Tadeusz Banachiewicz (1882 - 1954)

The beginning of Tadeusz Banachiewicz’s scientific career is considered to be the year 1903, when a brief note by student T. Banachiewicz appeared in the prestigious journal Astronomische Nachrichten, announcing the upcoming and rare event of the occultation of the star BD -6°6191 by the planet Jupiter.

Professor Banachiewicz highly valued observational work, and often paraphrased Descartes’ famous saying Cogito ergo sum to Observo ergo sum ("I observe, therefore I am"). In 1923, as director of the Astronomical Observatory of Jagiellonian University, he borrowed a 203mm diameter refractor from the Harvard College Observatory in Cambridge, USA. In the early 1920s, this refractor, nicknamed "The American" due to its origin, was the largest telescope in Poland and enabled the conduct of serious observations. At the Krakow observatory, Banachiewicz undertook two main observational programs: visual observations of eclipsing variable stars and the program of observing stellar occultations by the Moon.

The goal of the first program was to determine the moments of minima for eclipsing variable stars. These stars are typically binary systems, and the orbital motion of the components causes the observed periodic variations in brightness. Regular observations allowed for the determination of successive minima and the refinement of orbital period values. Sometimes, it was possible to obtain the entire light curve of the star. Changes in these periods indicated active astrophysical processes occurring in such systems. The results of these observations were published in the Supplemento ad Annuario Cracoviense as ephemerides of eclipsing variable stars. The second scientific program involved visual observations of stellar occultations by the Moon, with an accuracy of about 1/10 of a second. These observations were part of a larger international program and allowed for very precise tracking of the Moon's movement. The refractor brought by Banachiewicz played a key role in these programs and was the main instrument of the Krakow Observatory for nearly half a century.

In 1927, Banachiewicz constructed the chronocinematograph, which recorded the image of a solar eclipse and the precise timing of each phase of the event. In 1954, the professor described the chronocinematograph:

"It was my idea, realized with the help of Dr. K. Kordylewski. With the chronocinematograph (a film camera that captures the sky, synchronized with a chronometer and chronograph that precisely records the time of the observation), one can study total solar eclipses with extraordinary accuracy, utilizing the so-called Baily's beads, which were previously an obstacle to observations... (Just before the beginning and at the end of a total eclipse, bright points, known as Baily's beads, appear along the edge of the Moon's disk, caused by the Moon's irregular surface, including mountains and valleys)." [“Conversation about the stars with Professor Tadeusz Banachiewicz,” Stanisław Pagaczewski, Przekrój, 07.02.1954]

Banachiewicz developed the chronocinematographic method for observing solar eclipses by combining a specially designed film camera with a chronometer. For the first time, it was possible to simultaneously record the image and the exact timing of each stage of the eclipse. The chronocinematograph was used during expeditions to observe solar eclipses in Swedish Lapland (1927), the United States (1932), Greece, Japan, and Siberia (1936). Measurements based on observations of Baily’s beads allowed for the determination of the relative radii of the Sun and the Moon. In 1912, Professor Francisco da Costa Lobo recorded a film of a solar eclipse, which showed changes in the intensity of Baily’s beads. Also in 1912, Fr. Vles and J. Carvallo attempted to film the Sun during an eclipse along with a chronometer's hand, but this method did not provide accurate time measurements. Banachiewicz's idea was to use the eclipse phenomenon to conduct triangulation measurements across different continents. This method had an accuracy of about 35 meters between two points approximately 10,000 kilometers apart. Banachiewicz envisioned a continental geodetic network, which was a precursor to satellite geodesy.

Banachiewicz’s greatest scientific achievement was the development of the Krakowian calculus. It was a convenient and fast method of calculation in the "pre-computer" era. At the beginning of the 20th century, arithmometers, which were essentially created for Krakowian-based calculations, came into widespread use and reigned for many years. The creator of this new calculus described it as follows:

"The theory of Krakowians was developed through years of work and experience. It aimed to simplify complex astronomical calculations, requiring as little mental effort as possible. I developed this theory during my stay in Russia in 1917 and first applied it in my lectures at the University ofDorpat. The scientific foundations of this theory were published by me in 1923 in the Bulletin of the Polish Academy of Arts and Sciences. Today, this method is used worldwide, except in Australia. Among others, it has found wide application in China, where the director of the Astronomical Observatory in Shanghai, Professor Villemarqué, emphasized that its application enabled large- scale calculations for the first time." [“The Krakowian Theory—The World Embraces a Polish Method of Astronomical Calculations,” Dziennik Zachodni, 18.09.1949]

Like every field of the exact sciences, this calculus functions like a living organism, constantly growing and evolving. It was initially conceived to simplify certain complex astronomical calculations—today, its reach and usefulness extend to geodesy, engineering, and more. [“Second after Copernicus,” Eustachy Białoborski, Horyzonty Techniki, 3, 1955]

What are Krakowians used for? Professor Banachiewicz explains:

"Krakowians improved computational mathematics, steering it, if I may say so, towards practicality... Various engineering fields use Krakowians. This method is used for calculations in reinforced concrete constructions, geodetic computations, etc." [“Astronomy and Life,” Krystyna Zbijewska - interview with Tadeusz Banachiewicz, Dziennik Polski, 1953]

Krakowians introduced new methods for solving equations. In the 18th and 19th centuries, the field of spherical polygonometry was studied by such greats as Leonhard Euler, Carl Gauss, Gaspard Monge, and Delambre. Using Krakowians, Banachiewicz was the first to derive general formulas for spherical polygonometry, eliminating the need to divide polygons into triangles due to the availability of a direct solution. In the theory of rigid body rotations, the problem of decomposing a given rotation into three rotations around coordinate axes was solved with ease using Krakowians. [T. Banachiewicz, "Krakowian Calculus," 1959]

Krakowians evoked admiration from some and skepticism from others. Among the admirers was mathematician Antoni Chromiński, a friend of Banachiewicz, who wrote:

Warsaw, December 29, 1927

Dear Tadzio!

... my interest in the new polygonometry has grown immensely, and I decided to ask you for more detailed explanations regarding the specifics of the calculus. There was even a moment when I might have personally invaded your presence, eager to poke my nose into the retort where the works of various Jacobis, Cauchys, etc., were being melted down into Krakowians, noble in their simplicity, with just a few drops of the mixture from the "Euler-Gauss-Monge" company added, to shine in all their polygonometric glory. Circular No. 25, handed to me yesterday at the European, paralyzed my intentions, providing answers to almost all my pressing questions and inflaming my enthusiasm for these new computational simplifications to the point that my passion spread to Staś Rylke as well..."

[AUJ, DC 5]

Krakowians, unlike matrices, do not form an algebraic group under multiplication, and they have distinct properties and structure. Many considered Krakowians to be a superior and more convenient tool for complex computations. Krakowian calculus allowed for modifications to Gauss's method of least squares, making calculations faster, less prone to errors, and easier tocorrect. Banachiewicz emphasized the simplicity, ease, and reliability of Krakowian-based computations. Arithmometers were used for calculations for decades—one hand followed the written columns of numbers, while the other hand input them into the "machine." Before arithmometers, logarithmic slide rules were dominant. The Krakowian method, combined with arithmometers, greatly sped up and simplified calculations, allowing for the resolution of problems in astronomy, geodesy, geophysics, and engineering. Krakowians were an "economical computational scheme." Shortly after Pluto's discovery in 1930, Banachiewicz was the first to calculate its trajectory using his Krakowian methods, aiding in identifying the planetary nature of this newly discovered celestial body. Other observatories, using traditional methods, were unable to provide correct orbital parameters due to the limited number of Pluto observations. Even in the era of programmable electronic calculators and later computer processors, the simplicity, speed, and ease of error checking in Krakowian calculations remain relevant. Banachiewicz also modified and simplified Olbers' method of determining parabolic orbits, resulting in the Olbers-Banachiewicz method. He authored works on the theory of lunar libration as well. Professor Banachiewicz was a co-founder and the first director of The Polish Astronomical Society (PTA).

Biography

The life story of Tadeusz Banachiewicz, personally written by him for Jagiellonian University in 1920.

Tadeusz Banachiewicz was born in Warsaw on February 13, 1882, to his father, Artur, a landowner, and his mother, Zofia née Rzeszotarska. In 1900, he graduated with a silver medal from Warsaw’s Fifth Gymnasium, and in 1904, he completed the Mathematics Department at the University of Warsaw, earning the degree of Candidate in Mathematical Sciences and a gold medal for his thesis on practical astronomy. Enrolled at the University of Warsaw as an assistant in astronomy and geodesy, he studied in Göttingen in 1906-07, visiting various foreign observatories, and in 1907-08 he studied at the Pulkovo Observatory. In 1908-09, he served as an observer in Warsaw, and in 1910, after passing his master’s exams in Moscow, he accepted, due to political conditions, an invitation to work as an assistant at the Engelhardt Observatory near Kazan. There, he predicted in 1911 the occultation of a star by a satellite of Jupiter for South America and conducted numerous scientific expeditions in Russia, primarily to measure gravitational strength. In 1915, due to wartime events, he completed his habilitation at Kazan University. That same year, he left Kazan, habilitated again in Dorpat (now Tartu) after defending his dissertation "Three Essays on the Theory of Refraction," and became a private lecturer at the University of Dorpat. In 1917, he defended his thesis "On Gauss's Equation" in Dorpat for a degree in astronomy, after which he was appointed initially as a permanent Lecturer in Astronomy and later, in March 1918, as an Associate Professor at Dorpat University. In July 1918, during the university’s evacuation to Russia, he was invited to serve as a professor of astronomy in Voronezh. Previously, in May 1918, he had received an invitation to Krakow, where he has been a full professor of astronomy and director of the Observatory since the spring of 1919. On January 19, 1908, he became a member of the Scientific Society in Warsaw, and on May 28, 1920, a corresponding member of the Polish Academy of Learning. Krakow, June 16, 1920.

Tadeusz’s mother, Zofia née Rzeszotarska Banachiewicz (1852-1920), and his father, Artur (1840-1910), owned a family estate in Cychry near Warsaw, west of Grójec. Tadeusz spent his childhood on this estate, where the wooden manor house with 12 rooms and three kitchens was surrounded by chestnut trees, spruces, and lilacs. Tadeusz was the youngest of three siblings. Hisolder brother, Ignacy Jan (February 1875 - November 1940), settled in Zawiercie, working as an engineer at the Machine Factory, which produced pedestals for the chronokinematographs invented by Tadeusz Banachiewicz for filming solar eclipses. Ignacy died in the Dachau concentration camp. His sister, Zofia Anna (July 1878 - 1961), married Stanisław Domaszowski, a landowner in nearby Tułowice, and took over the family estate, managing it with her husband. From 1948 until her death, she lived in Krakow.

In 1900, Banachiewicz graduated from Warsaw’s Fifth Gymnasium with a silver medal. In the same year, he began his astronomical studies at the University of Warsaw’s Faculty of Mathematics and Physics. Already in January 1901, as a student, Banachiewicz conducted systematic astronomical observations, primarily of lunar occultations of stars. He graduated in 1904 with the title of Candidate in Sciences. His diploma thesis, "Studies on the Repsold Heliometer Reduction Constants of the Pulkovo Observatory," was awarded a gold medal by the university senate. In 1905, he continued his scientific work and began calculating the orbit of Comet 1905a, but the university was closed by the Russian authorities.

In 1906-07, he studied in Göttingen under Karl Schwarzschild. In 1907-08, he worked at the Pulkovo Observatory under Oskar Backlund, conducting astronomical observations and mathematical studies. After returning to Warsaw in 1908-09, he worked as a junior assistant at the Observatory. Preparing for his exams at the family estate, he completed his master’s exams in Warsaw in 1909 and Moscow in 1910.

The heliometer, a challenging instrument to use, was one in which Banachiewicz had substantial expertise. Consequently, in 1910, Professor Dmitri Ivanovich Dubyago offered him an assistant position at the Engelhardt Observatory near Kazan. His work in Kazan resulted in a series of five- year heliometric observations of the Moon, known in the literature as Banachiewicz’s Kazan series. Working in Kazan in 1911, Banachiewicz predicted a rare event—a star occultation by Ganymede, the largest moon of Jupiter. This event was visible in Chile, where 32 observational posts were organized. This rare occurrence was predicted and successfully observed and later served as the basis for Professor Józef Witkowski’s habilitation thesis in 1928. In 1912, Banachiewicz led an expedition to the Volga region to conduct gravimetric measurements. In 1915, he moved from Kazan to the Dorpat Observatory (now Tartu, Estonia) and in 1918 became its director. The same year, he returned to Warsaw, where he served as an acting professor of geodesy at the Warsaw University of Technology. On November 27, 1918, the Faculty of Philosophy at the Jagiellonian University sent a letter to the Ministry of Religious Denominations and Public Enlightenment in Warsaw, stating:

“Following the death of the esteemed Professor Maurycy Rudzki, the Astronomy Chair at the Faculty of Philosophy of the Jagiellonian University has been left vacant. The Faculty Commission thoroughly reviewed the matter and presented a unanimous recommendation to the Faculty Assembly, which was accepted unanimously at the meeting on November 8, 1918. The Faculty decided to recommend Mr. Tadeusz Banachiewicz, former Lecturer at the University of Dorpat, currently residing in Warsaw, to the Ministry as the Ordinary Professor of Astronomy and Director of the Astronomical Observatory.” [Jagiellonian University Archives, WF II 164]

In 1919, Banachiewicz arrived in Krakow and assumed the leadership of the Astronomical Observatory. However, the facility was in poor condition just months after Poland regained independence. Banachiewicz promptly began improving the situation. From 1920, he started publishing the "Krakow Observatory Circular." In a letter to the Dean in July 1921, he wrote:

"(...) We have initiated the publication of 'Circulars,' initially intended primarily for Polish astronomers, which have since taken on a more international character, though still quite modest. This publication facilitates receiving publications from sister institutions abroad for the Observatory.” [Jagiellonian University Archives, WF II 164]

In 1922, Banachiewicz began publishing the "Krakow Observatory Astronomical Yearbooks," followed by the "International Supplement to the Krakow Observatory Yearbooks" from 1923. These were eclipse predictions for variable stars, published in paper form until 2003 and later digitally. Today, "Acta Astronomica," initiated by Banachiewicz in 1925, continues to be published, with him as its editor-in-chief until his death in 1954. Banachiewicz was one of the founders of the Polish Astronomical Society. At the Society’s first congress (February 19-20, 1923) in Torun, Tadeusz Banachiewicz was elected its president.

In 1954, Professor Banachiewicz said about the observatory:

"For many years, the Observatory merely consumed the achievements of international science without significantly contributing to observational astronomy. In the last 30 years, this has changed. We have moved from consumers to ‘producers,’ despite limited financial resources and too few astronomers. Our specialty includes observations of variable stars and comets. Notably, we pride ourselves on discovering all six ‘Polish’ comets, beginning in 1925 when Polish astronomer Lucjan Orkisz first associated his name with a newly discovered comet.” [“A Conversation about Stars with Professor Tadeusz Banachiewicz,” Stanisław Pagaczewski, Przekrój, February 7, 1954]

The comet mentioned by Professor Banachiewicz was discovered at the remote station of the observatory on Łysina Hill in the Lubomir range near Myślenice. Established in 1922 at his initiative, it was Poland’s first mountain station for astronomical observation, where meteorological measurements were also conducted. The station was burned down by German troops on September 15, 1944. The discoverers of these six “Polish” comets were staff members of the Krakow Observatory: Lucjan Orkisz (1925), Antoni Wilk (1925, 1929, 1930, 1937), and Władysław Lis (1936).

In 1927, Banachiewicz began observing total solar eclipses using a chronokinematograph, a device he designed himself. He also initiated the broadcasting of radio time signals from the observatory, a practice that continued until 1984, when transmission was moved to Warsaw. As part of his involvement with the Baltic Geodetic Commission and the National Astronomical Institute he founded, Banachiewicz initiated Poland’s first gravimetric studies, measuring the intensity of Earth’s gravitational field. In a letter to the Ministry of Internal Affairs in July 1926, Banachiewicz wrote:

“In August and September of this year, the National Astronomical Institute will continue a leveling expedition from Krakow toward Warsaw along the Krakow-Kielce route. The purpose of this expedition is to precisely determine the altitude above sea level of various points along the route, which, aside from its scientific significance, holds great practical importance as it provides primary benchmarks for all future railway, hydrotechnical, and sewage projects, as well as for cartographic work, especially for military needs. The elevations determined by the expedition will be preserved on metal leveling markers embedded in permanent buildings.” [Jagiellonian University Archives, DC4]

From 1924 to 1926, Tadeusz Banachiewicz served as Vice President of the Geodetic Committee of the Baltic States and represented Poland in the committee.

From 1932 to 1938, he was Vice President of the International Astronomical Union (IAU), and from 1938 to 1952, he chaired the IAU’s Lunar Commission. The outbreak of war found him in Krakow, and on November 6, 1939, he was arrested along with other Jagiellonian University staff during the Sonderaktion Krakau and deported to the Sachsenhausen concentration camp, from which he returned three months later on February 9, 1940. According to his fellow inmates, Banachiewicz's conduct in the camp was marked by dignity and served as “an example of the stance a true man assumes in the face of barbarity, the enemy, and impending death” (Prof. Witold Krzyżanowski).

From 1932 until mid-1954, he maintained a diary he called “Daily Notes.” He was motivated to start writing the “Notes” by the marriage of his “right-hand man,” Dr. Kazimierz Kordylewski. Banachiewicz reacted poorly to the marriage plans of his associates, fearing that family obligations would overshadow scientific duties, force them to seek other income sources, and ultimately disrupt the work of a committed astronomer. Banachiewicz himself married quite late, at the age of 49. In 1931, he married his long-time friend Laura (Larissa) de Sołohub Dikyj, a Ukrainian painter and poet. Laura was born in Kapitołówka near Kharkiv. Her first husband, Mykola Dikyj, had passed away. The Banachiewiczes had no children. In 1933, Sylwiusz Arend named two newly discovered asteroids after them: asteroid Banachiewicza (1286) and Lorcia (1287), the latter from Laura’s nickname. Laura was arrested by the Polish Security Office on April 15, 1945, on suspicion of collaborating with the Nazis. She was released thanks to her husband’s intervention, but after nearly a month of grueling interrogations, she died of pneumonia on May 7, 1945, and was buried on May 28, 1945, at the Rakowicki Cemetery (section L south, grave 11). They had been married for 14 years.

In 1941, the management of observatories in the General Government was taken over by Dr. Kurt Walter from Potsdam, although he was officially appointed in February 1942. Banachiewicz was initially granted leave and later retired with permission to remain at work. In June 1944, under Walter’s pressure, he was forced to move from his official residence at Kopernika Street, where the observatory was located, to Limanowskiego Street. However, by February 1945, the apartment on the first floor of the observatory building was again available to the professor. He resumed his position as director of the Jagiellonian University Astronomical Observatory and remained there until his death. From 1945 to 1951, he held a professorship and chaired the Department of Higher Geodesy and Astronomy at the Polytechnic Faculties of the Mining Academy. Banachiewicz was fluent in multiple languages, though in university personnel surveys, he modestly described his foreign language skills as “fair.” He wrote in Russian, French, German, English, and Interlingua, the simplified Latin developed by Italian mathematician Giuseppe Peano.

As the city grew, conditions for conducting observations at the Kopernika observatory worsened each year. In 1953, Banachiewicz managed to secure Fort 38 Skała, a military fort dating from 1878 in Krakow’s Bielany district, from the army. The observatory officially opened there on May 24, 1954. After Professor Banachiewicz’s death, in 1964, the fort was designated the official headquarters of the observatory in celebration of the 600th anniversary of the Jagiellonian University. In June 1954, on Banachiewicz’s initiative, measurements during a solar eclipse were taken with the first 5-meter telescope. Due to illness, Banachiewicz himself did not participate in these observations. In May 1954, despite his declining health, he traveled to Leningrad (now St. Petersburg) to attend the inauguration of the Pulkovo Observatory, where he had once worked. He spent a month in a hospital there. In July, he returned to Krakow and was admitted to the State Clinical Hospital of the Medical Academy on Strzelecka Street, where he underwent surgery. Following postoperative pneumonia, he died on November 17, 1954, at the age of 72. He was buried on November 20, 1954, at Rakowicki Cemetery beside his wife. The following year, throughthe efforts of Docent Kazimierz Kordylewski, he was reinterred at the Crypt of the Distinguished in the Basilica of the Pauline Fathers at Skałka.