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index of the horary circle at the hour of the day, in the given place, where you are, turn the globe till the index points at the upper figure de XII. which done, fix the globe in that situation, and observe what places are exactly under the upper hemisphere 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. b) Prob.6.
given place; find the fun's place in the ecliptic (b) at that
time; which being brought to the east side of the horizon, set the index of the horary circle at noon, or the upper figure XII. and turning the globe about till the aforesaid 'place of the ecliptic touch the western side of the horizon, look upon the horary circle; and where the index points, reckon the mimber 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 same Time. (c) Prob. 3. the pole being raised (c) according to its latitude, and set the
Bring the place in which you are to the brazen meridian, index of the horary circle to the hour of the day at that time. Then bring the desired 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 shall be vertical to the fame.
Bring the given place to the brazen meridian, and mark what degree of
those Places of the Northern Frigid Zone, where the Sun begins then
Southern Frigid Zone, where he then begins to be totally absent. The day given (which must always be one of those either between the vernal equinox and the tummer folstice, or between the autumnal equi(d) Prob.6. the ecliptic, and marking the fame, bring it to the brazen
nox and the winter Yolstice), find (d) the sun's place in meridian, and reckon the like number of degrees from the north pole towards the equator, as there is between the equator and the sun's place in the ecliptic, making a mark where the reckoning ends. This done, turn the globe round, and all the places pafling under the said mark are those in which the fun begins to thine constantly without setting, upon the given day. For folution of the latter part of the problem, fet off the same distance trom the lovih pole up on the brazen meridian towards the cuator, as was formerly f: off from the north; then marking as before and turning the globe round, all places pafling under the mark are those where the sun begins his total disappearance 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 confiantly shines upon the said Place, and what Days he is absent, as also the first and
last Day of his Appearance. Bring the given place to the brazen meridian, and observing its latitude (a), elevate the globe accordingly; count the same number of degrees upon the meridian from each lide of (a) ProB. 2. the equator as the place is distant from the pole; and making marks where the reckonings end, turn the globe, and carefully observe what two degrees of the ecliptic pass 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 constantly shines above the horizon of the given place: and the opposite arch of the said circle will in like manner give the number of days in which he is totally absent, and also will point out which days those are. And in the interval he daily will rile and set. PROB. 13. The Month and Day being given, to find those Places on
the Globe, to which the Sun, when in the Meridian, shall be verti
cal on that Day. The sun's place in the ecliptic being found (b), bring (0) Prob. 6. the same to the brazen meridian, on which make a small mark exactly above the sun's place. Which done, turn the globe; and those places which have the sun vertical in the meridian, will successively pass under the said mark. Prog. 14. The Month and Day being given, to find upon what Point
of the Compass the Sun then rises and sets in any Place. Elevate the pole according to the latitude of the desired place, and, finding the fun's place in the ecliptic at the given time, bring the same to the eastern side of the horizon, and it will show the point of the compass upon which he then rises. By turning the globe about till his place coincides with the western side of the horizon, you may also see
that circle the exact point of his setting. PROB. 15. To know by the Globe the Length of the longest and shortest
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 hemisphere, to the east side of the horizon; ard setting the index of the horary circle at noon, turn the globe about till the sign 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 longest day, the complement of which to 24 hours is the extent of the shortest night. As for the thortest 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 those
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 set 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 observe what places are exactly under the upper semicircle of the brazen meridian; fo 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 place: are then in the lower semicircle of the meridian, in then it is midnight at the given time. After the same manner we may find those places that have any other particular hour at the time given, by moving the globe till the index points at the hour desired, and observing the places that are then under the brazen meridian.
PROB. 17. The Day and Hour being given, to find by tle Globe that
particular Place of the Earth to which the Sun is vertical at that Time.
The sun'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. same; then (b) find those places of the earth in whose ine
ridian the sun is at that infiant, and bring them to the brazen meridian; which done, observe that part of the earth which falls exactly under the aforesaid mark in the brazen meridian; for that is the particular place to which the sun is vertical at that time,
PROB. 18. The Day and Hour at any Place being given, to find all
those Places where the Sun is then rising, or setting, or in the Meridian; consequently all those Places which are enlightened at that
Time, and those which have Twilight, or dark Night. This problem cannot be solved by any globe fitted up in the common way, with the hour circle fixed upon the brass meridian, unless the sun be on or near either of the tropics on the given day. But by a globe fitted up with the hour-circle on its surface below the meridian, it may be solved for any day in the year, according to the following method.
Having found the place to which the sun is vertical at the given hour, if the place be in the northern hemisphere, 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 southern hemisphere, elevate the south pole accordingly; and bring the said place to the brazen meridian. Then, all those places which are in the western semicircle of the horizon have the sun rising to them at that time, and those in the eastern semicircle have it setting; to those under tbe upper semicircle of the brass meridian, it is noon; and to those under the lower semicircle, it is midnight. All those places which are above the horizon, are enlightened by the sun, and have the fun just 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 sun is vertical; and then laying it over any other place, observing what number of degrees on the quadrant are intercepted between the faid place and the horizon. In all those places that are 18 degrees below the western semicircle of the horizon, the morning twilight is just beginning; in all those places that are 18 degrees below the easiern femicircle of the horizon, the evening twilight is ending; and all those places that are lower than 18 degrees, have dark night.
If any place be brought to the upper semicircle of the brazen meridian, and ihe hour index be set to the upper XII. or noon, and then the globe be turned round eastward on its axis, when the place comes to the western semicircle of the horizon, the index will show the time of lunriting at that place; and when the fame place comes w the cattern fue
micircle of the horizon, the index will show the time of the fun's setting.
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 sun does not rise.
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 rise and set, 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 distance from the ecliptic, by applying the semicircle of position to her place in the zodiac. For the folution of the problem, eleyate the pole (a) according to the latitude of the given place; and (a) Prob. 2. the sun's place in the ecliptic at the time being (6) found, (6) PROB. 6. and marked, as also the moon's place at the same time, bring the sun's place to the brazen meridian, and set the index of the horary circle at noon; then turn the globe till the moon's place succeslively meet with the eaftern and western side of the horizon, as also the brazen meridian; and the index will point at those various times the particular hours of her riting, setting, and southing. PROB. 20. Two Places being given on the Globe, to find the true Dif
tance 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 distance from each other, reckoning every degree to be 691 English miles.
PROB. 21. A Place being given on the Globe, and its true Distance
from a second Place, to find what other places of the Earth are at the same Diftance from the given Place. Bring the given place to the brazen meridian, and elevate the pole according to the latitude of the said place; then fix the quadrant of altitude in the zenith, and reckon upon that quadrant the given distance between the firft and second place, provided the same be under 90 degrees; otherwise you must use the semicircle of position, and making a mark where the reckoning ends, and moving the said quadrant or femicircle quite round upon the surface of the globe, all places pafling under that mark are those desired.
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. Those places which lie on the equator have no latitude, it being there that the latitude begins; and those places which lie on the first meridian have no longitude, it being there that the longitude beyins. Consequently, that particular place of the earth where the first meridian interlects the equator, has neither longitude nor latitude.
3. All places of the earth equally enjoy the benefit of the sun, in respea 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 south, 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 sun is in the equinoctial : for, in all the elevations of the pole, Mort 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 or Aries and — Libra. For in every other part of the ecliptic, the circle of the sun's daily motion is divided into two unequal parts by the horizon.
7. The nearer any place is to the equator, the less 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 describes in the heavens every 24 houts, being cut more nearly equal in the former cate, and more unequal in the latter.
8. In all places lying upon any given parallel of latitude, however long or short the day and night be at any one of those places at any time of the year, it is then of the same length at all the rest; for in turning the globe round its axis (when rectified according to the sun's declination), all those places will keep equally long above and below the horizon.
9. The sun is vertical twice a year to every place between the tropics ; to those under the tropics once a year, but never any where else. For there can be no place between the tropics, but that there will be two points in the ecliptic, whose 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 sun 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 sun, when he is in the nearer tropic, continues 24 hours above the horizon without setting; because no part of that tropic is below their horizon. And when the sun is in the farther tropic, he is for the same length of time without rising; because no part of that tropic is above their horizon. But at all other times of the year, he rises and sets there, as in other places; because all the circles that can be drawn parallel to the equator, between the tropics, are more or less cut by the horizon, as they are farther from, or nearer to, that tropic which is all above the horizon ; and when the sun is not in either of the tropics, his diurnal course must be in one or other of those circles.
11. To all places in the northern hemisphere, from the equator to the polar circle, the longest day and shortett night is when the sun is in the northern tropic; and the shortest day and longest night is when the sun is in the fouthern tropic; because no circle of the fun's daily motion is so much above the horizon, and so little below it, as the northern tropic; and none so little above it, and so much below it, as the fuuthern. In the fouthern hemisphere, the contrary takes place.