AND laftly, it can never be vertical to the Places in the Temperate Zone, because no parallel defcribed by the Sun goes over thefe Places; and fo it is as to the Frigid Zones.

PROPOSITION V.

The Sun doth not fet nor rife for fome Day's to thofe in the Frigid Zones; and the more thofe Days are, the nearer the Place is to the Pole; fo that at the Pole it fets not for half a Year, and rises not all that time and thofe in the very arctic and antarctic Circle have one Day wherein the Sun fets not, and another wherein it rifes not but at other times it rifes and sets.

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TAKE a Place in the Frigid Zone, and elevate the Pole according to it's Latitude, and applying a Piece of Chalk, or a Pencil, to the North of the Horizon; that is, next the Pole; describe therewith a Parallel, by turning the Globe round, which will cut the Ecliptic in two Points, into which, and the intermediate Points, when the Sun comes it fets not: for all the Parallels thro thefe Points keep above the Horizon in the Rotation of the Globe. And if applied to the oppofite Notch, and a parallel Circle be defcribed, it will pafs thro' two Points of the Ecliptic; into which and the intermediate Points, when the Sun comes it rifes not above the Horizon; but it will be otherwife if the Place be taken in the other Frigid Zone. And fo as to thofe Places in the arctic and antarctic Circle, if the Globe be elevated to fix

ty fix Degrees thirty Minutes, and the Globe revolved, the first of Cancer welt then just touch the Horizon, and not fet; and fo will the first of Capricorn without rifing above it; but in the other Degrees of the Ecliptic it will fet and rife.

PROPO

PROPOSITION VI.

The Sun rifes and fets every Day to all Places in the Temperate and Torrid Zones.

TAKE any Place in thefe Zones, and elevate the Pole to it's Latitude, fo as the wooden Horizon may be the Horizon of that Place; then turning the Globe, you'll fee all the Points of the Ecliptic rife and fet and fo muft the Sun in thefe Points.

PROPOSITION VII.

Having a Place in the Torrid Zone, to find the two Days in which the Sun is vertical to it.

BRING the Place to the brafs Meridian, and obferve the Degree of it's Latitude, and turn the Globe 'till you find the Ecliptic pafs under that Degree in two Places, into which when the Sun comes It will be vertical to that Place; then find what time, or Day, of the Year the Sun comes to these two Points, from Tables, or from the wooden Horizon, or by the Method Chap. 22.

"TIS alfo plain in the Univerfal Maps; for drawing a Line thro' the Place, parallel to the Equator, it will cut the Ecliptic in two places alfo ; from which the two Days may be known.

BUT, without Globes and Maps, you may find the Latitude of the Place, in Degrees, and look in the Table of Declination for the fame Number of Degrees of Declination, and you'll have the two Days answering thereto.

Note, The Sun's Center, which is fixteen Degrees from it's Circumference, will be a few Days jooner or later, vertical to the Place, than the Cir cumference

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day.

cumference, in it's North or South Point at Mid

PROPOSITION VIII.

A Place being given in the Frigid Zone, to determine the Days in which the Sun doth not fet there, nor rife, and when thofe Days begin and end.

ON the Globe. Let the Place be brought to the Meridian, and the Pole elevated to it's Latitude; then, turning the Globe round, obferve the two Points in the Ecliptic which do not fet, or go under the Horizon; the first, that is next to Aries, fhows the firft Day of it's not fetting, and that next Libra the Day when it begins to rife, and the two Days in which the Sun is in thofe Points the Sun will only touch the Horizon, and it's Center will be a little above it; and thus the Days are found in which the Sun will be under the Horizon in the oppofite Part of the Year.

THIS may be done eafier by the Globe, tho' the reafon of it is not fo obvious. Find the Complement of the Latitude of the Place, and count fo many Degrees from the Equator, and mark what Points of the Ecliptic come under that Degree on the Meridian, and they will be found to be two Points, into which, or the intermediate Points, when the Sun comes, it will not fet: and fo you have an Arch, at the South, which fhows how long 'tis under the Horizon.

AFTER the fame way in the Maps; draw a Line thro' the Degree, that is as far from the Equator as the Place is from the Pole, and you'll fee what Point it cuts in the Ecliptic; in and between which when the Sun comes it doth not fet: and in the South part you fee how long 'tis under the Ho

rizon.

IF the Latitude of the Place be known, find the fame Degree and Minute in the Table of Declination, and againft it you'll have the Day in which it begins and ends the not fetting; and other two Days that have the fame South Declination in which it begins and ends the not rifing; the firft will be between the twenty first of June and the first of March; the other between the twenty firft of June and the twenty firft of September; and one of the laft between the twenty firft of September and twenty firft of December ; the other between that, and the twenty first of March.

THIS is to be understood of the Sun's Center which is fixteen Minutes above and below the Limb.

PROPOSITION IX.

Having the Day of the Year, to find thofe Places in which the Sun will then be vertical.

FROM the given Day, find the Sun's Place in the Ecliptic as in Chap. 22.

BRING the Sun's Place in the Ecliptic under the Meridian, and mark the Degree above it; and turning the Globe, obferve all the Places that pafs under that Degree will have the Sun vertical one after another and in the Maps find the Sun's Place in the Ecliptic, and draw a Line parallel to the Equator, either straight or curve, as the Map is, and all the Places it paffes over are thofe fought.

BY the Table of Declination find the Degree of Latitude of thofe Places, or, which is the fame, the Degree of Declination that Day; which being found, you'll have the Places by drawing a Line thro' thofe Degrees. FROPO

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PROPOSITION X.

Having the Day of the Year, to find thofe Places in which the Sun begins then not to fet and not to rife.

THE given Day must be between the twenty. first of March and twenty firft of June, or twenty first of September and twenty first of December.

FIND first the Sun's Place for that Day, which bring to the Meridian; and as many Degrees as are between it and the Equator, count fo many from the Pole towards the Equator; and draw a parallel Circle at that Diftance from the Pole: all the Places within it will fhow the firft, i. e. the Sun's not fetting there; and the like being drawn, as near the other Pole, will include the Places where it does not rife; and the Places under the two Parallels show where these two Changes begin. Then,

TO fhow the Truth of it; elevate the Pole according to the Latitude of any of the Places; and it will appear when the Sun's Place in the Ecliptic begins not to fet; and how long it continues fo; and when it begins not to rife in the South Part. The fame may be done by the Maps; taking the Declination of the Sun, which will reach from the Pole to the Parallel in which the Sun begins not to fet and fo likewife at the South.

AND by the Table of Declination you have the Latitude of the Places fought for.

PROPOSITION XI.

.

To calculate the Breadth and Quantity of each Zone, in Miles, or any known Measure.

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