plane be made to decline by any given num- 
ber of degrees from the meridian, towards 
the east or west : provided the declination be 
less than ninety degrees, or the reclination be 
less than the co-latitude of the place; and 
the axis of the sphere will be a gnomon, or 
stile, for the dial. But it cannot be a 
gnomon, when the declination is quite 90 
» degrees, nor when the reclination is equal to 
the co-latitude; because, in these two cases, 
[ the axis has no elevation above the plane of 
I the dial. , . 
And thus it appears, that the plane of 
[ every dial represents the plane of some great 
circle upon the earth ; and the gnomon the 
I earth’s axis ; whether it be a small wire, as in 
I the above figures, or the edge ot a thin plate, 
\ as in the common horizontal dials. 
The whole earth, as to its bulk, is but a 
I point, if compared to its distance trom the 
sun : and therefore, if a small sphere ot glass 
be placed upon any part ot the earth’s sur- 
face, so that its axis be parallel to the axis of 
the earth ; and the sphere have such lines 
upon it, and such planes within it, as above 
i described; it will shew the hours of the day 
J as truly as it it were placed at the eaitli s 
centre' and the shell of the earth were as 
transparent as glass. See tigs. 1 and 2. 
But because it is impossible to have a hol- 
] low sphere «t glass perfectly true, blown 
round a solid plane ; or if it' was, we could 
not get at the plane within the glass to set it 
j in any given position; we make use of a wire 
j sphere to explain the principles of dialing, 
j by joining twenty-four semicircles together 
J at the poles, and putting a thin Hat plate ol 
j brass within it. 
Dialing by the common terrestrial globe . — 
| A common globe, of twelve inches diameter, 
j has generally twenty-four meridian semi- 
} circles drawn upon it. It such a globe be 
elevated to the latitude of a given place, 
j and turned about until any one of these me- 
ridians cuts the horizon in the north point, 
where the hour of XII is supposed to be 
j marked; the rest of the meridians will cut 
the horizon at the respective distances ot all 
j the other hours from XII. I hen, if these 
I points of distance be marked on the horizon , 
and the globe be taken out ot the horizon, 
! and a Hat board or plate be put into its place, 
even with the surface ot the horizon ; and it 
straight lines be drawn from the centre of 
the board, to those points ot distance on the 
horizon which were cut by the twenty -tour 
meridian semicircles ; these lines will he the 
hour-lines of a horizontal dial for that lati- 
tude, the edge of whose gnomon must be in 
the very same situation that the axis of the 
globe was, before it was taken out of the 
horizon : that is, the gnomon must make an 
angle with the plane ot the dial, equal to the 
latitude of the place tor which the dial is 
made. 
It the pole of the globe be elevated to the 
co-latitude* of the given place, and any me- 
ridian be brought to the north point ot the 
horizon, the rest ot the meridians will cut the 
horizon in the respective distances of all the 
hours from XU, for a direct south dial, whose 
gnomon must make an angle with the plane 
* If the latitude he subtracted from 90 
degrees, the remainder is called the co-lati- 
tude, or complement of the latitude. See 
Geography. 
DIAL. 
of the dial, equal to the co-latitude of the 
place ; and the hours must be set the con- 
trary way on this dial, to what they are on 
the horizontal. 
But if your globe have more than twenty- 
four meridian semicircles upon it, you must 
take the following method for making hori- 
zontal and south dials by it. 
To construct a horizontal dial . — Elevate 
the pole to the latitude ot your place, anti 
turn the globe until any particular meridian 
(suppose the first) comes to the north point 
of the horizon, and the opposite meridian 
will cut the horizon in the south. I hen, set 
the hour-index to the uppermost XI l on its 
circle ; which done, turn the globe westward 
until fifteen degrees of the equator pass under 
the brasen meridian, and then the hour- 
index will be at I (tor the sun moves litteen 
degrees every hour) ; and the first meridian 
will cut the horizon in the number of degrees 
from the north point, that I is distant from 
XII. 'Burn on, until fifteen more degrees of 
the equator pass under the brasen meridian, 
and the hour-index will be then at II, and 
the lirst meridian will cut the horizon in the 
number of degrees that II is distant from 
XII: and so, by making fifteen degrees of 
the equator pass under the brus'en meridian 
for every hour, the lirst meridian of the 
globe will cut the horizon in t&e distances 
of all the hours from Xil to \ L w hich is 
just ninety' degrees ; and then you need go 
no farther; for the distances of XI; X, IX, 
VIII, VII, and VI, in the forenoon, are the 
same from XII, as the distances ot I, Jl, III, 
IV, V, and VI, in the afternoon: and these 
hour-lines continued through the centre, will 
give the opposite hour-lines on the other half 
of the dial : but no more of these lines need 
be drawn, than v. hat answer to the sun’s con- 
tinuance above the horizon ot your place on 
the longest day, which may be easily found. 
Thus, to make an horizontal dial for the 
latitude of London, which is about 51-§ de- 
grees north, elevate the north pole of the 
globe 514 degrees above the north point <?t 
the horizon, and then turn the globe, until 
the first meridian (which is that of London 
on the English terrestrial globe) cuts the 
north point of the horizon, and set the hour- 
index to XII at noon. 
Then, turning the globe westward until 
the index points successively to 1, II, HI, 
IV, V, and VI, in the afternoon; or until 
15, 30, 45, 60, 75, and 90 degrees of the 
equator pass under the brasen meridian, you 
will find that the first meridian of the globe 
cuts the horizon in the following numbers ot 
degrees from the north towards the east, 
viz° 1 1 1 , 244, 3S_i_ 534, 7 1J-, and 90 ; which 
are the respective distances ot the above 
hours from XII upon the plane of the hori- 
zon. 
To transfer these, and the rest of the hours, 
to a horizontal plane, draw the parallel right 
lines a c and b d (tig. 3) upon that plane, as 
far from each other as is equal to the intended 
thickness of the gnomon or stile ot the dial, 
and the space included between them will be 
the meridian or twelve-o’clock line on the 
dial. Cross this meridian at right angles with 
the six-o’clock line gh, and setting one foot 
of your compasses in the intersection a, as 
a Centre,, describe the quadrant g c with any 
500 
convenient radius or opening ol the com- 
passes ; then setting one foot in the inter- 
section b as a centre, with the same radius 
describe the quadrant,/ h, and divide each 
quadrant into ninety equal parts or degrees, 
as in the figure. r , , 
Because the hour-hnes are less distant 
from each other about noon, than in any 
other part of the dial, it is best to have the 
centres of these cjticidrants cit a little distance 
from the centre of the dial-plane, on the side 
opposite to XII, in order to enlarge the houi- 
distances thereabout under the same angles 
on the plane. 1 1ms, the centre oi the plane 
is at C, but the centres of the quadrants at a 
and b. 
Lay a ruler over the point h ; and keeping 
it there for the centre of all the afternoon 
hours in the quadrant f h ; draw the hour- 
line of I, through 111 degrees m the qua- 
drant; the hour-line of II, through 24| de- 
grees ; of III, through 38 T ‘ T degrees ; IV 
through 534, and V through 71 T V and bo- 
cause the sun rises about four m the morn- 
ing on the longest days at London, continue 
the hour-lines ot IV and V, in the after- 
noon, through the centre b to the opposite 
side of the dial. This done, lay the ruler to 
the centre a of the quadrant eg, and through 
the like divisions or degrees of that quadrant, 
viz. Ilf, 24L 33fL, 534, and 71J-, draw 
the forenoon hour-lines ot XI, X, IX, \ HI, 
and VII ; and because the sunsets not before 
ci<ditin the evening oil the longest days, con- 
tinue the hour-lines ot VII and V 111 in the 
forenoon, through the centre a, to \ II and 
VIII in the afternoon; and all the hour- 
lines will be finished on this dial; to which, 
the hours may be set, as in the figure. 
Lastly, through 514 degrees ot either qua- 
drant, and from Its centre, draw the right line 
a for the hypothenuse or axis of tiie gno- 
mon a g i\ and from g, let tall the perpen- 
dicular g i, upon the meridian line a i, and 
there will be a triangle made, whose sides 
are a g, gi , and i a. If a plate similar to this 
triangle be made as thick as the distance be- 
tween the lines a c and b d, and set upright 
between them, touching at a and b\ its hy- 
pothenuse a g will be parallel to the axis of 
the world, when the dial is tivdy r set, and 
will cast a shadow on the hour oi the day. 
The trouble of dividing the two quadrants 
may be saved, by means of a scale with a 
line of chords upon it : for if we extend the 
compasses from 0 to 60 degiees ot the line 
oi chords ; and with that extent, as a ladms, 
describe the two quadrants upon their respec- 
tive centres, the above distances may be taken 
with the compasses upon the line, and set 
off upon the quadrants. See Ixsirumesis 
MATHEMATICAL. 
To make an erect direct south dial . — ■ 
Elevate the pole to the co-latitude of your 
place, and proceed in all respects as above 
taught for the horizontal dial, from VI in the 
morning to VI in the afternoon ; only the 
hours must be reversed, as in figure 4, and 
the hypothenuse a g, ot the gnomon a gf, 
must make an angle with the dial-plane equal 
to the co-latitude of the place. As the sun 
can shine no longer on this dial, tnun horn, 
six in the morning until six hi the evening* 
there is no occasion for having any more than 
twelve hours upon it. 
To make an erect dud, dechmng from the 
