Dec 272020
 

Today is the birthday (1571) of Johannes Kepler, a German astronomer, mathematician, and astrologer (no doubt named after John the Apostle because this is his saint’s day https://www.bookofdaystales.com/san-juan/ ). Kepler is a key figure in the 17th-century scientific revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonices Mundi, and Epitome Astronomiae Copernicanae. These works also provided one of the foundations for Newton’s theory of universal gravitation which augmented Kepler’s concepts of planetary motion.

Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, and was mentioned in the telescopic discoveries of his contemporary Galileo Galilei. He was a corresponding member of the Accademia dei Lincei in Rome.

Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy). Kepler pulled together astronomical observations with mathematics and physics to build the foundations of astrophysics. He also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through reason. Kepler described his new astronomy as “celestial physics,” as “an excursion into Aristotle’s Metaphysics,” and as “a supplement to Aristotle’s On the Heavens,” transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics. When Newton said that he saw so far because he stood on the shoulders of giants, Kepler was one of those giants.

Delving into all that Kepler accomplished is way too much for a short blog post, so let me focus on his perhaps most famous formulation, his laws of planetary motion.  The three laws state that:

  1. The orbit of a planet is an ellipse with the Sun at one of the two foci.
  2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
  3. The square of a planet’s orbital period is proportional to the cube of the length of the semi-major axis of its orbit.

The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law helps to establish that when a planet is closer to the Sun, it travels faster. The third law expresses that the farther a planet is from the Sun, the slower its orbital speed, and vice versa. As such, Kepler refined the theories proposed by Copernicus.

If the eccentricities of the planetary orbits are taken as zero, then Kepler basically agreed with Copernicus:

1. The planetary orbit is a circle.
2. The Sun is at the center of the orbit.
3. The speed of the planet in the orbit is constant.

The eccentricities of the orbits of those planets, known to Copernicus and Kepler, are small, so the foregoing rules give fair approximations of planetary motion, but Kepler’s laws fit the observations better than does the model proposed by Copernicus. Kepler’s corrections are:

1. The planetary orbit is not a circle, but an ellipse.
2. The Sun is not at the center but at a focal point of the elliptical orbit.
3. Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed (closely linked historically with the concept of angular momentum) is constant.

If you are lost at this point – or don’t care about these points – I won’t beat you up, and I certainly won’t add any equations, or the like. It’s enough to be aware that the planetary orbits are elliptical rather than circular. Kepler shows us that physics is in a perpetual state of refinement (that never ceases). Newton added his bits and much later Einstein added his. Understanding is in a constant state of change, leading to a general acknowledgement that change is the only constant. Scientific theories never explain everything: there are always observations that cannot be accounted for by current theories. Hence the periodic revolutions in scientific thinking.

I will admit that my eyes have the habit of glazing over when I see something like r=p/1+ϵcosθ (or more complex) and it’s not because I do not understand the formula.  It’s because my interests do not lie in delving deeper into the implications.  There’s the nub of the matter. I accept the conclusions and move on. But . . . there are people like Kepler who are never satisfied. The work of Copernicus was fairly close to the truth, but the anomalies bothered Kepler and he worked tirelessly to get yet closer to the truth.  This is one of the reasons I get so aggravated with flat earthers and other science deniers.  They think that some vague intuitions based on limited sensory information can challenge the exhaustive work of dedicated professionals.  I despair – sometimes.

Kepler was born in Weil der Stadt, currently in the Stuttgart Region of the German state of Baden-Württemberg. Among other things, it is well-known for its Fasnetsküchle which will be available very soon (after Epiphany). Fasnetsküchle are similar to the so-called “Berliner,” or jelly doughnuts, or “Krapfen,” which are available year round. But the Swabian version is distinctly different: it must be flat and square or rectangular, never round nor as tall as a Berliner, and it’s not supposed to be filled with jam – it should be plain inside and out. True Swabians insist that Fasnetsküchle may not even be sprinkled with cinnamon or powdered sugar. But times change and you now find them with a dusting of sugar (and cinnamon).

Fasnetsküchle

Ingredients:

2 cups whole milk, warmed to 110F/43C
4½ teaspoons active dry yeast (two packages)
¾ cup and 1 pinch granulated sugar, divided
5 to 6 cups all-purpose flour, divided
2 eggs
1 teaspoon vanilla extract
1¼ teaspoons salt
4 tablespoons unsalted butter, melted
oil for deep- frying (lard is traditional)

Instructions:

Pour the warm milk into bowl. Stir in the yeast and a pinch of granulated sugar. Let stand for 5 to 10 minutes, or until it has become bubbly. Add 2 cups of flour to the mixture and stir with a wooden spoon until a smooth batter forms. Cover with plastic wrap and set in a warm spot for 30 minutes. By now the mixture should have risen and become bubbly.

In a medium bowl, whisk the eggs until pale yellow and frothy (about three minutes). Add the sugar, vanilla extract and salt, and whisk until combined and smooth.

Add the egg mixture to the dough and hand-knead until mostly combined. Add the melted butter and mix. Gradually add three more cups of flour to the mixture and continue to knead until very soft dough comes together (it will be rather slack and a bit sticky.) If necessary, add up to another cup of flour, a spoonful at a time, until the dough firms. Transfer the dough to a lightly greased bowl, cover with plastic wrap, or a kitchen cloth, and let it set in a warm spot until dough has doubled in size (20 to 30 minutes).

Remove the dough from the bowl and turn out on to a floured work surface. With your fingers, or a rolling pin, push down the dough into an even layer. Sprinkle flour on the dough and roll it out to about ½-inch thickness. If the dough doesn’t hold its shape and springs back, cover with a damp towel and let it rest for a few more minutes and try again.

Cut out 3 x 3 inch squares or 3 x 4 rectangles of dough. Transfer the dough pieces to parchment-lined baking sheets. Gather scraps of dough and again roll out and cut until you have used up all of the dough. Cover the baking sheets loosely with a dish-towel, plastic wrap and place in a warm, draft-free spot until they are almost doubled in size, about 30 minutes.

Meanwhile, heat at least 1½ to 2 inches or more of deep frying shortening or oil in a heavy-bottomed pot or deep skillet over medium heat to 350F/176C. Carefully lower about three or four Küchle into the oil one at a time (be sure not to over-crowd the pan) and fry until the bottom is golden brown. Carefully turn them over and continue to fry until the other side is golden brown.

Remove with a slotted spoon, and drain on a wire rack. Repeat for the remaining Küchle. They are best eaten warm.

Dec 142018
 

Today is the birthday (1546) of Tyge Ottesen Brahe, known in the English-speaking world as Tycho Brahe, a Danish nobleman, astronomer, and writer known for his accurate and comprehensive astronomical and planetary observations. He was born in the then-Danish (now Swedish) peninsula of Scania. His observations, done only with the naked eye before telescopes were available, were about five times more accurate than the best available observations at the time.

Tycho aspired to a level of accuracy in his estimated positions of celestial bodies of being consistently within a arcminute of their real celestial locations, and also claimed to have achieved this level. But, in fact, many of the stellar positions in his star catalogues were less accurate than that. To perform the huge number of multiplications needed to produce much of his astronomical data, Tycho relied heavily on a new technique called prosthaphaeresis, an algorithm for approximating products based on trigonometric identities that predated logarithms.

Although Tycho admired Copernicus and was the first to teach his theory in Denmark, he was unable to reconcile Copernican theory with the basic laws of Aristotelian physics, that he considered to be foundational. He was also critical of the observational data that Copernicus built his theory on, which he correctly considered to have a high margin of error. Instead, Tycho proposed a “geo-heliocentric” system in which the Sun and Moon orbited the Earth, while the other planets orbited the Sun. Tycho’s system had many of the same observational and computational advantages that Copernicus’ system had, and both systems could also accommodate the phases of Venus, although Galileo had yet to discover them. Tycho’s system provided a safe position for astronomers who were dissatisfied with older models but were reluctant to accept heliocentrism and the Earth’s motion. It gained a considerable following after 1616 when Rome declared that the heliocentric model was contrary to both philosophy and Scripture, and could be discussed only as a computational convenience that had no connection to fact. Tycho’s system also offered a major innovation: while both the purely geocentric model and the heliocentric model as set forth by Copernicus relied on the idea of transparent rotating crystalline spheres to carry the planets in their orbits, Tycho eliminated the spheres entirely. Kepler, as well as other Copernican astronomers, tried to persuade Tycho to adopt the heliocentric model of the solar system, but he was not persuaded. According to Tycho, the idea of a rotating and revolving Earth would be “in violation not only of all physical truth but also of the authority of Holy Scripture, which ought to be paramount.”

With respect to physics, Tycho held that the Earth was just too sluggish and heavy to be continuously in motion. According to the accepted Aristotelian physics of the time, the heavens (whose motions and cycles were continuous and unending) were made of “Aether” or “Quintessence.” This substance, not found on Earth, was light, strong, unchanging, and its natural state was circular motion. By contrast, the Earth (where objects seem to have motion only when moved) and things on it were composed of substances that were heavy and whose natural state was rest. Accordingly, Tycho said the Earth was a “lazy” body that was not readily moved. Thus while Tycho acknowledged that the daily rising and setting of the sun and stars could be explained by the Earth’s rotation, as Copernicus had said, he, nonetheless believed that, “such a fast motion could not belong to the earth, a body very heavy and dense and opaque, but rather belongs to the sky itself whose form and subtle and constant matter are better suited to a perpetual motion, however fast.”

With respect to the stars, Tycho also believed that, if the Earth orbited the Sun annually, there should be an observable stellar parallax over any period of six months, during which the angular orientation of a given star would change thanks to Earth’s changing position. (This parallax does exist, but is so small it was not detected until 1838, when Friedrich Bessel discovered a parallax of 0.314 arcseconds of the star 61 Cygni.) The Copernican explanation for this lack of parallax was that the stars were such a great distance from Earth that Earth’s orbit was almost insignificant by comparison. However, Tycho noted that this explanation introduced another problem: Stars as seen by the naked eye appear small, but of some size, with more prominent stars such as Vega appearing larger than lesser stars such as Polaris, which in turn appear larger than many others. Tycho had determined that a typical star measured approximately a minute of arc in size, with more prominent ones being two or three times as large. In writing to Christoph Rothmann, a Copernican astronomer, Tycho used basic geometry to show that, assuming a small parallax that just escaped detection, the distance to the stars in the Copernican system would have to be 700 times greater than the distance from the sun to Saturn. Moreover, the only way the stars could be so distant and still appear the sizes they do in the sky would be if even average stars were gigantic — at least as big as the orbit of the Earth, and of course vastly larger than the sun. And, Tycho said, the more prominent stars would have to be even larger still. And what if the parallax was even smaller than anyone thought, so the stars were yet more distant? Then they would all have to be even larger still. . . which, in fact, they are.

Kepler used Tycho’s records of the motion of Mars to deduce laws of planetary motion, enabling calculation of astronomical tables with unprecedented accuracy (the Rudolphine Tables) and providing powerful support for a heliocentric model of the solar system. Galileo’s 1610 telescopic discovery that Venus shows a full set of phases refuted the pure geocentric Ptolemaic model. After that it seems 17th-century astronomy mostly converted to geo-heliocentric planetary models that could explain these phases just as well as the heliocentric model could, but without the latter’s disadvantage of the failure to detect any annual stellar parallax that Tycho and others regarded as refuting it.

The three main geo-heliocentric models were the Tychonic, the Capellan with just Mercury and Venus orbiting the Sun such as favored by Francis Bacon, for example, and the extended Capellan model of Riccioli with Mars also orbiting the Sun whilst Saturn and Jupiter orbit the fixed Earth. But the Tychonic model was probably the most popular, albeit probably in what was known as ‘the semi-Tychonic’ version with a daily rotating Earth. This model was advocated by Tycho’s ex-assistant and disciple Longomontanus in his 1622 Astronomia Danica that was the intended completion of Tycho’s planetary model with his observational data, and which was regarded as the canonical statement of the complete Tychonic planetary system.

The ardent anti-heliocentric French astronomer Jean-Baptiste Morin devised a Tychonic planetary model with elliptical orbits published in 1650 in a simplified, Tychonic version of the Rudolphine Tables. Some acceptance of the Tychonic system persisted through the 17th century and in places until the early 18th century; it was supported (after a 1633 decree about the Copernican controversy) by “a flood of pro-Tycho literature” of Jesuit origin. Among pro-Tycho Jesuits, Ignace Pardies declared in 1691 that it was still the commonly accepted system, and Francesco Blanchinus reiterated that as late as 1728. Persistence of the Tychonic system, especially in Catholic countries, has been attributed to its satisfaction of a need (relative to Catholic doctrine) for “a safe synthesis of ancient and modern”. After 1670, even many Jesuit writers only thinly disguised their Copernicanism. But in Germany, the Netherlands, and England, the Tychonic system vanished from scientific literature much earlier.

No dish better suits the celebration of Tycho Brahe than spettekaka or spettkaka (spiddekaga in native Scanian) a dessert that originates in the province of Scania (Skåne) where he was born.  The name means “cake on a spit” which, as you will see from the video, exactly describes its production. A mixture consisting mainly of eggs, potato starch flour and sugar is squirted slowly on to a conical spit which is being rotated over an open fire or other heat source. So, a spinning dessert for an advocate of spinning bodies in space. Spettekaka can range in size anywhere from a few inches to several feet in height and over a foot in diameter. The very large cakes are served by sawing cuboids from the cake, leaving as much standing as possible. Spettekaka is frequently served accompanied by dark coffee, vanilla ice cream and port wine.

This video shows how spettekaka is made. Sorry it is in Swedish, but you’ll get the gist:

Feb 192016
 

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Today is the birthday (1473) of Nicolaus Copernicus a Renaissance mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe. The publication of this model in his book De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) just before his death in 1543 is considered a major event in the history of science, triggering the Copernican Revolution and making an important contribution to the Scientific Revolution. Here, mostly, I want to continue a discussion I began in this blog some time ago, trying to dispel some trenchant misconceptions about the reception of Copernicus’ work. It was NOT all scientists on one side (the “right” side) and all clergy on the other side (the “wrong” side). Many clergy were sympathetic to Copernicus and many scientists opposed him. This was abundantly clear when Galileo was tried for heresy: https://www.bookofdaystales.com/trial-galileo-think/.

Copernicus was born and died in Royal Prussia, a region that had been a part of the Kingdom of Poland since 1466. He was a polyglot and polymath who obtained a doctorate in canon law and also practiced as a physician, classics scholar, translator, governor, diplomat, and economist. Like the rest of his family, he was a third order Dominican.

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In Copernicus’ time, people were often called after the places where they lived. Like the Silesian village that inspired it, Copernicus’ surname has been spelled variously. The surname likely had something to do with the local Silesian copper-mining industry, though some scholars assert that it may have been inspired by the dill plant (in Polish, “koperek” or “kopernik”) that grows wild in Silesia. Numerous spelling variants of the name are documented for the astronomer and his relatives. The name first appeared as a place name in Silesia in the 13th century, where it was spelled variously in Latin documents. During his childhood, about 1480, the name of his father (and thus of his son) was recorded in Thorn as Niclas Koppernigk. At Kraków he signed himself, in Latin, Nicolaus Nicolai de Torunia (Nicolaus, son of Nicolaus, of Toruń). At Bologna, in 1496, he registered in the Matricula Nobilissimi Germanorum Collegii as Dominus Nicolaus Kopperlingk de Thorn. At Padua he signed himself “Nicolaus Copernik,” later “Coppernicus” His Latinized generally had two “p”s (in 23 of 31 documents extant), but later in life he used a single “p”. On the title page of De revolutionibus, Rheticus published the name as (in the Latin genitive) “Nicolai Copernici”.

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Some time before 1514 Copernicus made available to friends his “Commentariolus” (“Little Commentary”), a forty-page manuscript describing his ideas about the heliocentric hypothesis. Thereafter he continued gathering data for a more detailed work. About 1532 Copernicus had basically completed his work on the manuscript of Dē revolutionibus, but despite urging by his closest friends, he resisted openly publishing his views, not wishing—as he said—to risk the scorn “to which he would expose himself on account of the novelty and incomprehensibility of his theses.” His fears were justified. His heliocentric (sun-centered) hypothesis was elegant but lacked all proof. If the earth moves why don’t we fall off? What is pushing the earth if it moves? What keeps it in orbit? Copernicus and his contemporaries had no answers to these fundamental questions, nor did Galileo when he was put on trial for supporting Galileo. It was well over a century before Isaac Newton solved the puzzle.

Copernicus’ “Commentariolus” listed the “assumptions” upon which his heliocentric theory was based, as follows:

  1. There is no one center of all the celestial circles or spheres.
  2. The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere.
  3. All the spheres revolve about the sun as their midpoint, and therefore the sun is the center of the universe.
  4. The ratio of the earth’s distance from the sun to the height of the firmament (outermost celestial sphere containing the stars) is so much smaller than the ratio of the earth’s radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.
  5. Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth’s motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
  6. What appear to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion.
  7. The apparent retrograde and direct motion of the planets arises not from their motion but from the earth’s. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.

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These are, for the most part, quite reasonable assumptions and make the mathematics of the solar system so much simpler and more accurate. The latter pleased many clergy whose job it was to keep the calendar accurate and to set the timing of Easter annually based on equinoxes and full moons.

In 1533, Johann Albrecht Widmannstetter delivered a series of lectures in Rome outlining Copernicus’ theory. Pope Clement VII and several Catholic cardinals heard the lectures and were interested in the theory. On 1 November 1536, Cardinal Nikolaus von Schönberg, Archbishop of Capua, wrote to Copernicus from Rome:

Some years ago word reached me concerning your proficiency, of which everybody constantly spoke. At that time I began to have a very high regard for you. For I had learned that you had not merely mastered the discoveries of the ancient astronomers uncommonly well but had also formulated a new cosmology. In it you maintain that the earth moves; that the sun occupies the lowest, and thus the central, place in the universe. Therefore with the utmost earnestness I entreat you, most learned sir, unless I inconvenience you, to communicate this discovery of yours to scholars, and at the earliest possible moment to send me your writings on the sphere of the universe together with the tables and whatever else you have that is relevant to this subject.

So much for the false notion that the church opposed Copernicus. By then Copernicus’ work was nearing its definitive form, and rumors about his theory had reached educated people all over Europe. Despite urgings from many quarters, Copernicus delayed publication of his book, perhaps from fear of criticism—a fear delicately expressed in the subsequent dedication of his masterpiece to Pope Paul III. Scholars disagree on whether Copernicus’ concern was limited to possible astronomical and philosophical objections, or whether he was also concerned about religious objections. I’d like to believe that Copernicus, as a good scientist, was less concerned about religious objections than about objections from other scientists because his hypothesis was devoid of proof from the physics of the day.

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Copernicus was still working on De revolutionibus orbium coelestium (even if not certain that he wanted to publish it) when in 1539 Georg Joachim Rheticus, a Wittenberg mathematician, arrived in Frombork. Philipp Melanchthon, a close theological ally of Martin Luther, had arranged for Rheticus to visit several astronomers and study with them. Rheticus became Copernicus’ pupil, staying with him for two years and writing a book, Narratio prima (First Account), outlining the essence of Copernicus’ theory. In 1542 Rheticus published a treatise on trigonometry by Copernicus (later included in the second book of De revolutionibus).

Under strong pressure from Rheticus, and having seen the favorable first general reception of his work, Copernicus finally agreed to give De revolutionibus to his close friend, Tiedemann Giese, bishop of Chełmno (Kulm), to be delivered to Rheticus for printing by the German printer Johannes Petreius at Nuremberg (Nürnberg), Germany. While Rheticus initially supervised the printing, he had to leave Nuremberg before it was completed, and he handed over the task of supervising the rest of the printing to a Lutheran theologian, Andreas Osiander.

Osiander added an unauthorized and unsigned preface, defending the work against those who might be offended by the novel hypotheses. He explained that astronomers may find different causes for observed motions, and choose whatever is easier to grasp. As long as a hypothesis allows reliable computation, it does not have to match what a philosopher might seek as the truth.

Toward the close of 1542, Copernicus was seized with apoplexy and paralysis, and he died at age 70 on 24 May 1543. Legend has it that he was presented with the final printed pages of De revolutionibus orbium coelestium on the very day that he died, allowing him to take farewell of his life’s work. He is reputed to have awoken from a stroke-induced coma, looked at his book, and then died peacefully. This is a quaint story, even if fictitious, leading me to observe as a young professor that to get tenure I had to publish OR perish, but Copernicus published AND perished.

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Copernicus was reportedly buried in Frombork Cathedral, where archaeologists for over two centuries searched in vain for his remains. Efforts to locate the remains in 1802, 1909, 1939 and 2004 had come to nought. In August 2005, however, a team led by Jerzy Gąssowski, head of an archaeology and anthropology institute in Pułtusk, after scanning beneath the cathedral floor, discovered what they believed to be Copernicus’ remains. The find came after a year of searching, and the discovery was announced only after further research, on 3 November 2008. Gąssowski said he was “almost 100 percent sure it is Copernicus.” Forensic expert Capt. Dariusz Zajdel of the Polish Police Central Forensic Laboratory used the skull to reconstruct a face that closely resembled the features—including a broken nose and a scar above the left eye—on a Copernicus self-portrait. Zajdel also determined that the skull belonged to a man who had died around age 70—Copernicus’ age at the time of his death.

Polish cooking has evolved considerably since the time of Copernicus, and is markedly similar to the cuisines of Slavs and Germans in many respects. Rosół is a traditional Polish meat soup. The most popular variety is rosół z kury, or clear chicken soup. It is commonly served with fine noodles, in other words, chicken noodle soup. It is one of the most popular Polish soups and is served on family dinners and also is a traditional soup for weddings. It is also said to be a great remedy if one catches a cold. The name “rosół” derives from a dish made of salted meat (used for preservation before refrigeration) cooked in water to make it more edible. Later fresh meat was used instead of salted. Much later that dish of cooked meat became a soup.

There are lots of types of rosół, such as: rosół królewski (royal rosół), made of three meats: beef or veal, white poultry (hen, turkey or chicken) and dark poultry such as duck or goose, a few dried king boletes, one single cabbage leaf and variety of vegetables as parsley, celery, carrot, leek. The cooking must take at least six hours of sensitive boiling on small fire.

Rosół myśliwski (hunter’s rosół), made of variety of wild birds as well as pheasant, capercaillie, wood grouse, black grouse or grey partridge, with a small addition of roe deer meat, wild mushrooms, and 2-3 juniper berries.

Here is a rough translation of a recipe from 1682:

This is the way to cook Polish rosół: take beef meat or veal, hazel grouse or partridge, and whatever meat that can be cooked in rosół [not pork]. Soak it, lay in a pot, then strain and pour over meat, add parsley, butter, salt, and skim well. One has to know what to put in the rosół for it not to smell, that is, dill, onion or garlic, nutmeg, rosemary or pepper. Lime would spoil any rosół as well.

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In essence, therefore, you are talking about a Polish version of pot-au-feu. So your task is simply to choose your meats and vegetables, and take your time. I’d use equal quantities of stewing beef, bowling fowl, and duck. Place them in a big stock pot, cover with light stock or water, add coarsely cut carrot, celery and leek, plus some dried mushrooms, bring very slowly to a gentle simmer, and cook over the lowest heat for 6 hours. Skim the top as needed.

Refrigerate overnight.

In the morning remove any congealed fat. Reheat the pot and debone all the meats. Then serve meats, vegetable and broth in deep bowls with dark rye bread. You’re aiming for a very clear, clean, but flavorful broth.