index of the horary circle at the hour of the day, in the given place, or where you are, turn the globe till the index points at the upper figure of XII. which done, fix the globe in that fituation, and obferve what places are exactly under the upper hemifphere of the brazen meridian; for those are the places desired.

PROB. 8. To know the Length of the Day and Night in any Place of the Earth at any Time.

Elevate the pole (a) according to the latitude of the (a) PROB. 2. given place; find the fun's place in the ecliptic (b) at that (b) PROB.6. time; which being brought to the eaft fide of the horizon, fet the index of the horary circle at noon, or the upper figure XII. and' turning the globe about till the aforefaid place of the ecliptic touch the western fide of the horizon, look upon the horary circle; and where the index points, reckon the number of hours to the upper figure of XII. for that is the length of the day, the complement of which to 21 hours is the length of the night.

PROB. 9.
To know by the Globe, what o'Clock it is in any Part of the
World at any Time, provided you know the Hour of the Day where
you are at the fame Time.

Bring the place in which you are to the brazen meridian, (c) PROB. 3. the pole being raifed (c) according to its latitude, and set the index of the horary circle to the hour of the day at that time. Then bring the defired place to the brazen meridian, and the index will point. out the hour at that place.

PROB. 10. A Place being given in the Torrid Zone, to find the two Days of the Year in which the Sun fhall be vertical to the fame. Bring the given place to the brazen meridian, and mark what degree of latitude is exactly above it. Move the globe round, and observe the two points of the ecliptic that pafs through the faid degree of latitude. Search upon the wooden horizon (or by proper tables of the fun's annual motion) on what days he paties through the aforefaid points of the ecliptic; for thofe are the days required, in which the fun is vertical to the given place.

PROB. 11. The Month and the Day being given, to find by the Globe thefe Places of the Northern Frigid Zone, where the Sun begins then to fhine conftantly without fetting; as also thofe Places of the Southern Frigid Zone, where he then begins to be totally abfent. The day given (which muft always be one of thofe either between the vernal equinox and the fummer folftice, or between the autumnal equinox and the winter folftice), find (d) the fun's place in (d) PROB. C. the ecliptic, and marking the fame, bring it to the brazen meridian, and reckon the like number of degrees from the north pole towards the equator, as there is between the equator and the fun's place in the ecliptic, making a mark where the reckoning ends. This done, turn the globe round, and all the places paffing under the faid mark are thofe in which the fun begins to fhine conftantly without fetting, upon the given day. For folution of the latter part of the problem, fet off the fame diftance from the fouth pole upon the brazen meridian towards the equator, as was formerly foff from the north; then marking as before. and turning the globe round, all places paffing under the mark are thofe where the fun begins his total difappearance from the given day."

PROB. 12. A Place being given in either of the Frigid Zones, to find by the Globe what number of Days the Sun conftantly fhines upon the faid Place, and what Days he is abfent, as alfo the first and laft Day of his Appearance.

Bring the given place to the brazen meridian, and obferving its latitude (a), elevate the globe accordingly; count the fame number of degrees upon the meridian from each fide of (a) PROв. 2. the equator as the place is diftant from the pole; and making marks where the reckonings end, turn the globe, and carefully obferve what two degrees of the ecliptic país exactly under the two points marked on the meridian; first for the northern arch of the circle, namely, that comprehended between the two degrees marked, which being reduced to time, will give the number of days that the fun conftantly fhines above the horizon of the given place: and the oppofite arch of the faid circle will in like manner give the number of days in which he is totally abfent, and also will point out which days those are. And in the interval he daily will rife and

fet.

PROB. 13. The Month and Day being given, to find thofe Places on the Globe, to which the Sun, when in the Meridian, shall be vertical on that Day.

The fun's place in the ecliptic being found (b), bring (b) PROB. 6. the fame to the brazen meridian, on which make a small

mark exactly above the fun's place. Which done, turn the globe; and thofe places which have the fun vertical in the meridian, will fucceffively país under the faid mark.

PROE. 14. The Month and Day being given, to find upon what Point of the Compass the Sun then rifes and fets in any Place.

Elevate the pole according to the latitude of the defired place, and, finding the fun's place in the ecliptic at the given time, bring the fame to the eastern fide of the horizon, and it will fhow the point of the compafs upon which he then rifes. By turning the globe about till his place coincides with the western fide of the horizon, you may alfo fee upon that circle the exact point of his setting..

PROB. 15. To know by the Globe the Length of the longest and forteft Days and Nights in any Part of the World.

Elevate the pole according to the latitude of the given place, and bring the first degree of Cancer, if in the northern, or Capricorn, if in the southern hemifphere, to the eaft fide of the horizon; and fetting the index of the horary circle at noon, turn the globe about till the fign of Cancer touches the western fide of the horizon, and then observe upon the horary circle the number of hours between the index and the upper figure of XII. reckoning them according to the motion of the index; for that is the length of the longeft day, the complement of which to 24 hours is the extent of the fhortest night. As for the shortest day and longest night, they are only the reverse of the former.

PROB. 16. The Hour of the Day being given in any Place to find thofe Places of the Earth where it is either Noon or Midnight, or any other particular Hour, at the fame Time.

Bring the given place to the brazen meridian, and fet the index of the horary circle at the hour of the day in that place. Then turn about the globe till the index points at the upper figure of XII. and obferve what

places are exactly under the upper femicircle of the brazen meridian; for in them it is mid-day at the time given. Which done, turn the globe about till the index points at the lower figure of XII. and whatever places are then in the lower femicircle of the meridian, in them it is midnight at the given time. After the fame manner we may find thofe places that have any other particular hour at the time given, by moving the globe till the index points at the hour defired, and obferving the places that are then under the brazen meridian.

PROB. 17. The Day and Hour being given, to find by the Globe that particular Place of the Earth to which the Sun is vertical at that

Time.

The fun's place in the ecliptic' (a) being found, and (a) PROB. 6. brought to the brazen meridian, make a mark above the (b) PROB. 16. fame; then (b) find thofe places of the earth in whose meridian the fun is at that inftant, and bring them to the brazen meridian; which done, obferve that part of the earth which falls exactly under the aforefaid mark in the brazen meridian; for that is the particular place to which the fun is vertical at that time.

PROB. 18. The Day and Hour at any Place being given, to find all thofe Places where the Sun is then rifing, or fetting, or in the Meridian; confequently all thofe Places which are enlightened at that Time, and thofe which have Twilight, or dark Night.

This problem cannot be folved by any globe fitted up in the common way, with the hour circle fixed upon the brafs meridian, unless the fun be on or near either of the tropics on the given day. But by a globe fitted up with the hour-circle on its furface below the meridian, it may be folved for any day in the year, according to the following method.

Having found the place to which the fun is vertical at the given hour, if the place be in the northern hemifphere, elevate the north pole as many degrees above the horizon, as are equal to the latitude of that place: if the place be in the fouthern hemisphere, elevate the fouth pole accordingly; and bring the faid place to the brazen meridian. Then, all thofe places which are in the western femicircle of the horizon have the fun rifing to them at that time, and those in the eastern femicircle have it fetting; to thofe under the upper femicircle of the brafs meridian, it is noon; and to thofe under the lower femicircle, it is midnight. All thofe places which are above the horizon, are enlightened by the fun, and have the fun juft as many degrees above them as they themselves are above the horizon; and this height may be known, by fixing the quadrant of altitude on the brazen meridian over the place to which the fun is vertical; and then laying it over any other place, obferving what number of degrees on the quadrant are intercepted between the faid place and the horizon. In all thofe places that are 18 degrees below the western femicircle of the horizon, the morning twilight is juft beginning; in all thofe places that are 18 degrees below the eaftern femicircle of the horizon, the evening twilight is ending; and all thofe places that are lower than 18 degrees, have dark night.

If any place be brought to the upper femicircle of the brazen meridian, and the hour index be fet to the upper XII. or noon, and then the globe be turned round eastward on its axis,when the place comes to the western femicircle of the horizon, the index will fhow the time of funrifing at that place; and when the fame place comes to the eastern fe

micircle of the horizon, the index will show the time of the fun's fetting.

To those places which do not go under the horizon, the fun fets not on that day: and to those which do not come above it, the fun does not rife.

PROB. 19. The Month and Day being given, with the Place of the Moon in the Zodiac, and her true Latitude, to find the exact Hour when she will rife and fet, together with her fouthing, or coming to the Meridian of the Place.

The moon's place in the zodiac may be found readily enough at any time by an ordinary almanack; and her latitude, which is her diftance from the ecliptic, by applying the femicircle of pofition to her place in the zodiac. For the folution of the problem, elevate the

pole (a) according to the latitude of the given place; and (a) PROB. 2. the fun's place in the ecliptic at the time being (6) found, (b) PRCE. 6. and marked, as alfo the moon's place at the fame time,

bring the fun's place to the brazen meridian, and fet the index of the horary circle at noon; then turn the globe till the moon's place fucceffively meet with the eastern and western side of the horizon, as alfo the brazen meridian; and the index will point at thofe various times the particular hours of her rifing, fetting, and fouthing.

PROB. 20. Two Places being given on the Globe, to find the true Diftance between them.

Lay the graduated edge of the quadrant of altitude over both the places; and the number of degrees intercepted between them will be their true diftance from each other, reckoning every degree to be 69 English miles.

PROB. 21. A Place being given on the Globe, and its true Distance from a fecond Place, to find what other Places of the Earth are at the fame Distance from the given Place.

Bring the given place to the brazen meridian, and elevate the pole according to the latitude of the faid place; then fix the quadrant of alțitude in the zenith, and reckon upon that quadrant the given diftance between the first and fecond place, provided the fame be under 90 degrees; otherwise you must use the femicircle of pofition, and making a mark where the reckoning ends, and moving the faid quadrant or femicircle quite round upon the furface of the globe, all places paffing under that mark are thofe defired.

GEOGRAPHICAL OBSERVATIONS,

1. The latitude of any place is equal to the elevation of the pole above the horizon of that place, and the elevation of the equator is equal to the complement of the latitude, that is, to what the latitude wants of 90 degrees.

2. Thofe places which lie on the equator have no latitude, it being there that the latitude begins; and thofe places which lie on the first meridian have no longitude, it being there that the longitude begins. Confequently, that particular place of the earth where the firft meridian interfects the equator, has neither longitude nor latitude.

3. All places of the earth equally enjoy the benefit of the fun, in refpe of time, and are equally deprived of it.

4. All places upon the equator have their days and nights equally long, that is, 12 hours each at all times of the year. For although the fun declines alternately from the equator, towards the north and towards the fouth, yet, as the horizon of the equator cuts all the parallels of latitude and declination in halves, the fun must always continue above the horizon for one half a diurnal revolution about the earth, and for the other half below it.

5. In all places of the earth between the equator and poles, the days and nights are equally long, viz. 12 hours each, when the fun is in the equinoctial: for, in all the elevations of the pole, fhort of 90 degrees (which is the greatest), one half of the equator or equinoctial will be above the horizon, and the other half below it.

6. The days and nights are never of an equal length at any place between the equator and polar circles, but when the fun enters the figns

Aries and Libra. For in every other part of the ecliptic, the circle of the fun's daily motion is divided into two unequal parts by the horizon.

7. The nearer any place is to the equator, the lefs is the difference between the length of the days and nights in that place; and the more remote, the contrary;-the circles which the fun defcribes in the heavens every 24 hours, being cut more nearly equal in the former cafe, and more unequal in the latter.

8. In all places lying upon any given parallel of latitude, however long or fhort the day and night be at any one of thofe places at any time of the year, it is then of the fame length at all the reft; for in turning the globe round its axis (when rectified according to the fun's declination), all those places will keep equally long above and below the horizon.

9. The fun is vertical twice a year to every place between the tropics; to those under the tropics once a year, but never any where elfe. For there can be no place between the tropics, but that there will be two points in the ecliptic, whofe declination from the equator is equal to the latitude of that place; and there is but one point of the ecliptic, which has a declination equal to the latitude of places on the tropic which that point of the ecliptic touches; and as the fun never goes without the tropics, he can never be vertical to any place that lies without them.

10. In all places lying exactly under the polar circles, the fun, when he is in the nearer tropic, continues 24 hours above the horizon without fetting; because no part of that tropic is below their horizon. And when the fun is in the farther tropic, he is for the fame length of time without rifing; because no part of that tropic is above their horizon. But at all other times of the year, he rifes and fets there, as in other places; because all the circles that can be drawn parallel to the equator, between the tropics, are more or lefs cut by the horizon, as they are, farther izom, or nearer to, that tropic which is all above the horizon; and when the fun is not in either of the tropics, his diurnal courfe muft be in one or other of thofe eircles.

11. To all places in the northern hemisphere, from the equator to the polar circle, the longeft day and fhortett night is when the fun is in the northern tropic; and the fhorteft day and longeft night is when the fun is in the fouthern tropic; becaufe no circle of the fun's daily motion is fo much above the horizon, and fo little below it, as the northern tropic; and none fo little above it, and fo much below it, as the fouthern. In the fouthern hemifphere, the contrary takes place.