Epitome Astronomiae Copernicanae: Liber III, part 9
Of the poetic rising.
By what difference is the rising and setting of the stars treated in the various parts of this book? In the first part it was said of those things which happen to the stars daily, without consideration of the ecliptic and the motion of the Sun through it; of which was said in the second part, of the artificial day, of which in the third part, or of the different seasons of the year, of which in the fourth part; but now the risings of the stars are to be compared not only with the ecliptic, as just now, but also with the motion of the Sun through it, with the light of day and with the seasons of the year. There it was said of that rising and setting which the stars themselves make, or rather, according to Copernicus, the horizon of the world: but here will be treated the appearance and hiding, which has its cause from the Sun and from daylight.
How are the risings and settings considered in this place called? Commonly they are thought to be called poetic because poets use them in descriptions of times; to me this name does not seem to be of a genus but of a single species.
In what sense, then, are the words to rise and to set or depart used here? The sense of these phrases is twofold even in this place: one popular, when with the coming of night and the extinction of the light of day all the stars promiscuously are said to rise which before, although present, lay hidden under the light of day; and conversely, when light has risen, at the approach of the Sun, those stars are said to depart which, having shone and been seen before, are now hidden by the light of day, so that, though still present in the height of heaven, they can no longer be seen. The other signification is more restricted and proper to the art, and is taken of those stars which, on account of the annual motion of the Sun through the zodiac, undergo vicissitudes of rising and setting.
How many species of such risings are there? Today the common people count three species of poetic rising and setting: the cosmical, the acronychal and the heliacal.
What do they call cosmical rising and setting? Modern astronomers mark with the epithet cosmical the beginning of the day, for an obscure reason: as if that star rose cosmically which rises at sunrise, and that set cosmically which sets at sunrise. I define cosmical rising or setting simply and generally as that when a star, without regard to the Sun, emerges above the horizon of the world or descends below it.
What is acronychal rising or setting? Acronychal rising is when a star rises, emerging above the horizon, at one extremity or boundary of the night, that is, at its beginning, the Sun setting in the opposite region. With Pliny it is the evening rising. The common people of today add this definition of acronychal setting, when a star sets as the Sun sets, that is, together with the Sun. I define acronychal setting as when a star sets at the other extremity or boundary of the night, that is, at its end; with Pliny it is the morning setting.
What is heliacal rising and setting? A star rises heliacally, that is, begins to appear, when, having before lain hidden under the rays of the Sun, so that it rose and set at almost the same time as the Sun, it has on the next day emerged from the Sun’s rays so far that, the Sun lying hidden under the horizon, it can be seen first, just on the point of setting below the horizon or being extinguished (if it has risen from the horizon) by the coming of the light of day. A star sets heliacally, or is hidden, which having before been seen above the horizon, the Sun not being sunk much below it, has now so hidden itself in the Sun’s rays that on the next day, risen from the horizon or about to set beneath it, it can no longer be seen. The former would more rightly be called appearance or emergence, the latter hiding. (Pliny, Book XVIII, chapter 25: either by the coming of the Sun the stars are hidden and cease to be seen, or by its departure they bring themselves forth. Custom would have said emergence, better than rising, and hiding rather than setting.) So the Greeks say epitolē, not anatolē, likewise phasis, and kryphis or aphanismos in place of dysis. This species of rising and setting I think was once called by a special name poetic, as if feigned; because the stars do not truly rise or set, but only appear to rise or set.
What then will become of the common people’s cosmical rising and acronychal setting? I judge that those species, as the common people define them, are to be otherwise called, if any place at all is left to them in this part of the doctrine. Certainly they are not poetic, in the vulgar notion of this word; for what poets would use them, since they are not seen? Let them be called rather astronomical and named risings and settings with the Sun; Pliny seems to call them morning risings and evening settings, although the heliacal also come under the same name. So for the rising which they call cosmical, let the poet expect the heliacal rising nearest and coinciding, and for the common people’s acronychal setting, that is, with the setting Sun, let him anticipate the nearest heliacal setting.
Give the reasons why you think those species should be struck out. First, the names make for me, for of night there are not one only, as the common view holds, but two extremities, the beginning and the end, and Ptolemy calls planets acronychal all night, namely both rising at the beginning and setting at its end. And the design of him who devised this name seems to have been this, to show that the star then experiences things contrary to the Sun, namely rising at the beginning of the night when the Sun rises at the beginning of the day, and therefore setting when the Sun rises. And the word cosmical, what else does it sound but that which is opposed to the Sun, when it is asked in respect of what the star rises and sets, of the Sun or of the world, that is, of the horizon of the world? Next, among the chief stars, namely those that fall in the zodiac, the evening rising and the morning setting are joined in respect of time; why then should they be distinguished by surnames, so that the one should be called acronychal, the other cosmical? The same reasoning holds of morning rising and evening setting: why should I be accustomed to say, on the same day, the cosmical rising and the acronychal setting of the same star? Third, the rising and setting with the Sun are for the most part surrounded by emergence and hiding; what need is there to distinguish still more subtly and laboriously these narrow times by those cosmical risings and (in the common sense) acronychal settings? Finally, those which we call heliacal are seen, those which I call acronychal are themselves seen; they are suited to husbandmen, physicians, historians, poets for popular descriptions of times; but those spurious risings and settings with the Sun, which they enrich with the names, the former of cosmical, the latter of acronychal, are by no means seen, nor to be sought from the heavens but from the books of astronomers, nor recognised except by those who have learned astronomy. And so I have noted no approved writer who used these names in the common sense, nor even for popular descriptions of things; on the contrary Pliny and others, when in describing times they use these invisible risings and settings, both put other names, as has been said, and do it for another end, not to describe the times by popular marks, but to recall the abstruse causes of the seasons, drawn from astrology.
In what parts of the day do heliacal risings and settings fall? Fixed stars always, planets for the most part, are found to have emerged in the morning from the rays of the Sun, and in the evening to have vanished, sunk in the rays of the same; so that they are seen emerging in the region of the rising and are lost, hidden under the rays, at the setting. Except, however, First, the Moon always, and Mercury and Venus, when, like the Moon, they are swifter than the Sun itself and direct: for then (like the Moon) they are found in the evening to have emerged in the west, and in the morning to have disappeared in the east, hidden under the rays of the Sun.
Second, analogy also bids us make some exception within the polar circles, or in the frigid zones; namely, if the Sun and stars are in those signs which rise in inverted order and near the ecliptic; for if the Sun were sunk in them so deep below the horizon that the stars could shine out, not only the other species of risings and settings, but even the heliacal themselves would have all the reasons explained here changed.
How far must the Sun have departed from a fixed star that it can be seen free of the Sun’s rays? Although this matter has much variety, both as to the brightness of fixed stars and planets and as to the different disposition of the air through various places and times, and add also the different regions of the horizon, which are not equally illuminated by the twilight: yet craftsmen set down certain figures which agree as nearly as possible with the observations, namely these: first, that the Sun sunk in the vertical circle 19° below the horizon makes the beginnings and ends of the twilights; although Tycho Brahe requires not more than 16°, at the equinoctial rising at least, others 18°. Next, that the least fixed stars cannot be seen, in that region of the horizon which is toward the Sun, unless the Sun is sunk 18°. For stars of the sixth magnitude they set a depression of the Sun of 17°, for the fifth 16, for the fourth 15, for the third 14, for the second 13, for stars of the first magnitude 12°. The planets need a smaller depression of the Sun: Mars 11° 30′, Saturn 11°, Jupiter and Mercury 10°, Venus 5°. Although the unequal distance of the planets from the centre of the Earth seems to require much greater variety.
Granting that this observation is certain: I now desire to know how I may investigate in what degree of the ecliptic the Sun must be, so that, the star rising or setting by the motion of the world, the Sun itself may be depressed below the horizon by the due measure? In the sphere, a degree of the ecliptic that rises or sets with the star being placed on the rising or setting horizon, the vertical circle, prolonged beyond a quadrant by the due measure of degrees, is moved to and fro on the proposed horizon until it touches the ecliptic with its extremity: by that contact it shows the place of the Sun which it must occupy, that the proposed star may be able to rise or set heliacally.
I should like to be able to inquire the same by calculation. There is need, then, from the doctrine set forth, of knowledge of the degree of the ecliptic rising or setting with the proposed star, and of the angle which the ecliptic makes with the horizon in those parts. Then, C being the pole of the ecliptic, V the zenith, EOS the ecliptic, E the nonagesimal, O the rising point, we shall imagine a triangle OIS between the ecliptic OS, the horizon OI and the vertical IS, in which (always lying hidden under the horizon), besides the right angle OIS which the vertical makes with the horizon, there is given also the angle IOS which the ecliptic makes with the horizon at the point O, and the side IS opposite to it, namely the arc of the vertical VS when the Sun is sunk below the horizon. Wherefore the arc of the ecliptic OS opposite the right angle is also found, which arc is between O, the rising or setting point, and S, the Sun. For the sine of this arc of depression, prolonged by 5 ciphers and divided by the sine of the angle of the ecliptic and horizon, makes the quotient, which is the sine of the arc sought, to be added to the point of the ecliptic that rises with the star, and subtracted from that which sets with the star, and the place to be occupied by the Sun results.
In what order do the various risings and settings of the same fixed star follow one another? First, a star always rises with the Sun before it rises out of the Sun, and sets with the Sun later than it sets under the Sun’s rays. Second, when the latitude of the star is northern, the star first rises with the Sun, afterwards culminates with it, and last sets with the Sun; and in the same order it also makes its acronychal risings and settings. When the star is southern, the contrary happens; when the star is in the ecliptic itself, all three must coincide. Third, heliacal risings and settings also change order in different stars, both among themselves and with the said risings and settings with the Sun, but the common limit of this change is not the ecliptic, but lies with those stars which have so great a northern latitude that on one and the same day they can both rise and set heliacally. For stars which are more northern than these, in any longitude of the ecliptic, emerge earlier from the Sun’s rays, and are hidden under them afterwards, and that on days nearer to the culmination than are their risings and settings with the Sun. But stars which are more southern than the said limits are hidden earlier and emerge later, and in the intermediate time rise and set with the Sun, so that their heliacal risings and settings are farther distant from the culmination.
Take the diagram of this variety, for memory. KEOQS is the line of rising with the Sun. LNPDT is the line of heliacal rising. HMODV is the line of heliacal setting. IEPRX is the line of setting with the Sun. AB is the order of the signs, and the motion of the Sun and the succession of days. F is a southern star, the order of its appearances H, I, K, L. E is a star in the ecliptic, the order of its appearances M, E, N, for on the same day it both rises and sets with the Sun. The star C is northern, but more southern than D; at the same time it both rises with the Sun and sets heliacally, and conversely, namely in the order O, P. The star D first rises with the Sun, afterwards on the same day both rises and sets heliacally, again later sets with the Sun: namely in the order Q, D, R. The star G, more northern than D, first rises with the Sun, afterwards heliacally, then sets heliacally, finally with the Sun; the order of appearances S, T, V, X. The stars F, E, C lie wholly hidden for some time; the black colour indicates this. D is the last which on a single night, when the Sun is at E, lies wholly hidden, and is seen only momentarily in the morning and evening; it is the first of those which are seen on all the nights of the whole year, having two appearances on the same day, one daily and common or popular, when either by night they rise from the horizon, or, the light of day being extinguished, shine forth from on high, the other temporary, before or after the Sun, which occurs between the days of heliacal rising and setting.
By what method is the place found in which any star can both rise in the morning and set in the evening heliacally, the Sun being in any degree of the ecliptic? First, the right ascension ET and the declination ST of the Sun’s proposed place S are sought for each place. Second, from RS, the depression of the Sun below the horizon, as great as the magnitude of each star demands that, placed on the horizon, it may be seen first or last, and from the declination ST of the Sun’s place, the triangle LSN being taken here, on account of the southern declination, so that SN is the complement of the Sun’s depth, LS the complement of the declination, there is sought by the doctrine above the angle SLN or TI, and so I, a degree of the equator on the meridian, and the degree Q on the east are established; this is the oblique ascension of the star required, which, compared with the right ascension ET found before, yields the ascensional difference QT. Third, a new triangle is now formed by QB the rising or setting horizon without distinction, QT the equator and TB the circle of declination of the star placed on the horizon, having the same right ascension as the proposed place of the Sun: in which besides the right angle T the angle BQT is given, whose measure is AH, the altitude of the equator, and the side QT in the equator, which is the ascensional difference common to the Sun and the star. Multiply, therefore, its sine by the tangent of the altitude of the equator, and five last figures being cast off there results the tangent TB of the declination of the place sought for some star. From this declination TB and the right ascension ET above you have learned how to investigate the longitude and latitude.
Example. Let the Sun be in 0° of Capricorn, whose right ascension, as also that of the place to be sought, will be the same, 270°; the declination of the Sun is 23° 31′ 30″ south. Let the limit be sought for fixed stars of the first magnitude, at an altitude of the pole of 48° 16′. The depression of the Sun required is therefore 12°. Hence I seek the time:
From the nadir to the Sun 78°, depression 12°, sine 20791; subtract, because in the opposite hemisphere the declination is equivalent to northern.
(The versed sine itself serves here, because in the opposite hemisphere the declination is equivalent to northern.) 270° less 98° 28′ is 171° 32′, the right ascension of the midheaven. (Let it be morning.)
261° 32′, the oblique ascension of the horoscope. Take this from 270°, the difference tangent 7° 29′; this is the northern declination of the place sought, because the star is placed on the horizon, above the end of its right ascension, and its right ascension is 270°. This declination and this right ascension indicate the longitude 0° of Capricorn, the latitude 31°, the declinations of the Sun and of the star being simply added here.
A star of the first magnitude, therefore, near the Sun in 0° of Capricorn with latitude 31°, will on the same day both rise and set heliacally.
Let the Sun be in 0° of Cancer, with so great a northern declination, the rest remaining.
In our hemisphere, then, the triangle VPS is taken, and the side VS of altitude exceeds a quadrant and is 102°.
Therefore the sine of the depression of 12°, 20791, and the first sine 90820 are to be added; sum 111611;
the quotient, 182867, is the versed sine of an arc of 145° 58′, which take away from the ascension Oblique ascension of the horoscope 34° 2′.
Right ascension of the star 90° 0′.
Difference of ascensions 55° 58′, sine 82871; tangent of the altitude of the equator 89201.
82871 by 89201 gives 73922, the tangent of an arc of 36° 28′, which is the declination of the star sought, indicating a latitude of 12° 57′ north in 0° of Cancer: so great a latitude will a star of the first magnitude have that, the Sun being in 0° of Cancer, it both rises and sets on the same day.
Show the diversity of these appearances by the example of Arcturus. Tycho Brahe places Arcturus in 18° 40′ of Libra, latitude 31° 3′ north. Therefore its right ascension is 209° 24′. Mediation of the heavens 1° 34′ of Scorpio, declination 21° 19′ north. Hence the species of its risings and settings are computed by Maestlin, as the following table has:
Therefore from the time of the equinox almost to the solstice, namely from 23 March to 16 June, the star Arcturus is seen all night, but its rising above the horizon and setting below it cannot be seen because of the light of day. For on 23 March, rising at the very setting of the Sun, it spins out longer delays above the horizon than the Sun below. On the following days, at the Sun’s setting, Arcturus has already risen above the horizon, so that it is discovered with the other stars when the light of day is extinguished; and it is hidden by the light of the following day approaching, not yet setting. Meanwhile the Sun comes to 1° 34′ of Taurus; then Arcturus occupies the midheaven at the point of midnight, and its rising above the horizon and setting below it are distant by equal spaces from the beginning and end of daylight.
For the other stars situated in the south, then, the delays above the horizon are short, and they are therefore not seen all night, but seem both to rise and to set within the same night, the Sun being in their opposite; but Arcturus in this situation rises before the setting of the Sun and sets after its rising, conspicuous at neither time. On 16 June, although the night is shortest, Arcturus nevertheless ceases to be seen through the whole of it; for it sets at the very rising of the Sun, and thence, before the Sun, while it is still night, withdraws itself under the horizon from our eyes. So from 16 June to 25 November the setting of Arcturus falls in the night, passing little by little from the beginning of the night to its end: its setting is seen, therefore, for 5 whole months. Conversely, from 9 October its rising above the horizon unfolds itself from the Sun’s rays and its rising remains visible from that day until 23 March, when, as was said, it ceases to rise after the end of day and so in the night. Of these intervals the common space of time, which is between 9 October and 25 November, for 47 days, falls on both the nearest nights alike, both the rising of Arcturus above the horizon and its setting below it, and so both can be seen, the Sun passing nearest to Arcturus and culminating with it. But stars toward the south, on the contrary, when they have the Sun present, are plainly not seen. And the southern ones indeed are hidden earlier by the Sun’s rays in the evening, and go out later from the rays in the morning; Arcturus in the contrary order emerges in the morning earlier, on 9 October, and is hidden in the evening later, on 25 November.
How do writers use these risings and settings of the stars, and on what occasion? The Greek nations, and from their institution the Romans in antiquity, used a year mixed of lunar and solar, whence it happened that now they went ahead of the Sun and now followed it. Since, however, the seasons of the year do not return with an erroneous Calendar but with the Sun and the solstices, in order that rural, domestic and military works might each be done in its season, the ancients set forth the risings and settings of the stars in place of a Calendar, some from the said necessity, some for the sake of teaching, because copies of a Calendar could not be had in such plenty as today, and if they were set forth in public, could not be understood by countrymen, who were ignorant of letters and spent their time absent in the fields; but these signs could be observed even by the unlettered. Some, finally, sought ornament for their speech, as poets, who, luxuriating in a flowery kind of diction, are wont, as other things, so also times, to describe by their circumstances and as it were paint them, since of circumstances none is more beautiful than the risings and settings of so many stars, so various.
In how many ways are ancient times compared with modern for the sake of this marking by risings and settings of stars? The comparison is threefold. First, by reason of one and the same Roman Calendar. Second, by reason of the motion of the Sun in the ecliptic. Third, by reason of the very rising and setting of the stars. Of these the first and the last are of little use unless they are reduced to the middle one. For the first comparison is only historical or political, the last savours of astrological subtlety; but the middle one is rustic, domestic, medical, natural.
Why do you call the middle comparison alone natural? Do those risings of the stars, then, effect nothing? The ancients were indeed of the opinion that whatever more violent storms were wont to occur almost every year about the rising of any star were produced, or at least signified, by the rising or setting of that star. Hence arose among the Greeks the peculiar use of the words sēmainei, prosēmainei, episēmainei (it signifies, it signifies beforehand, it signifies besides), when they wished to say that this star was efficacious and produced a great commotion of the air. Pliny rendered the Greek word in Latin with the same use, saying it signifies or indicates: hence certain stars were called indicating beyond the rest, as the Dog. And the matter went so far that by metonymy the fixed seasons themselves were called stars, and Cicero complained of a very disturbed star of the equinox. Trees too are said to be star-struck, which are infested by hail, frost, blight, heat, diseases of the seasons; and the star-struck, that is, breathed upon by a star, who fall suddenly ill from a hidden cause, as if a plague had been sent from heaven or they had been struck suddenly by lightning. But Geminus refuted the opinion of the common people, and also of all the learned of his age, by natural and astronomical arguments; he lived before Christ. But no refutation of this opinion can be more manifest than that which our age has taught us, when the stars have departed from their former seats in the zodiac and rise in the following months, while the seasons return with the Sun and today come ahead of those their former signs; and now what Virgil sings is true:
They know their own sun, their own stars;
that is, any part of the year reckoned from the solstice retains its own nature, its own character and its own seasons, while the fixed stars migrate more and more on the following days.
Teach how to compare modern times with ancient from the same sign expressed in the rising or setting of stars. For this matter there is need of the longitude and latitude of the star and of an ephemeris of the Sun’s motion, adapted to the times of the writer, and in the form of the old Julian year extended backward. Then if the writer expresses a day of the Roman year and a rising or setting of a star under a certain elevation of the pole, the place of the Sun for that day is to be sought in the old ephemeris. Next the point of the ecliptic rising with the star, or setting with it, is to be sought, and by comparison of the Sun’s place with this co-rising point the credit of the writer will easily appear, and, if he wrote truly, the species of the rising or setting. So, if the same day of the Roman Calendar is taken up again even today, the sum of the political years will indeed be exact, but neither the season of the year nor the same stars will return on that day; and in respect of the turning year we shall have come beyond the proposed limit, while of the sidereal year we shall not yet have reached the limit. Second, therefore, to know the limit of the natural or tropical year as it returns, seek the place of the Sun, taken from the old ephemeris, in the ephemeris of our age, and the day of the Julian year on which you find it is to be compared, in respect of the same season, with the day which the writer recorded. The modern day will, however, come before the ancient in the order of the days of the Calendar. The season of the year will thus return the same, but not the same sign. But if third you desire to know on what day of the Julian year, and in what degree of the ecliptic the Sun being, the same rising or setting of the same star which the writer recorded will return today: seek again, by the present longitude and latitude of the proposed star, the degree of the ecliptic rising with it today or setting with it; by what interval this will follow the point rising or setting in the writer’s time (for it will follow), by almost that interval the Sun’s place in the ecliptic today will be later than its place on the day recorded by the writer of his age. Finally, the Sun’s place so found, if it is sought in the ephemeris of this age, will show the day of the Julian year to be compared with the writer’s day, in respect of the same star: the same rising will, that is, fall today later in the Julian year.
Is there no abridgement for so laborious a work? By how many days the Sun differs from the Julian Calendar has been said above, namely in 1767 years almost 13 days, which 13 days can be added to the day of the Julian year, extended backward to the age of Hipparchus, by constant observation: for there is no need here of a more scrupulous computation, nor must it be minded that in one part of the year, on account of the unequal motion of the Sun and the progress of the apogee, we are in excess, and in another somewhat in defect, which indeed down to these times is very little.
But the risings and settings of the stars, as they are of various species, so also through different climates, and through their declinations diminished or increased today by the Sun, and finally through the places of the ecliptic, of ascensions that are today longer or shorter in the oblique, vary much, so that more error lies here in abridgements. Yet here also we can come near the truth, by adding for the age of Hipparchus 12 days (as above) to the day in the Roman year on which the rising of each star was expressed. And since the suspicion is uncertain that the tropical year was once longer (of which in Book VII), it will do no harm, following the example of Tycho Brahe, to set the centuries between us and Hipparchus by the line and to continue the same proportion to the intermediate and more ancient times by the following little table, in which force is indeed done to the observations of Ptolemy in the column of the tropical year; for the 11 that he observed they give 12½. But of this in Book VII.
Which of all the stars is most celebrated among writers? The star of the Great Dog, called Sirius: for it is the greatest of the stars, and was most frequently observed by the Egyptians for the sake of prognostic; its rising was marked in Greece and Egypt by the blowing of the Etesian winds, a thing most celebrated among the ancient historians. In sum, whatever occurs naturally in that part of the year, on account of the heat grown to its height and now fading with the departure of the Sun, was ascribed to this star. As that summer grows oppressive, the seas are hot, the grapes are infested with the carbuncular disease, wines are changed, dogs are driven to madness, diseases set in, the cure of diseases proves difficult. Finally, that part of the year has for two thousand years now been surnamed the dog days.
Another notable star, however, precedes the rising of the Dog, a little smaller, which the Greeks call Procyon, Pliny the Little Dog or Canicula; when it has risen, we know that the Great Dog will follow very soon.
Declare the prescribed method by the example of those two stars. Tycho Brahe places Sirius, at the completion of the year 1600, in 8° 36′ of Cancer, with latitude 39° 30′ south. It is therefore among those stars which lie wholly hidden from the heliacal setting to the heliacal rising. Its right ascension, then, for the said year is 96° 53′, its declination 16° 11′ south, so that with the star itself 6° 19′ of Cancer mediates the heavens. Let the altitude of the pole be 48° 30′, as the tract of the Danube has, which is in the seventh climate, that through the Borysthenes. Therefore the ascensional difference of the star is 49° 29′, the oblique ascension 146° 22′, and the co-ascending point 13° 32′ of Leo; the angle between the ecliptic and the horizon 55° 10′. The oblique descension, however, is 47° 24′ and the co-descending point 26° 40′ of Taurus; the angle between the ecliptic and the horizon 50° 51′. With these angles and with the depth of the Sun, 12° (because the proposed star is of the first magnitude), there are found arcs of the ecliptic between the Sun and the horizon of 14° 40′ and 15° 33′, of which the former added to the co-rising point, the latter taken from the co-setting point, show the Sun’s places at the heliacal rising of the star, 28° 12′ of Leo, and at its setting, 11° 7′ of Taurus. Therefore today, the Sun being in 11° 7′ of Taurus, which happens on 21 April old style or 1 May new style, the Great Dog is hidden in the evening on the banks of the Danube, and on 7/17 May it sets with the Sun and remains concealed for three months, in the middle of which, namely on 18/28 June, it culminates with the Sun, when it has the Sun as near as it can. Thence on 27 July old style or 6 August new style it rises with the Sun, and a little later, in August, it appears again in the morning. It follows that for the rest of the time of the year through which it can be seen, it sets in the morning on 9/19 November, and rises in the evening on 23 January old style or 2 February new style.