514 
D I A 
D I A 
D I A 
from noon to midnight, it will pass over all 
those in the western. It is also farther evi- 
dent, that while the .sun is in the eastern he- 
misphere, it will be first below and then above 
the plane of the horizon, and vice versa 
on the other side. Again, when the sun 
is upon any of these hour-circles, by shining 
upon the axis it causes it to cast a shadow 
oft the contrary side, on the plane of the ho- 
rizon, on the lower or upper surface, as it is 
below or above the said plane. This shadow 
of the axis will be precisely in the line in 
which the plane of the hour-circle would in- 
tersect the plane of the horizon : if, there- 
fore, lines were drawn through the centre N, 
joining the points on each side the plane 
where the hour-circles touch it, as 4N4, 5 IS 5, 
6N6, &c. the shadow of the axis would fall on 
those lines at the beginning of each respec- 
tive hour, and thereby indicate the hour- 
circle the sun is in for every hour of the day. 
These lines are properly called hour-lines, 
and among the rest that which represents the 
hour of 12 at noon is NB, half the meridian 
line DB ; whence it appears that the hour- 
lines IS’l, N2, N3, &c. which serve for the 
afternoon, lie on the east side of the plane, 
and are numbered from the north to the east ; 
and on the contrary. 
It also appears, that as the sun’s altitude 
above the plane is greater or less, the num- 
ber of hour-circles the sun will possess above 
the horizontal plane will be also greater or 
less. Thus when the sun is at S in the equi- 
noctial, its diurnal path for that day being the 
equinoctial circle itself fEEQW, it is plain, ! 
since the arch TIE = EQ, the sun will apply j 
to six hour-circles below the horizon, and to 
six above it, in each half of the day ; and 
consequently that on this day the shadow will 
occupy but 12 of the hour-lines on each sur- 
face of the plane, beginning and ending at ! 
six. But when the sun is in the tropic of j 
Cancer, its diurnal path for that day being j 
the tropic itself, TCRF, it is manifest the 
sun in the forenoon ascends above the plane 
in passing between the hour-circles of 3 and 
4 in the morning, and descends below it in 
the afternoon between the hours of 8 and 9 : 
therefore on the summer tropic the shadow 
will pass over 16 of those hour-lines. On the 
contrary, when the sun is in the winter tropic 
at O, its path being then OGIII, it rises above 
the plane between 8 and 9, and leaves it be- 
tween 3 and 4. 
From what has been said it is evident, that 
if the circles be supposed removed, and only 
the horizontal plane remains, with the half of 
the axis above it in the same position as be- 
fore, then should we have constituted a ho- 
rizontal dial, every way the same with those 
in common use-, with only the addition of a 
smbslile to render the stile very firm. Hence 
appears the reason why the gnomon or stile 
in those dials in our latitude is always direct- 
ed to the north pole, and always contains 
such an angle PNB, with the hour of 12 line 
NB, as is equal to ihe latitude of the place. 
Lastly, the reason appears why the number 
of hour-lines on these dials exceeds not 1 6, and 
tiiey are all drawn from 6 to 12 and 6 again 
on the northern part, the rest on the south- 
ern; am ; why the hour-line of 6 lies directly 
east and west, as that of 12 does north and 
south. 
Dialling-globe, an instrument of brass 
or wood, with a plaive lilted to the horizon. 
and an index, so contrived as to give a clear 
illustration of the principles on which dials 
are made. 
Dialling-lines or scales, are gradu- 
ated lines placed on rulers or the edges of 
quadrants and other instruments, to expedite 
the construction of dials. These are, 1. A 
scale of six hours, which is only a double tan- 
gent, or two lines of tangents, each of 45°, set 
together in the middle, and equal to the 
whole line of sines, with the declination set 
against the meridian altitudes in the latitude 
of the place. 2. A line of latitudes, which is 
fitted to the hour-scale, and is made by this 
canon ; As the radius : to the chord of 90° 
: : so are the tangents of each respective de- 
gree of the line of latitudes : to the tangents 
of other arcs. And then the natural sines of 
these arches are the numbers, which taken 
from a diagonal scale of equal parts, shall 
graduate the divisions of the line of latitudes 
to any radius. The lines of hours and lati- 
tudes are general, for pricking down all dials 
with centres. 
The other scales are particular, and give 
the several requisites for all upright declining 
dials by inspection. They are, 1. A line of 
chords. 2. A line for fhe substile’s distance 
from the meridian. 3. A line for the stile’s 
height. 4. A line of the angle of 12 and 6. 
5. A line of inclination of meridians. See 
Dial. 
Dialling-sphere, an instrument made 
of brass, with several semicircles sliding over 
each other upon a moveable horizon, serving 
to demonstrate the nature of spherical tri- 
angles, as well as to give the true idea of 
drawing dials on all sorts of planes. 
DIALIUM, a genus of the monogynia 
order, in the cliandria class of plants. The 
corolla is pentapetalous ; no calyx; the sta- 
mina at the upper side of the receptacle. 
There is one species, a tree of the East In- 
dies. 
DIALOGISM, in rhetoric, is used for the 
soliloquy of persons deliberating with them- 
selves, as the following of Juno, in the first 
iEneid of Virgil: 
Mene incepto desistere vjetam, 
Nec posse Italia Teucrorum avertere regent,, 
Quippe vetor i'atis? Ike. 
In this sense it is distinguished from dia- 
logue. 
DIAMETER, in geometry, a right line 
passing through the centre of a circle, and 
terminated at each, side by the circumfer- 
ence thereof. The chief property of the di- 
ameter is, that it divides the circumference 
of a circle into two equal parts : hence we 
have a method of describing a semicircle 
upon any line, assuming its middle point for 
the centre, lire diameter is the greatest of 
all chords. For finding the ratio of the dia- 
meter to the circumference, see Circle. 
How to find the diameter of shot or shells. 
— For an iron ball, whose diameter is given, 
supposing a nine-pounder, which is nearly 
four inches, say the cube foot 2.08 (of nine 
pounds), is to lour inches, as the cube root of 
the given weight, is t6 the diameter sought. 
Or, if 4 be divided by 2.08, the cube root of 
9, the quotient 1 923 will be the diameter of 
a one-pound shot ; which being continually 
multiplied by the cube root of the given 
weight, gives the diameter required. Or by 
logarithms much shorter, thus: If the loga- 
rithm of 1.923, which is .283979, be con- 
stantly added to the third part of the loga- 
rithm of the weight, the sum will be the loga- 
rithm of the diameter. Suppose a shot to 
weight 24 pounds : add the given logarithm 
.283979 to .460070 the third part of the 
logarithm 1.38021 12 of 24, the sum .7440494 
will be the logarithm of the diameter of a shot 
weighing 24 pounds, which is 5.5468 inches. 
If the weight should be expressed by a 
fraction, the rule is still the same : for in- 
stance, the diameter of a 1-| pound ball, or 
1, is found by adding the logarithm .2839793 
found above, to .0586971 one-third of the 
logarithm of §• ; the sum .3426764 will be the 
logarithm ot the diameter required, i. e, 
2.2013 inches. 
As the diameter of the bore, or the caliber 
of the piece, is made l-20th part larger than 
that of the shot, according to the -present 
practice, the following table is computed. 
Diameters of the shots and calibers of English guns. 
lb. 
0 
1 
O 
3 
4 
5 
6 
7 
8 
9 
0 
0 
1 .923 
2.423 
2.775 
3.053 
3.288 
3.498 
3.679 
3.846 
4.000 
Diarn. 
0 
2.019 
2.544 
2.913 
3.204 
3.568 
3.668 
3.861 
4.038 
4.200 
Calib. 
1 
4.143 
4.277 
4.403 
4.522 
4.635 
4.743 
4.846 
4.945 
5.040 
5.131 
Diam. 
4.349 
4.4S0 
4.623 
4.74S 
4.866 
4.981 
5.088 
5.192 
5.292 
5.368 
Calib. 
2 
5.220 
5.305 
5.388 
5.409 
5.547 
5.623 
5.697 
5.769 
5.839 
5.908 
Diam. 
5.480 
5.570 
5.661 
5.742 
5.824 
5.893 
5.982 
6.057 
6.129 
6.203 
Calib. 
3 
5.975 
6.041 
6.105 
6.168., 
6.230 
6.290 
6.350 
6.408 
6.465 
6.521 
Diam. 
6.273 
6.343 
6.410 
6.475 
6.541 
6.604 
6.666 
6.707 
6.788 
| 6.846 
Calib. 
4 
6.576 
6.631 
6.684 
6.737 
6.789 
6.640 
6.890 
6.940 
6.989 
' 7.037 
Diam. 
6.904 
| 6.962 
7.018 
7,076 
7.128 
7.182 
| 7.234 
7.287 
I 7.338 
7.383 
Calib. 
