Epitome Astronomiae Copernicanae: Liber III, part 6
How is the measure of the artificial day and night accomplished? First, by compasses, if the circle of the natural day has been described in the sphere. For the proportion which the segments of any circle made by the horizon bear to each other in any place of the Earth is there also the proportion of the day to its night, the Sun being in that degree of the ecliptic through which the circle passes. The ancients held to this method chiefly in measuring the length of the day and night, both the longest and the shortest, because their circles, that is, the tropics, are expressed in the sphere, chiefly for this use. Second, by calculation and the equator circle, or by the oblique ascensions of the semicircles of the ecliptic, of which the one that precedes the place of the Sun has an oblique ascension that is the index and measure of the night, and the one that follows that of the day. And then exactly 15° of times of the equator make one mean or equinoctial hour, as if no addition were made; because we feign the Sun to rest in a single point of the ecliptic for the whole day.
What is the method of measuring that day or night which consists of many natural days? Because the circles of the natural days neither correspond in number to the days nor are expressed in the sphere, these are therefore set aside, and the arc of the ecliptic perpetually apparent is sought by the doctrine given in the second part. Then, by the theoretical doctrine or from the ephemeris, it is to be inquired how long the Sun is seen to remain in the arc found, making a continuous day or night.
Now set out the variety of artificial days and nights through the seven positions of the sphere noted in the second part. Under the equator, and from it as far as either polar circle, no day lacks its night and no night its day, which becomes a part of the natural day; with this difference, however, that under the equator all days are equal to their nights, but in those departing from it toward our north there arises an inequality of days, so that no day of the whole year is equal to another, except only two at a time, on which the Sun is in points equidistant from the solstitial point. For as one advances toward the pole the summer days begin little by little to grow, the nights to be contracted; conversely the winter days are contracted, the nights extended; so that always one of the summer days has one winter night of the opposite point equally long, or also of a point equally distant from the equinoctial point, and one summer night one winter day, the Sun being in the opposite part or in an equally distant part from the equinoctial point.
The order of the increases is this: from the winter solstice, when the day is shortest, the light begins little by little to grow, at first by insensible increases, but about the equinox very swiftly, and toward the summer solstice and the longest day again insensibly; thence the same order of decreases begins.
Further, this difference of the longest day from the shortest is little felt in places near the equator; under the tropic it is already three hours, beyond the tropic with us eight hours; further on it grows so much that under the polar circle it consumes the whole natural day, and there is now one day in summer which has no night, and one night in winter which has no day; for the Sun, emerging with half its orb at the very hour of noon, at once hides itself again.
Within the polar circle two kinds of artificial days and nights exist: for some days before and after the equinoxes have their nights, others on the contrary, this side of and beyond the solstice, coalesce into one day, the nights being shut out, and conversely certain nights this side of and beyond the solstice are continued into another without the interposition of any day, and the number of natural days in one such prodigious day is increased with the approach to the pole; so that under the pole there is at last a single day lasting through the whole half-year, and likewise a single night through the other half-year, and no day or night shorter than a natural one.
There is, however, this difference in those protracted days, that within the arctic polar circle in this age these continuous summer days are longer than the continuous winter nights, so that under the pole itself the day is eight days longer than the night; within the antarctic polar circle the contrary happens. The cause is in the slower motion of the Sun through the northern hemisphere than through the southern, as will be said in the theoretical doctrine.
Prove all these things, each and every one, both by the circles of the natural days and by the ascensions.
First, that from the equator as far as the polar circle no day lacks its night.
Because the zenith is outside the polar circle, the pole of the ecliptic is always toward the north for us, and therefore all the parts of the ecliptic, when they come to the meridian, are above the horizon, wherefore also all the opposite parts are below the horizon. The parallels, then, of all the parts, that is, all the circles of the natural days, are cut by the horizon, or all the points of the ecliptic rise and set and the Sun in all of them.
Second, that under the polar circle the longest day swells to 24 hours, as also the longest night.
For if the zenith falls on the polar circle, then the pole of the ecliptic comes to the zenith and the ecliptic then coincides with the horizon, when the colure of the solstices coincides with the meridian; so of the solstices one does not rise, the other does not set, and of the tropics one lies wholly hidden, the other wholly exposed: that one the measure of the longest night, this of the longest day. Thus with one half the whole equator ascends, with the other none; the Sun, therefore, being at the common termini of the halves, makes in one a day equal to the natural day and no night, in the other the contrary.
Third, that within the polar circle several natural days, though not all, and under the pole the whole half-year, coalesce into one artificial day or night.
Because the zenith, or pole of the horizon, is within the polar circle, it is at times midway between the pole of the equator and the pole of the ecliptic, and so the pole of the ecliptic is then lower toward the south, wherefore the arc of the ecliptic about the one solstice is, on the meridian, below the horizon, and therefore does not rise; the opposite arc, under the pole of the equator, is above the horizon and so does not set; there, then, the whole circles of the natural days which these arcs have lie hidden, here exposed; but the intermediate ones are cut by the horizon; under the pole none at all is cut, but half of them lies hidden, half exposed. Thus the ecliptic is cut by such a horizon into four arcs, of which the upper does not set, the lower does not rise, and the intermediate rise and set, and the Sun in them.
Fourth, that under the equator all days are equal to their nights.
Because the centres of the circles of the natural days are in the axis of the world, and the axis there is in the horizon, the horizon cuts all those circles into equal segments. So the ascensions of semicircles begun from anywhere are all equal to one another, and the semicircle before the Sun, the indication of night, always rises in an equal time with the semicircle after the Sun, the index of day.
Fifth, that outside the equator only two days of the year are equal to their nights, of the rest some longer than the nights, some shorter, and the shortest day for us is in Capricorn, the longest in Cancer.
For the equator alone, drawn through two opposite points of the ecliptic, has its centre in the plane of the horizon, and so it alone is cut in equal parts by the horizon. The centres of all the other parallels are either above or below the equator, because the axis of the world, which has those centres, is bisected by the equator; the greater part of those, therefore, is above, of these below, and the greatest of that one whose centre in the axis is most remote from the equator, and so either the most elevated or the most depressed. Thus in the oblique sphere only those halves of the ecliptic have equal ascensions which begin from the equinoctial points; the rest, begun elsewhere, have unequal ones. And indeed the semicircles whose beginnings are with us in the north have greater ascensions, because the ascensional difference of the beginning is subtracted and that of the end added; but the greatest ascension belongs to the one that begins from the beginning of Cancer, because the ascensional difference is there the greatest.
Sixth, that two days, the Sun being in points equally distant from the solstice, are equal to each other, and their nights likewise.
Because through such two points the same parallel is drawn. Thus, because the ascensions of semicircles begun from such two points are equal.
Seventh, that one summer day has a winter night equal to it, the Sun being equally distant from one of the equinoctial points.
For at such points the circles decline equally to either side, and are therefore cut by the horizon alternately in equal parts, so that as much of one is exposed as of the other is hidden, and conversely. Thus, because the ascensions of the semicircles of the ecliptic are equal to the descensions of the opposite semicircles. If, then, the Sun is at the beginning of such a semicircle, it remains above the horizon as long as it remains below it if it is at the end of that semicircle, namely after half a year.
Eighth, that the increases of days or nights are swiftest at the equinoxes, slowest at the solstices.
Because, since the ecliptic is most oblique at the intersections, the declination there grows most swiftly, but at the solstices it lingers, standing still, until from growing it becomes decreasing. And the distance of the circles of the natural days and the difference of their section by the horizon follow the quantity of the declination; the ascensional difference follows the same, varying the measures of day and night.
Have those long nights any remedies of darkness? There are many causes which prolong the light, with the Sun absent, in those places, and reduce the darkness to a narrow compass. First, every portion of the Sun illuminates, however small it be. The day therefore begins in popular estimation, and also ends, when the centre of the Sun is 15 minutes below the horizon; this cause adds 16 days to the time in which the Sun can be seen nearest within the polar circles. Then, because of refractions in the air, it happens that the Sun at times seems to rise sooner than usual. So the Dutch saw the Sun 14 days before its time when they wintered within the polar circle. Third, twilight lasts through the greater part of so long a night, because the Sun is not sunk deep for them at the middle of our day, and there are not more than 70 days on which twilights are extinguished in places under the pole. Fourth, the Sun being hidden among them, the Moon, as often as it passes through the exposed arc about the opposite of the Sun, spends the night with them at full orb, and then indeed longer when it strays from the ecliptic to the north. Fifth, the north pole also has a gain of eight days over the south, which it adds to its long day. Sixth, fiery openings in the sky, almost continual, add something, though I do not know whether from certain experience.
You said above that there are two kinds of hours, equinoctial and temporal or seasonal; say now what is the seasonal hour. It is exactly the twelfth part of any artificial day or of one night, and therefore the seasonal hours of long days or nights are long, of short ones short.
Whence are the hours called seasonal, temporal? From the four seasons of the year, into which the year is distinguished by the course of the Sun in the ecliptic, of which in the fifth part.
By what difference and for what reasons do men use one kind of hours rather than the other? The first cultivators of astronomy, living in places not so very far from the equator, did not perceive great differences between the longest day and the shortest night. Then, therefore, among the Chaldeans, Syrians and Jews (as in the Gospel), and also among the Greeks and Romans and afterwards among the Arabs, those unequal hours were in use, so that the number of the hours, twelve, should never vary. There was added also the custom of numbering the hours of the day from sunrise, so that, noon always keeping the same place at the sixth hour and not wandering through the hours, it was needful that the hours of each day be of the same number, twelve. But among us Europeans, since the differences of days are more evident, and in the north very unlike one another within a short interval of lands, and on some days there is no rising or setting at all, a method of numbering hours from noon and midnight, and using them equal the whole year, seemed more convenient; for this is more universal and easy to observe, and of great use in counting the length of day and night. There came also the invention of automatic clocks, which indicate equal hours more easily than unequal; and as all Europe is filled with machines of this kind, equal hours also have grown in use, and unequal hours have fallen into disuse.
Why were both day and night divided into 12 parts rather than into another number? It is likely that the first authors wished in this to imitate the nature of the year, in which twelve months are established by as many lunations, nearly. For from the same source it came about that the zodiac was divided into twelve signs and the as into as many parts or ounces, as was said in Book II. There is added the convenience of the number twelve, which has a half, a third, a fourth, a sixth and a twelfth, namely 6, 4, 3, 2, 1. Hermes Trismegistus is said to have chosen this number because the bull Apis, whom the Egyptians worship as a divinity, made water twelve times daily, and hence the hours were called ōrai from ouron, urine. Maestlin supposes that the custom was taken over from poultry, because they distribute their crowings, by night as by day, in twelve intervals.
You seem to fix different beginnings of the day; recount, then, the customs of the nations and the reasons of each concerning this beginning of the day. Although there is by nature no beginning of the day from the heavens themselves, yet on earth the differences of light and darkness, of the presence and absence of the Sun, and the change of one into the other, are manifest, which most regard as a kind of natural boundary. So the Jews begin from the evening, looking also, according to nature, to the order of creation: for when the world was already made, there was still darkness, to which light succeeded, and of evening and morning one day was made. The same is attributed to the Athenians, I think because the night was spent by the magistrates, who were changed from day to day, in meditation on those things which on the following day they were to do in their term of office, or because they kept the days of the month by the Moon, which begins to appear in the evening, at sunset. The Italian and Bohemian clocks savour of the same custom, which begin their 24 equal hours from the beginning of night and end them at the following sunset.
The peoples of the East, as was said, reckoned the day and the hours of the day from sunrise, because the whole nychthemeron is named from the day as the more important part, whose natural beginning is in the rising of the Sun. This numbering of hours the Romans imitated; the authors of the custom among the Babylonians seem to have been the Chaldean astrologers, imitating the week of the Jews, whose seven days they distributed among the dominions of the planets and ended the rule of each planet with the night at sunrise. And so Epiphanius too numbers the weekdays with the Christians, because Christ rose when the Sun was about to rise, which is the chief profession of the Christian dogma. Hence it is that the vigils of feasts, which are kept by night, are ascribed in the Roman Calendar to the day which precedes the feast. However, whether clocks or sacred or profane offices use this beginning or that, it comes about by the tacit consent of the common people that we divide the night between the two days that surround it in equal portions, as less conspicuous and less suited to the conduct of affairs, reckoning the night only as the common boundary of times, as if it were no time, because it is passed in cessation from business and in sleep, which is like death and unlike life. And so the Bohemians also assign what was done two or three hours after sunset not to the following but to the preceding day, caring nothing for the order of their clock; and among the Romans things written before daybreak were named from the following day, being declared written before this or that day. Astronomers, since they have no need of artificial days for their computations, look to the beginning of the natural day, taking promiscuously and as occasion arises either noon or midnight for the beginning, on account of the meridian circle, in which the right ascensions of the Sun’s place are the same through all places of the Earth, whereas the oblique ones in different horizons vary much. And they begin from midnight on account of the very reckonings of times, but from noon on account of the Ephemerides, in which are expressed the places of the planets which they hold in the heavens at the point of noon, which is equally distant from the beginning and end of the day; they think this more convenient, especially in the case of the Sun, on account of the observation of its meridian altitude, to which all astronomical operation is tied. This custom our clocks imitate, most of them in Germany, which return to the beginning of the number twelve both at midnight and, that the number of strokes may not be tedious, also at noon. And so our common people also are thoroughly accustomed to this reckoning, whence it comes that they divide the day into hours before and after noon.
You spoke of the distribution of the days of the week among the planets; I should like to hear the reason of it which the Chaldeans observed. Since the hours of the day are twelve and of the night as many, and the planets seven in this order: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon (for so they were numbered by them), they began from the first day of the Jewish week, assigning to the Sun, the author of the day, its first hour, to Venus the second, to Mercury the third, to the Moon the fourth; then returning to Saturn, they assigned to it the fifth hour, and so on in turn; so to it came also the twelfth and last hour of the day, wherefore the first of the night fell to Jupiter, and so it came about that the last of the night fell to Mercury; but the whole day thus far was named from the Sun, as that to which the first hour of that day was given. After Mercury the Moon follows, and so the first hour of the following day was given to the Moon, whence also the name of that whole day. By this method it came about that always the fourth planet from the former gave its name to the following day, and the first day was the Sun’s, the second the Moon’s, the third Mars’s, the fourth Mercury’s, the fifth Jupiter’s, the sixth Venus’s, the seventh and last, which was holy and solemn to the Jews, Saturn’s, the first and highest of the planets, with the greater congratulation of this game because the Jews by divine precept passed that day in rest and cessation from work, since Saturn too is the slowest of all the planets, as completing its course only in 30 years. Whence at last the Jews also, having received knowledge of the planets from the Chaldeans, gave Saturn a name from rest and the sabbath.
If the shortest night follows the longest day and each is divided into 12 equal hours, then the hours of the night too will be shorter than the hours of the day immediately preceding; is no injury, then, done to the planets, to which hours of the night so short fall? Indeed with us at the beginning of Cancer the last temporal hour of the day is twice as long as the first hour of the following night, yet the Babylonians did not observe the hours otherwise. The more recent writers, that they might dispose the hours more neatly and do no injury to any of the planets, contend that another distribution of the hours must be made, so that those are unequal even within one and the same day, and those alone equal which surround noon and midnight at equal intervals, so that in the example alleged the noon hour at least is double the hour of midnight, and the rest toward the rising and setting are brought little by little to equality, so that the last of the day is a little longer than the first of the night, and about the rising and setting through the whole year the temporal hours differ least from the equinoctial; by which method it would come about that at the equinoxes the temporal hours are again the same as the equal or equinoctial. Others, to whom this method seems laborious, contend that it is more consonant to follow nature in this inequality and to make the hours of absolutely all the days of the whole year unequal among themselves, so that the oblique ascension of each half sign in the ecliptic, or 15 degrees, begun from the place of the Sun, measures one temporal hour; by which method at the vernal equinox the shortest hours would be those surrounding the rising, the longest those surrounding the setting, and the inequality of the hours through the parts of the day would travel round in the yearly circuit. But sensible astrologers, who have also regard to nature, despise these dominions of the planets, and so judge the subtlety of these distributions to be idle.
Of twilights, an accident of the artificial night.
How do we inquire into the length of twilight? There must be given the altitude of the pole PR, the declination of the Sun ST, and the depth of the Sun below the horizon OS, from which twilight begins. This is fixed at 16, 18 or 19 degrees, as was said in the first book and will be said more fully in the fifth part. Taking, then, N the nadir and L the south pole, if the declination is southern, and the altitude of the Sun in the lower hemisphere OS as great as is for us the depth of the Sun; or if it is northern, taking the side in the vertical exceeding a quadrant and the upper hemisphere, there is sought by the doctrine of the first part TI or AT, the distance of the Sun from the semicircle of the meridian, there the lower, PI, which denotes to us midnight, here the upper, PA, which denotes to us noon, and it is compared with the hour of sunrise, counted from the same midnight or noon. Examples are in the fifth part.
What is the variety of twilights through places and times, with respect to astronomical causes? First, in the right sphere twilights are shortest, and through the whole year, as to celestial causes at least, nearly equal. For the Sun at the equinoxes ascends along the straightness of the vertical circle, which coincides with the equator, so that the ascension of the arc of the ecliptic between the horizon and the Sun is equal to its depth. Second, in oblique spheres the summer twilights are longest, the winter shortest, and the inequality, and the length of both, increases with the altitude of the pole itself. For a right-angled triangle is formed of the circle of the natural day, the horizon and the vertical, where the arc of the circle, subtended by the right angle QOS, is greater than the arc of the vertical OS, or the depth. And as with us the Sun in the summer signs quickly, in the winter slowly, acquires an altitude of 16, 18 or 19 degrees, so also in the other hemisphere this happens in the same parts of its year, which however coincide with the contrary parts of our year. In the summer signs, therefore, the Sun slowly becomes so deep as to extinguish the light of twilight, in the winter signs quickly. Third, under an altitude of the pole of 47°, 48° or 50° the solstitial twilights last all night. For when 19, 18 or 16 degrees are taken from the complement, 66½°, of the Sun’s greatest declination of 23½°, those arcs of the altitudes of the pole remain. This happens much more evidently and for a longer time at a still greater altitude of the pole. Thus the shortest twilight in the whole world, by these astronomical positions at least, has 1 hour 4′, 12′ or 16′, but the longest has no limit.
What is the chief use of the doctrine of artificial days? Astronomers, and geographers following them, distinguish the surface of the Earth into climates according to the increments of the day, and refer to them the celestial appearances, recording what different things belong to them in one climate and another. For where in the more recondite astronomy we speak thus, under this or that altitude of the pole, astronomers and geographers, speaking more popularly and to the common people, say in this or that climate.
What is the reason of this name? Klimata, from klinein, were called, as it were, inclinations, for those regions of the Earth which, from the places under the equator, having as it were a straight and balanced plain of the Sun, to which both poles are on the horizon, seem to slope toward either pole, so that one of the poles is seen to be elevated for them.
What, then, is a climate? It is a space or belt of the Earth, comprehended between two circles parallel to the equator, so far distant from each other that within them the excess of the longest day over its night can vary by one equinoctial hour.
Is it not enough to divide the whole surface of the Earth into five zones? The zones, separated from one another by the 4 primary parallels, which are the two tropics and the two polar circles, have a great breadth, as will be said in what follows. The ancients, therefore, disregarding the difference of zones, divided more concisely, by this new method, the whole breadth between the equator and the polar circle. The zones also divide the whole surface of the Earth, and are matters of more astronomical consideration; the climates, better known to geographers, were regarded only in the small part of the Earth which was known to the ancients, which did not exceed a semicircle in length and a quadrant in breadth.
With how many parallels is any climate described? With three: for two always bound any climate, but one, running through about the middle of the climate, has the mean length of day between the lengths at the beginning and the end. Yet one and the same parallel is always the beginning of one climate and at once the end of another.
Are the climates of equal breadth? By no means, for those which are nearer the equator are always broader.
Is the number of parallels and climates fixed? Since everything depends on the judgment of the geographers, it is no wonder that the number varies among different writers. Ptolemy at first arranged the parallels by half-hours of the difference between day and night, that is, by quadrants of the increments of the longest day, so that each climate increases the difference between day and night by one hour; when by this method he had come to the fourteenth parallel and the climates began to have half less of the breadth of the first, he suddenly fixed the following increments at double the former, namely half-hours, so that the climates again had the breadth of the first. At the nineteenth parallel the climates were again narrowed to half the former breadth; so between this and the twentieth he again fixed double the former increment, namely a whole hour. The same author continued the number of climates in the northern hemisphere as far as the seventh, in which he had begun to widen the parallels. The more recent writers, retaining the distance of one quarter-hour, number the parallels from the equator to the polar circle at 48, the climates at 24.
Where is the middle of the first climate placed? The first climate has in its middle a difference of two hours between the longest day and the shortest night, the second three hours, the third four, and so on in order.
Why did they not begin from the equator, placing the middle of the first climate where the difference of day and night is one hour, as in the following climate this difference is always one hour greater? The first portion of this uniform progression by whole hours, of the difference between the longest day and the shortest night, this side of and beyond the equator (as also the middle region under the equator itself, in whose middle this difference is nothing), was therefore not numbered among the climates, because some just space had also to be reckoned for the right position of the world and not inclined, with respect to which the other positions could be called klimata, that is, inclinations. So as elsewhere in arithmetic the numbers 2, 3, 4 and the rest are called numbers with respect to 1 (unity), but unity does not come into the count of numbers but is set as their beginning: so here also an inclination so great as made one hour in the middle was not counted as an inclination or climate. Another cause was added, that the interior places and those nearest the equator were less inhabited and known, since those who at that time wrote down the astronomical appearances were eager to adapt them to the use of the surrounding and known nations.
Did they name the climates only from numbers? On the contrary, a more frequent naming, and more suited to use, was from the more famous places lying about the middle of each climate. So these were their names: the climate through Meroë, through Syene, through Alexandria of Egypt, through Rhodes, through Rome, through the Pontus, through the Borysthenes. The southern ones could be named from the northern, of which the reasons are opposite, as the one opposite to that through Meroë, and so on.
What is the use of the doctrine of climates? Its chief use lies in explaining and understanding the writings of the ancient astronomers, geographers and physicians. Today their use is not so frequent, for instead of mentioning this or that climate we more commonly express the altitude itself of one or other pole.
How is the altitude of the pole investigated from a given climate? A climate being given, the difference of the day from the shortest night is given, for in the first climate this difference is two hours, in the second three, and so on in order. Let it be the seventh climate; the difference is eight hours, so that the shortest night has eight hours, the longest day sixteen; the semidiurnal time is eight hours, the excess therefore above the uniform (of 6 hours) is two hours, or 30° of the equator’s times. By what was handed down above, therefore, the ascensional difference is 30°. The same triangle QTS is therefore formed as above (page 225), by the horizon, the equator and the colure of the solstices, on which the Sun falls when it makes the longest day. The rest are as above; the special procedure is this:
The quotient 87066 gives the tangent of 41° 2′ 30″, the altitude of the equator. Therefore its complement, 48° 57′ 30″, is the altitude of the pole.
How, by the contrary way, is the climate known from the altitude of the pole? The ascensional difference, the Sun being at the solstice, is to be sought from the doctrines above, and from it the length of the day, which, compared with its night, gives the index of the climate.
Let the altitude of the pole be 41° 21′. The greatest ascensional difference will then be found to be 22° 30′, which make 1 hour 30′. The semidiurnal time is therefore 7 hours 30′. The day is 15 hours long, the night 9; they differ by 6 hours. This difference indicates the middle of the fifth climate, that through Rome.