PROPOSITION V.

The Latitude of a Place is equal to the Elevation of the Pole above the Horizon of that Place; which is thus demonftrated.

LET C be the Center of the Earth, (Fig. 30.) and L the Place brought to the Top of the Globe or Zenith, and P the Pole, HPLZ will be the Meridian, HZ á Diameter of the Horizon, PH the Elevation of the Pole, and QT the Diameter of the Equator, where the Meridian and Equator cut one another; then PQ will be a Quadrant, or ninety Degrees, P being the Pole of the Equator; and alfo LH will be ninety Degrees, L'being the Pole of the Horizon; then LH is equal PQ, and LP being taken from both, what remains, PH, LQ, will be equal.

COROLLARY

THE Latitude of the Place being given, there is known the Elevation of the Pole.

PROPOSITION VI.

Having the Latitude of one Place, to find all the other Places that have the fame Latitude.

ON the Globe: bring the Place to a Degree on the brass Meridian, and placing a Pencil there, turn the Globe, and the Pencil will defcribe a Circle paffing thro' all the Places of the fame Latitude.

AND in the Maps: draw a Line thro' the Place given that fhall be parallel to the Equator, and it will go thro' all the Places of the fame Lati

tude,

tude. But if it be a curvilinear Map, defcribe a Circle (whofe Center is the Pole of the Map) that fhall pass thro' the Place given; and find, as before, the feveral Places the Circle paffes through. But if not the Place, but the Latitude is given, extend the Compaffes from the Pole to that Degree of Latitude on the Side of the Map, and defcribe a Circle.

PROPOSITION VII.

To find a Meridian Line on a given Plane.

1. THERE are feveral ways; the easiest is to ufe a Magnetic Needle which will point North and South: but because in many Places it declines from the North, as we fhall fhow, it will not do it accurately; but if the Declination of the Needle be known, as it is in the chief Places, it may be found accurately enough, drawing firft the Meridian, which the Needle fhows, and taking the Degrees of the Declination with the Compaffes, fet them to the Eaft; if the Declination be weftward; and, vice verfâ; then draw a Line from the Point they reach to the Center, and it will be a true Meridian.

THERE is no need of this Pains if you have a Mariner's Compafs, wherein there is allowance made for all Declination in that Place for which 'tis made; for they that make the Inftrument, put the Flower de Luce, which is the Sign of the North not just above the Needle; but fo many Degrees from it as the Declination is.

2. BUT the Meridian Line is found better by the Stars. First, when the Sun fhines, fet up a Pin perpendicular to a Plane at twelve o'Clock, and the Shadow will fhow the Meridian. But

becaufe

SECT. VI. because the Hour is not exact enough; this way

is not perfectly true.

3. SET a Pin perpendicular to a Plane in the Forenoon, and mark the length of the Shadow; and in the Afternoon mark again, when the Shadow is of the fame Length, and draw a Line to the two Extremities of the Shadow, and bifect it by a perpendicular Line; which will be a meridian Line.

4. IF the Latitude of the Place be known, and the Sun's Altitude be taken, the meridian Line may be found by the Globe, thus: Draw a Line first on a Plane, and make it the diameter of a Circle, and the Line in which the Sun feems to be; then the Pole being elevated according to the Latitude; and the Sun's Place in the Ecliptic marked; and a Quadrant applied to the Top of the Globe, with the Sun's Altitude on it marked; then move the Globe and Quadrant both, 'till the Sun's Place and Degrees on the Quadrant meet; then see how many Degrees on the wooden Ho-. rizon between the brafs Meridian and the Quadrant, and cut off fo many on the Circle on the Plane, beginning at the end of the Diameter, either to the East or Weft, as the obfervation was made before or after noon, and draw a Line from the end of the Arch cut off, to the Center, and it will be a meridian Line. But it will be easier to obferve the Line in which the Sun is feen either when rifing or fetting; and bringing the Sun's Place on the Globe to the wooden Horizon, fee how many Degrees between it and the North or South, and turn the Line on the Plane fo many Degrees about, and it will be a meridian Line.

PRO

PROPOSITION VIII.

To place the Globe fo as the brass Meridian may be in the meridian Line.

FIND a meridian Line on the Plane, under the Globe, and turn it about 'till the brafs Meridian be just above it. But this is done eafier, if there be a Mariner's Compafs under it, which fhows the North and South Line.

THUS may Maps be placed alfo due North and South; of which there is ufe in Navigation.

PROPOSITION. IX.

To find the Latitude of a Place by the Sun or Stars.

THO' the Latitude is on the Earth, yet it cannot be found without the Sun or Stars.

1. OBSERVE how far the Sun is above the Horizon, or it's Distance from the Zenith at twelve o'clock; then fubftract the Sun's Distance from the Equator from the Zenith Distance, if the Sun be on the South Side of the Equator; but add it if on the North Side; and you have the Latitude. The Sun's Distance from the Equator, or the Declination, may be had from it's Place in the Ecliptic; or from Tables; or from the Globe, bringing the Place to the Sun under the brafs Meridian, then counting how far it is from the Equator.

2. IF the Sun be rifing or fetting you may find the Latitude by the Globe. Find the Point the Sun is then in, by the Sea-Compafs, which Mariners easily do, and find alfo the fame Point on the wooden Horizon; and having the Sun's Place in the Ecliptic, then raise the brass Meri

dian in the North of the wooden Horizon, or deprefs it 'till the Sun's Place fet or rife on that fame Point in the Horizon; and then fee how much the Pole is elevated, and it will be the Latitude of the Place.

Note, This Method will not do in the time of the Equinoxes, when the Sun is in the beginning of Aries or Libra; for then the Sun fets and rifes in all Places in one Point, i. e. West and Eaft.

3. TAKE the Altitude of the Sun at twelve o'Clock by the help of the Length of a Style fet perpendicular, and of it's Shadow, by which may be found the Angle at the Termination of the Shadow in the Triangle (Fig. 31.) ABC, that is, the Angle BCA; for as A B is to A C, fo is the Sine of go to the Tangent of the Angle ABC, the Sun's Altitude; from which may be found the Latitude of the Place, as in the first Method; and if the obfervation be made at the Equinox, then the Sun's Distance from the Zenith is the Latitude.

THUS Pliny writes, Chap. lxxii Lib. 2. that Rome was found in Latitude 41 degr. 25 min. and Carthage in Latitude 32 degr. 13 min.

4. IN the Night-time, when the Stars are feen, if we take with an Inftrument the Altitude of a Star in the Meridian, and know, from Tables, it's Declination; the Latitude may be found as if the Star were the Sun; as in the firft Method : but if the Star be between the Pole and the Ho rizon, and the Declination North, the Complement of the Declination is to be added to the first Altitude, and it gives the Latitude.

IF the Star be between our Zenith, and the South Part of the Horizon; and the Declination North; add the Declination to the Complement