DIAL. 
from the foot, or lowest part of the gno- 
mon, measure off at pleasure any distance, 
as a c, for the size of your dial : at c erect 
the perpendicular C D, and make the an- 
gle CAD equal, to the elevation of the 
equator ; then make a second triangle 
C D E, the angle at D being equal to that 
at A. Through E draw GH at right angles 
with A E. Carry on E B equal to E D, 
and with that distance as a radius, describe 
the quadrant EF from B as a centre. 
Measure off tiie proper angles from the 
point B, through the several parts of the 
quadrant, which is divided off into six 
equal parts; these will fall upon the pro- 
longed line G H, and give points thereon, 
through which lines being drawn from the 
centre A of the VI. o’clock line to the hour 
frame, the places of the several hours will 
be given. The gnomon is fixed at A, 
equal to A D E; being conformable to the 
co-latitude; or it may be simply a wire 
fixed at C, equal in length to C D, but 
perpendicular to the face of the dial ; some 
use large angular iron rods. This kind of 
dial is often seen on the sides of country 
church-steeples facing the south. 
To make an erect dial facing the north, 
invert the whole of that just described, 
making the gnomon point upwards instead 
of downwards, and causing all tile lower 
points to be transferred from left to right, 
and from right to left. This kind of dial 
will shew the hours before VI. A. M., and 
after VI. P. M. When such is wanted, 
the best way is to set up a stout post, with 
the planes of two dials back to back, they 
pointing due south and due north, respec- 
tively ; thus as the pin retires from one, it 
will set upon the other. 
We shall now instruct the reader how to 
make those scales, which are indispensable 
towards the attainment of perfection in 
this pleasing branch of study. 
The lines useful in dialling are, t, a line 
of chords ; 2, a line of latitudes ; 3, a line 
of sines ; and 4, a line of hours. They are 
all derived from the quadrant of a circle, 
as will be shewn in fig. 4. 
Describe a circle and divide it into four 
equal parts by the lines A B and C D, in- 
tersecting in the centre E. Draw the 
chords AC, C B, B D. Now divide the 
two segments, or quadrants, A D and C B, 
each into nine equal parts'; either of which 
contains 10 degrees. Placing one leg of 
your compasses at B for a centre, draw the 
several arcs from the quadrant subtended 
by the chord C B, so that they may fall 
upon that chord, which being numbered 
according as the several arcs correspond 
with the division on the quadrant, will 
give a line of chords gradually diminishing 
from B towards C ; all the intermediate 
degrees, or tlie measures of 10° each, thus 
obtained, may be removed in the same 
manner from the quadrant, if it be gra- 
duated accordingly. 
It will be proper to observe in this 
place that the chord of 60“ is the radius of 
a circle whose quadrant is subtended by 
90“ of the same scale : -hence a line of 
chords is easily made upon any circle, so 
that any part of that circle may be cut off 
at pleasure. This is essential in every 
branch of mathematics ; but in dialling it 
is indispensable to be known: the reader 
will have observed, that in forming the 
horizontal dial, the hour lines are drawn 
through particular points, so as to make 
the required angles. As he may be at a 
loss how to effect this on many occasions, 
we shall give an example in fig. 5, whereby 
every doubt, or difficulty will be removed. 
Let it be required to cut off an angle of 
40 degrees from the quadrant, w-hich ap- 
pertains to a circle for which we have not 
a line of chords in readiness. On the base 
line A B measure 60 degrees from any line 
of chords you may have at hand : it may ei- 
ther exceed, or be less than your base line ; 
we will suppose tire former ; in this case 
the base line must be prolonged to the mea- 
surement of 60“ from your scale, which will 
carry it on to Ci With that 60“, as a ra- 
dius, and from A, as a centre, describe the 
quadrant C D, concentric with the quadrant 
E B, from which you would cut off 40“. 
Now measure 40 degrees on your line of 
chords, and, placing one foot of the com- 
passes at C, carry the measurement to F, 
which will cause the angle F A C to mea- 
sure 40“, and the line F A will, at C, cut off 
40 degrees from (he quadrant E B. For an 
angle does not vary by prolongation ; there- 
fore, if the exterior quadrant is cut at 40“, 
the interior quadrant, being concentric 
therewith, must correspond with that divi- 
sion. 
We now proceed to the opposite quad- 
rant, which is not subtended by a chord, 
but is divided into nine equal parts, of ten 
degrees each. Draw from the several 
points of divi.sion on the quadrant eight 
lines, all parallel with E A, and falling on 
the radius E D ; this gives a line of sines, 
which is of veiy extensive use in various 
branches of mathematics. From A draw 
