G E O G R A P H Y. 
to the latitude, it will pafs through the nadir.—“For any 
liar or planet wliich paifes through D, Plate II. fig- 3 . 
the zenith, in its apparent diurnal revolution, mull dc- 
fcribe the circle D O ; whence its diftance from the equa¬ 
tor or declination will be E D. Btit E D is the dillaiice 
of the zenith from the equatbr, which, becaufe the ele¬ 
vation of the ; quator is equal to the complement of la- 
iitude, fo it is equal to the latitude. In like manner 
the reverie nuiy be fhewn. 
42. A heavenly body feen from any place, will never 
fet, from the diurnal motion of the earth, if the comple¬ 
ment of its declination towards the elevated pole be 
equal to, or lefs than, the latitude of the place : and it 
will never nlc, if the complement of its declination to¬ 
wards the deprefled pole be equal to, or lefs than, the 
latitude. Let P D, Plate II. fig-3, which is tire com¬ 
plement of declination of a body at D, and alfo the dif¬ 
tance ot the body at D Irom the pole, be equal to PO, 
the elevation ot the pole, or the latitude; it is manifell, 
that the body at its lowelt deprellion v/ill be no farther 
from the pole than the liorizon is, that is, will never 
be below it. In like manner the reverfe may be Hiewn. 
J-lence the latitvide of a place may be found, by obferv- 
ing the greatcft and lead altitude of a fixed Itar that ne¬ 
ver lets.—Let A, in the abovementioned tig. 3, be a ftar 
near the north pole, which in its daily motion defcribes 
th.e circle A B, without fetting. A quadrant being placed 
in the plane of the meridian, or along the meridian line, 
obferve its altitude when it is at A, and afterwards when 
at B; the difference of thefe altitudes isAB. And, 
lines tlie liar, in its revolution about the pole, is always 
at equal diftances from it, if A B be bifedled in P, this 
point will be the pole, and confequently PO will be 
the elevation of tiie pole. But, fince tlie lengths of the 
arcs AO, BO, have been found by obfervations, their 
diiTerence AB, and the half of tills difference, A P or 
B P, is known : and P O is equal to B P -p B O, or to 
AO — PA. Wiience the elevation of the pole, that is, 
the latitude, is equal to the fiim of the lealt altitude 
added to half the difference of tlie greateft and leaff alti¬ 
tude, or it is equal to the remainder arifing from fub- 
traiiting half the difference of the greateff and leaff alti¬ 
tudes from the greatelf altitude. 
Or, tlie latitude may be found from the fun’s meridian 
Rltitude and declination. If tlie fun’s meridian altitude, 
found by a quadrant, be CH, this altitude is equal to 
the fun’s declination C E, added to the elevation of tlie 
equator EH. 'I'herefore, if C E, the declination towards 
the elevated pole, be taken from the meridian altitude, 
tire remainder EH will be the elevation of the equator. 
But fince the elevation of tlie equator is the complement 
of latitude, the latitude is the complement of the eleva¬ 
tion ot the equator. This elevation, tiierefore, bein.o- 
found, the latitude of the place is known_Or, tlie hu 
titude of a place is equal to the fun’s meridian zenith, 
diftance, added to his declination, when he palfes the 
meridian between the zenitli and the equator. 
Example i. To find the latitude from an obfervation 
of the fun’s altitude, Auguft 7, 1776, at the oblervatory 
at Cambridge. 
Auparent meridian altitude of tlie fun’s 7 o 
lower limb.5 53° .46 8 
Sun’s apparent femi-diameter, from the f 
Ephemeris - - - - - .^°^5 50 
Apparent altitude of tlie fun’s centre - 54 i 
Dedudf for refraction - . - - o o 41 
.Altitude of the fun’s centre - - - 54 i Tj 
Zenitli diftance of tlie fun’s centre is found 7 
by fubtraCting the laft altitude from 90° i 
Add the fun’s declination . .16 13 57 
Latitude of the place - - 12 4^ 
Ex. 2. On the ift of December, 1793, the obferved 
VoL, Vlll. No. 50^. 
50' S. 
10 N. 
27 S. 
13 N. 
meridian altitude of Siritlis' was 59® 50'; required the 
latitude. 
Obferved altitude - - 59^ 
Therefore, Zenith diftance - - - 30 
Declination of Sirius - - 16 
Confequently, the latitude required - 13 
43. The two tropics, and two polar circles upon the 
furface of the earth, divide it into five parts called zones: 
the torrid zone lies between the two tropics; tlie tempe¬ 
rate zones between the tropics and polar circles ; and the 
frigid zones between the polar circles and tlie poles. 
44. At any place in the torrid zone the fun is vertical 
twice every year.—The fun in palling from the equator 
to tlie tropic of Cancer, 23^ degrees from the equator, 
lias every northern declination from o to 23^ ; and every 
place between the equator and the tropic of Cancer has 
i'ome northern latitude between o and 23^: therefore, in 
fome part of its courfe from the equator to the tropic 
ot Cancer, the fun mult have a declination equal to the 
latitude of every place between the equator and the 
tropic : wlience it mult be once in the zenith of every 
fucii place in its courfe towards the tropic of Cancer. 
For tlie fame reafon it iiiuft be once in the zenith of 
every fuch place in its courfe from the tropic to the 
equator. The like alfo happens on the fouthern fide of 
tile equator. 
43. The fun is vertical once every year at the places 
whicli lie in the tropics.—For the fun’s declination is 
then 23I degrees, equal to the latitude of the tropics. 
46. At the polar circles, the loiigeft day, and the longeft 
night, are twenty-fo.ur hours.—When the fun is in the tro¬ 
pic of Cancer, the complement of its doclinatioii towards 
the elevated pole is 66| degrees, equal to the latitude 
of the arctic poJar circle : on this day, therefore, the 
fun will not fet. Wlien the fun is in the tropic of Ca¬ 
pricorn, the complement of its declination towards the 
depreded pole will be 65 ^ degrees, equal to the latitude 
of the arctic pole ; whence the fun will not rife during 
that day. The fame happens with refpect to the ant¬ 
arctic circle. 
47. The longeft day, and the longeft night, are each 
of them more than twenty-four hour^, within the frigid 
zone. —For, while the fun’s complement of declination 
towards the elevated pole is lefs than tlie latitude of the 
place, the fun will not fet: while the complement of de¬ 
clination towards the depreded pole is lefs than the lati¬ 
tude of the place, it will not rife : but this miift be the 
cafe with refpedl to every place within the frigid zones, 
in fome part of the fun’s courfe towards the tropics. 
48. The lull is never vertical to any place in either of 
the temperate zones.—For the latitude of all places in 
the temperate zone, is greater than any declination of 
thelun. 
49. The longeft day, and the longeft night, in any part 
of the temperate zones, are lels than twenty-four hours; 
and the days and nights will be longer, the nearer the 
place is to the polar circles.—For the complement of 
the fun’s declination can never be lefs than, or equal to, 
the latitude of any place in tlie temperate zones; whence 
the fun will rife and fet every day within thefe zones. 
But the farther any place is removed from the equator, 
the nearer the latitude approaches to an equality with 
the complement of the fun’s greateft declination, when 
the day is twenty-four hours; that is, at the polar cir¬ 
cles.—.See Astronomy, vol. 11 . p. 369. 
30. At dift'ereut places, the hour of the day differs in 
proportion to the difference of longitude ; 15 degrees of 
longitude making the difl'erence of one hour in time ; 
13', one minute of time, 13"; one fecond of time; and 
it is feen at any given place fooner than at places w,hicli 
lie to the weft of it, and /aier-than at places which lie to 
the eaft of it.-—The fun in its daily apparent motion,^ 
which is from eaft to weft, luiift arrive at the meridian of 
anv given place, as London, fooner than it will arrive 
4 X at 
