510 
DIAL. 
south towards the east or west. — -'Elevate Hie 
pole to the latitude of vour place, and screw 
the quadrant of altitude to the zenith. Then 
if the dial declines towards the east (which we 
will suppose it to do at present), count in 
tne horizon the degrees of declination, from 
the east point towards the north, and bring 
tne lower end of the quadrant to that degree 
ef declination at which the reckoning ends. 
1 his done, bring any particular meridian of 
your globe (as suppose the first meridian) 
directly under the graduated edge of the 
upper part of the brasen meridian, and set 
the hour-index to XII at noon. Then, 
keeping the quadrant of altitude at the de- 
gree ot declination in the horizon, turn the 
globe eastward on its axis, and observe the 
•degrees cut by the first meridian in the qua- 
drant of altitude (counted from the zenith) 
as the hour-index comes to XI, X, IX, See. 
■in the forenoon, or as. 15, 30, 45, &c. de- 
grees of the equator pass under the brasen 
meridian at these hours respectively ; and 
the degrees then cut in the quadrant by the 
first meridian, are' the. respective distances 
of the forenoon hours from XII on the plane 
ot the dial. For the afternoon hours, turn 
the quadrant of altitude round the zenith until 
it comes to the degree in the horizon oppo- 
site to that where it was placed before ; 
namely, as far from the west point of the 
horizon towards the south, as it was set at 
first from the east point towards the north ; 
and turn the globe westward on its axis, until 
the first meridian comes to the brasen me- 
ridi :ii again, and the hour-index to XII : 
then, continue to turn the globe westward, 
and as the index points to the afternoon 
hours I, II, III, Sec. or as 15, 30, 45, &c. 
degrees of the equator pass* under the brasen 
-meridian, the first meridian will cut the qua- 
drant of altitude in the respective number 
ot degrees from the zenith, that each of these 
hours is from XII on the dial. And note, 
that when the first meridian goes off the qua- 
drant at the horizon, in the forenoon, the 
hour-index shews the time when the sun will 
come upon this dial: and when it goes off 
the quadrant in the afternoon, the index will 
point to the time when the sun goes off the 
dial. 
Having thus found all the hour-distances 
from XII, lay them down upon your dial- 
plate, either by dividing a semicircle into 
two quadrants of 90 degrees each beginning 
at the hour-line of XII, or by the line. of 
chords. 
In all declining dials, the line on which the 
stile or gnomon stands, commonly called the 
substile-line, makes an angle with the twelve- 
o’clock line, and falls among the forenoon 
hour-lines, if the dial declines toward the 
east; and among the afternoon hour-lines, 
when the dial declines towards the west ; 
that is, to the left hand from the 12-o’clock 
line in the former case, and to the right hand 
from it in the latter. 
To find the distance of the substile from 
the twelve-o’clock line. — If your dial declines 
from the south towards the east, count the 
degrees of that declination in the horizon 
from the east point toward the north, and 
bring the lower end of the quadrant of alti- 
tude to that degree of declination where the 
reckoning ends : then, turn the globe until 
the first meridian cuts the horizon in the like 
mimber-of degrees,, counted from the south 
point toward the east; and the quadrant and 
first meridian will then cross one another at 
right angles ; and the number of degrees of 
the quadrant which are intercepted between 
the first meridian and the zenith, is equal to 
the distance of the substile line from the 
twelve-o’clock line; and the number of de- 
grees of the first meridian, which are inter- 
cepted between the quadrant and the north 
pole, is equal to the elevation of the stile 
above the plane of the dial. 
If the dial declines westward from the south, 
count that declination from the east point of 
the horizon towards the south, and bring the 
quadrant of altitude to the degree in the ho- 
rizon at which the reckoning ends; both for 
finding the forenoon hours, and the distance 
of the substile from the meridian ; and for 
the afternoon hours, bring the quadrant to 
the opposite degree in the horizon, namely, 
as far from the west towards the north, and 
then proceed in all respects as above. 
Thus we have finished our declining dial: 
and in so doing, we made four dials, viz. 
1. A north dial, declining eastward by the 
same number of degrees; 2. A north ’dial, 
declining the same number west ; 3. a 
south dial, declining east ; and, 4. a south 
dial, declining west : only, placing the pro- 
per number of hours, and the stile or gnomon 
respectively, upon each plane. For, in the 
south-west plane, the substilar line falls 
among the afternoon hours : and in the south- 
east: of the same declination, among the fore- 
noon hours, at equal distances from XII, 
And so all the morning hours on the west 
decliner will be like the afternoon hours on 
the east decliner: the south-east decliner 
will produce the north-west decliner ; and the 
south-west decliner, the north-east decliner ; 
by only extending the hour-lines, stile, and 
substile, quite through the centre : the axis 
of the stile, or edge that casts the shadow on 
the hour of the day, being in all dials what- 
ever parallel to the axis of the world, and 
consequently pointing towards the north pole 
of the heavens in north latitudes, and towards 
the south pole in south latitudes. 
yin easy method for constructing of dials. 
— But because every one who would like to 
make a dial, may perhaps not be provided 
with a globe to assist him, and may probably 
not understand the method of doing it by 
logarithmic calculation ; we shall shew how 
to perform it by the plain dialing-lines, or 
scale of latitudes and hours (see fig. 5). 
Scales of this kind are sold by all mathe- 
matical instrument-makers. 
This is the easiest of ali mechanical me- 
thods, and by much the best, when the lines 
are truly divided: not only the half hours 
and quarters may be laid down by all of 
them, but every fifth minute by most, and 
every single minute by those where the line 
of hours is a foot in length. 
Having drawn a double meridian line 
ah, c d (fig. 6), on the plane intended for an 
horizontal dial, and crossed it at right angles 
by the six-o’clock line f e (as in fig. 3), take 
the latitude of your place with the com- 
passes, in the scale of latitudes, and set that 
extent from c to e, and from a to f on the 
six-o’clock line ; then, taking the whole six 
hours between the points of the compasses in 
the scale of hours, with that extent set one 
foot in the point e, and let. the other foot fall 
where it will upon the meridian line c d, as at 
d. Do the same from /to h, and draw the 
right lines e d and fh, each of which will be 
equal in length to the whole scale of hours. 
This done, setting one foot of the compasses 
in the beginning of the scale at XII, and ex- 
tending the other to each hour on the scale, 
lay off these extents from d to e for the after- 
noon hours, and from h to/ for those of the 
forenoon; this will divide the lines de and 
5/in the same manner as the hour-scale is 
divided, at 1, 2, 3, 4, 5, and 6; on which 
the quarters may also bq laid down, if re- 
quired. Then laying a ruler on the point 
c, draw the first five hours in the afternoon, 
from that point, through the dots at the nu- 
meral figures 1, 2, 3, 4, 5, on the line d e ; 
and continue the lines of IV and V through 
the centre c to the other side of the dial, 
for the like hours of the morning; which 
done, lay the ruler on the point a, and draw 
the last five hours in the forenoon through the 
dots 5, 4, 3, 2, 1, on the line / continu- 
ing the hour-lines of VII and VIII through 
the centre a to the other side of the dial, for 
the like hours of the evening; and set the 
hours to their respective lines as in the fi- 
gure. Lastly, make the gnomon the same 
way as taught above for the horizontal dial, 
and the whole will be finished. 
To make an erect south dud. — Take the 
co-latitude of the place from the scale of 
latitudes, and then proceed in all respects for 
the hour-lines as in the horizontal dial; only 
reversing the hours, as in fig. 2 ; and mak- 
ing the angle of the stile’s height equal to the 
co-latitude. 
The dialing-lines (fig. 5) are large enough 
for making a dial of nine inches or more in 
diameter, and they are drawn sufficiently exact 
for common practice, to every quarter of an 
hour. This scale may be cut off from the 
plate, and pasted upon wood or pasteboard, 
which will render it somewhat more exact 
than it is on the plate ; for being rightly di- 
vided upon the copper-plate, and printed off 
on wet paper, it shrinks as the paper dries ; 
but when it is wetted again, it stretches to Ibe 
same size as when newly printed; and if 
pasted on while wet, it will remain of that 
size afterwards. 
We shall now shew how to make a dial 
without these helps. Divide a quadrant 
into 90 equal parts or degrees for taking the 
proper angle of the stile’s elevation, which is 
easily done. 
To describe an horizontal dial. — With 
any opening of the compasses, as Z L (fig. 7), 
describe the two semicircles L F k and 
L Q k, upon the centres Z and z, where the 
six-o’clock line crosses the double meridian 
line, and divide each semicircle into twelve 
equal parts, beginning at L ; then connect 
the divis’ons which are equidistant from L, 
by the parallel lines K M, 1 N, II O, G P, 
and F Q. Draw V Z for the hypothenuse 
of the stile, making the angle VZE equal 
to the latitude of your place; and continue 
the line V Z to R. Draw the line R r pa- 
rallel to the six-o’clock line, and set off the 
distance a K from Z to Y, the distance b I * 
from Z to X, c II from Z to W, dg from 
Z to T, and e F from Z to S. Then draw 
the lines S ,v, T t, W tv, X .r, and Y y, each 
parallel to Rr, Set off the distance Y y 
from a to 11, and from / to 1 ; the distance 
.r X from b to 10, and from g to 2 ; iv W 
from c to 9, and from h to 3 ; t T from d to 
