# Tycho Brahe: a picture of scientific life and work in the sixteenth century/Chapter 8

CHAPTER VIII.
FURTHER WORK ON THE STAR OF 1572.
After the publication, or rather the completion, of the second volume of his book Tycho pushed on the preparation of the first volume on the new star, of which the printing began long before the manuscript was approaching completion. From many direct or indirect allusions to time in various places in the book, it appears that it was written in the years 1588 to 1592, and as Tycho had several times been inconvenienced by want of paper, he resolved to build a paper-mill on the south-western coast of the island, which could be driven by the water from the fish-ponds. This mill was finished in 1589 or 1590 and the same water-wheel which turned it could also be connected with a corn-mill and machinery for preparing skins. It was, however, by no means only the want of paper which delayed the completion of Tycho's book; it had come to embrace ​many branches of astronomy, and as the current observations continued to reveal imperfections in the values of astronomical constants handed down from antiquity, Tycho was unwilling to finish the book and deprive himself of the power of inserting in it further results of his work. The book was never issued in a complete state in his lifetime; only a very few friends or correspondents received incomplete copies or portions of the book; and after Tycho's death an important section (32 pp.), separately paged, was inserted at the end of the first chapter. When completed, the book numbered more than 900 pages, divided into three parts and a "conclusion;" and it bears many traces of having been both written and printed in the course of many years, succeeding sheets frequently before preceding ones. The first chapter deals with the apparent motion of the sun, the length of the year, the elements of the solar orbit, refraction, and gives tables for the motion of the sun. As there were a few pages to spare (the second chapter having been printed and paged first), Tycho determined to devote them to the lunar theory, though this had nothing to do with the determination of star places, and was not even mentioned in the title of the chapter; and as this subject grew in importance and difficulty, it eventually delayed the publication of the volume considerably. The second chapter describes the methods of determining the places of stars, investigates the amount of precession, and contains Tycho's own catalogue of star places. This finishes the first part of the book, and as we shall examine in our last chapter the various subjects dealt with, we may pass to the second part of Tycho's book, which is devoted to his own observations of the star of 1572.
​The third chapter describes the appearance of the star, the gradual fading of its light, the variation of colour; how it was seen by carriers, sailors, and similar people, a good while before the astronomers in their chimney-corners heard of it; then branches off into a mythological account of Queen Cassiopea, and gives a map of the constellation with the star in it. Tycho refers to the Aristotelean idea of the unchangeable nature of the heavens, and to the star of Hipparchus, which he believes to have been similar to his own star, and then to that of the Magi, which he says could not have been a star in the heavens, since it showed the way to a particular town, and even to a house, and was only seen by the wise men. He therefore summarily dismisses the idea that the star in Cassiopea should signify the return of Christ. Lastly, he mentions the stars said by Cyprianus Leovitius to have appeared in the years 945 and 1264. All these subjects we have dealt with in sufficient detail in the chapter on the new star, where the book of which we are now summarising the contents is frequently quoted.
In the fourth chapter are given descriptions and illustrations of the sextant with which he observed the star, and of the great quadrant at Augsburg. This chapter also contains the measured distance of the new star from twelve stars in Cassiopea, the distances inter se of most of these stars (from observations made at Hveen in 1578 and 1583), and a number of observations made with the Augsburg quadrant. As this instrument was designed and constructed by Tycho, he naturally wished to prove its excellence, and inserted a number of observed declinations of circumpolar stars (which give values for the latitude of Göggingen agreeing inter se within a minute), and the declinations of six zodiacal stars in equally good accordance with the results obtained at Hveen.
In the fifth chapter the co-ordinates of the star both ​with regard to the ecliptic and the equator are computed from its distance from the other stars in Cassiopea and the places of these stars as observed at Hveen. Seven different combinations give results of which the extremes differ only about half a minute. Tycho also gives the places of the twelve comparison stars according to Alphonso and Copernicus (i.e., Ptolemy), which differ in many cases upwards of a degree from his own. He then turns in the sixth chapter to the question as to where the star was situated in space, and proves in four ways that it was far beyond the planets, "in the eighth sphere." First, the shape, light, continual twinkling, immovability, daily revolution like the fixed stars, and its having lasted more than a year, prove that it was not a comet. Secondly, it had no parallax, as the distance from the pole and from neighbouring stars remained unaltered during the daily revolution, while the polar distance would have varied 1° 5′ if the star had been as near as the moon, 2′ 52″ if as near as the sun, and 16″ if at the distance of Saturn, with smaller variations in the distances from the other stars. Here he not only gives this indication of his idea of the distance of the planets, but also shortly alludes to his system of the world. He remarks that if the star was situated in the sphere of Saturn, and if we adopt the annual motion of the earth according to Copernicus, the star would in a year appear to move backwards and forwards (i.e., have an annual parallax) to the extent of about ten degrees, so that even followers of Copernicus must admit that the star was far beyond Saturn. The third proof of the great distance of the star is, that the meridian ​altitudes gave the same latitude (for Heridsvad and Göggingen) as other stars gave; and the fourth is, that observations at far-distant places gave results in good accordance inter se, as, for instance, his own and those of Munosius at Valencia. As Tycho has so often referred to the parallax of the moon, he verifies at the end of this chapter the value of Copernicus by computing the lunar parallax from six observations, three on the meridian and three at the nonagesimal point, where there is no parallax in longitude.
In the seventh and last chapter of the second part of the book Tycho attempts to calculate the diameter of the new star. He first recounts the crude ideas of his predecessors as to the diameters of the planets and fixed stars, on which he did not improve very much himself. He did not, however, place all the fixed stars at the same distance just beyond the orbit of Saturn, and he suggested that the fainter stars are probably at a far greater distance than the brighter ones, though even if they were at the same distance it would not follow that all the stars which we consider as belonging to one magnitude were equal in size, as Sirius and Vega are much larger than Aldebaran, which again is larger than Regulus. The apparent diameter of the sun Tycho had, in 1591, measured "through a canal 32 feet long," and in this way he found that at the apogee the diameter was barely 30′, and at the perigee slightly above 32′. The instrument was, according to Kepler, a screen on which the image of the sun fell through a small opening, and the "canal" must have been added merely to exclude stray light. The diameter of the moon Tycho generally ​determined by observing the difference of declination of the upper and lower limb; he adopts the mean diameter 33′. With these data he now calculates the real diameters of the sun and moon, making use of the old value of the solar parallax of 3′, which neither Copernicus nor he thought of discarding. The distance of the sun being 1150 semi-diameters of the earth, the semi-diameter of the sun will be 5.2 times that of the earth, and similarly the distance of the moon is 60 and its semi-diameter 0.29. For the planets he assumes apparent diameters from 2′ to 3′, and calculates from these their diameters and volumes in parts of those of the earth. For the fixed stars Tycho assumes smaller apparent diameters than other astronomers did before the invention of the telescope. With regard to the distance of the stars, he believes the greatest distance of Saturn to be 12,300 semidiameters of the earth (to arrive at which he sketches the theory of Saturn as mentioned above); and as he does not believe that there is a great void between the orbit of Saturn and the fixed stars, he places these at ​a distance of about 14,000, and the new star at least at 13,000 semidiameters. The apparent diameter of the new star at its first appearance he estimated at 31/2′, and its real diameter must therefore have been 71/8 times that of the earth, or somewhat greater than that of the sun. He does not think that the diminution of light was caused by the star having moved away from us in a straight line, partly because no celestial body moves in a straight line, partly because it would, when about to disappear, have been at the incredible distance of 300,000 semidiameters of the earth. The star must actually have decreased in size, so that it at the end of the year 1573 was about equal to the earth in size.
This finishes what Tycho has himself found by observation and speculation concerning the star of Cassiopea, and he next devotes the third part of his book, 300 pages, to an examination of the writings of other astronomers or authors about the star. First he discusses in Chapter VIII. the observations of those who could not find any parallax (the last book considered being his own little book of 1573, of which he reprints the greater part, omitting the astrological predictions); next he deals in Chapter IX. with those authors who thought they had found some parallax, but who did not place the star within the lunar orbit; and lastly, he deals with the writers "who have not brought out anything solid or important, and either maintained that the star was not new or that it was a comet or a sublunary meteor." His remarks are often written in a sarcastic style, with puns or play upon words, by which he perhaps meant to relieve the dulness of this far too lengthy part of the book. We have above, in our third chapter, given the reader some idea of these various classes of writers, and need not, therefore, here enter into further details about these chapters of Tycho's book.
​Finally, the "Conclusion" of the volume (pp. 787–816) gives first a rapid summary of the contents of the book, and then deals with two questions not yet touched upon, the physical nature of the new star and the astrological effect and signification, which the author did not wish to enter on in the body of the work, "as these matters are not subject to the senses, nor to any geometrical demonstration, but can only be speculated on." As to the nature of the star, Tycho considers that it was formed of "celestial matter," not differing from that of which the other stars are composed, except that it was not of such perfection or solid composition as in the stars of permanent duration. It was therefore gradually dissolved and dwindled away. It became visible to us because it was illuminated by the sun, and the matter of which it was formed was taken from the Milky Way, close to the edge of which the star was situated, and in which Tycho believed he could now see a gap or hole which had not been there before. This idea may to the modern reader seem absurd, but it should be remembered that the telescope had not yet revealed the true nature of the Milky Way, and Tycho's ideas about the latter were at all events a great advance from those of Aristotle (which he sharply attacks), according to which the Milky Way was merely an atmospheric agglomeration of stellar matter. With regard to the other question, the astrological signification of the star, Tycho had evidently considered it a good deal since he wrote his little book in 1573, and he does not on this occasion merely express himself in very general terms, but gives his opinion with more decision. As his prediction attracted a good deal of attention, particularly later when it seemed to have been fulfilled, it is worth while to give a short summary of it.
As the star of Hipparchus announced the extinction of the Greek ascendency and the rise of the Roman empire, ​so the star of 1572 is the forerunner of vast changes, not only in politics, but also in religious affairs, for the star was situated close to the equinoctial colure, which by astrologers is supposed to have something to do with religious matters. And as the star first shone with Jovial and clear light, and afterwards with Martial and ruddy light, the effect will first be peaceful and favourable, but afterwards become violent and tumultuous. And the religions which are full of "Jovial" splendour and pomp, after having for a long time dazzled ignorant people by their external magnificence and more than Pharisaic formalism, will, like that pseudo-star, fade and disappear. Though the star was so near the equinoctial colure that it nearly touched it with its rays, it was quite within the vernal quadrant, and it announces that some great light is at hand, just as the sun when past the vernal equinox conquers the darkness of night. And as the star was visible over most of the earth, so the effects of it will be felt over the greater part of the globe, though the northern hemisphere will be especially affected. With regard to the time when the influence of the star will begin to be felt, this will be nine years after the great conjunction of planets in April 1583, in the 21st degree of Pisces (because the direction of this and the star along the equator is 9°), or in other words, in 1592, and those who were born when the star appeared will about that time enter man's estate, and be ready for the great enterprise for which they are ordained. But if we take the direction along the zodiac, we find forty-eight years, after the lapse of which period the effect of the star will become strongest, and will last for some years, until 1632 or about that time, when the effect of the fiery trigon (which the star announced) will also be felt. The conjunction of 1583 concluded a cycle of planetary conjunctions, the seventh since the ​creation of the world. The first cycle ended at the time of Enoch, the second at the deluge, the third at the exodus from Egypt, the fourth at the time of the kings of Israel, the fifth at the time of Christ when the Roman empire was at its height, the sixth when the empire arose in the western world under Charlemagne, and the seventh and sabbath-like one was now coming. And as the first, third, and fifth "restitution" had been salutary to the world, the seventh, which had a particularly uneven number, will inaugurate a very happy state of things, a peaceful and quiet age such as that foretold by the prophets Isaiah (ch. xi.) and Micah (ch. iv.), when the lion shall eat straw like the ox, and the sucking child shall play on the hole of the asp, &c. As to the place on the earth from which this change will arise, it will be the one in the Zenith of which the star was at its first appearance, which Tycho assumes to have been at the time of the New Moon previous to the 11th November, when he noticed the star. The star was then on the meridian of places about 16° east of Uraniborg and in the Zenith of a place with north latitude 613/4. This fixes the ominous spot "in Russia or Moschovia where it joins the north-east part of Finland." Having devoted so much space to this matter, I must pass over the way in which Tycho finds Moschovia pointed out in the Prophets, the Revelation, and a certain ancient prophecy of Sibylla Tiburtina, found in 1520 in Switzerland.
That Tycho when writing of the religion distinguished by pomp and splendour which was soon to disappear was thinking of the Roman Catholic persuasion is beyond a ​doubt, and it is curious that the book in which we read this, though printed in Denmark, should eventually come to be published at Prague (where the religious war which he foretold raged furiously less than twenty years after his death) and was dedicated to the Roman Emperor! But it is more curious still that some of his other predictions seem to be fulfilled in the person of Gustavus Adolphus, the greatest champion of Protestantism in the seventeenth century. He was born in 1594 (only two years after the influence of the star should begin to be felt), and his glory was greatest in the year in which he fell, 1632, the very year mentioned by Tycho. He certainly was not born in Finland (for it is Finland and not the adjoining part of Russia which is indicated by 16° east of Uraniborg and 62° Latitude), but in Stockholm; but Finland was still a province of Sweden, and the yellow Finnish regiments were conspicuous for their bravery on many a blood-stained battlefield in Germany. No wonder that many contemporaries of Gustavus Adolphus were startled by these coincidences, and that the concluding part of Tycho's book was translated into several languages. But the star had a truer mission than that of announcing the arrival of an impossible golden age. It roused to unwearied exertions a great astronomer, it caused him to renew astronomy in all its branches by showing the world how little it knew about the heavens; his work became the foundation on which Kepler and Newton ​built their glorious edifice, and the star of Cassiopea started astronomical science on the brilliant career which it has pursued ever since, and swept away the mist that obscured the true system of the world. As Kepler truly said, "If that star did nothing else, at least it announced and produced a great astronomer."
* ↑ See, e.g., Progym., i. pp. 34, 52, 102, 335, 559, 710, 721, 745. In the appendix written by Kepler it is stated that the book was written between 1582 and 1592, but the printing cannot have commenced before 1588, and that the first chapter was written in 1588 is evident.
* ↑ In a letter to Rothmann (24th November 1589) Tycho mentions the mill as having been for some time at work. The inscription on a slab in the wall of the mill is given slightly different by Resen., Inscript. Hafn., 1668, p. 335 (Weistritz, i. p. 69), and in the Danske Magazin, ii. p. 265 (Weistritz, ii. p. 198); and according to the former it was begun in 1589 and completed in 1590; according to the latter, commenced 1590, finished 1592. But the former dates must be correct, as they agree with Tycho's statement that the mill was at work in 1589; and in the meteorological diary we read under 22nd July 1590: "Abiit Valentinus opere aggeris apud molendinum confecto." In March 1590 the widow of Steen Bille was ordered to allow Tycho to cut down an oak in the wood at Heridsvad for use in the mill (D. Magazin, ii. 264).
* ↑ The Catalogue was printed after the succeeding sheets, and the sheets KK. and LL. are therefore double ones, as the Catalogue filled more space than anticipated.
* ↑ The result adopted by Tycho is for 1573, AR 0° 26′ 24″, Decl. 61° 46′ 45″, while Argelander found 0° 28′ 6″ and 61° 46′ 23″ from a recomputation of the distance measures, using Bessel's and Bradley's star places. Astr. Nachr., lxii. No. 1482.
* ↑ On p. 414 he refers to the difficulty of finding the parallaxes of the outer planets, and how Mars was nearer than the sun. See above, p. 179.
* ↑ Progym., p. 470.
* ↑ Ibid., p. 471. Historia Cœlestis, p. 475 et seq. Tycho's mean diameter 31′ is exactly 1′ too small, and the difference between apogee and perigee is only 1′, as Kepler already found.
* ↑ Ad Vitell. Paral., cap. xi.; Opera omnia, ii. pp. 343–44, where Kepler quotes some observations made at Hveen in March and June 1578, giving 30′ 35″ and 29′ 53″. About the diopters of Hipparchus, see Halma's preface to the Almegist, vol. ii. p. lviii.
* ↑  The diameters of the planets are measured by pointing with the armillæ or a quadrant alternately to the upper and lower edge of the planet. See, e.g., Historia Cœlestis, p. 429, for a number of measures of Saturn. The diameters assumed are (Prog., pp. 475-76): Mercury 2′ 10″ at mean distance, 1,150 Venus 3′ 15″„„ 1,150 Mars 1′ 40″„„ 1,745 Jupiter 2′ 45″„„ 3,990 Saturn 1′ 50″„„ 10,550
* ↑ First mag. diameter 120″, second 90″, third 65″, fourth 45″, fifth 30″, sixth 20″ (ibid., pp. 481–82). Magini took the stars of the first mag. to be 10′ in diameter; Kepler made the diameter of Sirius 4′ (Opera, ii. p. 676); the Persian author of the Ayeen Akbery put the diameter of stars of the first mag. = 7′ (Delambre, Moyen Age, p. 238), so that Tycho's estimates were more reasonable than any of these.
* ↑ The ratio of the semidiameters of the deferent of Saturn and of the solar orbit he borrows from Copernicus. Compare above, p. 181, footnote $^1$.
* ↑ Pisces was supposed to be the sign of Palestine.
* ↑ "Septima hæc est trigonorum in integrum ab Orbe condito restitutio." About the trigoni see above, p. 49, footnote. The conjunction of Jupiter and Saturn in Sagittarius in December 1603 commenced a new cycle with a fiery trigon.
* ↑ See above, p. 50. Tycho now (Progym., p. 809) gives the time of New Moon as 7h. 312/3m. p.m.
* ↑ I possess an English translation which seems to be very scarce: "Learned Tico Brahæ his astronomicall Coniectur of the new and much Admired * which Appered in the year 1572," London, 1632, 26 pp. text, 5 pp. dedication ("To the High and Mighty Emperour Rvdolphvs the II. The Preface of the Heyres to Tycho Brahe"), and 2 pp. of epigrams by the translator and James VI. I have seen another copy in which there was a portrait of Gustavus Adolphus. Lalande has a German translation also printed in 1632, and there is a Dutch one printed at Goude in 1648 ("Generale Prognosticatie van het jaer 1572 tot desen tegenwoordigen Jare, alles in Latijn beschreven van Ticho Brahe") in the library of Trin. Coll., Dublin.
* ↑ "Certe si nihil aliud stella illa, magnum equidem astronomum significavit et progenuit." The last words in Kepler's Appendix to the Progymnasmata.