Having found the Sun’s place in the ecliptic, bring the same to themeridian, and note the degree over it; then turning the globe round, all places that pass under that degree will have the Sun vertical that day.
Bring the given place to the meridian, and mark what degree of latitude is exactly over it; then turning the globe about its axis, those two points of the ecliptic, which pass exactly under the said mark, are the Sun’s place; against which, upon the wooden horizon, you’ll have the days required.
Having found the Sun’s declination, and brought the first place (London) to the meridian, set the index to the given hour, then turn the globe about until the index points to XII at noon; which beingdone, that place upon the globe which stands under the point of the Sun’s declination upon the meridian, has the Sun that moment in the Zenith.
Having found the place where the Sun is vertical at the given hour, rectify the globe for that latitude, and bring the said place to the meridian.
Then all those places that are in the Western semicircle of the horizon, have the Sun rising at that time.
Those in the Eastern semicircle have it setting.
To those who live under the upper semicircle of the meridian, it is 12o’clock at noon. And,
Those who live under the lower semicircle of the meridian, have it at midnight.
All those places that are above the horizon, have the Sun above them, just so much as the places themselves are distant from the horizon; which height may be known by fixing the quadrant of altitude in the zenith, and laying it over any particular place.
In all those places that are 18 degrees below the Western side of the horizon, the twilight is just beginning in the morning, or the day breaks. And in all those places that are 18 degrees below the Eastern side of the horizon, the twilight is ending, and the total darkness beginning.
The twilight is in all those places whose depression below the horizon does not exceed 18 degrees. And,
All those places that are lower than 18 degrees, have dark night.
The depression of any place below the horizon is equal to the altitude of itsAntipodes, which may be easily found by the quadrant of altitude.
The Sun always illuminates one half of the globe, or that hemisphere which is next towards him, while the other remains in darkness: And if (as by thelast problem) we elevate the globe according to the Sun’s place in the ecliptic, it is evident, that the Sun (he being at an immense distance from the Earth) illuminates all that hemisphere, which is above the horizon; the wooden horizon itself, will be the circle terminating light and darkness; and all those places that are below it, are wholly deprived of the solar light.
The globe standing in this position, those arches of the parallels of latitude which stand above the horizon, are theDiurnal Arches, or the length of the day in all those latitudes at that time of the year; and the remaining parts of those parallels, which are below the horizon,are theNocturnal Arches, or the length of the night in those places. The length of the diurnal arches may be found by counting how many hours are contained between the two meridians, cutting any parallel of latitude, in the Eastern and Western parts of the horizon.
In all those places that are in the Western semicircle of the horizon, the Sun appears rising: For the Sun, standing still in the vertex (or above the brass meridian) appears Easterly, and 90 degrees distant from all those places that are in the Western semicircle of the horizon; and therefore in those places he is then rising. Now, if we pitch upon any particular place upon the globe, and bring it to the meridian, and then bring the hour index to the lower 12, which in this case, we’ll suppose to be 12 at noon; (because otherwise the numbers upon the hour circle will not answer our purpose) and afterwards turn the globe about, until the aforesaid place be brought to the Western side of the horizon; the index will then shew the time of the Sun rising in that place. Then turn the globe gradually about from West to East, and minding the hourindex, we shall see the progress made in the day every hour, in all latitudes upon the globe, by the real motion of the Earth round its axis; until, by their continual approach to the brass meridian (over which the Sun stands still all the while) they at last have noon day, and the Sun appears at the highest; and then by degrees, as they move Easterly the Sun seems to decline Westward, until, as the places successively arrive in the Eastern part of the horizon, the Sun appears to set in the Western: For the places that are in the horizon, are 90 degrees distant from the Sun. We may observe, that all places upon the Earth, that differ in latitude, have their days of different length (except when the Sun is in the equinoctial) being longer or shorter, in proportion to what part of the parallels stands above the horizon. Those that are in the same latitude, have their days of the same length; but have them commence sooner or later, according as the places differ in longitude.
It has been shewed in thelast problem, how to place the globe in such a position as to exhibit the length of the diurnal and nocturnal arches in all places of the Earth, at a particular time: If the globe be continually rectified, according as the Sun alters his declination, (which may be known by bringing each degree of the ecliptic successively to the meridian) you’ll see the gradual increase or decrease made in the days, in all places of the World, according as a greater or lesser portion of the parallels of latitude, stands above the horizon. We shall illustrate this problem by examples taken at different times of the year.
1. Let the Sun be in the first point of ♋ (which happens on the 21st ofJune) that point being brought to the meridian, will shew the Sun’s declination to be 23½ degrees North; then the globe must be rectified to the latitude of 23½ degrees; and for the better illustration of the problem, let the first meridian upon the globe be brought under the brass meridian. The globe being in this position, you’ll see at one view the length of the days in all latitudes, bycounting the number of hours contained between the two extreme meridians, cutting any particular parallel you pitch upon, in the Eastern and Western part of the horizon. And you may observe that the lower part of the arctic circle just touches the horizon, and consequently all the people who live in that latitude have the Sun above their horizon for the space of 24 hours, without setting; only when he is in the lower part of the meridian (which they would call 12 at night) he just touches the horizon.
To all those who live between the arctic circle and the Pole, the Sun does not set, and its height above the horizon, when he is in the lower part of the meridian, is equal to their distance from the arctic circle: For example, Those who live in the 83d parallel have the Sun when he is lowest at this time 13½ degrees high.
If we cast our eye Southward, towards the equator, we shall find, that the diurnal arches, or the length of days in the several latitudes, gradually lessen: The diurnal arch of the parallel ofLondonat thistime is 16½ hours; that of theEquator(is always) 12 hours; and so continually less, ’till we come to theAntarctic Circle, the upper part of which just touches the horizon; just those who live in this latitude have just one sight of the Sun, peeping as it were in the horizon: And all that space between the antarctic circle and the South Pole, lies in total darkness.
If from this position we gradually move the meridian of the globe according to the progressive alterations made in the Sun’s declination, by his motion in the ecliptic, we shall find the diurnal arches of all those parallels, that are on the Northern side of the equator, continually decrease; and those on the Southern side continually increase, in the same manner as the days in those places shorten and lengthen. Let us again observe the globe when the Sun has got within 10 degrees of the equinoctial; now the lower part of the 80th parallel of North latitude just touches the horizon, and all the space betwixt this and the pole, falls in the illuminated hemisphere: but all those parallels that lie betwixt this and the arctic circle, which before were wholly above the horizon, do now intersect it, and the Sun appearsto them to rise and set. From hence to the equator, we shall find that the days have gradually shortened; and from the equator Southward, they have gradually lengthened, until we come to the 80th parallel of the South latitude; the upper part of which just touches the horizon; and all places betwixt this and the South Pole are in total darkness; but those parallels betwixt this and the antarctic circle, which before were wholly upon the horizon, are now partly above it; the length of their days being exactly equal to that of the nights in the same latitude in the contrary hemisphere. This also holds universally, that the length of one day in one latitude North, is exactly equal to the length of the night in the same latitude South; andvice versa.
Let us again follow the motion of the Sun, until he has got into the equinoctial, and take a view of the globe while it is in this position. Now all the parallels of latitude are cut into two equal parts by the horizon, and consequently the days and nights are of equal lengths,viz.12 hours each, in all places of the world; the Sun rising and setting at six o’clock, excepting under the twoPoles, which now lieexactly in the horizon: Here the Sun seems to stand still in the same point of the heavens for some time, until by degrees, by his motion in the ecliptic, he ascends higher to one and disappears to the other, there being properly no days and nights under the Poles; for there the motion of the Earth round its axis cannot be observed.
If we follow the motion of the Sun towards the Southern tropic, we shall see the diurnal arches of the Northern parallels continually decrease, and the Southern ones increase in the same proportion, according to their respective latitudes; the North Pole continually descending, and the South Pole ascending, above the horizon, until the Sun arrives into ♑, at which time all the space within the antarctic circle is above the horizon; while the space between the arctic circle, and its neighbouring Pole, is in total darkness. And we shall now find all other circumstances quite reverse to what they were when the Sun was in ♋; the nights now all over the world being of the same length that the days were of before.
We have now got to the extremity of the Sun’s declination; and if we follow him through the other half of the ecliptic, and rectify the globe accordingly, we shall find the seasons return in their order, until at length we bring the globe into its first position.
The two foregoing problems were not, as I know of, published in any book on this subject before; and I have dwelt the longer upon them, because they very well illustrate how the vicissitudes of days and nights are made all over the world, by the motion of the Earth round her axis; the horizon of the globe being made the circle, separating light and darkness, and so the Sun to stand still in the vertex. And if we really could move the meridian, according to the change of the Sun’s declination, we should see at one view, the continual change made in the length of days and nights, in all places on the Earth; but as globes are fitted up, this cannot be done; neither are they adapted for the common purposes, in places near the equator, or any where in the Southern hemisphere. But this inconvenience is now remedied (at a smalladditional expence) by the hour circle being made to shift to either Pole; and some globes are now made with an hour circle fixed to the globe at each Pole between the globe and meridian, so as to have none without side to interrupt the meridian from moving quite round the wooden horizon.
Because the Sun, by his motion in the ecliptic, alters his declination a small matter every day; if we suppose all the torrid zone to be filled up with a spiral line, having so many turnings; or a screw having so many threads, as the Sun is days in going from one tropic to the other: And these threads at the same distance from one another in all places, as the Sun alters his declination in one day in all those places respectively: This spiral line or screw will represent the apparent paths described by the Sun round the Earth every day; and by following the thread from one tropic to the other, and back again, we shall have the path the Sun seems to describe round the Earth in ayear. But because the inclinations of these threads to one another are but small, we may suppose each diurnal path to be one of the parallels of latitude, drawn, or supposed to be drawn upon the globe. Thus much being premised, we shall explain thisProblem, by placing the globe according to some of the most remarkable positions of it, as before we did for the most remarkable seasons of the year.
In thepreceding problem, the globe being rectified according to the Sun’s declination, the upper parts of the parallels of latitude, represented theDiurnal Arches, or the length of the days all over the world, at that particular time: Here we are to rectify the globe according to the latitude of the place, and then the upper parts of the parallels of declination are the diurnal arches; and the length of the days at all times of the year, may be here determined by finding the number of hours contained between the two extreme meridians, which cut any parallel of declination in the Eastern and Western points of the horizon; after the same manner, as before we found the length of the day in the several latitudes at a particular time of the year.
1. Let the place proposed be under the equinoctial, and let the globe be accordingly rectified for 00 degrees of latitude, which is called a direct position of the sphere. Here all the parallels of latitude, which in this case we will call the parallels of declination, are cut by the horizon into two equal parts; and consequently those who live under the equinoctial, have the days and nights of the same length at all times of the year; and also in this part of the Earth, all theStarsrise and set, and their continuance above the horizon, is equal to their stay below it,viz.12 hours.
If from this position we gradually move the globe according to the several alterations of latitudes, which we will suppose to be Northerly; the lengths of theDiurnal Archeswill continually increase, until we come to a parallel of declination, as far distant from the equinoctial, as the place itself is from the Pole. This parallel will just touch the horizon, and all the heavenly bodies that are betwixt it and the Pole never descend below the horizon. In the mean time, while we are moving the globe, the lengths of the diurnalarches of the Southern parallels of declination, continually diminish in the same proportion that the Northern ones increased; until we come to that parallel of declination which is so far distant from the equinoctial Southerly, as the place itself is from the North Pole. The upper part of thisParalleljust touches the horizon, and all the Stars that are betwixt it and the South Pole never appear above the horizon. And all the nocturnal arches of the Southern parallels of declination, are exactly of the same length with the diurnal arches of the correspondent parallels of North declination.
2. Let us take a view of the globe when it is rectified for the latitude ofLondon, or 51½ degrees North. When the Sun is in the tropic of ♋, the day is about 16½ hours; as he recedes from this tropic, the days proportionably shorten, until, he arrives into ♑, and then the days are at the shortest, being now of the same length with the night, when the Sun was in ♋,viz.7½ hours. The lower part of that parallel of declination, which is 38½ degrees from the equinoctial Northerly, just touches the horizon; and the Stars that are betwixt this parallel and the North Pole, never set to us atLondon. In likemanner the upper part of the Southern parallel of 38½ degrees just touches the horizon, and the Stars that lie betwixt this parallel and the Southern Pole, are never visible in this latitude.
Again, let us rectify the globe for the latitude of theArctic Circle, we shall then find, that when the Sun is in ♋, he touches the horizon on that day without setting, being 24 hours compleat above the horizon; and when he is inCapricorn, he once appears in the horizon, but does not rise in the space of 24 hours: When he is in any other point of the ecliptic, the days are longer or shorter, according to his distance from the tropics. All the Stars that lie between the tropic ofCancer, and the North Pole, never set in this latitude; and those that are between the tropic ofCapricorn, and the South Pole, are always hid below the horizon.
If we elevate the globe still higher, the circle ofperpetual Apparitionwill be nearer the equator, as will that ofperpetual Occultationon the other side. For example, Let us rectify the globe for the latitude of 80 degrees North: when the Sun’s declination is 10degrees North; he begins to turn above the horizon without setting; and all the while he is making his progress from this point to the tropic of ♋, and back again, he never sets. After the same manner, when his declination is 10 degrees South, he is just seen at noon in the horizon; and all the while he is going Southward, and back again, he disappears, being hid just so long as before, at the opposite time of the year he appeared visible.
Let us now bring the North Pole into the Zenith, then will the equinoctial coincide with the horizon; and consequently all the Northern parallels are above the horizon, and all the Southern ones below it. Here is but one day and one night throughout the year, it being day all the while the Sun is to the Northward of the equinoctial, and night for the other half year. All the Stars that have North declination, always appear above the horizon, and at the same height; and all those that are on the other side, are never seen.
What has been here said of rectifying the globe to North latitude,holds for the same latitude South; only that before the longest days were, when the Sun was in ♋, the same happening now when the Sun is in ♑; and so of the rest of the parallels, the seasons being directly opposite to those who live in different hemispheres.
I shall again explain some things delivered above in general terms, by particular problems.
But from what has been already said, we may first make the following observations:
1.All places of the Earth do equally enjoy the benefit of the Sun, in respect of time, and are equally deprived of it, the Days at one time of the Year, being exactly equal to the Nights at the opposite season.2.In all places of the Earth, save exactly under the Poles, the Days and Nights are of equal length(viz.12 hours each) when the Sun is in the equinoctial.3.Those who live under the equinoctial, have the days and nights of equal lengths at all times of the year.4.In all places between the equinoctial and the Poles, the days and nights are never equal, but when the Sun is in the equinoctial points♈and♎.5.The nearer any place is to the equator, the less is the difference between the length of the artificial days and nights in the said place; and the more remote the greater.6.To all the inhabitants lying under the same parallel of latitudes the days and nights are of equal lengths, and that at all times of the year.7.The Sun is vertical twice a year to all places between the tropics; to those under the tropics, once a year; but never any where else.8.In all places between the Polar Circles, and the Poles, the Sun appears some number of days without setting; and at the opposite time of the year he is for the same length of time without rising; and the nearer unto, or further remote from the Pole, those places are, the longer or shorter is the Sun’s continued presence or absence from the Pole.9.In all places lying exactly under the Polar Circles, the Sun, when he is in the nearest tropic, appears 24 hours without setting; and when he is in the contrary tropic, he is for the same length of time, without rising; but at all other times of the year, he rises and sets there, as in other places.10.In all places lying in the (Northern/Southern) hemisphere, the longest day and shortest night, is when the Sun is in the (Northern/Southern) tropic, and on the contrary.
1.All places of the Earth do equally enjoy the benefit of the Sun, in respect of time, and are equally deprived of it, the Days at one time of the Year, being exactly equal to the Nights at the opposite season.
2.In all places of the Earth, save exactly under the Poles, the Days and Nights are of equal length(viz.12 hours each) when the Sun is in the equinoctial.
3.Those who live under the equinoctial, have the days and nights of equal lengths at all times of the year.
4.In all places between the equinoctial and the Poles, the days and nights are never equal, but when the Sun is in the equinoctial points♈and♎.
5.The nearer any place is to the equator, the less is the difference between the length of the artificial days and nights in the said place; and the more remote the greater.
6.To all the inhabitants lying under the same parallel of latitudes the days and nights are of equal lengths, and that at all times of the year.
7.The Sun is vertical twice a year to all places between the tropics; to those under the tropics, once a year; but never any where else.
8.In all places between the Polar Circles, and the Poles, the Sun appears some number of days without setting; and at the opposite time of the year he is for the same length of time without rising; and the nearer unto, or further remote from the Pole, those places are, the longer or shorter is the Sun’s continued presence or absence from the Pole.
9.In all places lying exactly under the Polar Circles, the Sun, when he is in the nearest tropic, appears 24 hours without setting; and when he is in the contrary tropic, he is for the same length of time, without rising; but at all other times of the year, he rises and sets there, as in other places.
10.In all places lying in the (Northern/Southern) hemisphere, the longest day and shortest night, is when the Sun is in the (Northern/Southern) tropic, and on the contrary.
Having rectified the globe according to the latitude, bring the Sun’s place to the meridian, and put the hour index to 12 at noon; then bring the Sun’s place the Eastern part of the horizon, and the index will shew the time when the Sun rises. Again, turn the globe until the Sun’s place be brought to the Western side of the horizon, and the index will shew the time of Sun-setting.
The hour of Sun-setting doubled, gives the length of the day; and the hour of Sun-rising doubled, gives the length of the night.
Let it be required to find when the Sun rises and sets atLondonon the 20th ofApril. Rectify the globe for the latitude ofLondon, and having found the Sun’s place corresponding toMaythe 1st,viz.♉ 10¾ degrees, bring ♉ to 10¾ degrees to the meridian, and set the index to 12 at noon; then turn the globe about ’till ♉ 10¾ degrees be brought to the Eastern part of the horizon, and you’ll find the index point 4¾ hours, this being doubled, gives the length of the night 9½ hours. Again, bring the Sun’s place to the Western part of the horizon, and the index will point 7¼ hours, which is the time of Sun-setting; this being doubled, gives the length of the day 14½ hours.
Note, The longest day at all places on the (North/South)side of the equator, is when the Sun is in the first point of (Cancer/Capricorn) Wherefore having rectified the globe for the latitude, find the time of Sun-rising and setting, and thence the length of the day and night, as in thelast problem, according to the place of the Sun: Or, having rectified the globe for the latitude, bring the solstitial point of that hemisphere, to the East part of the horizon, and set the index to 12 at noon; then turning the globe about ’till the said solstitial point touches the Western side of the horizon, the number of hours from noon to the place where the index points (being counted according to the motion of the index) is the length of the longest day; the complement whereof to 24 hours, is the length of the shortest night, and the reverse gives the shortest day and the longest night.
If from the length of the longest day, you subtract 12 hours, thenumber of half hours remaining, will be theClimate: Thus that place where the longest day is 16½ hours, lies in the 9thClimate. And by the reverse, having theClimate, you have thereby the length of the longest day.
Bring the solstitial point to the meridian, and set the index to 12 at noon; then turn the globe Westward, ’till the index points at half the number of hours given; which being done, keep the globe from turning round its axis, and slide the meridian up or down in the notches, ’till the solstitial point comes to the horizon, then that elevation of the Pole will be the latitude.
If the hours given be 16, the latitude is 49 degrees; if 20 hours, the latitude is 63¼ degrees.
Having rectified the globe according to the latitude, turn it about until some point in the first quadrant of the ecliptic (because the latitude is North) intersects the meridian in the North point of the horizon; and right against that point of the ecliptic on the horizon, stands the day of the month when the longest day begins.
And if the globe be turned about ’till some point in the second quadrant of the ecliptic cuts the meridian in the same point of the horizon, it will shew the Sun’s place when the longest day ends, whence the day of the month may be found, as before: Then the number of natural days contained between the times the longest day begins and ends is the length of the longest day required.
Again, turn the globe about, until some point in the third quadrant of the ecliptic cuts the meridian in the South part of the horizon; that point of the ecliptic will give the time when the longest night begins. Lastly, turn the globe about, until some point in the fourth quadrant of the ecliptic cuts the meridian in the South point of the horizon; and that point of the ecliptic will be the place of the Sun when the longest night ends.
Or, the time when the longest day or night begins, being known, their end may be found by counting the number of days from that time to the succeeding solstice; then counting the same number of days from the solstitial day, will give the time when it ends.
Find a point in the ecliptic half so many degrees distant from the solstitial point, as there are days given, and bring that point to themeridian; then keep the globe from turning round its axis, and move the meridian up or down until the aforesaid point of the ecliptic comes to the horizon; that elevation of the Pole will be the latitude required.
If the days given were 78, the latitude is 71½ degrees.
This method is not accurate, because the degrees in the ecliptic do not correspond to natural days; and also because the Sun does not always move in the ecliptic at the same rate; however, such problems as these may serve for amusements.
In theforegoing problem, by the length of the day, we mean the time from Sun-rising to Sun-set; and the night we reckoned from Sun-set, ’till he rose next morning. But it is found by experience, thatTotal Darknessdoes not commence in the evening, ’till the Sun has got 18 degrees below the horizon; and when he comes within the same distanceof the horizon next morning, we have the firstDawn of Day. This faint light which we have in the morning and evening, before and after the Sun’s rising and setting, is what we call theTwilight.[4]Having rectified the globe for the latitude, the zenith, and the Sun’s place, turn the globe and the quadrant of altitude until the Sun’s place cuts 18 degrees below the horizon (if the quadrant reaches so far) then the index upon the hour circle will shew the beginning or ending of twilight after the same manner as before we found the time of the Sun-rising and setting, inProb. 18. But by reason of the thickness of the wooden horizon, we can’t conveniently see, or compute when the Sun’s place is brought to the point aforesaid. Wherefore the globe being rectified as above directed, turn the globe, and also the quadrant of altitude, Westward, until that point in the ecliptic, which is opposite to the Sun’s place, cuts the quadrant in the 18th degree above the horizon; then the hour index will shew the time when day breaks in the morning. And if you turn the globe and the quadrant ofaltitude, until the point opposite to the Sun’s place cuts the quadrant in the Eastern hemisphere, the hour hand will shew when twilight ends in the evening. Or, having found the time from midnight when the morning twilight begins, if you reckon so many hours before midnight, it will give the time when the evening twilight ends. Having found the time when twilight begins in the morning, find the time of Sun-rising, byProb. 18, and the difference will be the duration of twilight.
Thus atLondonon the 12th ofMaytwilight begins at three quarters past one o’clock: The Sun rises at about half an hour past four: Whence the duration of twilight now is 2¾ hours, both in the morning and evening. On the 12th ofNovember, the twilight begins at half an hour past six, being somewhat above an hour before Sun-rising.
Let the place be in the Northern hemisphere; then if the complement ofthe latitude be greater than (the depression) 18 degrees, subtract 18 degrees from it, and the remainder will be the Sun’s declination North, when total darkness ceases. But if the complement of the latitude is less than 18 degrees, their difference will be the Sun’s declination South, when the twilight begins to continue all night. If the latitude is South, the only difference will be, that the Sun’s declination will be on the contrary side.
Thus atLondon, when the Sun’s declination North is greater than 20½ degrees, there is no total darkness, but constant twilight, which happens from the 26th ofMayto the 18th ofJuly, being near two months. Under the North Pole the twilight ceases, when the Sun’s declination is greater than 18 degrees South, which is from the 13th ofNovember, ’till the 29th ofJanuary: So that notwithstanding the Sun is absent in this part of the world for half a year together, yet total darkness does not continue above 11 weeks; and besides, theMoonis above the horizon for a whole fortnight of every month throughout the year.
Bring the Sun’s place to the meridian, and mark the number of degrees contained betwixt that point and the equator; then count the same number of degrees from the nearest Pole (viz.the North Pole, if the Sun’s declination is Northerly, otherwise the South Pole) towards the equator, and note that point upon the meridian; then turn the globe about, and all the places which pass under the said point, are those where the Sun begins to shine constantly, without setting on the given day. If you lay the same distance from the opposite Pole towards the equator, and turn the globe about, all the places which pass under that point, will be those where the longest night begins.
The Latitude of the place being given, to find the hour of the day when the Sun shines.
If it be in the summer, elevate the Pole according to the latitude, and set the meridian due North and South; then the shadow of the axis will cut the hour on the Dial plate: For the globe being rectified in this manner, the hour circle is a trueEquinoctial Dial; the axis of the globe being theGnomon. This holds true inTheory, but it might not be very accurate in practice, because of the difficulty in placing the horizon of the globe truly horizontal, and its meridian due North and South.
If it be in the winter half year, elevate the South Pole according to the latitude North, and let the North part of the horizon be in the South part of the meridian; then the shade of the axis will show the hour of the day as before: But this cannot be so conveniently performed, tho’ the reason is the same as in the former case.
To find the Sun’s altitude, when it shines, by the Globe.
Having set the frame of the globe truly horizontal or level, turn the North Pole towards the Sun, and move the meridian up or down in thenotches, until the axis casts no shadow; then the arch of the meridian, contained betwixt the Pole and the horizon, is the Sun’s altitude.
Note, The best way to find the Sun’s altitude, is by a little quadrant graduated into degrees, and having sights and a plummet to it: Thus, hold the quadrant in your hand, so as the rays of the Sun may pass through both the sights, the plummet then hanging freely by the side of the instrument, will cut in the limb the altitude required. These quadrants are to be had at the instrument-makers, with lines drawn upon them, for finding the hour of the day, and the azimuth; with several other pretty conclusions, very entertaining for beginners.
The Latitude and the Day of the Month being given, to find the hour of the day when the Sun shines.
Having placed the wooden frame upon a level, and the meridian due North and South, rectify the globe for the latitude, and fix a needle perpendicularly over the Sun’s place: The Sun’s place being brought tothe meridian, set the hour index at 12 at noon, then turn the globe about until the needle points exactly to the Sun, and casts no shadow, and then the index will shew the hour of the day.
Having rectified the globe for the latitude, the zenith, and the Sun’s place, turn the globe and the quadrant of altitude, so that the Sun’s place may cut the given degree of altitude: then the index will show the hour, and the quadrant will cut the azimuth in the horizon. Thus, if atLondon, on the 21st ofAugust, the Suns altitude, be 36 degrees in the forenoon, the hour of the day will be IX, and the Sun’s azimuth about 58 degrees from the South part of the meridian.
The Sun’s Azimuth being given, to place the Meridian of the Globe due North and South, or to find a Meridian Line when the Sun shines.
Let the Sun’s azimuth be 30 degrees South-Easterly, set the horizon of the globe upon a level, and bring the North Pole into the zenith; then turn the horizon about until the shade of the axis cuts as many hours as is equivalent to the azimuth (allowing 15 degrees to an hour) in the North-West part of the hour circle,viz.X at night, which being done, the meridian of the globe stands in the true meridian of the place. The globe standing in this position, if you hang two plummets at the North and South points of the wooden horizon, and draw a line betwixt them, you will have a meridian line; which if it be on a fixed plane (as a floor or window) it will be a guide for placing the globe due North and South, at any other time.
Rectify the globe for the latitude, the zenith, and the Sun’s place, then the number of degrees contained betwixt the Sun’s place and thevertex, is the Sun’s meridional zenith distance; the complement of which to 90 degrees, is the Sun’s meridian altitude. If you turn the globe about until the index points to any other given hour, then bringing the quadrant of altitude to cut the Sun’s place, you will have the Sun’s altitude at that hour; and where the quadrant cuts the horizon, is the Sun’s azimuth at the same time. ThusMaythe 1st atLondon, the Sun’s meridian altitude will be 61½ degrees; and at 10 o’clock in the morning, the Sun’s altitude will be 52 degrees, and his azimuth about 50 degrees from the South part of the meridian.
Having rectified the globe for the latitude, the zenith, and the Sun’s place, take a point in the ecliptic exactly opposite to the Sun’s place, and find the Sun’s altitude and azimuth, as by thelast problem, and these will be the depression and the altitude required. Thus, if the time given be the 1st ofDecember, at 10 o’clock at night, thedepression and azimuth will be the same as was found in thelast problem.