D I A 
D I A 
To find the altitude of an?/ place by obser- 
tted ion . — The latitude of any place is equal 
to the elevation of the pole above the hori- 
zon of that place. Therefore it is plain, that 
if a star was lixed in the pole, there would 
be required to find the latitude, but to take 
the altitude of that star with a good instru- 
ment. But although there is no star in the 
pole, yet the latitude may be found by taking 
the greatest and least altitude of any star that 
never sets: for if half the difference between 
these altitudes be added to the least altitude, 
or subtracted from the greatest, the sura or 
remainder will be equal to the altitude of the 
poh' at the place of observation. 
But because the length of the night must 
be more than 12 hours, in order to have two 
such observations ; the sun’s meridian alti- 
tude and deciinatipn are generally made use 
of for finding the latitude, by means of its 
complement, which is equal to the elevation 
of the equinoctial above the horizon ; and if 
this complement be subtracted from 90 de- 
grees, the remainder will be the latitude, 
concerning which the following rules seem to 
take in all the various cases. 
1. If the sun has north declination, and is 
on the meridian, and to the south of your 
place, subtract the declination from the me- 
ridian altitude (taken by a good quadrant), 
and the remainder will be the height of the 
equinoctial or complement of the latitude 
north. 
Example. 
Suppose the sun’s meridian 
altitude 42® 20' south 
And his declination, subt, 10 15 north 
Remains the complement of 
the latitude 32 5 
Which subtract from 90 0 
And the rem. is the latitude 57 55 north. 
2. If the sun has south declination, and is 
southward of vour place at noon, add the 
declination to the meridian altitude; the 
gum, if less than 90 degrees, is the comple- 
ment of the latitude north ; but if the sum 
exceeds 90 degrees, the latitude is south; 
and it 90 be taken from that sum, the re 
mainder will be the latitude. 
Examples. 
Sun’s meridian altitude 
60® 30' north 
Sun’s declination, add 
20 
10 north 
Complement of the latitude 
80 
40 
Subtract from — 
90 
0 
Remains the latitude 
9 
20 south. 
Sun’s meridian altitude 
70° 20' north 
Sun’s declination, add — 
23 
20 north 
The sum is — 
93 
40 
Prom which subtract 
90 
0 
Remains the latitude 
3 
40 north. 
The sun’s meridian altitude 
65° 
1 O' south 
The sun’s declination, add 
15 
30 
south 
Complement of the latitude 
80 
40 
Subtract from 
90 
0 
Remains the latitude 
9 
20 north. 
The sun’s meridian altitude 
80° 40’ 
south 
The sun’s declination, add 
20 
10 
south 
The sum is — 
100 
50 
From which subtract 
90 
0 
Remains the latitude 
10 
50 
south. 
D I A 
Examples, 
4. If the sun has south declination, and is 
north of your place at noon, subtract the de- 
clination from the north meridian altitude, 
and the remainder is the complement of the 
latitude south. 
Example. 
Sun’s meridian altitude 
Sun’s declination, subtract 
50° 30’ north 
20 10 south 
Complement of the latitude 32 20 
Subtract this from 90 0 
And the rem. is the latitude 57 40 south. 
5. It the sun has no declination, and is 
south of your place at noon, the meridian 
altitude is the complement of the latitude 
north : but if the sun be then north of your 
place, his meridian altitude is the comple- 
ment of the latitude south. 
Examples, 
Sun’s meridian altitude 38 3 * * * * * 9 30' south 
Subtract from 90 0 
Remains the latitude 
Sun’s meridian altitude 
Subtract from 
51 30 north. 
38° 30' north 
90 0 
Remains the latitude 5 1 30 south. 
6. If you observe the sun beneath the 
pole, subtract his declination from 90 degrees, 
and add the remainder to his altitude ; the 
sum is the latitude. 
Example. 
Sun’s declination — 20® 30t 
Subtract from — . 90 0 
Remains — — - 69 30 > 
Sun’s altitude below the pole 10 20) 
add 
3. If the sun has north declination, and is 
on the meridian north of your place, add the 
declination to the north meridian altitude ; 
the sum,. if less than 93 degrees, is the com- 
plement of the lat itude sout h : but if the sum 
is more than 90 degrees, subtract 90 from it, 
and the remainder is the latitude north. 
Vol. 1. 
The sum is the latitude 79 50. 
Which is north or south, according as the 
sun’s declination is north or south: for when 
the sun has south declination, lie is never seen 
below the -north pole ; nor is he ever seen 
below the south pole, when his declination 
is north. 
7. If the sun be in the zenith at noon, and 
at the same time lias no declination, you are 
t lien under the equinoctial, and so have no 
latitude. 
8. If the sun be in the zenith at noon, and 
has declination, the declination is equal to 
the latitude, north or south. These tw< 
cases are so plain, that they require no ex 
amples. 
DIALECTICS, dialectica, in the literary 
history of the antients, that branch of logf< 
which taught the rules and modes of reason 
' ins. 
51 ' 
DIALLAGE, in mineralogy, called also 
resplendent hornblende. This stone was 
called smaragdite by Saussure, from the re- 
semblance it has to emerald. It is never 
crystallized. Its texture is foliated, and it is 
easily divided into plates. The laminae are 
inflexible, and the' specific gravity is 3. The 
colour in some cases is line green; in others 
it has the grey colour, and metallic lustre, of 
mica: it assumes all the shades of colour be- 
tween these two extremes. According to 
Yauquelin, it. is composed of 
50.0 silica 
13.0 lime 
1 1.0 alumina 
7.5 oxide of chromium 
6.0 magnesia 
5.5 oxide of iron 
1 .6 oxide of copper. 
94.2 
DIALLING, the art of constructing all 
manner of dials. See Dial. 
Having described the most useful dials 
under the word Dial, we now proceed to 
explain the philosophical principles of the art 
of dialling. In order to this, therefore, we 
are to consider, that as the time which passes 
between any meridian’s leaving the sun, and 
returning to it again, is divided into 24 hours, 
so it we conceive a sphere to be constructed 
with twenty-four of these meridians, the sun 
wili orderly come upon one of them at the 
beginning of every hour. Such a sphere may 
be represented by the figure PDSB (fig. 
it), where the several meridians are repre- 
sented by P 1 S, P2S, P 3 S, and so on to 
twenty-four in all; since these meridians di- 
vide the equinoctial into twenty-four equal 
parts, each part will contain just 15°, because 
15x24=360, the whole circle; and since 
all the meridians pass through the poles of 
the world, the planes of those meridians all 
intersect each other in one common line P S, 
which is the axis of the sphere, therefore the 
said axis P S is in the plane of each of the 
twelve meridians. Suppose Z to be the 
zenith of any place, and DWBE the plane 
of the horizon fixed within the sphere, con- 
structed with the twelve meridians, 1, 1 ; 
2,2; 3,3; 4, 4 ; .&c. then will the axis of 
the sphere PS passthrough the centre of the 
plane at N ; so that one half N P will be 
above the plane, and the other half N S be- 
low it. Suppose now this dialling-sphere to 
be suspended by the point Z, and moved 
about so as to have the points D and B ex- 
actly in the south and north points of the 
horizon, and E and \V in (he east and west 
points, then will the sphere have a situation 
every way similar to that of the earth and 
heavens with respect to the given place, and 
the axis ot the sphere to that of the earth, 
l he sun, therefore, sliming on such a sphere, 
will be attended with all the same incidents, 
and produce all the same effects, as would 
happen it the said sphere were at the centre 
of the earth, or the centre N of the sphere 
coincided with the centre of the earth, be- 
cause the distance between the surface and 
centre of the earth is insensible at the dis- 
tance of the sun. Now it is evident, as the 
sun revolves about such a sphere, it will 
every hour be upon one half or other of the 
twelve hour-circles, viz. from midnight to 
-noon, it will be on those parts of the circles 
[which are in the eastern hemisphere ; anti 
3 T 
