shall be wanting, that may, in 
the least, contribute to so desirable an end :”—So far 
the preface. 
“It will be sufficient, for my purpose, to make use 
of no more lines and ares than are represented in Fig. 2. 
Bird’s me- 
thod of 
graduation. 
PLATE Plate CCLX XXII. 
a The requisites for the performance of this work are as 
follow :—A scale of equal parts, by which the radius may 
be measured to 0.001 of an inch, must be provided. My 
scale is 90 inches long, each inch divided into 10, conti- 
guous to which are nonius divisions, viz. 10.1 inches di- 
vided into 100 equal parts, shewirg 0.001 of an inch ; 
and, by the assistance of a magnifying glass, of one inch 
i ngth, a third of 0.001 may be taken off by estima- 
ton. 
* Bird received the sum of £560, by certificate, from the Commissioners of Longitude, for his method of nie together with. 
that of constructing mural quadrants; the latter of "which was published soon afterwanda ‘ j = ; } ; 2 
GRADUATION. 
Provide five beam compasses, to which magnifying Or 
glasses, of ie more than one inch focal length, Gola te ! 
applied. Let the longest beam be sufficient to draw the ,~ 
arcs, and. measure the radius; the 2d, to measure the p02 
chord of 42° 40’; the 3d, to measure the chord of 30° ; 
the 4th, 10° 20’; the 5th, 4° 40’; and if'a 6th, to mea~ Px. 
sure 15°, be made use of; so much the better, cen 
I have, for the sake of a round number; mentioned ¥ig- 
above, that the radius cf the mural-are in the Royal’ Ob- 
servatory at Greenwich is eight feet ; but, as I shall here 
put down the lengths of the several chords made use’ of'in 
the dividing, it will be necessary to note the exact radius ' 
in inches and decimal parts. © eet 18s ANION 
The radius of the arc of 90°, at the points, = 95.938 
inches, from which the following numbers were computed, 
viz. 49.6615 inches = chord of 30°, — 25.0448 inches = 
chord of 15° — 17.279047 inches, = chord of 10° 20'— 
7.81186 inches, = chord of 4° 40’, and 69.80318 inches, 
= chord of 42° 40'. Having drawn the several ares, 
between which the divisions were to be cut, the radius and 
the lengths of the above chords were taken by the beam 
compasses, which, together with the scale, mere laid upon 
the quadrant, where they wemained till the neat morning, . 
during which time the dour of the room was kept locked. 
Before sun-rise I remeasured the radius, which required 
some correction ; the beam being of white fir, and the scale 
of brass, which probably contracted, while the beam re- 
mained unaltered. The other beam compasses also re- 
quired correction. evr 
Now the quedrant and scale being of the same tempe= 
rature, the faint arc 6, d, was Ati and, with a very 
fine prick-punch, the point a was made. ' With the 
same beam compass, unaltered, I laid off, from a to é, 
the chord of 60°, making also a fine point. With the 
chord of 30°, ae was bisected inc. Now, one point of © 
the beam compass, containing 60°, was fixed ine; and 
with the other was marked the point r, or 90°. Neat, 
nith the beam compass, containing 15°, mas bisected er 
inn, or 75°. From n was laid off the chord of 10° 20’, — 
and from x, 4° 40! ; which lwo last chords joined exactly 
in g, being the point of 85° 20'. Now each degree 
being to be divided into 12 parts, or every 5’, therefore 
85X12 + 4= 1024, a number divisible by continual bis 
sections. The last chord computed was 42° 40!, with 
which ag was bisected ino; ao and og were bisected 
by trials. But whoever undertakes to divide a large qua- 
drant, will do well to compute also the chord of 21° 207; 
but for this chord any of the beam compasses already pro- 
vided, which will take in the length, may be used. The 
point g being found as above, I Dae mp by continual 
bisections, till I had the number required, viz. 1024. To 
fill up the space between -g and r, containing 56 divisions, 
the chord of 64 divisions was laid off from g towards d, 
and divided, like the rest, by continual beseclions, as was 
also from a towards b. The points 30°, 60°, 75°, and 90°, 
fell in without any sensible inequality. 
Here it is necessary to mention in what manner the 
bisecting and pointing were performed. Having the 
chord of 42° 40’ in the beam compass, and one point 
placed in a, with the other a faint arch of about of 
an inch in length was made in o. Again, one point of 
the beam compass was placed in g, and with the other 
the aforesaid faint arch was intersected. Here, as in” 
all other places, great care was used to make the points — 
exactly in the arc to be divided, and also in the inter- 
section. 
/ ‘te “ae! “ 
—— 
