Seek for the given longitude in the equator, and bring that point to
the meridian; then count from the equator on the meridian the degree of
latitude given, towards the arctic and antarctic Pole, according as the
latitude is Northerly or Southerly, and under that degree of latitude
lies the _Place_ required.
PROB. II. _To find the Difference of Latitude
betwixt any two given Places._
Bring each of the places proposed successively to the meridian, and
observe where they intersect it, then the number of degrees upon
the meridian, contained between the two intersections, will be the
_Difference of Latitude_ required. Or, if the places proposed are on
the same side of the equator, having first found their latitudes,
subtract the lesser from the greater; but if they are on contrary sides
of the equator, add them both together, and the difference in the first
case, and the sum in the latter, will be the difference of latitude
required.
Thus the difference of latitude betwixt _London_ and _Rome_ will be
found to be 9¾ degrees; betwixt _Paris_ and _Cape Bona Esperance_ 83
degrees.
PROB. III. _To find the Difference of
Longitude betwixt any two given Places._
Bring each of the given places successively to the meridian, and see
where the meridian cuts the equator each time; the number of degrees
contained betwixt those two points, if it be less than 180 degrees,
otherwise the remainder to 360 degrees, will be the difference of
longitude required. Or,
Having brought one of the given places to the meridian, bring the
index of the hour circle to 12 o’clock; then having brought the other
place to the meridian, the number of hours contained between the place
the index was first set at, and the place where it now points, is the
difference of longitude in time betwixt the two places.
Thus the difference of longitude betwixt _Rome_ and _Constantinople_
will be found to be 19 degrees, or 1 hour and a quarter; betwixt
_Mexico_ and _Pekin_ in _China_, 240 degrees, or 9⅓ hours.
PROB. IV. _Any Place being given to find all
those Places that are in the same Latitude with the
same Place._
The latitude of any given place being marked upon the meridian, turn
the globe round its axis, and all those places that pass under the same
mark are in the same latitude with the given place, and have their
days and nights of equal lengths. And when any place is brought to
the meridian, all the inhabitants that lie under the upper semicircle
of it, have their Noon or mid-day at the same point of absolute time
exactly.
PROB. V. _The day of the Month being given;
to find the Sun’s Place in the Ecliptic, and his
Declination._
1. _To find the Sun’s Place_: Look for the day of the month given in
the kalendar of months upon the horizon, and right against it you’ll
find that sign and degree of the ecliptic which the Sun is in. The
Sun’s place being thus found, look for the same in the ecliptic line
which is drawn upon the globe, and bring that point to the meridian,
then that degree of the meridian, which is directly over the Sun’s
place, is the _Declination_ required; which is accordingly either North
or South, as the Sun is in the Northern or Southern signs. Thus,
_Sun’s Place._ _Declination._
Deg. Min. Deg. Min.
_April 23_ ♉ 3 00 12 32 N.
_July 31_ ♌ 7 51 18 20 N.
_October 26_ ♏ 2 49 12 28 S.
_January 20_ ♒ 0 49 20 07 S.
PROB. VI. _To rectify the Globe for the
Latitude, Zenith, and the Sun’s Place._
1. _For the Latitude_: If the place be in the Northern hemisphere,
raise the arctic Pole above the horizon; but for the South latitude you
must raise the antarctic; then move the meridian up and down in the
notches, until the degrees of the latitude counted upon the meridian
below the Pole, cuts the horizon, and the globe is adjusted to the
latitude.
2. _To rectify the Globe for the Zenith_: Having elevated the globe
according to the latitude, count the degrees thereof upon the meridian
from the equator, towards the elevated Pole, and that point will be the
zenith or the vertex of the place; to this point of the meridian fasten
the quadrant of altitude, so that the graduated edge thereof may be
joined to the said point.
3. Bring the Sun’s place in the ecliptic to the meridian, and then set
the hour index to XII at Noon, and the globe will be rectified _to the
Sun’s Place_. If you have a little mariner’s compass, the meridian of
the globe may be easily set to the meridian of the place.
PROB. VII. _To find the Distance between any
two given places upon the Globe, and to find all
those places upon the globe that are at the same
distance from a given place._
Lay the quadrant of altitude over both the places, and the number of
degrees intercepted between them being reduced into miles, will be the
distance required: Or, you may take the distance betwixt the two places
with a pair of compasses, and applying that extent to the equator,
you’ll have the degrees of distance as before.
_Note_, A _geographical mile_ is the ¹/₆₀th part of a degree; whereof
if you multiply the number of degrees by 60, the product will be the
number of geographical miles of distance sought; but to reduce the
same into _English_ miles, you must multiply by 70, because about 70
_English_ miles make a degree of a great circle upon the superficies of
the Earth.
Thus, the distance betwixt _London_ and _Rome_ will be found to be
about 13 degrees, which is 780 geographical miles.
If you rectify the globe for the latitude and zenith of any given
place, and bring the said place to the meridian; then turning the
quadrant of altitude about, all those places that are cut by the same
point of it, are at the same distance from the given place.
PROB. VIII. _To find the angle of position of
Places, or the angle formed by the meridian of one
Place, and a great circle passing through both the
Places._
Having rectified the globe for the latitude and zenith of one of the
given places, bring the said place to the meridian, then turn the
quadrant of altitude about, until the fiducial edge thereof cuts the
other place, and the number of degrees upon the horizon, contained
between the said edge and the meridian, will be the angle of position
sought.
Thus, the angle of position at the _Lizard_, between the meridian of
the _Lizard_ and the great circle, passing from thence to _Barbadoes_
is 69 degrees South-Westerly; but the angle of position between the
same places at _Barbadoes_, is but 38 degrees North-Easterly.
_SCHOLIUM_
The angle of position between two places is a different thing from
what is meant by the bearings of places; the _Bearings_ of two places
is determined by a sort of spiral line, called a _Rhumb Line_, passing
between them in such a manner, as to make the same or equal angles
with all the meridians through which it passeth; but the _angle_ or
_position_ is the very same thing with what we call the azimuth in
astronomy, both being formed by the meridian and a great circle passing
thro’ the zenith of a given place in the heavens, then called the
azimuth, or upon the Earth, then called the angle of position.
From hence may be shewed the error of that geographical paradox, _viz._
If a place A bears from another B due West, B shall not bear from A
due East. I find this paradox vindicated by an author, who at the
same time gives a true definition of a rhumb line: But his arguments
are ungeometrical; for if it be admitted that the East and West lines
make the same angles with all the meridians through which they pass,
it will follow that these lines are the parallels of latitude: For
any parallel of latitude is the continuation of the surface of a
_Cone_, whose sides are the radii of the sphere, and circumference of
its base the said parallel; and it is evident, that all the meridians
cut the said surface at right (and therefore at equal) angles; whence
it follows, that the rhumbs of East and West are the parallels of
latitude, though the case may seem different, when we draw inclining
lines (like meridians) upon paper, without carrying our ideas any
farther.
PROB. IX. _To find the_ Antœci, Periœci, _and_
Antipodes _to any given place._
Bring the given place to the meridian; and having found its latitude,
count the same number of degrees on the meridian from the equator
towards the contrary Pole, and that will give the place of the
_Antœci_. The globe being still in the same position, set the hour
index to XII at noon, then turn the globe about ’till the index points
to the lower XII; the place which then lies under the meridian, having
the same latitude with the given place, is the _Periœci_ required. As
the globe now stands, the _Antipodes_ of the given place are under
the same point of the meridian, that its _Antœci_ stood before: Or,
if you reckon 180 degrees upon the meridian from the given place,
that point will be the _Antipodes_. Let the given place be _London_,
in the latitude of 51½ degrees North, that place which lies under the
same meridian and the latitude 51½ degrees South, is the _Antœci_;
that which lies in the same parallel with _London_, and 180 degrees of
longitude from it, is the _Periœci_, and the _Antipodes_ is the place
whose longitude from _London_ is 180 degrees, and latitude 51½ degrees
South.
PROB. X. _The Hour of the Day at one place
being given; to find the correspondent Hour (or
what o’Clock it is at that time) in any other
place._
The difference of time betwixt two places is the same with their
difference of longitude; wherefore having found their difference
of longitude, reduced into time (by allowing one hour for every
15 degrees, _&c._) and if the place where the hour is required
lies (Easterly/Westerly) from the place where the hour is given,
(add/subtract) the difference of longitude reduced into time (to/from)
the hour given; and the sum or remainder will accordingly be the hour
required. Or,
Having brought the place at which the hour is given to the meridian,
set the hour index to the given hour; then turn the globe about until
the place where the hour is required comes to the meridian, and the
index will point out the hour at the said place.