_. Tm the followin pages I shall not only describe the 
T process int ividing the mural arc in the Royal 
bse , but endeavour, also, to make the descrip- 
* tthe chord should be taken a little too long, or too 
_ short, so that the intersection be made on one side or 
i. the other of the arc to be divided, it will not a 
_ an inequality, provided the point be made in the mid- 
Tvtbocmencine tee short Ries; except at the point vA 
85°. 20', where great care must be used in taking the chords 
from the scale, Great care must also be used in pointin 
__ thtersections in general, being more difficult than a single 
line. But here i must not be understood to mean a single 
line made by one point of the compass ; for, in all bisec- 
tions, the to be pointed must be laid off from left 
to right, and from right to left ; and if any error arises 
from an alteration of the beam compass, it will be shewn 
double. 
- In dividing, the points of the beam compass should 
never be brought nearer together than two or three 
inches, except near the ends of the arch or line to be di- 
vided ;-and there spring-dividers, having round points, 
which may be put in and taken out occasionally, will 
best answer the p / 
' The next thing to es —— ae method of 
making the points. The prick-punch, for this purpose, 
must be rok nanees sla and round, the conical point 
to make a pretty acute angle; and as the points here- 
with to be made, should not exceed 0.001 of an inch, 
shen linear divisions are to hee esas a magni- 
1 lass of 4 inch foca s used 5 b 
fire sioee f of a8 the impression, or bekaket, 
made by the points of the beam compass, will be very 
conspicuous ; and, if the said impression be not too faint, 
feeling, as well as seeing, will greatly contribute to make 
the points properly. f 
It is scarce nec to.say any thing about the arc 
of 96°. I shall only mention, that it contains 1536 di- 
visions; is to be divided into three equal parts, in the 
same manner as the arc of 90°. Each third > contains 
_ 512 divisions ; which number ‘is divisible continually 
by 2, and gives 16 in each 96th part of the whole arc. 
~ This arc of 96; (so far as 1 know,) was first applied 
to the iron quadrant in the vt he Observatory, in the 
year 1725, by my late worthy friend, Mr George 
Graham. It was not only a severe check upon that 
t mechanic, but will be so to all others, who divide 
e two arcs, upon one and the same instrument ; yet, 
if the above instructions be strictly followed, the agree- 
ment between the two will be surprising, and differ 
i little from the truth. 
} the next step is to cut the linear divisions from the 
i ints. The best instrument for this purpose is the 
\ stat compass, having both its points conical, and very 
| . Draw a tangent to the arc 6 d, suppose at e, it 
i will intersect the arc x y in g; this will be the distance 
: between the points of the beam compass fo cut the di- 
| visions (nearly at right angles to the arc bd.) 
( Lodge that point of the beam compass next your right 
| hand, in the point : 3 let the other fall freely into the 
arc, XY; ss gently with your upon the scren- 
head, whch fultess ihe pes Ey rag pie must be 
conver, and right over the point;) and, with the point 
towards the right hand, cut the divisions.—JIn this man- 
ner you must proceed with the rest. 
aving finished the divisions of the limb, the nonius 
divisions are next to be divided. Chuse any part of the 
arch, where there’is a coincidence of the 90 and 96 
arches, which let be at e: Draw the faint arcs s/ 
and i #, which may be continued to any length towards 
SS SY 3 EE a Ee Ee 
GRADUATION. 
865 
A, upon which the nonius divisions must be divided in Original 
points ; a tangent line, as before, intersecting this are, Graduation. 
gives the distance of the points in the beam-compass. ~~. 
ow as the nonius divisions of the arc 90° subdivide jyoq of 
the divisions of the limb of the mural are at Greenwich to graduation. 
halfa minute, 11 divisions of the limb being equal to 10 Piatx 
upon the nonius plate (a number which only 5 and 2 ccLxxxi. 
will divide,) recourse must again be had to comjntation, ¥ig- 2 
Measure the radius of the arc, and compute the chord of 
16, or rather 82, of the nonius divisions ; the quantity of 
an are equal thereto, may be easily had by the following 
proportion: As 10 div. : 55! (the number of minutes in 
11 divisions of the limb) = : 82 div. : 2° 56, the chord of 
which must be computed, and taken from the scale of 
equal parts: But as different subdivisions by the no- 
- nlus may be required, /et n= number of nonius divisions, 
m = number of minutes taken in by the nonius, b = 16, 
82 or 64, and x=are sought ; then as n:m::b: x. 
Lay off with the beam-compass, having the length of 
the tangent between the points, the point q from e, and 
the chord of 32 Sram q; towards the left hand, and divide 
by continual bisections, 10 of those divisions, counting 
Jrom q to the left, will be the points required. As the 
number of nonius divisions for the 96 arch should al~ 
ways be 16, 82, &c. I need only mention, that the 
extremes may be laid off from the divisions of the limb, 
without computation. 
Now the place upon the chamfered edge of the no- 
nius plate, where the nonius is to begin, may be found 
in the following manner. Measure the distance of the 
quadrant centre, from the axis of the telescope ; this dise 
tance from the axis of the telescope at the eye-end, will be 
the pe fer thé first division of the nonius, where draw 
@ faint line from the centre. The greater accura 
with which this ts laid off; the nearer to the axis of the 
tube will be the intersection of the wires, in the common 
Socus of the object and eye-glasses. 
I will suppose that no instrument-maker will fix to 
the telescope the nonius, and centre-plates, without 
steady-pins, as well as screws. Screw the centre-plate 
of the telescope very fast: put the nonius plate upon 
the steady-pins, without screws, and put the telescope 
upon the quadrant: make fast the nonius plate to the 
arch with two pair of hand-vices, and take the tele~ 
scope away. Now with one point of a beam-compass, in 
the centre of the quadrant, ‘and the other at the middle of 
the nonius plate, draw a faint arch from end to end: 
Where this arch cuts the faint line before-mentioned, 
make a fine point: From this point lay off on each side 
another, which may bé at any distance in the arch ; only 
care must be taken, that they be equally distant from the 
middle point: From the two last make a faint intersec- 
lion as near as possible to either of the chamfered edges 
of the nonius plate: Through this intersection, the first 
division of the nonius must be cut. 
Put the telescope again upon the centre of the qua- 
drant, the steady-pins into the nonius plate as before ; 
unscrew the hand-vices, and bring the last-mentioned in- 
terseclion to e or 60° upon the limb, where fasten it again 
with the hand vices, and take away the telescope. Now, 
from the point before divided, the nonius divisions 
must be cut; by lodging the left hand point of the 
beam-compass in the point upom the arch, and cutting 
with the right. 
Here great care must be taken, to cut the first divi- 
sion of the nonius through the point of intersection ; 
which may be done by altering the distance of the 
points in the beam-cempass, if necessary: This will 
not sensibly affect the perpendicularity of the divisions, 
provided the intersection be placed very near to e, or 60°. 
