‘ 
Original 
366 
Having cut the nonius divisions, suppose of the. 90 
Graduation are, take up the plate, polish off the bur, and fasten it 
—v"_ to the limb, as before; but here 
reat. care must be 
taken to make the first division of the nonius coincide 
with the 60th deg. so as to appear one line; and the: 
nonius of the 96 arc may be cut in the same manner, 
making the first division coincide with 64 = 60° upon 
the limb. 
Now, take up the plate, and dram, a tangent, at the 
point in the faint arc in the middle of the nonius. plate ; 
and with a distance about a quarter of au inch er 
than the nonius, lay off from the tangent point another 
in the tangent line; also. lay. off this distance from the 
centre of the collar. at the object end of the. telescope, 
and makea fine point: Then. extend the beam-compass. 
nearly the whole length, of the nonius, or centre plate 
(which should reach, at least, half an inch. beyond the 
telescope, on the contrary side), and lay off other points 
in the tangent line before mentioned, and in a line 
passing through the centre of the quadrant, at right 
angles to the telescope. 
Now screw the two plates to the telescope, and. draw 
lines by the edge of a steel-ruler through the correspon-~ 
dent points, to which lines the plates must be carefully: 
filed.. Then the ends of the plates will be in lines pa~ 
rallel to each other, and to the axis of the tube, which 
affords ar excellent mechanical method of finding the 
line of’ collimation of the telescope. 
The apparatus used for this purpose by the late Mr, 
Graham, was a box equal in length to. the telescope, 
having deep sides, to prevent its bending by its own, 
weight. The ends were of hard wood.) Instead. of 
which, I use iwo flat piecesof brass, which I can move, 
according to different lengths required ; and by the help 
of a small spirit-level, these pieces of brass may be fined in 
one and the same plane. This, apparatus should stand 
firm upon the ground, where a distant and. distinct ob- 
ject can be seen. Rest the ends of the nonius and cen- 
tre plates upon the two pieces, of brass, and observe 
what point of the object is cut at the intersection of the 
horizontal and vertical wires. Invert the telescope,, 
and if the horizontal wire does not cut the same point 
of the object, it must be altered by the screws for that 
purpose, half the, difference. . By repeating this, you 
may approximate extremely near the truth. 
» In the middle, between the 90 and 96 arches of the 
mural quadrant, in the royal observatory, is an arch.of 
oints (96), which are used with a silver wire, of about 
E00 in an inch, carried by asmall frame, screwed to the 
end of the nonius.plate. When the wire, in an obser- 
vation, falls between two points, it must, by the micro- 
meter screw, be made to bisect the nearest point to the 
left hand, the instrnment shewing the cenith distance ; 
and the minutes and seconds shewn by the micrometer 
addéd, Ifthe next point to the right hand be bisected, 
the minutes and seconds must be subtracted. This arch 
of points was divided in every respect like the other 
arch of 96. 
Having gone through the whole process of dividing 
the cua arc, &c. it will be necessary to shew some rea- 
sons why this kind of management hath succeeded better 
than any other, as far as I either know or have heard. 
After I had found by experience, that the expansion of 
the instruments to be divided, occasioned by the inereasin 
heat of the sun, or a contraction by a decrease thereof 
was the grand difficulty with which Ihad to struggle, espe- 
cially when two or three hours were required to lay off the 
principal points ; I immediately set about contriving how 
to lay them. off in the least time possible, i. e. before any ex- 
pansion or contraction could take place ; and as the heat 
5 
GRADUATION. 
of three or four persons in the room may produce the same ¢ 
sun, I never admit were - Gi 
A 2h 
this 
points being but few in number, the divisions may be 
Sextants, or octants, for observing the distance of the 
moon from the fixed stars, should be divided by the — 
foregoing method, great accuracy being bh” 
instead of dividing sextants to every 20! the li 
as is commonly done, they should be divided to 15',a chord 
of 64° might be laid off, and divided by continual, bisece 
tions, This would, in some measure, crowd the limt 
with divisions ; but it. would shorten the nonius; for’ 
15, instead of 20, would shew one minute... | 
In dividing either arches or 
ight lines, a number 
(which will divide continually by 2) greater 
exthan is re. 
quired upon the are or line, is the best. to begin with,’ 
and may be used in dividing a circle, by laying off 
chord of the difference. _ Suppose it was: to di« 
vide a circle into 54 MY eal be ¥ 
10=10°.30'; the chord of which laid off must be add 
ed to 360°, and it willbe 360° 410° 30’, to be divi 
into 64 equal parts, 54.of which will complete the cir 
If the are of 10° 30’ be laid off from a dividing plate, 
it will answer the same. purpose. Senciss } os 
Analogous to the foregoing method, my scale of equal 
parts mas divided. I took *%2 of an iach in_a, beam 
compass, laid the scale which I took it from, the brass 
scale to be divided, and the beam compass in a ro 1 
cing the north, where they lay the whole night. . 
next morning, after correcting the lengths, the above +. 
were laid off three times (the brass being long eno 
to take it in); then, having in other ‘compasses 256, 
128, and 64, I bisected the three spaces of 512 with all 
the expedition I could, Having now only 64 inches in 
the last beam compass, any Rake: or unequal expan- 
sion was not to be feared ; therefore worked by conti- 
nual bisections till I had done. The linear di i p 
were cut from the points, with a beam compass, as bene 4 
described. , ; 5 a 
The nonius divisions of this scale contains *,% | 
inch, which were divided into 100 in the follo 4 
manner : 4s 100 : 101 :: 256 : 258.56 tenths of an inch, 
the integer inthis case being ;';. Suppose the scaletobe 
numbered at every inch from left to right ; then b= 
ly against *,, to the left of 0, was.made a fine point, 
from which was laid off 258.56 to the right hand... This 
was taken from a scale 3 feet in length, which was divi- 
ded after the common meth the error was so 
od ; but 
small as to vanish at the other extremity ofthe nonius, 
when divided continually be 2. Siding A's Se 
