511 
DIAL. 
distances B a, B b, B c, kc. be taken in the 
compasses from B, and set uppn this line in 
the same manner as directed for the line of 
chords, it will make a line of latitudes B C, 
equal in length to the line of chords A B, and 
of an equal number of divisions, but very 
unequal as to their lengths. 
Draw the right line D G A, subtending the 
quadrant D A; and parallel to it, draw the right 
line r s, touching the quadrant D A at the 
numeral figure 3. Divide this quadrant into 
six equal parts, as 1 , 2, 3, &c. and through 
these points. of division draw right lines from 
the centre E to the line r s, which will divide 
it at the points where the six hours are to 
be placed, as in the figure. If every sixth 
part of the quadrant be subdivided into four 
equal parts ; right lines drawn from the 
centre through these points of division, and 
continued to the line r.s, will divide each 
hour upon it into quarters. 
A dial on a card. — In fig. 9, we have the 
representation of a portable dial, which may 
be easily drawn on a card, and carried in a 
pocket-book. The lines a d, a b, and h c, of 
the gnomon, must be cut quite through the 
card ; and as the end a b of the gnomon is 
raised occasionally above the plane of the 
dial, it turns upon the uncut line c d as on a 
hinge. The dotted line A B must be slit 
quke through the card]; and the thread must 
be put through the slit, and have a knot tied 
behind, to keep it from being easily drawn 
out. On the other end of this thread is a 
small plummet D, and on the middle of it a 
small bead for shewing the time of the day. 
To rectify this dial, set the thread in 
A F B by the arcs 10 10, 20 20, &c. and this j the slit right against the day 7 of the month, 
will be a line of chords, divided into 90 un- ' and stretch the thread from the day of the 
equal parts; which, if transferred from the j month over the angular point where the 
line back again to the quadrant, will divide curve-lines meet at XII ; then shift the 
if equally. It is plain by tire figure, that the bead to that point on. the thread, and the 
distance from A to 60 in the line of chords, j dial will be rectified.. 
is just equal to A E, the radius of the circle 
from which that line is made ; for if the arc 
6t) 60 be continued, of which A is the centre. 
<5, and from i to 4 ;. 5 S from, e to 7, and from 
n to 5. Then laying a ruler to the centre 
Z, draw the forenoon hour-lines through the 
points 11, 10, 9, 8, 7; and laying it to the 
centre r, draw the afternoon lines through 
the points 1, 2, 3, 4, .5 ; continuing the fore- 
noon lines of VII and VII 1 through the cen- 
tre Z, to the opposite side of the dial, for the 
like afternoon hours ; and the afternoon 
lines IV and V through the centre s, to the 
opposite side, for the like morning hours. 
Set the hours to these lines as in the-figure, 
and then, erect the stile or gnomon ; and the 
horizontal dial will be finished. 
To construct a south dial, draw the line 
V Z, making an angle with the meridian 
Z L equal to" the co-latitude of your place; 
and proceed in all respects as in the above 
I horizontal dial for the same latitude, revers- 
ing the hours, and making the elevation of the 
gnomon equal to the co-latitude. 
| We shall now,, to render this article com- 
! plete, explain the method of constructing the 
dialing-lines, and some others. 
With any opening of the compasses, as 
E A (fig. 8), according to the intended 
length of the scale, describe the circle A D 
j C B, and cross it at right angles by the di- 
: aineters C E A and D E B. Divide the 
quadrant A B first into nine equal parts, and 
then each part into ten ; so shall the qua- 
drant be divided into ninety equal parts or 
degrees. Draw the right line A E B for the 
chord of this quadrant, and setting one foot 
of the compasses in the point A, extend the. 
other to the several divisions of the qua- 
drant, and transfer these divisions to the line 
To find the hour of the day, raise the 
gnomon (no matter how much or how little), 
and hold the edge of the dial next the 
it goes exactly through tire centte E of the j g Qomon towards the sun, so that the upper- 
arc A B. 
And therefore, in laying down any num- 
ber of degrees on a circle by the line of 
chords, you must first open the compasses, 
so as to J take in just 60 degrees upon that 
line, as from A to 60: and then, with that 
extent as a radius, describe a circle which 
will be exactly of the same size with that 
from which the line was divided : which 
done, set one foot of the compasses in the 
beginning of the chord line, as at A, and ex- 
tend the other to the number of degrees you 
want upon the line, which extent, applied to 
the circle, will include the like number, of 
degrees upon it. 
Divide the quadrant C D into 60 equal 
parts, and from each point of division draw 
right lines as i, k, l, k c. to the line C E ; 
all perpendicular to. that line, and parallel to 
D E, which will divide E G into a line of 
sines; and although these are seldom put 
among the dialing-lines on a scale, yet they 
assist in drawing the line of latitudes. For, 
if a ruler be laid upon the point D, and over 
each division in the line of sines, it will di- 
vide the quadrant C B into 90 unequal parts, 
as B a, a b, kc. shewn by the right lines 
10 a, 20 b, 30 c, kc. drawn along live edge 
of the ruler. If the right lineB C be drawn, 
subteuding^ this quadrant, and the nearest 
most edge of the shadow of the gnomon may 
just cover the shadow-line; and the bead 
then playing freely on the face of the dial, by 
the weight of the plummet, will shew the 
time of the day among the hour-lines, as it 
is forenoon or afternoon. 
To find the time of sun-rising and setting, 
move the thread among the hour-lines, until 
it either covers some one of them, or lies pa- 
rallel betwixt any two ; and then it will cut 
the time of sun-rising among the forenoon 
hours, and of sun-setting among the after- 
noon hours, on that day of the year for which 
the thread is set in the scale of months. 
To find the sun’s declination, stretch the 
thread from the day of the month over the 
angular point at XII, and it will cut the sun’s 
declination, as it is north or south, for that 
day, in the arched scale of. north and south 
declination. 
To find on what days the sun enters the 
signs; when the bead, .as above rectified, 
moves along any of the curve lines which 
have the signs of the zodiac marked upon 
them,. the sun enters those signs on the days 
pointed out by the thread in the scale of 
months. 
The construction of this dial is very easy, 
especially if the reader compaies it all ubrq 
with fig. 10, as he reads the following expla^ 
nation of that figure. 
Draw the occult line A B (fig. 10), pa- 
rallel to the top of the card, and cross it at 
right angles with the six-o’clock line I. C D ; 
then upon C, as a centre, with the radius 
C A, describe the semicircle A E L, and di- 
vide it into twelve equal parts (beginning at 
A), as A r, A s, kc. and from these points of 
division, draw the hour-lines r, s, t, u, v, L, 
zv, and x, all parallel to the six-o’clock line 
E C. If each part of the semicircle be sub- 
divided into four equal parts, they will give 
the half-hour lines and quarters, as in fig. 9. 
Draw the right line A S D o, making the an- 
gle S A B equal to the latitude of your place. 
Upon the centre A describe the arch It S E, 
and set off upon it the arcs S It and S T, each 
equal to 9,3\ degrees, for the sun’s greatest 
declination ; and divide them into 23| equal- 
parts, as in fig. 9. Through the intersection 
D of the lines E C D and A D o, draw the 
right line F D G at right angles to A D o . 
Lay a ruler to the points A and It, and draw 
the line A It F through 23^ degrees of south 
declination in the arc S It ; and then laying 
the ruler to the points A and T, draw the- 
line ATG through 23£ degrees of north 
declination in the arc S T : so shall the lines- 
A It F and A T G cut five line F D G in the 
proper length for the scale of months. Upon, 
the centre D, witli the radius D F, describe 
the semicircle FoG; and divide it into six 
equal parts, F m, m n, n o, kc. ami from,; 
these points of division draw the right lines rn h, 
n i, p A:, .and q l, each parallel to o I). Thun, 
setting one foot of the compasses in the 
point F, extend the other to A, and describe 
the arc A z H for the tropic of VJ ; with the. 
same extent, setting one toot in G, describe 
the arc A E O for the tropic • of - ‘5 . N-ext 
setting one foot in the point li , and extending. 
I the other to A, describe the arc A C I fer- 
tile beginnings of the 'signs sj? and f ; . and 
with the same extent, setting one foot 'in the 
point /, describe the arc A N for the begin- 
nings of the signs rr and Set one foot 
in the point i, and having extended the other 
to A, describe the arc A K for the beginnings:* 
of the signs X and Y\\; and with the same* 
extent, set one foot in k, and describe the 
arc A M for the beginnings of the signs ^ 
and Tt£. Then, setting one foot in the point 
D, and extending the other to A, describe ■ 
the curve A L for the beginnings of. <y> and; 
; and the signs will be finished. This 
done, lay a ruler from the point A over t he 
sun’s declination in the arch R S T (found by 
the following table) for every fifth day of the • 
year ; and where the ruler cuts the line 
F D G, make marks ; and place the days of 
the months right against these marks, in the 
manner shewn by fig. 9. Lastly, draw the 
shadow-line P Q, parallel to the occult line 
A B ; make the gnomon, and set the hours' 
to their respective lines, as in fig. 9, and the 
dial will be finished. 
The following table shews the sun’s place 
and declination, in degrees -and minutes, at 
the noon of every day of the second year 
after leap-year ; which is a mean between 
those of leap-year itself, and the first and. 
third years after. It is useful for inscribing 
the months and their days on sun-dials, and 
also for finding the latitudes of places. 
